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GSMsimA MATLAB Implementation of a

GSM Simulation Platform

Arne Norre Ekstrøm & Jan H. MikkelsenInstitute of Electronic Systems,

Division of Telecommunications, Aalborg University,Fredrik Bajers Vej 7A, DK-9220 Aalborg Øst, Denmark

Telephone: +45 96 35 86 53Fax: +46 98 15 67 40E-mail: aneks / hmi @kom.auc.dk

December, 1997

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Preface

This technical report documents a MATLAB toolbox – GSMsim – developed as part of a re-search effort on CMOS front-end RF-IC design. GSMsim provides a mean for evaluating theperformance of both transmitter and receiver front-ends in a GSM system. The performanceevaluation is of the Monte-Carlo type, and is based on a BER measure calculated by comparinga random input bit sequence and the resulting sequence estimated by the receiver. The toolboxincludes baseband functionalities from both transmitter and receiver. The modular structure ofthe toolbox is designed for easy addition of user defined functionalities. The individual simu-lation parts developed are described using a mixture of pseudo code and MATLAB notations.Test results are provided whenever appropriate.

The toolbox is implemented using MATLAB Version 5.1.0.421 on SOL2. The entire MATLABtoolbox may be retrieved from the URL:

http://www.kom.auc.dk/TELE/SW-packages/matlab/GSMsim.tar.gz

It is the hope of the authors that this toolbox will turn out useful in future research projects aswell as related student projects.

Arne Norre Ekstrøm & Jan Hvolgaard MikkelsenAalborg University, December 1997

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Forord

Denne tekniske rapport beskriver en MATLAB toolbox – GSMsim – udviklet som et led iforskning indenfor CMOS front-end RF-IC design. GSMsim åbner mulighed for at evaluereperformancen af både sender og modtager front-ends i et GSM system. Performance evaluerin-gen er af Monte-Carlo typen, og er baseret på den BER der kan udregnes ved sammenligning afen tilfældig input bit sekvens og den resulterende sekvens estimeret af modtageren. Toolboxeninkluderer baseband funktionaliteter fra både sender og modtager. Den modulære struktur aftoolboxen er designet med henblik på let tilføjelse af brugerdefinerede funktioner. I dokumen-tationen er de individuelle dele af toolboxen beskrevet ved hjælp af en blanding af pseudo kodeog MATLAB notation. Der er anført testresultater hvor forfatterne har fundet det tjeneligt.

Toolboxen er implementeret ved hjælp af MATLAB Version 5.1.0.421 på SOL2. Toolboxenkan hentes på følgende URL:

http://www.kom.auc.dk/TELE/SW-packages/matlab/GSMsim.tar.gz

Forfatterene håber at toolboxen vil vise sig anvendelig i fremtidige forskningsprojekter såvelsom relaterede studenterprojekter.

Arne Norre Ekstrøm & Jan Hvolgaard MikkelsenAalborg Universitet, December 1997

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Contents

1 Introduction 1

1.1 Approach and Conceptual Transceiver Structure . . . . . . . . . . . . . . . . . 1

1.1.1 Overall Transmitter Structure . . . . . . . . . . . . . . . . . . . . . . 3

1.1.2 Overall Receiver Structure . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Transmitter Background 5

2.1 Data Generation, Channel Encoding, Interleaving, and Multiplexing . . . . . . 5

2.1.1 Data Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Channel Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.3 Interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.4 Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 GMSK-Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Differential Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Transmitter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 Receiver Background 21

3.1 Synchronization, Channel Estimation, and Matched Filtering . . . . . . . . . . 22

3.2 Minimum Least Square Error (MLSE) Detection . . . . . . . . . . . . . . . . 25

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3.3 De-Multiplexing, De-Interleaving and Channel Decoding . . . . . . . . . . . . 31

3.3.1 De-Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.2 De-Interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3.3 Channel Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Receiver Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4.1 Test of mf.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4.2 Test of viterbi_detector.m . . . . . . . . . . . . . . . . . . . . 38

4 Use of the GSMsim Toolbox 39

4.1 Installation of GSMsim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2 Syntax of the Major Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2.1 Syntax of data_gen.m . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.2 Syntax of channel_enc.m . . . . . . . . . . . . . . . . . . . . . . 43

4.2.3 Syntax of interleave.m . . . . . . . . . . . . . . . . . . . . . . . 44

4.2.4 Syntax of gsm_mod.m . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2.5 Syntax of channel_simulator.m . . . . . . . . . . . . . . . . . 46

4.2.6 Syntax of mf.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2.7 Syntax of viterbi_init.m . . . . . . . . . . . . . . . . . . . . . 48

4.2.8 Syntax of viterbi_detector.m . . . . . . . . . . . . . . . . . . 49

4.2.9 Syntax of DeMUX.m . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2.10 Syntax of deinterleave.m . . . . . . . . . . . . . . . . . . . . . 51

4.2.11 Syntax of channel_dec.m . . . . . . . . . . . . . . . . . . . . . . 52

4.3 The GSMsim_demo.m Function . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.4 The GSMsim_demo_2.m Function . . . . . . . . . . . . . . . . . . . . . . . 54

4.5 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

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4.6 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

A Transmitter Implementations 63

A.1 Data Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.1.1 Input, Output, and Processing . . . . . . . . . . . . . . . . . . . . . . 64

A.2 Channel Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.2.1 Input and Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.2.2 Internal Data Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.2.3 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.3 Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66


A.4 Multiplexer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67


A.5 GMSK-Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

A.5.1 Input and Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

A.5.2 Internal Data Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

A.5.3 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

B Receiver Implementations 71

B.1 Synchronization, Channel Estimation, and Matched Filtering . . . . . . . . . . 71

B.1.1 Input and Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

B.1.2 Internal Data Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

B.1.3 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

B.2 Viterbi Detector (MLSE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75


B.2.2 Internal Data flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

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B.2.3 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

B.3 De-multiplexer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

B.3.1 Input, Output and Processing . . . . . . . . . . . . . . . . . . . . . . . 85

B.4 De-Interleaver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

B.4.1 Input, Output, and Processing . . . . . . . . . . . . . . . . . . . . . . 86

B.5 Channel Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86


B.5.2 Internal Data Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

B.5.3 Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

C Source code 93

C.1 burst_g.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

C.2 data_gen.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

C.3 channel_enc.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

C.4 interleave.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

C.5 diff_enc.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

C.6 gmsk_mod.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

C.7 gsm_mod.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

C.8 ph_g.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

C.9 make_increment.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

C.10 make_next.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

C.11 make_previous.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

C.12 make_start.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

C.13 make_stops.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

C.14 make_symbols.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

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C.15 mf.m (Renamed to mafi.m) . . . . . . . . . . . . . . . . . . . . . . . 108

C.16 viterbi_detector.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

C.17 viterbi_init.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

C.18 DeMUX.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

C.19 deinterleave.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

C.20 channel_dec.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

C.21 channel_simulator.m . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

C.22 GSMsim_demo.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

C.23 GSMsim_demo_2.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

C.24 gsm_set.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

C.25 T_SEQ_gen.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

C.26 GSMsim_config.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

C.27 make_interleave_m.m . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

C.28 make_deinterleave_m.m . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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1Introduction

WITHIN the last decade the high frequency electronic design community has displayeda renewed interest in CMOS (Complementary Metal Oxide Semiconductor) integrated

circuits. This is primarily due to the cost effectiveness of CMOS implementations when com-pared to for instance Bipolar, BiCMOS, or GaAs (Gallium Arsenide) implementations. Also,CMOS design has the potential of low voltage and low power operation. These are key wordsof significant – and increasing – importance, especially in the design of portable handsets forcellular radio communications.

The use of CMOS is in most wireless equipment limited to DSP (Digital Signal Processing)applications and low frequency analog designs [18]. The potential of CMOS for high frequencyapplications motivates much of todays research in integrated circuit design. As a result, designspresenting high frequency CMOS applications are starting to emerge [1, 4, 5, 7, 19]. At higherfrequencies the analog signal processing limitations of CMOS are more apparent [17]. Here,moving traditional analog signal processing tasks to the digital domain may prove advantageousfor CMOS. Hence, to fully evaluate the performance potential of RF-IC CMOS based front-ends it is advantageous to take a system level approach. To accomplish this it is chosen toconsider the GSM (Global System for Mobile Communication) system, as this currently is themost wide spread of all the cellular systems [2]. Also, GSM is a system with very well definedspecifications.

1.1 Approach and Conceptual Transceiver Structure

The intention is hence to develop a software platform capable of generating a series of appropri-ate GSM data blocks and subsequently perform correct reception of these. Complex baseband

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representation is chosen as this reduces the required simulation sample rate and thus also theoverall simulation time and memory consumption. Moreover, it is chosen to implement the toolas an MATLAB [13] toolbox, as this provides an easy entry to implementing the simulationtool. Also, an excellent graphics tool is readily at hand when using MATLAB. This makesillustrating and verifying the product an easy task.

To analyze specific front-end architectures and designs for GSM operation one just have toinsert a software description of the receiver – or transmitter – prior to running the demodulator.The front-end description must, of course, comply with some predefined interface restrictions.The toolbox described consists of baseband parts only. More specificly, the parts included areillustrated in Figure 1.1, where a conceptual block diagram of a GSM transmitter and receiversystem is sketched. Only the highlighted blocks are implemented.

Figure 1.1: Conceptual block diagram for a GSM transmitter/receiver system.Only the six highlighted blocks are included in the toolbox.

The voice interfaces – including microphone, speech encoder/decoder, and loudspeaker – arenot intended to be included in the toolbox. Instead, to supply the input signal to the channel en-coder/interleaver random bits are generated, as Figure 1.2 displays. By comparing this randominput sequence with the reconstructed sequence delivered by the channel decoder/de-interleaverblock the BER (Bit Error Rate) performance of the system is estimated.

The RF-Tx, RF-Rx, and the mobile channel blocks are optional as to the closed loop structureof the toolbox. If run without any of these blocks the simulation proceeds flawless. The toolboxprovides for easy inclusion of user defined RF blocks and mobile channel. The toolbox mayhence be seen as a three part tool consisting of a data transmitter part, a receiver part, and anoverall simulation flow control part. Each of these three separate parts consists of one or moreMATLAB functions.


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Figure 1.2: Block diagram illustrating the data structure of the implemented soft-ware. Dashed blocks are optional in the simulation runs.

1.1.1 Overall Transmitter Structure

The overall structure of the implemented transmitter is illustrated in Figure 1.3. The transmitteris, as illustrated, made up of four distinct functional blocks.

Figure 1.3: Display of the overall structure of the transmitter part of the toolbox.The input and output labels, TRAINING�OSR� I� and Q all relateto actual parameters used in the implementations.

To provide an input data stream to the channel encoder/interleaver a sequence of random databits is generated by the random bit generator. This sequence is – after processing – then ac-cepted by the MUX which splits the incoming sequence to form a GSM normal burst. Asthis burst type requires that a training sequence is included this also must be supplied. Thisis in Figure 1.3 illustrated by the TRAINING parameter. The term TRAINING is alsoused throughout the software implementations to represent the training sequence. Upon havinggenerated the prescribed GSM normal burst data structure the MUX returns this to the GMSK-modulator, where GMSK is short for Gaussian Minimum Shift Keying. The GMSK-modulatorblock performs a differential encoding of the incoming burst to form a NRZ (Non Return toZero) sequence. This modified sequence is then subject to the actual GMSK-modulation afterwhich, the resulting signal is represented as a complex baseband signal using the correspondingI and Q signals. The number of sample values per data bit, OSR � rb, is left as an user definable


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parameter. It is here customary to operate using four samples per bit, hence, an OSR of four isnormally used [15].

The actual theory behind the transmitter blocks, the parsing of parameters, and the data flowswithin the transmitter implementations are described in detail in Chapter 2.

1.1.2 Overall Receiver Structure

The overall structure of the implemented data receiver is illustrated in Figure 1.4. Here threefunctional blocks are designed in order to implement the data receiver.

Figure 1.4: Display of the overall structure of the data receiver part of the toolbox.The input and output labels, r� OSR� TRAINING�Lh� and dec dataall relate to actual parameters used in the implementations.

The demodulator accepts a GSM burst, r, using a complex baseband representation. Based onthis data sequence, information concerning the oversampling rate OSR, the training sequenceTRAINING, and the desired length of the receiving filter, Lh, the demodulator determines themost probable bit sequence. This demodulated sequence is then used as input to the DeMUXwhere the bits are split in order to retrieve the actual data bits from the sequence. The remainingcontrol bits and the training sequence are here discharged. As a final operation to retrieve theestimated transmitted bits channel decoding and de-interleaving is performed. It is important tonote that the parameter values of OSR and TRAINING used in the receiver must equal thoseused in the transmitter.

The parsing of parameters and data flows within the receiver functions are described in detail inChapter 3.

In Chapter 4, the topics of installation and use of the GSMsim toolbox is covered.

After this very general introduction to the implemented toolbox the following two appendicesprovide a summary of the theory behind the functions and the actual structure of the imple-mented functions are also presented in detail. The blocks indicated in Figure 1.2 as beingoptional are not considered further in the document.

The MATLAB source code used for implementing the central parts of GSMsim is included inAppendix C.


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2Transmitter Background

This chapter presents the functional structure of the implemented transmitter as well as presentsthe individual MATLAB functions developed as part of the transmitter implementation. Theoverall structure of the transmitter, presented in Figure 1.3, is used to indicate where the variousfunctions belong in the transmitter data flow. The implemented functions are described withrespect to input/output parameters and the underlying theory. For a full description of the actualimplementations please refer to Appendix A.

This chapter is divided into three sections. The first section describes the implemented datagenerator, channel encoder, interleaver and multiplexer while the second section addresses thedifferential encoder and the GMSK-modulator implementations. Finally, the third section de-scribes some of the tests performed to verify the operation of the transmitter implementation.

2.1 Data Generation, Channel Encoding, Interleaving, andMultiplexing

The generation of data and the tasks of interleaving the data, performing the channel encod-ing, and multiplexing the resulting data segments are implemented in three separate blocks.These blocks then make sure that a correct GSM normal burst bit format structure is generated.This is done by first generating a series of random bits which, in turn, are inserted in a pre-scribed frame structure. To implement this combined operation four functions, data_gen.m,channel_enc.m, interleave.m, and burst_g.m, are used. These functions are shownin Figure 2.1.


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Figure 2.1: Illustration of the transmitter implementation. The relations betweenblocks and actual implemented functions are indicated.

2.1.1 Data Generation

The function data_gen.m is in fact a very simple function as it is based on the rand func-tion included as a default function in MATLAB. As input data_gen.m accepts an integer,INIT L, representing the desired length of the random bit sequence that the function is to re-turn as output. The variable name tx data is used to return the random data output. Note thatthe data are generated using the MATLAB function, rand, which produces up to �� randomnumbers before repeating itself. As described in section 2.1.2 a single GSM data block uses�� random bits. The maximum number of blocks that may be simulated before rand starts torepeat itself can be found to

Blocksmax ��

�� (2.1)

This number of burst is more than enough to secure prober statistics for the simulations.

2.1.2 Channel Encoding

The purpose of the channel encoder is to provide the GSM receiver with the ability to detecttransmission errors and eventually correct some of these. This is to improve the transmissionquality from a bit error point of view. Various encoding standards are used in GSM dependingon the mode of transmission. The encoding implemented here goes for the burst type TCH/FS(Traffic CHannel Full rate Speech) which is a normal speech burst.

The channel encoding is here implemented by the function channel_enc.m. As its input,tx block, the channel_enc.m accepts a 260 bit long vector. The content of tx block isencoded to produce a 456 bit long vector which then is returned as output using the variablename tx enc.

More specificly channel_enc.m splits the incoming 260 information bits into three different


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classes, i.e. class Ia, class Ib, class II, depending on the importance of the bits. For instance, anytransmission errors in the class Ia bits effect the overall speech quality more severely than errorsin class II bits. Due to this variation in bit importance the different classes of bits are encodedaccordingly. The channel encoding scheme utilized in GSM is illustrated in Figure 2.2.

Figure 2.2: Channel encoding in GSM. A total of 196 redundant bits are added.

The channel encoding scheme is thus as follows. The 50 most significant class I bits, the classIa bits, are extracted from the sequence and parity encoded. The parity encoder used in GSM isa systematic cyclic encoder based on three check bits. Systematic means that the parity bits areadded to the original class Ia bit sequence. This way the class Ia bits are left unchanged and theresulting code word has the structure

V � f�k data bits��r check bits�g (2.2)

The generator polynomial used in the encoder has a length of 4 bits and is given as [9]

Gx � x� � x � � � G � f��g (2.3)

The check bits are found as the remainder, rx, of the division

xr �Dx

Gx� Qx �

rx

Gx� (2.4)

where the number of check bits is given by r, Dx represents the data bits intented for encodingand Qx the division quotient. The remainder, rx, is then directly used to form the check bitsequence required in generating V .

The multiplication xr �Dx is equivalent to shifting Dx r places to the left. Also, the imple-mentation makes use of a default function, deconv.m, provided by MATLAB to perform thedivision.


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After parity encoding of the class Ia bits these are recombined with the class Ib bits and a tailsequence of four zeros is finally added. The resulting class I sequence, now consisting of 189bits, is then feed to the convolution encoder.

The convolution encoder takes a block of k bits as input and returns a block of n bits as output.The rate of the encoder, defined as the ratio k�n, is in the GSM system specified to be ��.In the convolution encoding scheme each output bit, cn, is depending not only on the inputbit presently being encoded, bk, but also on some of the previous input bits. The number ofinput bits required in the processing of encoded output bit is called the constraint length of theencoder. GSM specifies a constraint length of 5 in its encoding scheme defined as

c�k � bk � bk�� bk��

c�k�� bk � bk�� bk�� bk��

where � implies modulo 2 addition, and

k � f�� g and bk � � for �� k � � (2.5)

As the convolution encoder is defined as a rate �� encoder two output bits are generated forevery input bit, hence the two expressions. When operated as a shift register the convolutionencoder takes on the form illustrated in Figure 2.3.

Figure 2.3: The convolution encoder scheme used in GSM for encoding ofTCH/FS bursts. All additions are modulo 2 additions.

The combined channel encoder implementation is found in Enclosure A.

The two encoding schemes in the channel encoder are tested separately. Both the parity and theconvolution encoder operates as expected. As an example, a typical input/output scenario forthe combined encoder is illustrated in Figure 2.4. Notice that the output rate is twice the inputrate.

Figure 2.4 illustrates the encoding of the 25 first bits of input data and, as such, the effects ofparity encoding is not displayed.


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Figure 2.4: Typical input/output scenario of the combined channel encoder. Theseed value used in data_g.m is 931316785.


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2.1.3 Interleaving

The interleaver shuffles the bits contained in the data blocks output from the channel encoder,and distributes them over a number of bursts. The input variable is thus tx enc, and the outputis delivered to a number of instances of the variable tx data. The purpose of this procedure isto ensure that the errors that appear in a received data block are uncorrelated. The motivationfor reducing the correlation between bit errors is that the convolution code used to protect theclass I bits has better performance when errors are not correlated [16]. Correlation between biterrors can occur in for example fading conditions.

The interleaver operates according to the following two formulas [15]

b � �� T mod � � t � �� t mod � mod �� (2.6)

B � T � b mod � div �� (2.7)

which imply that bit number t in tx data intended for burst number T is found in instanceB of tx enc as bit number b. In the above x mod y is the remainder of the division x�y,and x div y is the corresponding quotient. The operation of (2.6) and (2.7) are illustrated byFigure 2.5.

Figure 2.5: Illustration of the interleaving prosess as described by (2.6) and (2.7).

It can be realized by writing (2.6) and (2.7) out for a significant number of bursts, that theinterleaver can be implemented so that it operates at two code blocks at a time. For eachinterleaving pass four sets of tx data are returned. These data are further processed in themultiplexer, which is described in the next section. Since two instances of tx enc contain twotimes 456 bit, and four set of tx data contain 456 bit, it is evident that all the bits containedin the input to the interleaver are not represented in the output. This is solved by passing eachcode block to the interleaver two times. In practice this is done by implementing a queue ofcode blocks, as illustrated in Figure 2.6.

The interleaver is implemented in the MATLAB function interleave.m, and the four setsof tx data, are returned in a matrix for convenience. For speed optimization the interleavingpositions are precalculated in the implementation. This precalculation is implemented in thefunctions make_interleave_m.m and make_deinterleave_m.m


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Figure 2.6: Operation of the interleaver, aided by a queue. The interleaver readsout the entire content of the queue. The queue has two slots, and ineach interleaving pass a new block is pushed into the queue, and theeldest block is discarded.

2.1.4 Multiplexing

The input to the Multiplexer is tx data, and the output is given in tx burst. What the mul-tiplexer does, is to take tx data from the interleaver, and place it appropriately in a framestructure. The GSM-recommendations dictate specific burst structures for different transmis-sion purposes. The implemented burst, referred to as a GSM normal burst, has the structuredisplayed in Figure 2.7.

Figure 2.7: The prescribed GSM normal burst structure. The number of bits ineach part of the burst is indicated by the integers above the individualparts.

From Figure 2.7 is is clear that the GSM normal burst is made up of � � �� bits in total. Of these 148 bits, � � �� are pure data bits. Hence, burst_g.m mustaccept a total of 114 bits as input when a normal burst is considered. Of the 114 data bits inputto the multiplexer only �� bits are true information bits, as can be seenfrom section 2.1.3. 65 information bits out of a total of 148 transmitted bits corresponds to atransmission efficiency of approximately 44%.

The bit patterns included below the burst sequence in the figure indicate that these parts havepredefined patterns that must be complied with. For instance, the tail bits must constitute ofthree zeros, f��g, while the control bits can be selected at random as these are left unusedin the normal burst. The training bit sequence can be any of eight prescribed ones. Thus,to form this burst structure the multiplexing involves tx data as well as a training sequence,TRAINING. These are then ordered in the correct manner and supplemented by tail and


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CTRL bits to form the correct output format returned using the variable name tx burst.

2.2 GMSK-Modulation

The implemented GMSK-modulator is made up of three functions, namely diff_enc.m,gmsk_mod.m, and ph_g.m, as illustrated in Figure 2.8.

Figure 2.8: The functions diff_enc.m, gmsk_mod.m, and ph_g.m are allrelated to the GMSK-modulator implementation.

These three functions implement two separate tasks, as both a differential encoding of the burstsequence as well as the actual GMSK-modulation is performed. These two operations aredescribed further in the following sections.

2.2.1 Differential Encoding

The output from the MUX, burst, is a binary {0, 1} bit sequence. This sequence is is firstmapped from the RTZ (Return To Zero) signal representation to a NRZ representation beforebeing input to the GMSK-modulator. This task is accomplished by the function diff_enc.m.

GSM makes use of the following combined differential encoding and level shifting scheme,where d � f�� g and a � f�� g represent input and output sequences, respectively[10]

�d�n� � d�n�� d�n� ��

(2.8)

a�n� � �� d�n��To avoid the start condition problem the GSM-recommendation [10] prescribes that an infinitelength sequence of all ones are assumed to precede the burst to be processed. Hence, whencalculating a��, and thereby also �d��, it may be assumed that d�� is one.


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The above encoding scheme is directly implemented in diff_enc.m where the variablesburst and diff enc data are used to represent the input and output sequences, respectively.That is to say, that burst equals d and diff enc data equals a when comparing (2.8) to theactual implementation.

2.2.2 Modulation

After the differential encoding of the information burst the signal is GMSK-modulated. This isimplemented by the function gmsk_mod.m where a complex baseband representation of themodulated signal is obtained.

GMSK is a modulation form derived from the very similar MSK (Minimum Shift Keying). Bothare variants of the more general CPFSK (Continuous Phase Frequency Shift Keying) modulationforms.

Mathematically the generation of a MSK-signal may be described as

st� a �

s�Ec

Tbcos f��fct ��t� ag � (2.9)

where Ec is the bit energy, fc the carrier frequency, and �t� a the information carrying phaseof the MSK signal. Through the use of a complex baseband notation fc may be removed fromthe expression whereby Sine and Cosine values of �t� a is sufficient in describing the signal.This may be seen from the general complex baseband definition

st� a � A � cos f��fct ��t� ag� A �sct� a cos f��fctg � sst� a sin f��fctg� � (2.10)

where A describes the carrier amplitude and �t� a the phase modulation of the carrier. Also,in obtaining (2.10) the following definition is introduced

�st� a � sct� a � j � sst� a � ej��t�a

� cos f�t� ag� j � sin f�t� ag � (2.11)

which represents the complex envelope of the modulated signal. From (2.11) it is clear that bytaking the Cosine and the Sine of �t� a two low-pass baseband signals results, the in-phase,I , and the quadrature-phase, Q, signals, respectively. These two low-pass signals fully describethe original signal as described by (2.9).

Making use of the following pulse shaping function, pt, definition

pt �

�� cos

��t�Tb

��Tb � t � Tb

� otherwise�(2.12)


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the in-phase and quadrature phase components, sct� a and sst� a, may be rewritten using thefollowing linear form [8]

sct� a � pt act �X

n even

ac�n� � pt� nTb (2.13)

sst� a � pt ast �Xn odd

as�n� � pt� nTb� (2.14)

where the weighted impulse responses, act and ast, are given as

act �X

n even

ac�n��t� nTb� ac�n� � cos��n� (2.15)

ast �Xn odd

as�n��t� nTb� as�n� � sin��n�� (2.16)

where � is the Dirac pulse function and ��n� is given as

��n� ��

�

n��Xk�

a�k� (2.17)

To further simplify the MSK-baseband description a complex sequence, I , is introduced wherethe complex data symbols are given as

I�n� ej��n � cos��n� � j � sin��n� � ac�n� � j � as�n� (2.18)

Based on this complex definition the MSK-baseband representation may be described as onesingle convolution [3]

�st� I � pt at �Xn

I�n� � pt� nTb� (2.19)

whereat �

Xn

I�n� � �t� nTb (2.20)

Returning to the definition in (2.18) it is found that I�n� alternating assumes real and imaginaryvalues. This is a direct result of ��n� � f�� g. This leads to the following recursiveMSK-mapping definition [3]

I�n� � j � I�n� �� a�n� �� (2.21)

where

I�n� � f�� j��jga�n� � f��g

Further, in the GSM-recommendations [10] a differential encoding scheme is prescribed. Incor-porating this encoding with the MSK-description in (2.19) an OQAM (Offset Quadrature Am-plitude Modulation) MSK-model, including the GSM differential encoding, is obtained. Thismodel is illustrated in Figure 2.9.


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Figure 2.9: Final OQAM-model for MSK including the differential encoding pre-scribed in GSM.

This simplified MSK-representation comes in handy when trying to understand the structure ofthe data detector presented in Section 3.2.

In GMSK the phase shift are made smoother than in for instance MSK. This results in a morenarrow frequency spectrum. The price paid for the desirable bandwidth reduction is ISI (InterSymbol Interference) which results in an increased BER. A GMSK-signal can be generatedusing different approaches, e.g. the approach illustrated in Figure 2.9 with an appropriate choiceof pt. The implementation used here is some what different as illustrated in Figure 2.10.

Figure 2.10: GMSK-baseband modulator implementation.

From Figure 2.10 it is seen that the symbol sequence, �, is convolved with gt, which is afrequency pulse function, and then multiplied with �, resulting in the generation of the phasefunction �t� �.

The phase function, �t� a, may be written as [10]

�t� a �Xi

a�i��hZ t�i�

��

gd� (2.22)

where h the modulation index which for GSM equals 1/2. The frequency pulse function, gt,is mathematically defined as a convolution in time of a rectangular pulse, vt, and a Gaussianfunction, hgt

g�t � vt hgt� (2.23)

where [10]

vt �

��Tb for � � jtj � Tb�� otherwise

(2.24)


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hgt ��p

��Tbexp

� �t��T �

b

where �

pln �

��BTb(2.25)

The 3 dB bandwidth, B, of the Gaussian function is specified by the normalized bandwidth,BTb, which is specified to 0.3 for GSM [10]. The ideal Gaussian function has an infinite timeduration, t � ��. For reasons of signal processing this signal is truncated to a specificlength, L where OSR and L then determine the number of samples used to represent the bellshaped Gaussian pulse. Typically, a value higher than 3 is chosen for L [12]. To make thefrequency pulse function causal it is time shifted by an amount of LTb��. This results in thefollowing truncated frequency pulse

gt � g��t� LTb

�

�� wLt where wLt �

�� for � � t � LTb� otherwise

(2.26)

To provide this information the function ph_g.m is used. Based on two input parameters,BTb, and OSR the function calculates the required values of the frequency and phase shapingfunctions gt and qt, respectively. These values are returned using the output parametersg fun and q fun for the frequency and phase functions, respectively.

The different stages in generating the truncated frequency pulse function, gt, and eventual thephase smoothing response function, qt, are shown in Figure 2.11. The first two plots, Figures2.11a and 2.11b, illustrate functions that are made use of internally to the function ph_g.mwhile Figures 2.11c and 2.11d illustrate the output functions g fun and q fun, respectively.

Please note that the function is implemented assuming a truncation length, L, of 3. Hence,ph_g.m returns � �OSR samples of gt and qt within the interval 1 to 4 t�Tb.

Having generated the required shaping information the function gmsk_mod.m performs theactual calculation of the phase value �t� a. This is done by a sliding window approach wherethe gt function is slid across the input sequence while accumulating the previous phase infor-mation.

The structure of the implemented GMSK-modulator is, however, based on gmsk_mod.m call-ing the ph_g.m function and as a result a few extra input parameters are required. To performcorrectly gmsk_mod.m requires four input parameters need to be specified. These are the dif-ferential encoded information sequence, burst, the bit duration, Tb, the normalized bandwidth,BTb, and the simulation oversample ratio, OSR. Of these four input parameters the two, BTb,and OSR, are passed on to ph_g.m.

The resulting phase function is evaluated through Sine and Cosine to obtain the in-phase, I , andquadrature phase, Q, values returned by the function. The variables i and q are used to returnthe in-phase and the quadrature signals, respectively.


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Figure 2.11: Step-by-step illustration of the generation of the phase smoothingfunction. a) The rectangular pulse, b) the Gaussian bell shape. c)The resulting frequency pulse function, and d) the equivalent phaseshaping function.


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2.3 Transmitter Test

To test the operation of the implemented transmitter two time-domain tests and a single fre-quency domain test are carried out.

First the result of a time domain test of the relationship between the I andQ signals is illustratedin Figure 2.12.

Figure 2.12: I and Q baseband outputs from the implemented modulator whengiven a random input sequence.

From this the I and Q signals are seen to display the expected behavior. When compared withother visualizations found in relevant literature the in-phase and quadrature phase signals arefound to resemble these. Furthermore, as the I and Q signals are given as cos� and sin�,respectively, the following relation must be fulfilled at all times

I�n �Q�n � cos�� sin�� (2.27)

This relation has been tested in MATLAB and the result shows that the I and Q signals arecorrectly related as a result of � is obtained for every sample value tested.

A second time domain test is performed by feeding the modulator a sequence consisting of allones. This is equivalent to transmitting a GSM frequency correction burst. As every one of thetransmitted ones eventually adds �� to the phase of the signal four bits are required before thesignal returns to its initial phase state. The rate of the input sequence then determines the speedof this phase rotation. Hence, when delivered such a sequence the modulator should return asinusoidal signal of frequency rb�� for both I and Q channels. Due to the Sine/Cosine relationthe Q channel should trail the I channel by an amount of one Tb. This is illustrated in Figure2.13.


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Figure 2.13: I and Q (dashed) signals when the modulator is given a sequence ofall ones.

Figure 2.13 illustrates the I and Q channels over a time period of 20 Tb’s. From this the mod-ulation is seen to operate as expected as the signals display periods having a time durations of4 Tb’s, which of course equals rb��. Thus the time domain test indicate that the performance ofthe system is acceptable.

Also, a frequency test is performed to analyze the spectral properties of the baseband signal,as produced by the implemented modulator. The resulting spectrum is compared to the GSMrequirements and to other reported spectrums [14].

As the resulting power spectrum, shown in Figure 2.14, reveal some filtering need to be imple-mented in order to fully comply with the GSM 05.05 requirements [11]. This tx-filtering is notimplemented in GSMsim.


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Figure 2.14: The power spectrum generated by the modulator. The spectrum isgenerated by averaging over 10000 spectras produced by GMSKmodulated sequences each 1024 bits long. In the simulation a sam-ple rate of fs � �� rb is used. The dashed line represents the GSM05.05 requirement [11].


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3Receiver Background

The receiver implementation used in the GSMsim toolbox is shown in Figure 3.1. In the diagrampresented in the Figure 3.1 the demodulator block part of the data receiver is expanded comparedto the diagram illustrated in Figure 1.4. Hence, the demodulator part of Figure 1.4 is expandedinto three separate blocks.

In this chapter the theory underlying the function of the implementation is given a short intro-duction.

Figure 3.1: Block diagram of the receiver implementation used in the GSMsimtoolbox.

As described in Chapter 1, the receiver implementation does not include a front-end, since theoriginal intention with the toolbox is to provide for easy simulation of user defined front-ends.This has the effect that no channel selection, or filtering, is done, since the implementation ofsuch vary with the front-end implementation.

The contents of this chapter is divided into four sections. The first section describes, synchro-nization, channel estimation, and matched filtering. The second section introduces the theory


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underlying the MLSE (Minimum Least Square Error) implementation. The third section con-tains a short introduction of the de-multiplexer, de-interleaver, and channel decoder. None ofthe three sections provide an in depth treatment of the subjects, but rather provide for a sum-mary of the used techniques. The last section contains a description of tests performed on thereceiver implementations.

3.1 Synchronization, Channel Estimation, and Matched Fil-tering

Synchronization, channel estimation, and matched filtering is done in a two step process. Thisis illustrated in Figure 3.2. For the matched filter to operate correctly the synchronization andchannel estimation must be done first.

Figure 3.2: Illustration of how the synchronization, channel estimation, andmatched filtering is divided into two parts.

As can be seen from Figure 3.2 both the channel estimator and the matched filter have thesampled received signal, r, as input. r is a sampled sequence which is expected to contain thereceived GSM burst. Also, the oversampling factor, OSR, described as fs�rb, with fs being thesample frequency, and rb the symbol rate, is input to both of these two blocks. Finally, thesetwo blocks have Lh as input, where Lh is the desired length of the channel impulse responsemeasured in bit time durations. The channel estimator passes an estimate of the channel im-pulse response, h, to the matched filter. Also, the channel estimator passes the sample numbercorresponding to the estimated beginning of the burst in r.

To interface correctly with the MLSE implementation mf.m must return a down-sampled –one sample per symbol – version of the now matched filtered burst. Also, the MLSE requiresinformation concerning the matched filter. This information is supplied by also returning theimpulse response autocorrelation, i.e. Rhh.


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To understand the operation of mf.m, recall from earlier that a training sequence is insertedin each burst. The method used for obtaining synchronization is based on the mathematicalproperties of this training sequence.

The training sequence, TRAINING, used in GSMsim is as follows [15]

TRAINING � �� (3.1)

for which the following MSK-mapped equivalent, TSEQ, is used

TSEQ � (3.2)

�� j� ��j� ��j�� j��j��j� �� j� ��j� �� j� ��j� ��j�� j��j��This sequence is one of eight predefined training sequences when a normal burst is considered.Now, from TSEQ the central sixteen MSK-symbols are picked and referred to as TSEQC . IfTSEQC is extended by placing five zeros in both ends, a sequence, TSEQE , is obtained. This isdone in order to obtain equal length vectors that, when evaluated using the following MATLABcommand

stem(abs(xcorr(T_SEQ_E, T_SEQ))),

produces a result similar to that presented in Figure 3.3.

Figure 3.3: Cross correlation between TSEQ and the extended version of TSEQC .n represents the number of samples that the two sequences have beendisplaced in calculating the correlation value.

What Figure 3.3 illustrates is that

RTSEQC �TSEQ�

��

�� for n � �� for n � f��g� otherwise�

(3.3)


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where the question mark represents the undefined correlation noise that is found outside of theinterval n � ��.

The result presented in Figure 3.3 may be verified through manual calculations, using the fol-lowing

RTSEQC �TSEQ�n� � TSEQC �� TSEQ� (3.4)

where denotes convolution, and TSEQC �� is T �

SEQCwith its elements reversed. This property

is useful since the received signal corresponding to the transmission of the training sequence,here called rTSEQ, may be written as

rTSEQ � TSEQ h� w� (3.5)

where h is the channel impulse response, and w is unknown additive noise. If convoluting thiswith TSEQC �� then the following is obtained

rTSEQ TSEQC �� TSEQ TSEQC �� h� w TSEQC �� (3.6)

�

��h� w TSEQC �� for n � �

w TSEQC �� for n � f��g (3.7)

��

��h for n � �� for n � f��g � (3.8)

The approximation leading from (3.7) to (3.8), is based on the assumption that the noise, w iswhite and the knowledge that TSEQ has white noise like properties, as illustrated by Figure 3.3.It is indicated by the above, that if an entire burst containing TSEQ is considered, then similarcalculations can be done. Thus, if an entire burst is convoluted by TSEQC �� it is seen that anestimate of the channel impulse response is present in the result, called v. Also, it is observedthat the estimate of the impulse response that is contained in v is likely to be more powerfulthan the neighboring contents of v. This is due to the factor sixteen and the zero samples. Thisknowledge leads to the sliding window technique, which allows for both channel estimation andsynchronization at the same time.

The sliding window technique uses the fact that in the GSM system coarse synchronization ispresent on the basis of dedicated synchronization bursts. This coarse synchronization is usedfor sampling a time interval of the received signal, in which the desired burst is likely to befound. This, possibly oversampled, sample sequence is referred to as r.

The first step in the sliding window technique is to convolute r with TSEQC ��, to obtain asignal v

v � r TSEQC �� (3.9)

Here, v is an intermediate result, and all samples in v are immediately squared to yield an energyestimate e

e�n� � v�n�� (3.10)


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Now the window energy, we, is found using

we�m� �m�LXkm

e�k�� (3.11)

for all but the last L samples in e, where L � Lh OSR � �. The sample mmax in wecontaining the highest energy value is estimated as corresponding directly to the first sample ofthe channel impulse response in v. From mmax, and the known oversampling ratio, it is nowpossible to extract an estimate of the channel impulse response, and also calculate the beginningof the burst.

Note from the above that the obtained channel impulse response estimate, h, cannot be anylonger than five Tb’s. This is due to the number of zero samples surrounding the peak in (3.3).In the present implementation the length of h measured in bit time durations has been limited,as is expressed by Lh

Lh � f�� g� (3.12)

In this context, it is worth noting that the number of samples in h is given as OSR � Lh � �,and not Lh.

In the described procedure the entire r sequence is processed. In the actual implementation,however, only a sub-sequence is processed. This is possible since the location of the trainingsequence within a GSM burst is known. Refer to Section B.1 for details on this.

Having obtained sample synchronization, and an estimate of the channel impulse response, thematched filtering can be done as

Y � r h�� (3.13)

Along with the filtering of r down sampling is done as well. This is needed since r contains atleast fs�rb as many samples as desired in Y . Recall here that Y must contain one sample perMSK symbol in the received burst. In this work a special technique is used so that the obtainedsynchronization is not lost during the matched filtering described by (3.13).

All the functions described in this chapter are implemented in a single MATLAB function,called mf.m. The actual implementation of mf.m is described in Section B.1.

3.2 Minimum Least Square Error (MLSE) Detection

The part of the receiver that handles the actual detection of the received sequence is the MLSE(Minimum Least Square Error) Detector. Here, the MLSE is implemented as a Viterbi equalizerbased on the modified Ungerboek algorithm [3]. The placement of the MLSE in the receiver isshown in Figure 3.4.

As shown in Figure 3.4, the MLSE input is interfaced by two blocks internally in the receiver.These two blocks are the matched filter, and the channel estimator. The input to the MLSE is


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Figure 3.4: The placement of the MLSE in the overall receiver structure.

the matched filtered and down sampled signal, referred to as Y , along with Rhh which is theautocorrelation of the estimated channel impulse response. Y is a sequence of samples, andcontains one sample for each transmitted symbol. The output of the MLSE, rx burst, which isan estimate of the most probable sequence of transmitted binary symbols.

The MLSE, as it is implemented here, operates on basis of the system shown in Figure 3.5c. Tounderstand the figure, recall the alternative OQAM transmitter model described earlier on page13.

Figure 3.5a, included for comparison, represents the implemented system. The implementedmodulator structure is merely one of a number of possible solutions, in fact, the structure shownin Figure 3.5b can be used with the same result. This is exploited in Figure 3.5c where the MLSEis shown as an Viterbi detector which assumes a system where a stream of MSK-symbols aretransmitted trough an extended mobile channel. This extended channel is purely fictive andcovers the full signal path from the output of the MSK-mapper to the input of the matchedfilter. The MSK-symbols may be obtained from the binary sequence to be transmitted, andvice versa. It is thus sufficient to find the transmitted sequence of MSK-symbols, and then mapthese symbols to binary information. Therefore, the Viterbi detector estimates the sequence ofMSK-symbols input to the extended mobile channel.

In order for the implemented algorithm to work the system bounded by the label I and thematched filter output in Figure 3.5c is required to have a causal impulse response, h, of fi-nite duration Lh. This requirement seems reasonable when considering the real life scenario.Furthermore, it is required that this impulse response does not change significantly during thereception of a GSM burst.

With these requirements the bounded system may be considered as a finite state machine witheach state, to the discrete time n, only depending on the previous Lh MSK-symbols in I . Thatis, the MSK-symbols trigger the state shifts of the machine and thus, the next state is uniquelydetermined by the present MSK-symbol in I . The state of the machine to the time n is referred


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Figure 3.5: Various representations of a general baseband transmission system. a)The transmission system showing the implemented system. b) Thesystem as it is described using the OQAM model. c) The system onwhich the MLSE is based.


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to as �n� and is represented as

�n� � �I�n�� I�n� �� I�n� Lh � �� (3.14)

in which the right hand side is the sequence of the last Lh MSK-symbols. In general states, forwhich I�n� assumes one of the values�j or j, are referred to as complex. Likewise states whereI�n� assumes one of the values �� or �, are referred to as real. This is to prove useful later inthis section.

In order to find the number of legal states, recall from the description of the OQAM receiver onpage 13, that four MSK-symbols exist, namely �� j and �j. Also, recall from the above,that a state is described by the last Lh symbols. Additionally, recall from the description of theOQAM receiver on page 13 that if the symbol I�n� to the time n is real, then I�n�� is complex,and vice versa. From this it is evident, that the number of states, M , is given by

M � �Lh�� (3.15)

which is the number of possible states at any time. In the above, �n� is thus contained in a setof states consisting of M states. If referring to the individual states as sm, then this set can beexpressed as

�n� � fs�� s�� sMg� (3.16)

The concept that �n� belongs to a set of states, which may be numbered from � to M , is useddirectly in the implementation done in the present work. Internally in the program a state isuniquely identified by an integer, called the state number, and not by MSK-symbols. Referringto (3.15), and observing that Lh is limited to four – or less – it is seen that the number of statesin the state machine is thirty two or less. In the implementation there is no consciously prede-fined mapping between the MSK-symbols and the state numbers. Alternatively to a predefinedmapping, a mapping table is constructed at runtime. This mapping table can be referred to forretrieval of the MSK-symbols whenever they are needed. The lookup is done using the statenumber as an index. Using the state number representation a mutation of the present state toobtain the legal previous and next states requires a call to the integer to symbols mapping table,followed by the actual mutation. In order to avoid the undesirable overhead associated with this,a set of transition tables are constructed. These transition tables can be used to obtain the legalnext states or previous states by using the present state number as an index. Apart from limitingthe legal previous and next states relative to a single state, it is possible to reduce the number oflegal states to any discrete time. This is due to the fact that it is possible to determine a uniquestart state of the algorithm [15]. Since the MSK-symbols are shifting between complex and realvalues, knowledge of the start state effectively limits the number of legal states at any time toM��. To see this refer to the formal state representation given by (3.14). In consequence of thisit can for example be stated that if the start state, to n � � is complex then the state to n � ��is also complex.

Having established the state concept, the problem of finding the most probable sequence ofMSK-symbols now changes to locating the most probable path trough a state trellis. The con-cept of a state trellis is illustrated in Figure 3.6 for Lh � �. Note that actual state trellises have


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M � �� different states and just as many transitions as there are samples in Y . This is aresult of Y containing one sample per transmitted symbol.

Figure 3.6: The transmission of a sequence of MSK-symbols using Lh � � and atransmitted sequence equal to I � ��j� �� j� �� j��. The describedstate machine assumes a new state to each discrete time n.

When operating with the trellis concept, it should be noted that all states have two legal nextstates. This can be realized by recalling that

I�n� � f��g � I�n� � fj��jg� (3.17)

which in turn implies that all states have only two legal previous states.

Turning the attention to the method for finding the most probable path trough the trellis, theconcept of an metric is introduced. To all discrete times n, all states m have an associatedsurvivor metric. In the present implementation of the metric calculation, the rule is, that thehigher the metric value the better. The term survivor stems from the fact that two paths leadto every state. Each path results in a metric for the state. The survivor metric is the highestvalued of the two metrics. The metric of a path to a state is found by taking the metric of theprevious state in the path, and then adding a contribution generated by the transition from theprevious state to this state. The concept of survivor metrics is illustrated in Figure 3.7. Theactual computation of the metric increment related to a state transition – referred to as a gain,Gain, in the metric – is is done on the basis of the following formula [3]

GainY �n�� sa� sb � � fI��n�Y �n�g

�� I��n�

n��Xmn�Lh

I�m�Rhh�n�m�

�� jI�n�j�Rhh�� (3.18)

where sa and sb is previous and present state, respectively, described by their MSK-symbols.Yn is the n’th sample in Y . Note from (3.18) that only the values of Rhh ranging from index �


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to Lh are used. For speed optimization (3.18) is reduced to

GainY �n�� sa� sb � fI��n�Y �n�g � ��I��n�

n��Xmn�Lh


�� (3.19)

which results in the same decisions being made.

Figure 3.7: Illustration of survivor metrics. a) The survivor metric is found bytaking the metric of the two legal previous states, and adding the con-tributions from the transitions. b) The survivor is the path with thehighest valued metric.

The task of finding the most probable sequence, as illustrated in Figure 3.7b, may hence beformulated as follows.

To find the most probable path trough the trellis, start at the predetermined startstate, and continue to the end of the state trellis. While traversing the trellis con-stantly compute survivor metrics for all legal states to all discrete times. Further-more, record, for all of these states to each discrete time, the previous state that waschosen as contributor to the survivor metric for the individual state. Having pro-cessed the entire state trellis, the state with the highest metric, at the final discretetime, is chosen to be the last state in the most likely sequence of states. Havingfound the final state, lookup what state was the previous state, and continue in thismanner until the entire sequence of states in the most likely path is established.

From the sequence of states the sequence of symbols is readily found from the first elementof the MSK-symbols which make up each state. The MSK-symbols may readily be MSK de-mapped to obtain a NRZ representation. This de-mapped sequence then needs to be differentialdecoded and subsequently transformed into the binary RTZ representation. However, by usingthe following relation the MSK-symbols may be transformed directly into a differential decodedNRZ representation [15]

rx burst�n� � Iest�n��j � rx burst�n� �� Iest�n� �� (3.20)

Hence, (3.20) implements both the MSK de-mapping as well as the differential decoding.


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It is, in (3.20), necessary to identify a start value for rx burst�� and Iest��. From earlier work[15] these are both known to equal unity. In (3.20) the variable rx burst is in NRZ format. Thetransformation to RTZ is done by adding unity to all elements and then divide by two.

The Viterbi detector is implemented in MATLAB. The implementation is split into two func-tions. The splitting is motivated by the fact that the data structures used by the algorithm do notdepend on Y . Thus initialization of state translation tables, need not be done more than oncefor all the bursts in a simulation. Details about the implementation, including a pseudo codedescription of the algorithms, are given in Appendix B.2.

3.3 De-Multiplexing, De-Interleaving and Channel Decoding

The tasks of de-multiplexing, de-interleaving and decoding the data, are implemented in threeseparate blocks. The overall task of these three blocks is to regenerate the transmitted coded datablocks. This functionality is implemented via three MATLAB functions channel_dec.m,deinterleave.m, and DeMUX.m. These functions, and their relation to the block diagram,are shown in Figure 3.8.

Figure 3.8: Illustration of the receiver implementation. The relations betweenblocks and actual implemented functions are indicated.

3.3.1 De-Multiplexing

The de-multiplexer is the first functional block to follow the Viterbi equalizer block in theimplemented receiver. The placement of the de-multiplexer in the receiver structure is illustratedin Figure 3.8.

The input to the de-multiplexer is rx burst, which is output from the MLSE, as described in theprevious section. The output from the de-multiplexer is the contents of the two data fields in a


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standard GSM burst. These data are returned in a variable called rx data. Refer to Section 2.1,and Figure 2.7 on page 11, for an description of a GSM burst as used in the GSMsim toolbox.The de-multiplexer is simple in its function, since all that needs to be done is to locate the datafields in rx burst, and then copy these to rx data. In this implementation the data fields arelocated by using the sample numbers, e.g. the first data field is found in rx burst� � ��.

3.3.2 De-Interleaving

The de-interleaver reconstructs the received encoded data, rx enc, from the received data,rx data. The operation is the inverse of the interleaver, and may thus be considdered as anreordering of the shuffeled bits.

The de-interleaver operates according to the following two formulas [15]

R � � �B � b mod � (3.21)

r � � � � � b mod �� b mod � div �� (3.22)

which provide the information that bit number b for rx enc instance numberB, may be retrievedfrom rx data corresponding to burst number R at position r.

It can be realized by writing (3.21) and (3.22) for a significant number of code blocks, that thede-interleaver can be implemented so that it operates on eight sets of rx data at a time. Foreach de-interleaving pass one instance of rx enc is returned. Since rx enc contains 456 bit,and eight sets of rx data contain two times 456 bit, it is evident that all the bits contained inthe input to the de-interleaver are not represented in the output. This is solved by passing eachset of rx data to the interleaver two times. In practice this is done by implementing a queue ofrx data sets, as illustrated in Figure 2.6.

The interleaver is implemented in the MATLAB function interleave.m. The two timesfour sets of rx data, are passed to the function in matrix form for convenience.

3.3.3 Channel Decoding

The coding scheme utilized in the GSM system may be viewed as a two level coding where aninner and an outer coding is made use of. This is illustrated in Figure 3.10

The inner coding scheme is here made up of the GMSK-modulation and demodulation whilethe outer code is a regular convolution encoding scheme.

The outer code used in GSM, and described in Section 2.1.2, is based on a rate 1/2 convolutionencoder using a constraint length of 5. This implements a finite state machine on which is itpossible to predetermine legal state transitions as was described in Section 3.2. This way it is


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Figure 3.9: Operation of the de-interleaver, aided by a queue. The de-interleaverreads out the entire content of the queue. The queue has two timesfour slots, and in each interleaving pass four new sets of rx data arepushed into the queue, and the eldest four instances are discarded. Oneinstance of rx enc is returned in each pass.

Figure 3.10: Illustration of the two level coding scheme utilized in the GSM sys-tem.


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possible to build a state transition diagram that may be used in the decoding of the receivedsequence. Such a state transition diagram is illustrated in Figure 3.11.

Figure 3.11: State transition diagram for the GSM system.

The state transition diagram of Figure 3.11 is deduced from the transmitter encoder with statesordered in a binary manner. That is, state 1 represents the situation where the encoder has allzeros in its registers, i.e. s� � f� � � �g, while state 2 is given as s� � f� � � �g. This way it ispossible to characterize the encoder completely.

The optimum decoder for a convolution encoded signal is the Viterbi decoder [6] as it representsa recursive optimal solution to the problem of estimating a state transition sequence of a finite-state Markov process. As the principle of the Viterbi decoder has been described in Section 3.2,where the GMSK demodulation is described, this is not addresses further here.

Only the metric used in determining the most probable sequence is of interest as this differ fromthe one used in the mentioned GMSK demodulator. As the convolution decoder operates onbinary information a much simpler metric definition is used. At any particular discrete timeinstance, k, a set of metrics is given by [6]

�sk� �k��Xi�

��i� (3.23)

where sk� � fs�� s�� s�� skg represents a given sequence of states and �i represents the i’thstate transition. The metric increase definition does, in principle, not differ much from the


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definition in (3.19), page 30. Only, here the simple Euclidean distance measure is used todetermine the metric increase for a given state transition. Hence, the following definition stands

��i � yk � xk�

� xorybink � xbink � (3.24)

where ybink is the received binary symbol and xbink the binary symbols expected to cause a givenstate transition.

The simplification in (3.24) is possible as the decoder operates on binary information signal.The calculation of this increase in the metric value for a given state transition is illustrated inFigure 3.12.

Figure 3.12: Illustration of the metric calculations that compromises part of thechannel decoder implementation.

Based on the principle illustrated in Figure 3.12 and the principle of a survivor metric the entiretrellis structure is formed as was the case in the GMSK demodulator.

Having determined the end state with the smallest metric value the trellis is backtracked todetermine the most probable state sequence. This sequence may then be decoded to retrieve thedecoded estimated transmitted bit sequence.

Note, that as the channel decoder operates on input dibits and outputs bits the data rate is reducedby a factor of two.


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3.4 Receiver Test

To test the operation of the implemented receiver various tests have been carried out. Duringthe implementation of the individual blocks testing has been performed on all levels. Here onlythe high level tests are presented.

Also, due to the complexity of the implemented data receiver the test results presented here areseparated into two sections. The first test considers the matched filter implementation and thesecond considers the implemented Viterbi detector.

3.4.1 Test of mf.m

Testing the mf.m function implies at least two tests. A test of the actual channel impulseresponse estimation and a test of the synchronization included in the function.

To test the calculation of the impulse response a burst is generated, differentially encoded andmapped to a MSK-representation. This signal is the applied to an artificial channel and the fedto the matched filter. By comparing the artificial impulse response with the estimated one thispart of mf.m may be verified. The test has been carried out using numerous impulse responsesof varying lengths. The result of two of these tests are shown in Figure 3.13.

What Figures 3.13a and 3.13b show is that for channel impulse responses of lengths equal to 4Tb’s a correct estimation is achieved. This result goes for impulse responses of lengths equal to� � Tb � � in fact. As the length of the responses exceed 5 Tb’s errors are introduced as Figures3.13c and 3.13d reveal. This result is not surprising when Figure 3.3 is recalled. From this figureit is clear that correct estimation can only be expected for impulse responses of lengths less that,or equal to, 5 Tb’s. When this value is exceeded the correlation no longer produces only zerovalues besides Rhh��, as Figure 3.3 shows. As a result the correlation limitations of the trainingsequence start to affect the channel estimate.

The synchronization implemented in mf.m is tested using two approaches. First, variouslengths of random samples are inserted in front and after the generated burst. Using the samechannel impulse response for all received bursts the matched filter function is able to establishcorrect synchronization. This is verified manually by comparing the burst start parameter ofthe function with the known correct value. Using the same verification approach the same burstis evaluated using different channel impulse responses. The response types are here chosen as[1 0 0 0 0], [0 1 0 0 0], etc. This way the synchronization may also be tested.

For both test approaches the synchronization is found to operate correctly. As the estimatedimpulse response also is calculated correctly the complete mf.m implementation is found tooperate correctly.


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Figure 3.13: The results from two mf.m tests. Real parts and imaginary parts ofthe actual response, h, and the estimated response, h est, are com-pared. Actual values are indicated using ’o’ while the estimated val-ues are indicated using ’*’. a) Real parts using a Lh of 4. b) Imagi-nary parts using a Lh of 4. c) Real parts using a Lh of 6. d) Imaginaryparts using a Lh of 6.


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3.4.2 Test of viterbi_detector.m

The Viterbi detector has been tested in two major tests. In the first test the detector is fed asequence of non-distorted MSK-symbols. This is done using an OSR of 1 and the followingimpulse response

h � �� (3.25)

and Lh is set to � and the corresponding value of

Rhh � �� (3.26)

is used. With these settings the metric of the final survivor path should be 148. To realize this,observe that 148 transitions exist. Also, the metric gain for a single transition should equal

GainY �n�� sa� sb � fI��n�Y �n�g � ��I��n�

n��Xmn�Lh


��

� �� (3.27)

The test is done by slight rewrites of the code, and using the auxiliary MATLAB test-scriptviterbi_ill.m. The result of the test is that the best path has the total metric 148, indicatingcorrect operation. Also, the algorithm identifies this correctly, and does flawless mapping fromthe survivor path and back to the transmitted binary symbols. From this test, it is concludedthat the metrics of a given previous survivor state is transferred correctly to the correspondingpresent state, and that the mapping from a path to binary information is correct. Thus, whatmay be referred to as the basic functionality and control flow within the algorithm is workingas specified.

Having verified the control and data flow of the algorithm via the first test, a second test, in-tended to verify the values calculated inside the algorithm, is done. During this test, it has beenverified, by comparing results found by hand calculations against those calculated by the pro-gram, that the gain values are calculated correctly. In this test, Rhh � �� was used tokeep the complexity low. The test showed that values calculated by hand yield the same resultsas those found in internal data structures.


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4Use of the GSMsim Toolbox

This chapter describes the installation and use of the GSMsim toolbox. As is described in theforegoing part of this work, the GSMsim toolbox consists of 11 major functions – plus someminor sub-functions – intended to be directly interfaced by the user. To summarize, thesefunctions are:

data_gen.m: Generates random data for transmission.channel_enc.m: Performs the parity and convolutional encoding of the data

bits.interleave.m: Interleavs the encoded data sequences.gsm_mod.m: Modulates the bursts and does multiplexing as well.mf.m: Performs channel estimation, synchronization, matched fil-

tering and down sampling.channel_simulator.m: Performs simulation of transmitter front-end, channel and

receiver front-end.viterbi_init.m: Sets up data structures for the Viterbi detector to use.viterbi_detector.m: Implements a hard decision only MLSE based on Unger-

boeck’s modified Viterbi algorithm.DeMUX.m: Does simple demultiplexing of the received data sequence.deinterleave.m: Takes care of de-interleaving the received data sequences.channel_dec.m: Performs the channel decoding.

Together these functions constitute a minimal GSM simulation base. To obtain a full GSMsimulation platform RF-parts and channel models need to be added. Addition of components iseasily done due to the modular implementation of the existing functions.


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NOTE: The function channel_simulator is intended for replacement by userimplemented functions, and should NOT, under any circumstances, be used forscientific purposes.

The first part of this chapter describes some details about installing the GSMsim toolbox ona user level. If you desire to do a system level installation, the procedure you need to followis likely to be similar. In the second part of the chapter a brief description of the syntax of themajor functions listed above is presented. After this the chapter contain a description of twodemos GSMsim_demo.m and GSMsim_demo_2.m which are included in the toolbox. Thelast two sections in this chapter contain profiling and convergence information.

4.1 Installation of GSMsim

The GSMsim toolbox is distributed as a GNU zipped tape archive. The procedure of extractingand installing GSMsim is illustrated here by a step by step example. The example assumes that

� The GSMsim distribution file is available as: ~/tmp/GSMsim.tar.gz

� The directory, where GSMsim is intended to be installed is: ~/matlab/

� Standard UNIX tar is available

� Standard GNU gunzip is available

� Emacs is available

� A UNIX shell, like BASH, is available

� The file ~/matlab/startup.m is automaticly executed at MATLAB startup

The first step is to change to the desired directory location

cd ~/matlab

Then unpack the distribution

gunzip -c ~/tmp/GSMsim.tar.gz | tar xvf -

In the next step, edit the file ~/matlab/startup.m, using your favorite text editor. Forexample issue the command

emacs ~/matlab/startup.m &

Then insert the lines


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startdir=pwd ;cd ~/matlab/GSMsim/config ;GSMsim_config ;eval( [ ’cd ’ startdir ] ) ;

at the top of ~/matlab/startup.m. Having inserted these lines save the file and exit youreditor. In emacs, this is done by issuing the key sequence

C-x C-s C-x C-c

This concludes the installation of GSMsim. In order to test the installation, start MATLAB ina shell. This is done by simply typing matlab, at the prompt, and pressing Enter. WhenMATLAB has started, you may test the installation by issuing the command

GSMsim_demo(10,2)

at the MATLAB prompt. If a result similar to the one shown in Figure 4.1 appear, then theinstallation is a success.

Figure 4.1: Illustration of how to test a GSMsim installation.

4.2 Syntax of the Major Functions

This section serves as a reference guide for the implemented functions. The aim is to supplysufficient information for the toolbox to be useful.


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4.2.1 Syntax of data_gen.m

Matlab Call Syntax:

[ tx_data ] = data_gen(INIT_L)

Input Parameters:

INIT_L: An integer indicating the number of bits to be generated.

Output Parameters:

tx_data: The generated data,


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4.2.2 Syntax of channel_enc.m

Matlab Call Syntax:

[ tx_enc ] = channel_enc(tx_block)

Input Parameters:

tx_block: A 260 bits long vector containing the raw and non processed datasequence intended for transmission.

Output Parameters:

tx_enc: A 456 bits long vector containing the now encoded data sequence.This includes parity encoding, addition of check bits, and convo-lution encoding.


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4.2.3 Syntax of interleave.m

Matlab Call Syntax:

[ tx_data_matrix ] = interleave(tx_enc0,tx_enc1)

Input Parameters:

tx_enc0: The previous instance of tx_enc returned from the channelcoder.

tx_enc1: The latest instance of tx_enc returned from the channel coder.

Output Parameters:

tx_data_matrix:The four sets of tx_data produced in a single interleaver pass.Each set is placed in a row of the matrix. The first row containthe instance of tx_datawhich is to be transmitted first, and rowfour contains the instance of tx_datawhich is to be transmittedlast.


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4.2.4 Syntax of gsm_mod.m

Matlab Call Syntax:

[ tx_burst , I , Q ] =gsm_mod(Tb,OSR,BT,tx_data,TRAINING)

Input Parameters:

Tb: Bit time in seconds.OSR: Oversampling ratio. Here the oversampling ratio is defined as:

fs�rb, where fs is the sample frequency, and rb is the bit rate.BT: Bandwidth bit time product. Usually ��.tx_data: The contents of the data fields in the burst to be transmitted, rep-

resented as a binary row vector, using ones and zeros.TRAINING: Training sequence which is to be inserted in the burst. Repre-

sented as a row vector. Binary format is used in the form of onesand zeros.

Output Parameters:

tx_burst: The entire transmitted burst, represented as an binary row vector,using ones and zeros.

I: In-phase part of modulated burst. The format is a row vector ofreal floating point numbers.

Q: Quadrature part of modulated burst. The format is a row vector ofreal floating point numbers.


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4.2.5 Syntax of channel_simulator.m

Matlab Call Syntax:

[ r ] = channel_simulator(I,Q,OSR)

Input Parameters:

I: In-phase part of modulated burst. The format is a row vector ofreal floating point numbers.

Q: Quadrature part of modulated burst. The format is a row vector ofreal floating point numbers.

OSR: Oversampling ratio.

Output Parameters:

r: Complex baseband representation of the received GMSK-modulated signal. The format is a row vector consisting of com-plex floating point numbers.


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4.2.6 Syntax of mf.m

Matlab Call Syntax:

[ Y, Rhh ] = mf(r,Lh,T_SEQ,OSR)

Input Parameters:

r: Complex baseband representation of the received GMSK-modulated signal as it is returned from the channel simulator. Theformat is a row vector consisting of complex floating point num-bers.

Lh: The desired length of the matched filter impulse response mea-sured in bit time durations.

T_SEQ: A MSK-mapped representation of the 26 bits long training se-quence used in the transmitted burst, i.e. the training sequenceused in the generation of r.

OSR: Oversampling ratio.

Output Parameters:

Y: Complex baseband representation of the matched filtered anddown converted received signal. Represented as a complex val-ued row vector.

Rhh: Autocorrelation of the estimated channel impulse response. Rep-resented as a Lh+1 elements long complex valued column vectorstarting with Rhh[0], and ending with Rhh[Lh].


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4.2.7 Syntax of viterbi_init.m

Matlab Call Syntax:

[ SYMBOLS , PREVIOUS , NEXT , START , STOPS ] =viterbi_init(Lh)

Input Parameters:

Lh: The length of the matched filter impulse response measured in bittime durations.

Output Parameters:

SYMBOLS: State number to MSK symbols translation table.NEXT: Present state to next state transition table.PREVIOUS: Present state to previous state transition table.START: Start state number.STOPS: Set of legal stop states.


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4.2.8 Syntax of viterbi_detector.m

Matlab Call Syntax:

[ rx_burst ] = viterbi_detector(SYMBOLS,NEXT,PREVIOUS,START,STOPS,Y,Rhh)

Input Parameters:

SYMBOLS: State number to MSK symbols translation table.NEXT: Present state to next state transition table.PREVIOUS: Present state to previous state transition table.START: Start state number.STOPS: Set of legal stop states.Y: Complex baseband representation of the matched filtered and

down converted received signal. Represented as a complex val-ued row vector.

Rhh: Autocorrelation of the estimated channel impulse response. Rep-resented as a Lh+1 elements long complex valued column vectorstarting with Rhh[0], and ending with Rhh[Lh].

Output Parameters:

rx_burst: The most likely sequence of symbols. Representation is a rowvector consistent of binary symbols, represented as zeros andones.


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4.2.9 Syntax of DeMUX.m

Matlab Call Syntax:

[ rx_data ] = DeMUX(rx_burst)

Input Parameters:

rx_burst: The received GSM burst as estimated by the Viterbi detector.

Output Parameters:

rx_data: The contents of the data fields in the received burst.


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4.2.10 Syntax of deinterleave.m

Matlab Call Syntax:

[ rx_enc ] = deinterleave(rx_data_matrix)

Input Parameters:

rx_data_matrix:A matrix containing eight instances of rx_data. Each instanceis aligned in a row. The data are arranged so that the eldest in-stance of rx_data is kept in row number one, and the latestarrived instance is kept in row number eight.

Output Parameters:

rx_enc The received code block, as reconstructed from the eight instancesof rx_data.


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4.2.11 Syntax of channel_dec.m

Matlab Call Syntax:

[ rx_block, FLAG_SS, PARITY_CHK ] = channel_dec(rx_enc)

Input Parameters:

rx_enc: A 456 bits long vector containing the encoded data sequence asestimated by the Viterbi equalizer. The format of the sequencemust be according to the GSM 05.03 encoding scheme.

Output Parameters:

rx_block: A 260 bits long vector containing the final estimated informationdata sequence.

FLAG_SS: Indication of whether the correct stop state was reached. Flag isset to ’1’ if an error has occurred here.

PARITY_CHK: The 3 parity check bit inserted into the transmitted bit sequence.


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4.3 The GSMsim_demo.m Function

GSMsim_demo.m is a implementation of an example of a GSM simulation platform basedon the major functions described in the beginning of this chapter, but leaving out the channelcoding and interleaving. This reduced simulation is useful, for example, in the case where typeII performance is of primary interest. The call syntax of the function is

GSMsim_demo(LOOPS,Lh)

where LOOPS indicate how many times the function is to process ten GSM bursts. The algo-rithm which form the basis for GSMsim_demo.m is

viterbi_initfor n=1:LOOPS do

for n=1:10 dodata_gengsm_modchannel_simulatormfviterbi_detectorDeMUXCount errors.

end forUpdate display.

end forPresent simulation result on screen.

Note, that the function processes ten bursts between each screen update. This is motivated bythe fact that in networked environments, as Aalborg University, screen updates may take upunreasonable much time. This is worth remembering when implementing custom simulationscripts. In general the GSMsim_demo.mmay serve as a starting point for creating such scripts.


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4.4 The GSMsim_demo_2.m Function

GSMsim_demo_2.m is an example of a GSM simulation which includes all the functionsavailable in the GSMsim toolbox. That is to say that channel coding and interleaving is alsoincluded, in contrast to what is the case in GSMsim_demo. Also GSMsim_demo_2, includesan example of how to create a simulation log. The call syntax of GSMsim_demo_2 is

GSMsim_demo_2(NumberOfBlocks,Lh,LogName)

where NumberOfBlocks regulates how many instances of tx_block that is processed ina simulation, and LogName indicates a basename which is to be used for the name of thesimulation log. The simulation script will output a log to a file called

“LogName”_”NumberOfBlocks”_Lh.sim

The basic algorithm of GSMsim_demo_2 is

viterbi_initfor n=1:NumberOfBlocks dodata_genchannel_encinterleavefor generated bursts dogsm_modchannel_simulatormfviterbi_detectorDeMUX

end fordeinterleavechannel_decCount errors.Update logfile.Update display.

end forPresent simulation result on screen.

During the simulation a status report is continuously updated at the screen, showing the progressalong with the remaining simulation time. Note that the simulation log is saved during thesimulation, and not at the end of the simulation. This provide for recovery of the simulationresults in the case of a system crash or other failures.

Using the GSMsim_demo_2.m four Bit Error Rates are produced


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Type Ia BER: The Bit Error Rate within the decoded type Ia bits.

Type Ib BER: The Bit Error Rate within the decoded type Ib bits.

Type II BER: The Bit Error Rate within the unprotected type II bits.

Type II BER-CHEAT: This Bit Error Ratio is constructed by considering all the bits in thereceived blocks as unprotected type II bits, and is thus the same as the Type II BER butwith a much more substantial statistical basis.

All the results are measured in percent.

4.5 Performance

The GSMsim_demo_2.m is useful for evaluating which part of an simulation takes the majorpart of the time. This is done by using the profile command available in MATLAB version5. The profiling is done for Lh � f�� g. The results are shown in Figures 4.2, 4.3 and 4.4.

Figure 4.2: Profile for GSMsim_demo_2.m usingLh � �, the simulation is donefor 100 blocks.

As it can be seen from Figures 4.2, 4.3 and 4.4 it is not advisable to include channel encodingin the simulations if type I bit error rates are not of specific interest. Note that tables describingcoding gain for various coding techniques do exist [16].


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4.6 Convergence

This section aims to illustrate the simulation length required for the resulting BER estimates toconverge. In order to get estimates of the convergence for all types of Bit Error Rates producedby the GSMsim toolbox the GSMsim_demo_2 script is used.

To illustrate the convergence of the results three simulations are run for �� blocks equaling�� bursts. In the three simulations Lh is set to �� and �, respectively. In order to get animpression of the convergence, the four Bit Error Rates described in Section 4.4 are plotted inFigures 4.5, 4.6 and 4.7.

Figure 4.5: The convergence properties, illustrated by using Lh � �. The top lineis the type II-cheat BER curve. Immediately bellow this line is theactual type II BER curve. Both type I curves are almost at the zeroline. The simulation result is plotted for each tenth simulated burst.


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Figure 4.6: The convergence properties, illustrated by using Lh � �. The twotype II BER curves are almost identical, and are located at the top ofthe graph. Likewise, the two type I curves are almost identical. Thesimulation result is plotted for each tenth simulated burst.


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Figure 4.7: The convergence properties, illustrated by using Lh � �. The type IIerror curves are nearly equal, and tend to converge to about ��. Thetop curve represents type Ib errors. The type Ia curve is second fromthe top. The simulation result is plotted for each tenth simulated burst.


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References

[1] Asad A. Abidi. CMOS-only RF and Baseband Circuits for a Monolithic 900 MHz Wireless Transceiver. InBipolar Circuits & Tech. Mtg., pages 35–42, October 1996.

[2] Julian Bright; Stephen McClelland; Bhawani Shankar. Microwave in Europe: Trends Shaping the Future.Microwave Journal, September 1996.

[3] Johan Brøndum. GSM data receiver structures. Technical report, Institute for Electronic Systems Departmentof Communication Technology, 1993.

[4] Jan Crols & Michel S. J. Steyaert. A Single-Chip 900 MHz CMOS Receiver Front-End with a High Perfor-mance Low-IF Topology. IEEE Jour. of Solid-State Circuits, 1995.

[5] Jan Crols & Michiel Steyaert. A Full CMOS 1.5 GHz Highly Linear Broadband Downconversion Mixer.IEEE Jour. of Solid-State Circuits, 30(7):736–742, jul 1995.

[6] G. David Forney, Jr. The Viterbi Algorithm. In Proceedings of the IEEE, volume 61, pages 268–273, march1973.

[7] Armond Hairapetian. An 81 MHz IF Receiver in CMOS. In 1996 IEEE Int. Solid-State Circuits Conference,pages 56–57, 1996.

[8] Simon Haykin. Communication Systems. John Wiley & Sons, 2 edition, 1983.

[9] European Telecommunications Standards Institute. GSM 05.03: Channel Coding. Version: 4.6.0, July 1993.

[10] European Telecommunications Standards Institute. GSM 05.04: Modulation. Version: 4.6.0, July 1993.

[11] European Telecommunications Standards Institute. Digital cellular telecommunications system (Phase 2);Radio transmission and reception (GSM 05.05). Ninth Edition, November 1996.

[12] Benny Madsen. Data-Receiver For the Pan-European Mobile Telephone System (GSM). EF 226, IndustrialResearch Project, The Danish Academy of Technical Sciences, September 1990.

[13] The MathWorks, Inc., Cochituate Place, 24 Prime Park Way, Natick, Mass. 01760. MATLAB ReferenceGuide.

[14] Michel Mouly and Marie-Bernardette Pautet. The GSM System for Mobile Communications. M. Mouly etMarie-B. Pautet, 1992.

[15] Anders Østergaard Nielsen, Henrik Refsgaard Hede, Klaus Ingemann Pedersen, Michael Hedelund Ander-sen, Thomas Almholdt, and Troels Emil Kolding. DSP realtime implementation of GSM testbed system.Student Report by group 870 at Department of Communication Technology, Institute for Electronic Systems,Aalborg University, June 1995.

[16] John G. Proakis. Digital Communications. McGraw-Hill Book Company, 2 edition, 1989.

[17] Behzad Razavi; Kwing F. Lee; Ran H. Yan. Design of High-Speed, Low-Power Frequency Dividers andPhase-Locked Loops in Deep Submicron CMOS. IEEE Jour. of Solid-State Circuits, 30(2):101–109, feb1995.

[18] Jans Sevenhans & Dirk Rabaey. The Challenges for Analogue Circuit Design in Mobile Radio VLSI Chips.Microwave Engineering Europe, pages 53–59, may 1993.

[19] Chung-Yo Wu & Shuo-Yuan Hsiao. The Design of a 3-V 900-MHz CMOS Bandpass Amplifier. IEEE Jour.of Solid-State Circuits, 32(2):159–168, February 1997.


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ATransmitter Implementations

AS described previously the implemented transmitter consists of three blocks made up of inall five MATLAB functions. The functions of these and their placement in the transmitter

structure is illustrated in Figure A.1.

Figure A.1: Illustration of the five implemented functions constituting the trans-mitter. Also included is a sixth function that combines the other fivefunctions into a single transmitter function call.

As shown in Figure A.1 a sixth function is added to the transmitter implementation. This is doneto allow for a single function call to access the entire transmitter. It should be noted here thatwhile the GMSK-modulator returns only I and Q as outputs the variable tx burst is a resultof the gsm_mod.m function. The variable tx burst is in fact the output sequence returnedby the MUX block. Hence, tx burst contains the burst sequence as it is found prior to bothdifferential encoding and modulation. The syntax and the required input and output parameters


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of gsm_mod.m are describen in Section 4.2.4.

Due to the simplicity of the transmitter implementation this is described as a whole here. Thisis opposed to describing the five functions in individual appendices. The following two sectionsthus describe the data generator and multiplexer and the GMSK-modulator implementations,respectively.

A.1 Data Generator

The data generator is implemented by the MATLAB function data_gen.m. This functionserves to produce random data to the channel encoder. This is to emulate the speech encoder.

A.1.1 Input, Output, and Processing

The data generator block has the following inputs:

INIT L: An integer determining the number of random data bits that thedata_gen.m routine is to return.

The corresponding output is:

tx block: The random bits generated by the function.

A.2 Channel Encoder

The channel encoder operation is implemented by the MATLAB function channel_enc.m.The task of this function is to implement the outer encoding required for use in the GSM system.

A.2.1 Input and Output

The channel encoder makes use of the following input parameter

tx block: A 260 bits long vector contaning the data sequence intended fortransmission.


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The corresponding output from channel_enc.m is

tx enc: The resulting 456 bits long vector contaning the encoded data se-quence.

A.2.2 Internal Data Flow

Besides from the above mentioned information carrying parameters the channel encoder alsooperates some internal information.

The GSM encoding scheme operates using two levels of bits where the more important arethose that affects the speach quality the most. These bits, termed class I bits, are furthermoresplit into class Ia and classe Ib bits. This separation is also made use of in channel_enc.mwhere the variables c�, c�a, c�b, and c� are used to represent the class I, the class Ia, the classIb, and the class II bits, respectively.

A.2.3 Processing

First the input, tx block, is split into the different classes

c�a � tx block� � ��c�b � tx block�� c� � tx block��

Having split the data the c�a bits are parity encoded using three check bits. Due to the syntax ofthe MATLAB function deconv�m some post processing is required to have the parity bit resultin binary format.

g � �� d � �c�a � � ��q� r� � deconvd� gL � lengthrout � absrL� � � Lfor n � � � lengthout do

if ceiloutn�� flooroutn�� thenoutn � �

elseoutn � �

end ifend for


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c�a � �c�a out�

The next step is to recombine the class I bits and then perform the convolutional encoding ofthese.

c� � �c�a c�b � � � ��register � zeros�� data seq � �registerc��enc a � zeros�� enc b � zeros�� encoded � zeros�� for n � � � �� doenc an � xorxordata seqn� �� data seqn� �� data seqnenc temp � xordata seqn� �� data seqn� �enc bn � xorxorenc temp� data seqn� �� data seqnencoded� n� � � enc anencoded� n � enc bn

end for

Finally the now encoded class I bits are recombined with the class II bits to form the final output.

tx enc � �encoded c��

A.3 Interleaver

As described in Section 2.1.3 the interleaver is implemented in the function interleave.m.The purpose of the interleaver is to ensure that the bit errors that occur in the received encodeddata blocks are uncorrelated.


The interleaver has two input variables

tx enc�: The previous code block returned from the channel coder.tx enc�: The latest GSM code block returned from the channel coder.

The output from the interleaver is


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tx data matrix:The four sets of tx data produced in a single interleaver pass.Each set is placed in a row of the matrix. The first row contain theinstance of tx data which is to be transmitted first, and row fourcontains the instance of tx data which is to be transmitted last.

The interleaver is externally aided by a queue, which administrates the propper alignment ofthe tx block variables. Internally the interleaver simply perform a number of copy operationsas described by the formulas in (2.6) and (2.7) in Section 2.1.3. The file interleave.m isconstructed by the aid of the following lines

Blocks � �BitsInBurst � ��out � fopen�interleave�tmp�� w�for T � � � � do

for t � � � BitsInBurst dob � mod�� modT� � � t �� modt� �� B � floorT �modb� ��fprintfout�� tx data matrix�d��d � tx enc�d�d�

nn�� T � �� t� �� B � �� b� �end for

end forfcloseout

A.4 Multiplexer

The multiplexer operation is implemented by the MATLAB function burst_g.m. The oper-ation of this function serve to produce GSM burst frames according to the prescribed formatsdictated in the GSM recommendations [10].


The multiplexer block has the following input

tx data: A 114 bit long data sequence.TRAINING: A 26 bit long MSK representation of the desired training sequence

to be included in the GSM burst.

The corresponding output from burst_g.m is


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tx burst: The required GSM burst bit sequence including tail, control, andtraining sequence bits.

The implementation is done in a simple way as

TAIL � ��CTRL � ��tx burst �

�TAIL tx data� � �� CTRL TRAINING CTRL tx data�� TAIL�

after which poin the variable tx burst contains a valid GSM normal burst, which is then mod-ulated as described in the next section.

A.5 GMSK-Modulator

The GMSK-modulator operation is implemented by three MATLAB functions, which are nameddiff_enc.m, ph_g.m, and gmsk_gen.m respectively. The combined operation of thesefunctions serves to differential encode the GSM burst, as received from burst_g.m, andperform the GMSK-modulation according to the prescriptions dictated in the GSM recommen-dations [10].

A.5.1 Input and Output

The combined GMSK-modulator has the following inputs

tx burst: The required GSM burst bit sequence including tail, control, andtraining sequence bits as returned by the burst_g.m routine.

Tb: Bit time duration in seconds.OSR: Oversampling ratio. Here the oversampling ratio is defined as:

fs�rb, where fs is the sample frequency, and rb is the bit rate.BT : Bandwidth bit time product. Usually ��.

The corresponding output from gmsk_mod.m is:

i � q: In-phase and quadrature-phase parts of modulated burst, respec-tively.


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A.5.2 Internal Data Flow

Besides from the above mentioned information carrying parameters the GMSK-modulator blockalso exchanges some internal information. More specifically, the following parameters are usedto parse internal information

diff enc data: The differential encoded version of the GSM normal burst. Thisvariable is returned as output from diff_enc.m and serves asinput to gmsk_mod.m.

L: The truncation length used to limit the time duration of the oth-erwise infinite length Gaussian pulse. This value is in ph_g.mdefined to 3.

g fun: The resulting L times OSR values of the resulting frequencypulse function as returned by pg_g.m.

A.5.3 Processing

The bursts are differentially encoded before the actual modulation. This come into expressionin the following

burst � diff enctx burst�I� Q� � gmsk modburst� T b� OSR� BT

As gmsk_mod.m makes use of the sub-function ph_g.m presenting the code for this mightbe appropriate in illustrating how these two functions are interlinked. Thus, the detailed imple-mentation is as follows

�g� q� � ph gTb� OSR� BT bits � lengthburstfor n � � � bits dof resn� � �OSR � � � n� � �OSR

� f resn� � �OSR � � � n� � �OSR � burstn � gend fortheta � � � cumsumf resI � costhetaQ � sintheta

At this point the variables I and Q contain the in-phase and the quadrature-phase outputs fromthe GMSK-modulation, respectively.


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BReceiver Implementations

AS described previously the implemented receiver is separated into two main blocks. Onethat handles the task of synchronization, channel estimation, as well as matched filter-

ing and another block handling the decoding of the received and matched filtered signal. Toimplement this a total of eight MATLAB functions are generated. These functions and theirplacement in the receiver structure is illustrated in Figure B.1.

Note in Figure B.1, that the MLSE block which was shown in the, otherwise similar, Figure 3.1has been explicitly divided into two blocks as discussed in Section 3.2, page 31. Further-more, Figure B.1 shows that the VA block consists of several functions, in fact seven in all.The matched filter, channel estimation and synchronization are, however, implemented in asingle function. Hence, the following sections describe the matched filter and channel estima-tion/synchronization as a combined block while the VA is described in a separate section.

B.1 Synchronization, Channel Estimation, and Matched Fil-tering

The combined task of synchronizing the received burst, performing the channel estimation andmatched filtering is here implemented in a single function mf.m. The combined operation ofthese tasks aims to remove the transmitter pulse shaping and channel effects through equalizingas well as to find the optimum sample points in the received burst.


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Figure B.1: Illustration of the ten implemented functions constituting the receiverdata detector.

B.1.1 Input and Output

The operations combined in mf.m result in the following inputs:

r: Complex baseband representation of the received GMSK modu-lated signal.

Lh: The desired length of the matched filter impulse response mea-sured in bit time durations.

T SEQ: A MSK-modulated representation of the 26 bits long training se-quence used in the transmitted burst, i.e. the training sequenceused in the generation of r.

OSR: The oversample ratio defined as fs�rb.

The corresponding outputs from mf.m is:

Y : A complex baseband representation of the matched filtered anddown converted received signal.

Rhh: The autocorrelation of the estimated channel impulse response.The format is a Lh�� element column vector starting withRhh��and ending with Rhh�Lh�


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B.1.2 Internal Data Flow

To link the three different tasks included in mf.m a number of internal variables are made useof. Two of these are T�� and r sub, where the former contains the 16 most central bits of theotherwise 26 bits long training sequence, TSEQ. The latter, r sub, contains a sub-set of thereceived burst r. This sub-set is chosen in a manner that ensures that the training sequence partof the received burst is present in r sub. This is done by not only extracting the sixteen mostcentral bit time durations of r but rather extract extra samples preceding – and also succeeded– the central sixteen bit time durations, as illustrated in Figure B.2.

The two extra sequences each correspond to a time period of approximately 10 Tb. If the 16most central training sequence bits are not located within the resulting sub-set the GSM networkguard time is exceeded and the received burst would be corrupted by burst collision anyways.Hence, instead of searching for the training sequence through out the entire received burst, onlyr sub needs to be evaluated.

Figure B.2: Extraction of r sub from r.

On basis of these two sub-sequences, T�� and r sub, the function mf.m forms a channel esti-mate, chan est, by calculating the cross correlation between the sub-sequences. From chan esta power estimate sequence, power est, is calculated to determine the most likely channel im-pulse response estimate which is stored in the variable h est. As a final internal parameter thevariable burst start is used. This value, representing the sample number in r corresponding tothe first bit of the transmitted burst, is used in performing the actual matched filtering.

B.1.3 Processing

The first part of mf.m, where the two sub-sequences are formed, takes the form

T�� conjT SEQ� � ��r sub � rstart sub � end sub,


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where the parameters start sub and end sub are calculated according to the guard time require-ments indicated above.

From these two sub-sequences a chan est sequence is calculated. Within this sequence thechannel impulse response estimate is to be found

chan est � zeros�� lengthr sub� OSR � ��for n � � � lengthchan est dochan estn � r subn � OSR � n�OSR � �� T��

end for

The location of the channel impulse response estimate – within the sequence chan est – isfound by forming a power sequence based on chan est. This new sequence, power est, isevaluated using a sliding window approach using a window length of WL. Searching throughthis power sequence the maximum power window is located and the impulse response estimateis extracted

WL � OSR � L� �search � abschan est�

for n � � � lengthsearch� WL� � dopower estn � sumsearchn � n�WL� �

end for�peak� sync w� � maxpower esth est � chan estsync w � sync w �WL� �

The next task is to synchronize the received burst, that is to say to find the first sample in rthat corresponds to bit one in the transmitted burst. Recall, that the channel impulse response isfound by cross correlating a received sequence with a known sequence, the training sequence.This implies that the sample number corresponding to the maximum value of h est directlyserves as an indication of the location of the first bit in T�� as this is located within r. Takinginto account that only a sub-sequence of r has been used the sample corresponding to the firstbit in r, burst start, may be derived

�peak� sync h� � maxabsh estsync T�� sync w � sync h� �burst start � start sub� sync T�� OSR � �� burst start � burst start� � �OSR � �

The first calculation of burst start may seem unclear at first. This is mostly due to the MAT-LAB notation where zero cannot be used to index vectors. Hence, the plus and minus onesserve to compensate for this index problem.


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The last burst start calculation compensates for a delay inherently introduced in the transmitteras a result of the shaping operation of GMSK. As each bit is stretched over a period of 3 Tb –with it’s maximum phase contribution in the last bit period – a delay of 2 Tb is expected. Thiscorresponds to burst start being misplaced by � � OSR which then is corrected in the abovecode.

Having determined the channel impulse response estimate h est and having established burstsynchronization through burst start the received burst may be matched filtered. The code re-sponsible for the output generation is as follows

R temp � xcorrh estpos � lengthR temp � ��Rhh � R temppos � OSR � pos� L �OSRm � lengthh est� �r extended � �zeros�� L r zeros�� m�for n � � � �� doY n � r extendedL � burst start� n� � �OSR

� L� burst start� n� � �OSR�m � conjh estend for

Finally, the function returns Rhh and Y as outputs for the subsequent data detector, i.e. theViterbi detector.

B.2 Viterbi Detector (MLSE)

As described previously, the Viterbi detector is implemented in two blocks. This two functionconcept is motivated by the fact that the setup of internal tables does not need to be done foreach burst, as they can be reused. The split up is illustrated in Figure B.1.

The MLSE is interfaced by the matched filter and the channel estimator. The input to theMLSE is the matched filtered and down sampled signal, Y , along with Rhh and Lh which arethe autocorrelation of the estimated channel impulse response and its duration measured in bittime durations, respectively. The format of Rhh is special, as described in the following SectionB.2.1. Y is a sequence of samples with one sample for each transmitted symbol. The output ofthe MLSE, rx burst, is an estimate of the most likely sequence of transmitted binary bits.


The total Viterbi detector, as constructed by the two blocks illustrated in Figure B.1, has thefollowing inputs:


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Y : A sequence of samples as they are returned from the matched fil-ter. It is expected to be a complex valued vector, with one samplecorresponding to each MSK-symbol.

Rhh: The autocorrelation of the channel impulse response as estimatedby the mf.m routine. It is expected that Rhh is a complex valuedsequence of samples represented as a column vector. Also it isexpected that Rhh contains Lh � � samples. The layout of Rhh is:Rhh � �Rhh�� Rhh�� Rhh�Lh��.

Lh: The number of elements in Rhh minus one. This is needed due tothe splitting of the function, as will emerge later.

The corresponding output is:

rx burst: The estimated bit sequence.

The splitting of the algorithm is done so that elements independent of the received burst are onlyprocessed once. Specifically, Lh determines the state structures used by the algorithm. Thesestates and related variables are thus setup only once.

B.2.2 Internal Data flow

In this section the interface between the two blocks constituting the Viterbi detector is de-scribed. In the following the two blocks are referred to by their MATLAB function names asviterbi_init and viterbi_detector respectively. The interface between these twofunctions is illustrated in Figure B.3.

As can be seen in Figure B.3 viterbi_init has only Lh as input. The output is used onlyby viterbi_detector. The output consists of the following variables:


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Figure B.3: Illustration of the interface between the two functionsviterbi_init and viterbi_detector. The figure alsoillustrates the block names of the MATLAB functions. Note that theblock labeled Init is equal to viterbi_init, and the block labeledVA is equal to viterbi_detector.

SYMBOLS: State number to MSK-symbols mapping table. Row s containsthe MSK-symbols corresponding to a state. Taking n as the timereference the state is referred to as �n�, i.e. the state to dis-crete time n. Say that �n� � �, then the MSK-symbols I��n �

corresponding to state �n� is related to SYMBOLS so thatI��n � � �I�n�� I�n�� I�n� Lh�� SYMBOLS(7,:).

PREV IOUS: This is a state to legal previous state mapping table. The legalstates, here called LEGAL, that may proceed state number s areobtained from PREV IOUS as LEGAL � PREVIOUS(s,:).

NEXT : This is a state to legal next state mapping table. The legal states,here called LEGAL, that may succeed state number s are ob-tained from NEXT as LEGAL � NEXT s� �.

START : The start state of the Viterbi algorithm. This is a single integer,since the start state of the Viterbi detector is uniquely determined.

STOPS: The set of legal stop states for the Viterbi detector. This is anarray of integers, since the stop states are limited, but not alwaysunique.

The resulting list of input variables feed to the VA block is thus

SYMBOLS�NEXT� PREV IOUS� START� STOPS� Y� Rhh


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all of which are described above. The resulting output is rx burst, which also is describedabove.

B.2.3 Processing

The setup of the pre-calculable tables and values, related to the Init block, is done by the MAT-LAB function viterbi_init. viterbi_init is implemented as a sequence of calls to anumber of sub-functions, as described by the following piece of code

SYMBOLS � make symbolsLhPREV IOUS � make previousSYMBOLSNEXT � make nextSYMBOLSSTART � make startLh� SYMBOLSSTOPS � make stopsLh� SYMBOLS

The sub-functions are described individually in the following. As described the state numberto MSK-symbols translation table is to be setup. This is done using the following algorithm,which is implemented in the MATLAB function make_symbols

SYMBOLS � �� j��j�for n � � � Lh � � doSYMBOLS =��SYMBOLS�� j� SY MBOLS�� SYMBOLS�� j� SYMBOLS��

end forif isrealSYMBOLS�� thenSYMBOLS � flipudSYMBOLS

end if

The if-structure ensures that state number one begins with a complex MSK-symbol. This fea-ture is used to cut in half the number of calculations required by the Viterbi detector. From theSYMBOLS-table the NEXT -table is created by direct search using the following approach

�states� elements� � sizeSYMBOLSfor this state � � � states dosearch vector � SYMBOLSthis state� � � elements � �k � �for search � � � states do

if search matrixsearch� � �� search vector thenk � k � �NEXT this state� k � search

end if


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end forend for

which is implemented as the MATLAB function make_next. Likewise the PREV IOUS-table is constructed as

�states� elements� � sizeSYMBOLSfor this state � � � states dosearch vector � SYMBOLSthis state� � � elementsk � �for search � � � states do

if search matrixsearch� � �� search vector thenk � k � �PREV IOUSthis state� k � search

end ifend for

end for

The above is implemented as the MATLAB function make_previous. As previously notedthe state number corresponding to the start state is determined at runtime. This is done usingthe MSK-representation of the start state which is shown in Table B.1 [15].

Lh ��

� �� j�� j� �� j� �� j�

Table B.1: The MSK-representation of the legal start states of the Viterbi detector.

The returned value is stored in the variable START , and is determined using the followingstrategy

if Lh �� thenstart symbols � �� j�

else if Lh �� thenstart symbols � �� j� ��

else if Lh �� thenstart symbols � �� j� �� j�

end ifSTART � �while START NOT FOUND doSTART � START � �


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if SYMBOLSSTART� � �� start symbols thenSTART NOT FOUND � �

end ifend while

The location of the integer corresponding to the start state is handled by the MATLAB functionmake_start. The stop state of the Viterbi detector is not always uniquely defined but isalways contained within a limited set. The legal stop states are listed in Table B.2 for theconsidered values of Lh [15].

Lh ��

� f�� j�g� f�� j� ��g� f�� j� �� j�� j� �� j�g

Table B.2: The MSK-representation of the legal stop states of the Viterbi detector.

From Table B.2 the state numbers corresponding to the stop states are stored in STOPS usingthe following method

if Lh �� thenstop symbols � �� j�count � �

else if Lh �� thenstop symbols � �� j� ��count � �

else if Lh �� thenstop symbols � �� j� �� j�� j� �� j�count � �

end ifindex � �stops found � �while stops found � count doindex � index � �if SYMBOLSindex� � �� stop symbolsstops found� �� thenstops found � stops found� �STOPSstops found � index

end ifend while

This is implemented in MATLAB by the function called make_stops. This concludes thedescription of the retrieval of the variables returned from viterbi_init. In the following


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viterbi_detector, which contain the actual implementation of the Viterbi detector, isdescribed. Unlike viterbi_init, viterbi_detector is run for all bursts and, thus, itis implemented as a single function. This is done in order to avoid the overhead associated witha function call.

It should be clear that the Viterbi detector identifies the most probable path trough a state trellis.The trellis involves as many state shifts as the number of MSK-symbols in a GSM-burst, whichequals ��. This is also the number of elements in Y . The assumption which form the basis forthe algorithm is that the metric of a state to the time n can be calculated from

� The n� �’th state and its associated metric.

� The n’th present state.

� The metric of the n’th element in Y .

Referring to the previous state as p and to the present state as s then the metric of state s isexpressed as

METRICs� n � maxpfV aluen� �� p �GainYn� s� pg� (B.1)

which implies that the metric of state number s, to the time n, is found by choosing the previousstate number p so that the metric is maximized. It is here chosen to assign the initial state themetric value �. The initial state is referred to as state number �. Based on this all that needs tobe done is to calculate the gain from state to state. The gain is calculated using

GainY �n�� ss� sp � fI��n�y�n�g � ��I��n�

n��Xmn�Lh


�� (B.2)

as has been presented earlier. With the variable definitions above, and introducing MATLABnotation, this becomes

GainY n� s� p � fSYMBOLSs� �� Y ng� fSYMBOLSs� �� SYMBOLSp� � �Rhhg� (B.3)

Note that the last part of (B.3) is independent of Y , but rather depends on the previous sym-bols. Thus the same calculations have to be done each time the algorithm considers a shiftfrom state a to state b. Since this is done approximately seventy times per burst, a consider-able speedup can be expected from pre-calculating that last part of (B.3). Thus, before start-ing the actual VA algorithm viterbi_detector internally does pre-calculation of a tablecalled INCREMENT which represents these values. The layout of increment is so thatINCREMENT a� b � fSYMBOLSb� �� SYMBOLSa� � �Rhhg represents the pre-calculable increment when moving from state a to state b. The pseudo code for setting up thistable is


R-97-1004 December 1997

�M�Lh� � sizeSYMBOLSfor n � � � M dom � NEXT n� �INCREMENT n�m � SYMBOLSm� �� SYMBOLSn� � �Rhh� � Lh��m � NEXT n� �INCREMENT n�m � SYMBOLSm� �� SYMBOLSn� � �Rhh� � Lh��

end for

Having established a method for calculating the metric of the states it is possible to find the met-rics of the final states. This is done by starting at the predefined start state, and then calculate thegains associated with all 148 state shifts, while summing up the gain values of each path. How-ever, as described in connection with (B.1), arriving at a state requires a choice between twocandidates. Thus, for all states it is important to save information of which state is the chosenprevious state. The chosen previous state is also referred to as the survivor. In the present im-plementation this done in a table. Since �� state shifts, and M states exist the table is M times148 elements big. The state that leads to state s at the time n is stored in SURV IV ORs� n.However, since the start state of the algorithm is bounded, initialization is required. As can beseen from Table B.1 it takes Lh symbols to remove the effect of the constraint introduced by thestart state. This initialization is described by the following piece of pseudo code

PS � STARTS � NEXT START� �METRICS� � � GainY n� S� PSSURV IV ORS� � � STARTS � NEXT START� �METRICS� � � GainY n� S� PSSURV IV ORS� � � STARTCOMPLEX � �for N � � � Lh do

if COMPLEX thenCOMPLEX � �

elseCOMPLEX � �

end ifSTATE CNTR � �for PS � PREV IOUS STATES doSTATE CNTR � STATE CNTR � �S � NEXT PS� �METRICS�N � METRICPS�N � � �GainY n� S� PSSURV IV ORS�N � PSUSEDSTATE CNTR � SSTATE CNTR � STATE CNTR � �S � NEXT PS� �


R-97-1004 December 1997

METRICS�N � METRICPS�N � � �GainY n� S� PSSURV IV ORS�N � PSUSEDSTATE CNTR � S

end forPREV IOUS STATES � USED

end for

Having initialized the algorithm the remainder of the states are processed using the followingtechnique

PROCESSED � Lh

if not COMPLEX thenCOMPLEX � �PROCESSED � PROCESSED � �N � PROCESSEDfor S � � � � � M doPS � PREV IOUSS� �M� � METRICPS�N � � �GainY n� S� PSPS � PREV IOUSS� �M� � METRICPS�N � � �GainY n� S� PSif M� M� thenMETRICS�N � M�SURV IV ORS�N � PREV IOUSS� �

elseMETRICS�N � M�SURV IV ORS�N � PREV IOUSS� �

end ifend for

end ifN � PROCESSED � �while N � lengthY do

for S � � � � � M � � doPS � PREV IOUSS� �M� � METRICPS�N � � �GainY n� S� PSPS � PREV IOUSS� �M� � METRICPS�N � � �GainY n� S� PSif M� M� thenMETRICS�N � M�SURV IV ORS�N � PREV IOUSS� �


end if


R-97-1004 December 1997

end forN � N � �for S � � � � � M doPS � PREV IOUSS� �M� � METRICPS�N � � �GainY n� S� PSPS � PREV IOUSS� �M� � METRICPS�N � � �GainY n� S� PSif M� M� thenMETRICS�N � M�SURV IV ORS�N � PREV IOUSS� �


end ifend forN � N � �

end while

Note in the above, that the first if structure, which ensures that an equal number of states remainsfor the while loop to process.

Now the remaining task is to identify the received symbols. This involves determining the re-ceived sequence of MSK-symbols. The algorithm used for that task is

BEST LEGAL � �for FINAL � STOPS do

if METRICFINAL� STEPS BEST LEGAL thenBEST LEGAL � METRICFINAL� ��S � FINAL

end ifend forIEST STEPS � SYMBOLSS� �N � STEPS � �while N � doS � SURV IV ORS�N � �IEST N � SYMBOLSS� �N � N � �

end while

Finally, the MSK-symbols are to be translated to a sequence of binary data bits and returned inrx burst. To do this the following is employed

rx burst� � IEST ��j � � � �


R-97-1004 December 1997

for n � � � STEPS dorx burstn � IEST n�j � rx burstn� � � IEST n� �

end forrx burst � rx burst� ��

This concludes the description of the viterbi_detector, and thus of the implementationof the Viterbi detector.

In summary it is repeated that the present implementation is made up by two functions, namelyviterbi_init and viterbi_detector. The job of viterbi_init is to setup trans-lation and transition tables, along with other information, for use by viterbi_detector.viterbi_detector handles all the processing of the received data.

B.3 De-multiplexer

The de-multiplexer is simple in its implementation, since all that needs to be done is to extract tosub-vectors directly from a burst and then return these two vectors as a single continued vector.

B.3.1 Input, Output and Processing

The input to the function is:

rx burst: The estimated bit sequence, in the same format as it is returnedby the function viterbi_detector.m.

and the corresponding output is:

rx data: The de-multiplexed data bits.

The de-multiplexing is implemented by a single line of MATLAB code:

rx data � �rx burst� � �� rx burst� � ��

B.4 De-Interleaver

As described in Section 3.3.2 the de-interleaver is implemented in the MATLAB function calleddeinterleave.m. The purpose of the de-interleaver is to reorder the bits which was initially


R-97-1004 December 1997

shuffeled by the interleaver. As is the case with the interleaver, it is possible to implement thede-interleaver in a simple manner, resulting in a low computational burden at runtime.

B.4.1 Input, Output, and Processing

The de-interleaver takes eight instances of rx data as its input:

rx data matrix:A matrix containg eight instances of rx data. Each instance isaligned in a row. The data are arranged so that the eldest instanceof rx data is kept in row number one, and the latest arrived in-stance is kept in row number eight.

The output from the de-interleaver is:

rx enc: The received code block, as reconstructed from the eight instancesof rx data.

The de-interleaver is externally aided by a queue, which administrates the propper alignment ofthe rx data instances. Internally the de-interleaver simply perform a number of copy operationsas described by the formulas in (3.21) and (3.22) in Section 3.3.2. The file deinterleave.mis constructed using the following lines

BitsInBlock � ��out � fopen�deinterleave�tmp�� w�B � �for b � � � BitsInBlock doR � � B �modb� �r � � mod� b� �� floormodb� ��fprintfout�� rx enc�d � rx data matrix�d��d� nn�� b� �� R � �� r � �

end forfcloseout

Implementing the de-interleaver in this way, with pre calculated indexes, proves to be muchfaster than when the indexes are calculated at runtime.

B.5 Channel Decoder

The channel decoder operation is implemented by the MATLAB function channel_dec.m.The task of this function is to implement the outer decoding required for use in the GSM system.


R-97-1004 December 1997


The channel decoder makes use of the following input parameter

rx enc: A 456 bits long vector contaning the encoded data sequence asestimated by the SOVA. The format of the sequency must be ac-cording to the GSM 05.03 encoding scheme

The corresponding output from channel_enc.m is

rx block: The resulting 260 bits long vector decoded data sequence.FLAG SS: Error flag. Due to the structure of the encoding scheme the

decoder should end in the same state as it starts of in. If this isnot the case the decoded output contains errors. If an error hasoccured FLAG SS is set to ’1’.

PARITY CHK: Estimate of the 3 parity check bit inserted in the transmitter.

B.5.2 Internal Data Flow

Besides from the above mentioned information carrying parameters the channel decoder alsooperates using some internal information.

As is the case in the channel encoder two levels of bits are dealt with. The separation into classI, c�, and class II bits, c�, is nessesary as only the class I bits are encoded.

Furthermore a number of matrices and vectors are generated to help keep track of the differentpaths in the state trellis and the corresponding metrics. These variables are termed STATEand METRIC, respectively. Also, to destinguish between legal and illegal state transitionstwo matrices, NEXT and PREV IOUS, are set up to determine wich two states a given statemay switch to next and what states that are allowed to lead to a given state, respectively.

In order to enable the calculation of the metric a matrix, DIBIT , is set up. When, in thechannel encoder, a transition from one state to another state occurs two bits, here referred to asdibits are output. Which one of the four possible dibit combinations that are output for a giventransition is stored in the DIBIT matrix. In close relation to this matrix a BIT matrix is alsorequired. The structure of BIT is just as that of the DIBIT matrix only here the content is theone bit binary input that is required for a given state transition. Hence, the BIT matrix is usedin mapping state transition information to actual binary – and decoded – information.


R-97-1004 December 1997

B.5.3 Processing

First the input, rx enc, is split into the different classes and the various internal variables areinitialized

c� � rx enc� � ��c� � rx enc��

START STATE � �END STATE � �

STATE � zeros�� METRIC � zeros��

NEXT � zeros�� zeroin � �onein � for n � � � � � �� doNEXT n� � � �zeroin onein�NEXT n � �� NEXT n� �zeroin � zeroin � �onein � onein � �

end for

PREV IOUS � zeros�� offset � �for n � � � � doPREV IOUSn� � � �n � offset n � offset� ��offset � offset� �

end forPREV IOUS � �PREV IOUS� � �� PREV IOUS� � ��

Having split the data the c� bits are decoded using the Viterbi algorithm. check bits. To reducethe number of calculations the run of the Viterbi is split into to parts. The first part is a runin where only the known legal next states are used in the metric calculations. This is run for4 strate transitions. From that point on all states in the state trellis are in use and the previouslegal states are used in stead.

V ISITED STATES � START STATEfor n � � � � dorx DIBITXy � c�� n � �rx DIBITxY � c�� n� � � �for k � � � lengthV ISITED STATES do


R-97-1004 December 1997

PRESENT STATE � V ISITED STATESknext state� � NEXT PRESENT STATE� �next state� � NEXT PRESENT STATE� �symbol � � DIBIT PRESENT STATE� next state �symbol � � DIBIT PRESENT STATE� next state �

if symbol � �� thenLAMBDA � xorrx DIBITXy� � � xorrx DIBITxY� �

end ifif symbol � �� thenLAMBDA � xorrx DIBITXy� � � xorrx DIBITxY� �



end if

METRICnext state �� METRICPRESENT STATE� � � LAMBDA





end if

METRICnext state �� METRICPRESENT STATE� � � LAMBDASTATE�next state �� next state �� n� � � PRESENT STATE

if k �� thenPROCESSED � �next state � next state ��

elsePROCESSED � �PROCESSED next state � next state ��

end ifend for


R-97-1004 December 1997

V ISITED STATES � PROCESSEDMETRIC�� METRIC�� METRIC��

end for

Having completed the run in process of the Viterbi algorithm all 16 states are now consideredusing the PREV IOUS table

for n � � � �� dorx DIBITXy � c�� n � �rx DIBITxY � c�� n� � � �for k � � � �� doprev state � � PREV IOUSk� �prev state � � PREV IOUSk� �symbol � � DIBIT prev state �� ksymbol � � DIBIT prev state �� k





end if





end if


R-97-1004 December 1997

METRIC � � METRICprev state �� LAMBDA �METRIC � � METRICprev state �� LAMBDA �

if METRIC � � METRIC � thenMETRICk� � � METRIC �STATEk� n� � � prev state �

elseMETRICk� � � METRIC �STATEk� n� � � prev state �

end ifend for

METRIC�� METRIC�� METRIC��

end for

Having build the state transition trellis finding the most probable sequence of states is now amatter of backtracking through the trellis. This gives the state transition sequence that then ismapped to binary information which when combined with the class II bits gives the final de-coded information signal.

STATE SEQ � zeros�� STOP METRIC� STOP STATE� � minMETRIC�� STATE SEQ�� STOP STATEfor n � �� doSTATE SEQn � STATESTATE SEQn� �� n� �

end forSTATE SEQ � �START STATE STATE SEQ�

for n � � � lengthSTATE SEQ� � doDECONV DATAn � BIT STATE SEQn� STATE SEQn � �

end for

DATA Ia � DECONV DATA� � ��PARITY CHK � DECONV DATA�� DATA Ib � DECONV DATA�� TAIL BITS � DECONV DATA��

rx block � �DATA Ia DATA Ib c��


R-97-1004 December 1997


R-97-1004 December 1997

CSource code

This Chapter contains the source code for GSMsim. The more simple code, such as the oneused for generating the illustrations in the present work, is not included.


R-97-1004 December 1997

Sour

ceco

deC

.1:burst_g.m

1functiontx_burst=burst_g(tx_data,TRAINING)

2%

3%burst_g:

This

functiongeneratesa

bit

sequencerepresenting

4%

ageneralGSM

informationburst.Includedare

tail

5%

and

ctrlbits,

databitsand

atrainingsequence.

6%

7%

The

GSMburst

containsatotal

of148

bitsaccounted

8%

for

inthe

followingburststructure(GSM

05.05)

9%

10%

[TAIL|

DATA

|CTRL

|TRAINING|CTRL

|DATA|

TAIL]

11%

[3

|57

|1

|26

|1

|57

|3

]12

%13

%[TAIL]

=[000]

14%

[CTRL]

=[0]or

[1]

here[1]

15%

[TRAINING]is

passedtothefunction

16%

17%SYNTAX:

tx_burst=

burst_g(tx_data,TRAINING)

18%

19%INPUT:

tx_data:

The

burstdata.

20%

TRAINING:The

Trainingsequencewhichis

tobe

used.

21%

22%OUTPUT:

tx_burst:A

complete148bits

longGSM

normalburstbinary

23%

sequence

24%

25%GLOBAL:

26%

27%SUB_FUNC:None

28%

29%WARNINGS:None

30%

31%TEST(S):

Functiontested

32%

33%AUTHOR:

Jan

H.Mikkelsen/

ArneNorre

Ekstrøm

34%EMAIL:

[email protected]/[email protected]

35%

36%$Id:

burst_g.m,v1.6

1997/12/1715:32:23aneksExp

$37 38

TAIL=

[00

0];

39CTRL=

[1];

40 41%COMBINETHE

BURSTBIT

SEQUENCE

42%

43tx_burst=[TAIL

tx_data(1:57)CTRLTRAININGCTRL

tx_data(58:114)TAIL];

Sour

ceco

deC

.2:data_gen.m

1function[tx_data]=

data_gen(INIT_L);

2%

3%

data_gen:

Thisfunctiongeneratesablockofrandomdatabits.

4%

5%

SYNTAX:

[tx_data]=data_gen(INIT_L)

6%

7%

INPUT:

INIT_L:

Thelengthofthegenerateddatavector.

8%

9%

OUTPUT:

tx_data:Anelementvectorcontaningtherandomdata

10%

sequenceoflengthINIT_L.INIT_Lisavariable

11%

setbygsm_set.

12%

13%

SUB_FUNC:

None

14%

15%

WARNINGS:

None

16%

17%

TEST(S):

Functiontested.

18%

19%

AUTOR:

ArneNorreEkstrøm/JanH.Mikkelsen

20%

EMAIL:


21%

22%

$Id:data_gen.m,v1.61997/09/2211:46:29aneksExp$

23%

24 25%

GENERATEinit_lRANDOMBITS.FUNCTIONISBASEDONTHATRANDRETURNS

26%

UNIFORMLYDISTRIBUTEDDATAINTHEINTERVAL[0.0;1.0].

27%

28tx_data=

round(rand(1,INIT_L));


R-97-1004 December 1997

Sour

ceco

deC

.3:channel_enc.m

1function[tx_enc]=chan_enc(tx_block)

2%

3%chan_enc:

This

functionacceptsa260

bitslong

vectorcontaningthe

4%

data

sequenceintendedfor

transmission.The

lengthof

5%

the

vectoris

expandedbychannelencodingto

forma

data

6%

blockwith

alengthof456

bitsas

requiredin

anormal

7%

GSM

burst.

8%

9%

[ClassI

|ClassII

]10

%[

182

|78

]11

%12

%[

ClassIa

|ClassIb

|Class

II]

13%

[50

|132

|78

]14

%15

%The

ClassIa

bitsare

separatlyparity

encodedwhereby3

error

16%

controlbits

areadded.Subsequently,theClass

Iabits

are

17%

combinedwith

theClassIb

bitsfor

convolutionalencoding

18%

accordingto

GSM05.05.The

ClassII

bitsare

leftunprotected

19%

20%SYNTAX:

[tx_enc]=

channel_enc(tx_block)

21%

22%INPUT:

tx_block

A260bits

longvectorcontaningthe

datasequence

23%

intendedfortransmission.

24%

25%OUTPUT:

tx_enc

A456bits

longvectorcontaningthe

encodeddata

26%

sequence

27%

28%SUB_FUNC:

None

29%

30%WARNINGS:

None

31%

32%TEST(S):

Parityencoding-

testedto

operatecorrectly.

33%

Convolutionencoding-tested

tooperatecorrectly.

34%

35%AUTHOR:

Jan

H.

Mikkelsen/

Arne

NorreEkstrøm

36%EMAIL:


37%

38%$Id:

channel_enc.m,v1.9

1998/02/1210:48:31aneks

Exp$

39 40L=length(tx_block);

41 42%INPUT

CHECK

43%

44ifL

~=

260

45disp(’

’)

46disp(’Inputdata

sequencesizeviolation.Programterminated.’)

47disp(’

’)

48break;

49end

50 51%SEPARATEINPUT

INRESPECTIVECLASSES

52%

53c1a=

tx_block(1:50);

54c1b=

tx_block(51:182);

55c2=

tx_block(183:260);

56 57%PARITY

ENCODING.THREECHECKBITS

AREADDED

58%

59g=[1

011];

60d=[c1a

00

0];

61[q,r]

=deconv(d,g);

62 63%

ADJUSTRESULTTO

BINARYREPRESENTATION

64%

65L

=length(r);

66out

=abs(r(L-2:L));

67for

n=1:length(out),

68if

ceil(out(n)/2)~=floor(out(n)/2)

69out(n)=

1;

70else

71out(n)=

0;

72end

73end

74 75c1a

=[c1aout];

76 77%

CLASSI

BITS

ARECOMBINEDAND4TAILBITS,{0000},AREADDEDAS

78%

PRESCRIBEDINTHE

GSMRECOMMENDATION05.03

79%

80c1

=[c1ac1b

00

00];

81 82%

CONVOLUTIONALENCODINGOFTHERANDOMDATABITS.THEENCODINGIS

83%

ACCORDINGTO

GSM05.05

84%

85register=

zeros(1,4);

86data_seq=

[registerc1];

87enc_a

=zeros(1,189);

88enc_b

=zeros(1,189);

89encoded=

zeros(1,378);

90 91for

n=1:189,

92enc_a(n)=

xor(xor(data_seq(n+4),data_seq(n+1)),data_seq(n));

93enc_temp=

xor(data_seq(n+4),data_seq(n+3));

94enc_b(n)=

xor(

xor(enc_temp,data_seq(n+1)),data_seq(n));

95encoded(2*n-1)=

enc_a(n);

96encoded(2*n)=enc_b(n);

97clearenc_temp

98end

99 100

%PREPAREDATA

FOROUTPUT

101

%10

2tx_enc=

[encodedc2];

103


R-97-1004 December 1997

Sour

ceco

deC

.4:interleave.m

1function[tx_data_matrix]=

interleave(tx_enc0,tx_enc1)

2%

3%interleave:

4%

This

functionperformsinterleavingof

twoinformation

5%

blocks,each

containing456

bitsof

information.Output

6%

is

an

matrixwith4

rows,each

containing114

bitsof

7%

informationforinclusionin

an

GSMburst.

8%

9%SYNTAX:

[tx_data_matrix]

=interleave(tx_enc0,tx_enc1)

10%

11%INPUT:

tx_enc0:

12%

Thefirstblock

inan

interleavingpass.

13%

tx_enc1:

14%

Thesecondblock

inan

interleavingpass.

15%

16%OUTPUT:

tx_data_matrix:

17%

Amatrix

containing114

bitsof

datain

eachrow,

18%

readyto

besplitinto

twoand

passedto

burst_g.m

19%

20%WARNINGS:Not

all2

x456bits

arerepresentedin

theoutput,this

is

21%

exactelyas

specifiedinthe

recommadations.

22%

23%TEST(S):

interleave->

deinterleave=

0Errors.

24%

25%AUTHOR:

Jan

H.Mikkelsen/

ArneNorre

Ekstrøm

26%EMAIL:


27%

28%$Id:

interleave.m,v1.4

1997/11/2011:10:42aneks

Exp$

29tx_data_matrix(1,1)=tx_enc1(1);







































































100

tx_data_matrix(1,72)=tx_enc0(189);

101


102


103


104


105


106


107


108


109


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115


116


117


118


119


120


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R-97-1004 December 1997

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R-97-1004 December 1997

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R-97-1004 December 1997

381


382


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R-97-1004 December 1997

Sour

ceco

deC

.5:diff_enc.m

1functionDIFF_ENC_DATA=

diff_enc(BURST)

2%

3%diff_enc:

Thisfunctionacceptsa

GSM

burstbit

sequenceand

4%

performsa

differentialencodingof

thesequence.The

5%

encodingis

accordingtothe

GSM05.05

recommendations

6%

7%

Input:D(i)

8%

Output:A(i)

9%

10%

D’(I)=

D(i)

(+)D(i-1)

;(+)=

XOR

11%

D(i),D’(i)=

{0,1}

12%

A(i)=

1-

2*D’(i)

13%

A(i)=

{-1,1}

14%

15%SYNTAX:

[diff_enc_data]=

diff_enc(burst)

16%

17%INPUT:

burst

Abinary,(0,1),bit

sequence

18%

19%OUTPUT:

diff_enc_data

Adifferentialencoded,(+1,-1),version

20%

of

theinput

burstsequence

21%

22%SUB_FUNC:

None

23%

24%WARNINGS:

None

25%

26%TEST(S):

Functiontested

27%

28%AUTHOR:

Jan

H.Mikkelsen/

ArneNorre

Ekstrøm

29%EMAIL:


30%

31%$Id:

diff_enc.m,v1.5

1998/02/1210:49:36aneksExp$

32 33L=length(BURST);

34 35%INTERMEDIATEVECTORSFOR

DATAPROCESSING

36%

37d_hat=

zeros(1,L);

38alpha=

zeros(1,L);

39 40%DIFFERENTIALENCODINGACCORDINGTOGSM

05.05

41%AN

INFINITESEQUENCEOF

1’ENSAREASSUMED

TO

42%PRECEEDTHE

ACTUALBURST

43%

44data=

[1BURST];

45forn

=1+1:(L+1),

46d_hat(n-1)=

xor(data(n),data(n-1));

47end

48alpha=

1-

2.*d_hat;

49 50%PREPARINGDATA

FOROUTPUT

51%

52DIFF_ENC_DATA=

alpha;

Sour

ceco

deC

.6:gmsk_mod.m

1function[I,Q]=

gmsk_mod(BURST,Tb,OSR,BT)

2%

3%

gmsk_mod:

ThisfunctionacceptsaGSMburstbitsequenceand

4%

performsaGMSKmodulationofthesequence.The

5%

modulationisaccordingtotheGSM05.05recommendations

6%

7%

SYNTAX:

[i,q]=

gmsk_mod(burst,Tb,osr,BT)

8%

9%

INPUT:

burst

Adifferentialencodedbitsequence(-1,+1)

10%

Tb

Bitduration(GSM:Tb=3.692e-6Sec.)

11%

osr

Simulationoversampleratio.osrdeterminesthe

12%

numberofsimulationstepsperinformationbit

13%

BT

Thebandwidth/bitdurationproduct(GSM:BT=0.3)

14%

15%

OUTPUT:

i,q

In-phase(i)andquadrature-phase(q)baseband

16%

representationoftheGMSKmodulatedinputburst

17%

sequence

18%

19%

SUB_FUNC:

ph_g.m

Thissub-functionisrequiredingeneratingthe

20%

frequencyandphasepulsefunctions.

21%

22%

WARNINGS:

Sub-functionph_g.massumesa3xTbfrequencypulse

23%

truncationtime

24%

25%

TEST(S):

Functiontestedusingthefollowingrelations

26%

27%

i)

28%

29%

I^2+

Q^2=Cos(a)^2+Sin(a)^2=1

30%

31%

ii)

32%

33%

Whentheinputconsistsofall1’stheresultingbaseband

34%

outputsthefunctionshouldreturnasinusoidalsignalof

35%

frequencyrb/4,i.e.asignalhavingaperiodetimeof

36%

approximately4*Tb=4*3.692e-6s=1.48e-5sforGSM

37%

38%

AUTHOR:

JanH.

Mikkelsen/ArneNorreEkstrøm

39%

EMAIL:


40%

41%

$Id:gmsk_mod.m,v1.51998/02/1210:50:10aneksExp$

42 43%

ACCUIREGMSKFREQUENCYPULSEANDPHASEFUNCTION

44%

45[g,q]=

ph_g(Tb,OSR,BT);

46 47%

PREPAREVECTORFOR

DATAPROCESSING

48%

49bits

=length(BURST);

50f_res=

zeros(1,(bits+2)*OSR);

51 52%

GENERATERESULTINGFREQUENCYPULSESEQUENCE

53%

54for

n=

1:bits,

55f_res((n-1)*OSR+1:(n+2)*OSR)=f_res((n-1)*OSR+1:(n+2)*OSR)+BURST(n).*g;

56end

57 58%

CALCULATERESULTINGPHASEFUNCTION

59%

60theta=

pi*cumsum(f_res);


R-97-1004 December 1997

61 62%PREPARE

DATAFOR

OUTPUT

63%

64I=cos(theta);

65Q=sin(theta);

Sour

ceco

deC

.7:gsm_mod.m

1function[

tx_burst,I,Q]=gsm_mod(Tb,OSR,BT,tx_data,TRAINING)

2 3%

GSM_MOD:

ThisMatLabcodegeneratesaGSMnormalburstby

4%

combiningtail,ctrl,andtrainingsequencebitswith

5%

twobloksofrandomdatabits.

6%

Thedata

bitsareconvolutionalencodedaccording

7%

to

theGSMrecommendations

8%

Theburstsequenceisdifferentialencodedandthen

9%

subsequentlyGMSKmodulatedtoprovideoversampled

10%

IandQ

basebandrepresentations.

11%

12%

SYNTAX:

[tx_burst,I

,Q

]=

gsm_mod(Tb,OSR,BT,tx_data,TRAINING)

13%

14%

INPUT:

Tb:Bit

time,setbygsm_set.m

15%

OSR:Oversamplingratio(fs/rb),setbygsm_set.m

16%

BT:BandwidthBittimeproduct,setbygsm_set.m

17%

tx_data:The

contentsofthedatafieldsinthebursttobe

18%

transmitted.Datafieldonecomesfirst.

19%

TRAINING:The

Trainingsequencewhichistobeinsertedinthe

20%

burst.

21%

22%

OUTPUT:

23%

tx_burst:The

entiretransmittedburstbeforedifferential

24%

precoding.

25%

I:Inphasepartofmodulatedburst.

26%

Q:Quadraturepartofmodulatedburst.

27%

28%

WARNINGS:No

interleavingorchannelcodingisdone,andthusthe

29%

GSMrecommadationsareviolated.Datasimulationsdoneusing

30%

thisformatcanonlybeusedforpredictingClassIIperformance.

31%

32%

AUTHOR:

JanH.


33%

EMAIL:


34%

35%

$Id:gsm_mod.m,v1.101997/12/1715:29:27aneksExp$

36 37%

GENERATEBURSTSEQUENCE(THISISACTUALLYTHEMUX).

38%

39tx_burst=

burst_g(tx_data,TRAINING);

40 41%

DIFFERENTIALENCODING.

42%

43burst

=diff_enc(tx_burst);

44 45%

GMSKMODULATIONOF

BURSTSEQUENCE

46%

47[I,Q]

=gmsk_mod(burst,Tb,OSR,BT);


R-97-1004 December 1997

Sour

ceco

deC

.8:ph_g.m

1function[G_FUN,Q_FUN]=

ph_g(Tb,OSR,BT)

2%

3%PH_G:

This

functioncalculatesthe

frequencyandphase

functions

4%

requiredfor

theGMSK

modulation.The

functionsare

5%

generatedaccordingto

theGSM

05.05recommendations

6%

7%SYNTAX:

[g_fun,q_fun]

=ph_g(Tb,osr,BT)

8%

9%INPUT:

Tb

Bit

duration(GSM:Tb

=3.692e-6Sec.)

10%

osr

Simulationoversampleratio.osr

determinesthe

11%

number

ofsimulationstepsper

informationbit

12%

BT

The

bandwidth/bitdurationproduct(GSM:

BT=

0.3)

13%

14%OUTPUT:

g_fun,q_fun

Vectorscontaningfrequencyand

phase

15%

functionoutputs

whenevaluatedat

osr*tb

16%

17%SUB_FUNC:None

18%

19%WARNINGS:Modulationlengthof

3isassumed!

20%

21%TEST(S):

Testedthrough

functiongsmk_mod.m

22%

23%AUTHOR:

Jan

H.Mikkelsen/

ArneNorre

Ekstrøm

24%EMAIL:


25%

26%$Id:

ph_g.m,v1.61998/02/1210:50:54aneksExp

$27 28

%SIMULATIONSAMPLEFREQUENCY

29%

30Ts=

Tb/OSR;

31 32%PREPARINGVECTORSFOR

DATAPROCESSING

33%

34PTV=

-2*Tb:Ts:2*Tb;

35RTV=

-Tb/2:Ts:Tb/2-Ts;

36 37%GENERATEGAUSSIANSHAPED

PULSE

38%

39sigma=

sqrt(log(2))/(2*pi*BT);

40gauss=

(1/(sqrt(2*pi)*sigma*Tb))*exp(-PTV.^2/(2*sigma^2*Tb^2));

41 42%GENERATERECTANGULARPULSE

43%

44rect=

1/(2*Tb)*ones(size(RTV));

45 46%CALCULATERESULTINGFREQUENCYPULSE

47%

48G_TEMP=

conv(gauss,rect);

49 50%TRUNCATINGTHE

FUNCTIONTO3xTb

51%

52G=G_TEMP(OSR+1:4*OSR);

53 54%TRUNCATIONIMPLIESTHAT

INTEGRATINGTHE

FREQUENCYPULSE

55%FUNCTIONWILL

NOTEQUAL

0.5,HENCETHE

RE-NORMALIZATION

56%

57G_FUN=

(G-G(1))./(2*sum(G-G(1)));

58 59%CALCULATERESULTINGPHASEPULSE

60%

61Q_FUN=

cumsum(G_FUN);


R-97-1004 December 1997

Sour

ceco

deC

.9:make_increment.m

1function[INCREMENT]

=make_increment(SYMBOLS,NEXT,Rhh)

2%

3%MAKE_INCREMENT:

4%

This

functionreturnsa

lookuptablecontainingthe

5%

metric

incrementsrelatedto

movingfrom

staten

tom.

6%

The

datais

arrangedso

thatthe

incrementaccosiated

7%

with

amovefromstate

ntom

is

locatedin

8%

INCREMENT(n,m).Tominimizecomputationsonlylegal

9%

transitionsare

considdered.

10%

11%SYNTAX:

[INCREMENT]

=make_increment(SYMBOLS,NEXT,Rhh)

12%

13%INPUT:

SYMBOLS:The

tableof

symbolscorrespondingthe

thestate-

14%

numbers.

15%

NEXT:

Atransitiontablecontainingthenext

legal

16%

states,as

it

isgeneratedby

thecode

make_next.

17%

Rhh:

The

autocorrelationas

estimatedbymf.m.

18%

19%OUTPUT:

INCREMENT:

20%

The

incrementtableas

describedabove.

21%

22%SUB_FUNC:None

23%

24%WARNINGS:There

isno

syntaxcheckingon

inputor

output.

25%

26%TEST(S):

By

hand,againstexpectedvalues.

27%

28%AUTOR:

Jan

H.

Mikkelsen/

Arne

NorreEkstrøm

29%EMAIL:


30%

31%$Id:

make_increment.m,v1.61997/09/2211:39:34aneksExp

$32 33

%IN

THIS

PEACEOF

CODETHE

SYNTAXCHECKINGISMINIMAL

34%THIS

HASBEEN

CHOSENTO

AVOIDTHE

OVERHEAD.RECALL

THAT

35%THIS

CODEIS

EXECUTEDEACHTIME

ABURSTIS

RECEIVED.

36 37%FIND

THENUMBER

OFSYMBOLSTHAT

WEHAVE

38%

39[M,Lh]=size(SYMBOLS);

40 41%INITIALIZETHE

INCREMENTMATRIX

42%

43INCREMENT=zeros(M);

44 45%RECALL

THATTHE

ISEQUENCEAS

IT

ISSTORED

INSTOREDAS:

46%[I(n-1)I(n-2)

I(n-3)...I(n-Lh)]

47%

48%ALSO

RECALLTHAT

RhhIS

STOREDAS:

49%[Rhh(1)Rhh(2)

Rhh(3)...Rhh(Lh)]

50%

51%THE

FORMULATO

USEIS:

52%INCREMENT(n,m)

53%=

54%real(conj(I(n))*(I(n-Lh)*Rhh(Lh)+I(n-Lh+1)*Rhh(Lh-1)+...+I(n-1)*Rhh(1))

55%

56%THEY

CANTHUS

BE

MULTIPLIEDDIRECTLYWITH

EACHOTHER

57 58%LOOP

OVERTHE

STATES,AS

FOUNDIN

THEROWS

INSYMBOLS.

59%

60forn=1:M,

61%

ONLYTWO

LEGALNEXTSTATESEXIST,SOTHELOOPISUNROLLED

62%

63m=NEXT(n,1);

64INCREMENT(n,m)=real(conj(SYMBOLS(m,1))*SYMBOLS(n,:)*Rhh(2:Lh+1).’);

65m=NEXT(n,2);

66INCREMENT(n,m)=real(conj(SYMBOLS(m,1))*SYMBOLS(n,:)*Rhh(2:Lh+1).’);

67end


R-97-1004 December 1997

Sour

ceco

deC

.10:

make_next.m

1function[NEXT

]=make_next(SYMBOLS)

2%

3%MAKE_NEXT:

4%

This

functionreturnsalookuptablecontaininga

mapping

5%

betweenthe

presentstateand

thelegal

nextstates.

6%

Each

rowcorrespondto

astate,

andthe

twolegal

states

7%

relatedto

staten

is

locatedinNEXT(n,1)and

in

8%

NEXT(n,2).Statesare

representedby

theirrelated

9%

numbers.

10%

11%SYNTAX:

[NEXT]

=make_next(SYMBOLS)

12%

13%INPUT:

SYMBOLS:The

tableof


thestate-

14%

numbers.

15%

16%OUTPUT:

NEXT:

The

transitiontable

describingthelegalnext

17%

statesasdescribedabove.

18%

19%SUB_FUNC:None

20%

21%WARNINGS:None

22%

23%TEST(S):

The

functionhasbeen

verifiedtoreturn

theexpected

24%

results.

25%

26%AUTOR:

Jan

H.Mikkelsen/

ArneNorre

Ekstrøm

27%EMAIL:


28%

29%$Id:

make_next.m,v1.3

1997/09/2208:13:29aneks

Exp$

30 31%FIRST

WENEED

TOFIND

THENUMBER

OFLOOPS

WESHOULDRUN.

32%THIS

EQUALSTHE

NUMBEROFSYMBOLS.ALSO

MAXSUMIS

NEEDEDFOR

33%LATER

OPERATIONS.

34%

35[states

,maxsum

]=size(SYMBOLS);

36 37search_matrix=SYMBOLS(:,2:maxsum);

38maxsum=maxsum-1;

39 40%LOOP

OVERTHE

SYMBOLS.

41%

42forthis_state=1:states,

43search_vector=SYMBOLS(this_state,1:maxsum);

44k=0;

45for

search=1:states,

46if

(sum(search_matrix(search,:)==search_vector)==maxsum)

47k=k+1;

48NEXT(this_state,k)=search;

49if

k>

2,

50error(’Error:identifiedtoomany

nextstates’);

51end

52end

53end

54end

Sour

ceco

deC

.11:

make_previous.m

1function[

PREVIOUS]=make_previous(SYMBOLS)

2%

3%

MAKE_PREVIOUS:

4%

Thisfunctionreturnsalookuptablecontainingamapping

5%

betweenthepresentstateandthelegalpreviousstates.

6%

Eachrow

correspondtoastate,andthetwolegalstates

7%

relatedtostatenislocatedinPREVIOUS(n,1)andin

8%

previous(n,2).Statesarerepresentedbytheirrelated

9%

numbers.

10%

11%

SYNTAX:

[PREVIOUS]=make_previous(SYMBOLS)

12%

13%

INPUT:

SYMBOLS:Thetableofsymbolscorrespondingthethestate-

14%

numbers.

15%

16%

OUTPUT:

PREVIOUS:

17%

Thetransitiontabledescribingthelegalprevious

18%

statesasdescribedabove.

19%

20%

SUB_FUNC:None

21%

22%

WARNINGS:None

23%

24%

TEST(S):

Verifiedagainstexpectedresult.

25%

26%

AUTOR:

JanH.


27%

EMAIL:


28%

29%

$Id:make_previous.m,v1.31997/09/2208:14:27aneksExp$

30 31%

FIRSTWE

NEEDTO

FINDTHENUMBEROFLOOPSWESHOULDRUN.

32%

THISEQUALS

THENUMBEROFSYMBOLS.ALSOMAXSUMISNEEDEDFOR

33%

LATEROPERATIONS.

34%

35[

states,

maxsum]=size(SYMBOLS);

36 37maxsum=maxsum-1;

38search_matrix=SYMBOLS(:,1:maxsum);

39 40%

LOOPOVER

THESYMBOLS.

41%

42for

this_state=1:states,

43search_vector=SYMBOLS(this_state,2:maxsum+1);

44k=0;

45forsearch=1:states,

46if(sum(search_matrix(search,:)==search_vector)==maxsum)

47k=k+1;

48PREVIOUS(this_state,k)=search;

49if

k>

2,

50error(’Error:identifiedtoomanypreviousstates’);

51end

52end

53end

54end


R-97-1004 December 1997

Sour

ceco

deC

.12:

make_start.m

1function[START

]=make_start(Lh,SYMBOLS)

2%

3%MAKE_START:

4%

This

codereturnsa

statenumbercorrespondingto

thestart

5%

state

asit

is

foundfromLh.

Themethod

isto

use

thetable

6%

of

symbolicstartstatesasit

islisted

inthe

reportmade

7%

by

95gr870T.Forthe

tablelookupsare

madein

SYMBOLS.in

8%

order

tomap

fromthe

symbolrepresentationto

the

statenumber

9%

representation.

10%

11%SYNTAX:

[START]

=make_start(Lh,SYMBOLS)

12%

13%INPUT:

SYMBOLS:The

tableof


thestate-

14%

numbers.

15%

Lh:

Length

ofthe

estimatedimpulseresponse.

16%

17%OUTPUT:

START:

The

numberrepresentationof

the

legalstartstate.

18%

19%SUB_FUNC:None

20%

21%WARNINGS:The

tableof

symbolicrepresentationshas

notbeen

verified

22%

but

is

useddirectlyas

itis

listedin

thereport

made

23%

by

95gr870T.

24%

25%TEST(S):

The

functionhasbeen

verifiedtoreturn

astate

number

26%

which

matchesthesymbolicrepresentation.

27%

28%AUTOR:

Jan

H.

Mikkelsen/

Arne

NorreEkstrøm

29%EMAIL:


30%

31%$Id:

make_start.m,v1.2

1997/09/2211:40:17aneks

Exp$

32 33%WE

HAVEN’TFOUND

ITYET.

34%

35START_NOT_FOUND=

1;

36 37%OBTAIN

THESYMBOLSFROM

Lh.THIS

ISTHE

TABLELISTEDIN

THE

REPORTMADE

38%BY

95gr870T.(SATEREPRESENTATIONISSLIGHTLYCHANGED).

39%

40ifLh==1,

41start_symbols=

[1

];

42elseifLh==2,

43start_symbols=

[1

-j

];

44elseifLh==3,

45start_symbols=

[1

-j

-1

];

46elseifLh==4,

47start_symbols=

[1

-j

-1

j];

48else

49fprintf(’\n\nError:Illegalvalue

ofLh,

terminating...’);

50end

51 52%NOW

MAP

FROMTHE

SYMBOLSTOA

STATENUMBER

BYSEARCHING

53%SYMBOLS.

54%

55START=0;

56whileSTART_NOT_FOUND,

57START=START+1;

58if

sum(SYMBOLS(START,:)==start_symbols)==Lh,

59START_NOT_FOUND=0;

60end

61end


R-97-1004 December 1997

Sour

ceco

deC

.13:

make_stops.m

1function[STOPS

]=

make_stops(Lh,SYMBOLS)

2%

3%MAKE_STOPS:

4%

This

codereturnsa

statenumbercorrespondingto

theset

of

5%

legal

stopstatesas

foundfrom

Lh.The

methodis

touse

thetable

6%

of

symbolicstopstatesasit

islisted

inthe

reportmade

7%

by

95gr870T.Forthe

tablelookupsare

madein

SYMBOLS.in

8%

order

tomap

fromthe

symbolrepresentationto

thestate

number

9%

representation.

10%

11%SYNTAX:

[STOPS]

=make_stops(Lh,SYMBOLS)

12%

13%INPUT:

SYMBOLS:The

tableof


thestate-

14%

numbers.

15%

Lh:

Lengthof

the

estimatedimpulseresponse.

16%

17%OUTPUT:

STOPS:

The

numberrepresentationof

theset

of

legalstop

18%

states.

19%

20%SUB_FUNC:None

21%

22%WARNINGS:The

tableof

symbolicrepresentationshasnot

beenverified

23%

but

isused

directlyasitis

listedin

thereportmade

24%

by

95gr870T.

25%

26%TEST(S):

The

functionhasbeen

verifiedtoreturn

astate

number

27%

which

matchesthesymbolicrepresentation.

28%

29%AUTOR:

Jan

H.Mikkelsen/

ArneNorre

Ekstrøm

30%EMAIL:


31%

32%$Id:

make_stops.m,v1.2

1997/09/2211:44:21aneks

Exp$

33 34%OBTAIN

THESYMBOLSFROM

Lh.THIS

ISTHE

TABLELISTEDIN

THE

REPORTMADE

35%BY

95gr870T.(SATEREPRESENTATIONISSLIGHTLYCHANGED).

36%

37ifLh==1,

38stop_symbols=

[-1

];

39count=1;

40elseifLh==2,

41stop_symbols=

[-1

j];

42count=1;

43elseifLh==3,

44stop_symbols=

[-1j1];

45count=1;

46elseifLh==4,

47stop_symbols=

[[

-1

j1-j];[-1

j1

j]

];

48count=2;

49else

50fprintf(’\n\nError:IllegalvalueofLh,

terminating...’);

51end

52 53%NOW

THATWE

HAVETHE

SYMBOLREPRESENTATIONTHE

REMAININGJOBIS

54%TO

MAP

THEMSK

SYMBOLSTOSTATE

NUMBERS

55%

56index=

0;

57stops_found=0;

58whilestops_found<count,

59index=index+1;

60if

sum(SYMBOLS(index,:)==stop_symbols(stops_found+1,:))==Lh,

61stops_found=stops_found+1;

62STOPS(stops_found)=index;

63end

64end


R-97-1004 December 1997

Sour

ceco

deC

.14:

make_symbols.m

1function[SYMBOLS

]=

make_symbols(Lh)

2%

3%MAKE_SYMBOLS:

4%

This

functionreturnsa

tablecontainingthemapping

5%

from

statenumbersto

symbols.Thetable

iscontained

6%

in

amatrix,andthe

layoutis:

7%

8%

--

9%

|Symbolsfor

state1

|10

%|

Symbolsfor

state2

|11

%:

12%

:13

%|

Symbolsfor

stateM

|14

%-

-15

%16

%Where

Mis

the

totalnumberof

states,andcan

be

calculated

17%

as:

2^(Lh+1).Lhis

the

lengthofthe

estimatedimpulse

18%

response,as

foundin

themf-routine.In

thesymbolsfor

19%

astatenumbertheorder

isas:

20%

21%

I(n-1)

I(n-2)I(n-3)...I(n-Lh)

22%

23%

Each

ofthe

symbolsbelongto

{1,

-1

,j,

-j

}.

24%

25%SYNTAX:

[SYMBOLS]=

make_symbols(Lh)

26%

27%INPUT:

Lh:

Length

ofthe

estimatedimpulseresonse.

28%

29%OUTPUT:

SYMBOLS:The

tableof


thestate-

30%

numbers,as

describedabove.

31%

32%SUB_FUNC:None

33%

34%WARNINGS:None

35%

36%TEST(S):

Comparedresult

againstexpectedvalues.

37%

38%AUTOR:

Jan

H.

Mikkelsen/

Arne

NorreEkstrøm

39%EMAIL:


40%

41%$Id:

make_symbols.m,v1.6

1997/09/2211:38:57aneks

Exp$

42 43%THIS

CODECANNOT

HANDLELh=1or

Lh>4.

44%

45ifLh==1,

46error(’GSMsim-Error:Lh

isconstrainedto

bein

the

interval[1:4].’);

47elseifLh

>4,

48error(’GSMsim-Error:Lh

isconstrainedto

bein

the

interval[1:4].’)

49end

50 51%make

initiatingsymbols

52%

53SYMBOLS=[1;j;

-1

;-j];

54%

55forn=1:Lh-1

56SYMBOLS=[[SYMBOLS(:,1)*j,SYMBOLS]

;[

SYMBOLS(:,1)*(-j),SYMBOLS

]];

57end

58%

59%NOW

WE

NEEDTO

ASSURETHATTHE

STATERELATEDTO

THE

NUMBERONE

60%IS

COMPLEX.THIS

ISREQUIREDBY

THEIMPLEMENTATIONOFTHE

VITERBI

61%

ALGORITHM.

62%

63if

isreal(SYMBOLS(1,1)),

64SYMBOLS=flipud(SYMBOLS);

65end


R-97-1004 December 1997

Sour

ceco

deC

.15:

mf.m(Renamedtomafi.m)

1function[Y,Rhh]

=mafi(r,L,T_SEQ,OSR)

2%

3%MAFI:

This

functionperformesthe

tasksof

channelimpulse

4%

responsestimation,bitsyncronization,matched

5%

filteringand

signalsampleratedownconversion.

6%

7%SYNTAX:

[y,

Rhh]=

mafi(r,Lh,T_SEQ,OSR)

8%

9%INPUT:

rComplexbasebandrepresentationof

thereceived

10%

GMSKmodulatedsignal

11%

Lh

Thedesiredlengthofthe

matchedfilterimpulse

12%

responsemeasuredinbit

timedurations

13%

T_SEQ

AMSK-modulatedrepresentationof

the26

bitslong

14%

trainingsequenceused

in

thetransmittedburst,

15%

i.e.the


in

thegenerationof

r16

%OSR

Oversamplingratio,definedas

f_s/r_b.

17%

18%OUTPUT:

YComplexbasebandrepresentationof

thematched

19%

filteredanddownconvertedreceivedsignal

20%

21%

Rhh

Autocorrelationofthe

estimatedchannelimpulse

22%

response.The

formatis

aLh+1unitlong

columnvector

23%

startingwithRhh[0],and

endingwithRhh[Lh].

24%

Complexvalued.

25%

26%SUB_FUNC:None

27%

28%WARNINGS:The

channelestimationisbased

onthe

16most

central

29%

bits

ofthe

trainingsequenceonly

30%

31%TEST(S):

Testedmanuallythroughtest

scriptmf_ill.m

32%

33%AUTOR:

Jan

H.Mikkelsen/

ArneNorre

Ekstrøm

34%EMAIL:


35%

36%$Id:

mafi.m,v1.11998/10/0110:20:21hmi

Exp$

37 38DEBUG=0;

39 40%PICK

CENTRAL16

BITS[

B|C|A]AS

COMPROMISE

41%AND

PERFORMCOMPLEXCONJUGATION

42%

43T16=

conj(T_SEQ(6:21));

44 45%EXTRACTRELEVANTPART

OF

THERECEIVEDSIGNAL.USING

46%GUARD

TIMESAS

GUIDELINESIMPLIESEXTRACTINGTHE

PART

47%STARTINGAPPROXIMATELYAT10

Tb’sBEFORE

THE16

MOST

48%CENTRALTRAININGSEQUENCEBITS

ANDENDING

APPROXIMATELY

49%10

Tb’sAFTER.

ASSUMETHATBURSTSTEND

TO

BECENTEREDIN

50%A

SAMPLESTREAM.

51%

52GUARD=

10;

53center_r=round(length(r)/2);

54start_sub=center_r-(GUARD+8)*OSR;

55end_sub=center_r+(GUARD+8)*OSR;

56 57%YOU

MAYWANT

TO

ENABLETHISFOR

SPECIALDEBUGGNIG

58%

59%start_sub=1;

60%end_sub=length(r);

61 62r_sub=

r(start_sub:end_sub);

63 64if

DEBUG,

65%

DEBUGGING,VERIFIESTHATWEPICKTHERIGHTPARTOUT

66%

67count=1:length(r);

68figure

69plot(count,real(r));

70plug=start_sub:end_sub;

71holdon;

72plot(plug,real(r_sub),’r’)

73holdoff;

74title(’Realpartofrandr_sub(red)’);

75%pause;

76end

77 78%

PREPAREVECTORFOR

DATAPROCESSING

79%

80chan_est=

zeros(1,length(r_sub)-OSR*16);

81 82%

ESTIMATECHANNELIMPULSERESPONSEUSINGONLYEVERY

83%

OSR’thSAMPLEIN

THERECEIVEDSIGNAL

84%

85for

n=

1:length(chan_est),

86chan_est(n)=r_sub(n:OSR:n+15*OSR)*T16.’;

87end

88 89if

DEBUG,

90%

DEBUGGING,PROVIDESAPLOTOFTHEESTIMATEDIMPULSE

91%

RESPONSEFORTHE

USERTOGAZEAT

92figure;

93plot(abs(chan_est));

94title(’Theabsoultevalueofthecorrelation’);

95%pause;

96end

97 98chan_est=

chan_est./16;

99 100

%EXTRACTINGESTIMATEDIMPULSRESPONSBYSEARCHINGFORMAXIMUM

101

%POWERUSING

AWINDOWOFLENGTHOSR*(L+1)

102

%10

3WL

=OSR*(L+1);

104

105

search=

abs(chan_est).^2;

106

for

n=

1:(length(search)-(WL-1)),

107

power_est(n)=

sum(search(n:n+WL-1));

108

end

109

110

if

DEBUG,

111

%DEBUGGING,SHOWS

THEPOWERESTIMATE

112

figure;

113

plot(power_est);

114

title(’Thewindowpowers’);

115

%pause;

116

end

117

118

%SEARCHINGFORMAXIMUMVALUEPOWERWINDOWANDSELECTINGTHE

119

%CORRESPONDINGESTIMATEDMATCHEDFILTERTAPCOEFFICIENS.ALSO,

120

%THESYNCRONIZATIONSAMPLECORRESPONDINGTOTHEFIRSTSAMPLE

121

%IN

THET16

TRAININGSEQUENCEISESTIMATED

122

%12

3[peak,sync_w]=

max(power_est);

124

h_est=

chan_est(sync_w:sync_w+WL-1);


R-97-1004 December 1997

125

126

[peak,sync_h]=

max(abs(h_est));

127

sync_T16=sync_w

+sync_h

-1;

128

129

ifDEBUG,

130

%DEBUGGING,SHOWSTHE

POWERESTIMATE

131

figure;

132

plot(abs(h_est));

133

title(’Absolutevalueof

extractedimpulse

response’);

134

%pause;

135

end

136

137

%WE

WANT

TOUSE

THEFIRST

SAMPLEOFTHE

IMPULSERESPONSE,AND

THE

138

%CORRESPONDINGSAMPLESOF

THERECEIVEDSIGNAL.

139

%THE

VARIABLEsync_wSHOULDCONTAINTHE

BEGINNINGOF

THEUSED

PARTOF

140

%TRAININGSEQUENCE,WHICH

IS3+57+1+6=67BITSINTO

THEBURST.

THATIS

141

%WE

HAVE

THATsync_T16EQUALSFIRSTSAMPLE

INBIT

NUMBER67.

142

%14

3burst_start=

(start_sub+

sync_T16-

1)

-(OSR

*66+

1)

+1;

144

145

%COMPENSATINGFOR

THE2

Tb

DELAYINTRODUCEDINTHE

GMSKMODULATOR.

146

%EACH

BITIS

STRECHEDOVER

APERIODOF

3Tb

WITHITS

MAXIMUMVALUE

147

%IN

THE

LASTBIT

PERIOD.HENCE,burst_startIS2

*OSRMISPLACED.

148

%14

9burst_start=

burst_start-

2*OSR+

1;

150

151

%CALCULATEAUTOCORRELATIONOFCHANNELIMPULSE

152

%RESPONS.DOWN

CONVERSIONISCARRIEDOUT

AT

THESAME

153

%TIME

154

%15

5R_temp=

xcorr(h_est);

156

157

pos=

(length(R_temp)+1)/2;

158

159

Rhh=R_temp(pos:OSR:pos+L*OSR);

160

161

%PERFORM

THEACTUALMATCHEDFILTERING

162

%16

316

4m=

length(h_est)-1;

165

166

%A

SINGLEZERO

IS

INSERTEDINFRONTOF

rSINCETHERE

ISAN

EQUAL

167

%NUMBER

OFSAMPLESIN

r_subWE

CANNOTBE

TOTALLYCERTAINWHICH

168

%SIDE

OF

THEMIDDLETHAT

ISCHOSEN

THUSAN

EXTRASAMPLEIS

169

%NEEDED

TOAVOID

CROSSINGARRAYBOUNDS.

170

%17

1GUARDmf=

(GUARD+1)*OSR;

172

r_extended=

[zeros(1,GUARDmf)r

zeros(1,m)zeros(1,GUARDmf)];

173

174

%RECALL

THATTHE

’OPERATORIN

MATLABDOES

CONJUGATION

175

%17

617

7forn=1:148,

178

aa=GUARDmf+burst_start+(n-1)*OSR;

179

bb=GUARDmf+burst_start+(n-1)*OSR+m;

180

Y(n)

=r_extended(aa:bb)*h_est’;

181

end

Sour

ceco

deC

.16:

viterbi_detector.m

1function[

rx_burst]=viterbi_detector(SYMBOLS,NEXT,PREVIOUS,START,STOPS,Y,Rhh)

2%

3%

VITERBI_DETECTOR:

4%

Thismatlabcodedoestheactualdetectionofthe

5%

receivedsequence.Asindicatedbythenamethealgorithm

6%

is

theviterbialgorithm,whichisaMLSE.Atthistime

7%

theapprochistouseUngerboecksmodifiedalgorithm,and

8%

to

returnhardoutputonly.

9%

10%

SYNTAX:

[rx_burst]

11%

=12

%viterbi_detector(SYMBOLS,NEXT,PREVIOUS,START,STOPS,Y,Rhh)

13%

14%

INPUT:

SYMBOLS:

Thetableofsymbolscorrespondingthethestate-

15%

numbers.Formatasmadebymake_symbols.m

16%

NEXT:

Atransitiontablecontainingthenextlegal

17%

states,asitisgeneratedbythecodemake_next.m

18%

PREVIOUS:Thetransitiontabledescribingthelegalprevious

19%

statesasgeneratedbymake_previous.m

20%

START:

Thestartstateofthealgorithm.

21%

STOPS:

Thelegalstopstates.

22%

Y:

Complexbasebandrepresentationofthematched

23%

filteredanddownconvertedreceivedsignal,asit

24%

isreturnedbymf.m

25%

Rhh:

Theautocorrelationasestimatedbymf.m

26%

27%

OUTPUT:

rx_burst:Themostlikelysequenceofsymbols.

28%

29%

SUB_FUNC:make_increment

30%

31%

WARNINGS:None.

32%

33%

TEST(S):

Testedwithnonoise,perfectsyncronization,andchannel

34%

estimation/filtering.(Refertoviterbi_ill.m)

35%

36%

AUTOR:

JanH.


37%

EMAIL:


38%

39%

$Id:viterbi_detector.m,v1.71997/11/1812:41:26aneksExp$

40 41%

KNOWLEDGEOF

LhANDMISNEEDEDFORTHEALGORITHMTOOPERATE

42%

43[

M,

Lh]

=size(SYMBOLS);

44 45%

THE

NUMBEROFSTEPSINTHEVITERBI

46%

47STEPS=length(Y);

48 49%

INITIALIZETABLES(THISYIELDSASLIGHTSPEEDUP).

50%

51METRIC=

zeros(M,STEPS);

52SURVIVOR=

zeros(M,STEPS);

53 54%

DETERMINEPRECALCULATABLEPARTOFMETRIC

55%

56INCREMENT=make_increment(SYMBOLS,NEXT,Rhh);

57 58%

THE

FIRSTTHINGTO

DOISTOROLLINTOTHEALGORITHMBYSPREADINGOUT

59%

FROM

THE

STARTSTATETOALLTHELEGALSTATES.

60%


R-97-1004 December 1997

61PS=START;

62 63%NOTE

THATTHE

STARTSTATEIS

REFERREDTO

ASSTATE

TOTIME

064

%AND

THATIT

HAS

NOMETRIC.

65%

66S=NEXT(START,1);

67METRIC(S,1)=real(conj(SYMBOLS(S,1))*Y(1))-INCREMENT(PS,S);

68SURVIVOR(S,1)=START;

69 70S=NEXT(START,2);

71METRIC(S,1)=real(conj(SYMBOLS(S,1))*Y(1))-INCREMENT(PS,S);

72SURVIVOR(S,1)=START;

73 74PREVIOUS_STATES=NEXT(START,:);

75 76%MARK

THENEXT

STATESAS

REAL.N.B:COMPLEXINDICATESTHE

POLARITY

77%OF

THE

NEXTSTATE,E.G.

STATE2

ISREAL.

78%

79COMPLEX=0;

80 81forN

=2:Lh,

82if

COMPLEX,

83COMPLEX=0;

84else

85COMPLEX=1;

86end

87STATE_CNTR=0;

88for

PS

=PREVIOUS_STATES,

89STATE_CNTR=STATE_CNTR+1;

90S=NEXT(PS,1);

91METRIC(S,N)=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N))-INCREMENT(PS,S);

92SURVIVOR(S,N)=PS;

93USED(STATE_CNTR)=S;

94STATE_CNTR=STATE_CNTR+1;

95S=NEXT(PS,2);

96METRIC(S,N)=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N))-INCREMENT(PS,S);

97SURVIVOR(S,N)=PS;

98USED(STATE_CNTR)=S;

99end

100

PREVIOUS_STATES=USED;

101

end

102

%AT

ANY

RATEWE

WILLHAVE

PROCESSEDLh

STATESAT

THISTIME

103

%10

4PROCESSED=Lh;

105

106

%WE

WANTAN

EQUALNUMBER

OFSTATESTOBE

REMAINING.THENEXT

LINESENSURE

107

%THIS.

108

%10

911

0if~COMPLEX,

111

COMPLEX=1;

112

PROCESSED=PROCESSED+1;

113

N=PROCESSED;

114

for

S=2:2:M,

115

PS=PREVIOUS(S,1);

116

M1=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N)-INCREMENT(PS,S));

117

PS=PREVIOUS(S,2);

118


119

if

M1>

M2,

120

METRIC(S,N)=M1;

121

SURVIVOR(S,N)=PREVIOUS(S,1);

122

else

123

METRIC(S,N)=M2;

124


125

end

126

end

127

end

128

129

%NOWTHAT

WE

HAVEMADETHERUN-INTHERESTOFTHEMETRICSARE

130

%CALCULATEDINTHE

STRAIGHTFORWARDMANNER.OBSERVETHATONLY

131

%THERELEVANTSTATESARECALCULATED,THATISREALFOLLOWSCOMPLEX

132

%ANDVICE

VERSA.

133

%13

4N=PROCESSED+1;

135

whileN

<=

STEPS,

136

forS

=1:2:M-1,

137

PS=PREVIOUS(S,1);

138


139

PS=PREVIOUS(S,2);

140


141

ifM1

>M2,

142

METRIC(S,N)=M1;

143


144

else

145

METRIC(S,N)=M2;

146


147

end

148

end

149

N=N+1;

150

forS

=2:2:M,

151

PS=PREVIOUS(S,1);

152


153

PS=PREVIOUS(S,2);

154


155

ifM1

>M2,

156

METRIC(S,N)=M1;

157


158

else

159

METRIC(S,N)=M2;

160


161

end

162

end

163

N=N+1;

164

end

165

166

167

%HAVINGCALCULATEDTHEMETRICS,THEMOSTPROBABLESTATESEQUENCEIS

168

%INITIALIZEDBYCHOOSINGTHEHIGHESTMETRICAMONGTHELEGALSTOP

169

%STATES.

170

%17

1BEST_LEGAL=0;

172

for

FINAL=

STOPS,

173

if

METRIC(FINAL,STEPS)>BEST_LEGAL,

174

S=FINAL;

175

BEST_LEGAL=METRIC(FINAL,STEPS);

176

end

177

end

178

179

%UNCOMMENTFORTEST

OFMETRIC

180

%18

1%

METRIC

182

%BEST_LEGAL

183

%S

184

%pause

185

186

%HAVINGFOUNDTHE

FINALSTATE,THEMSKSYMBOLSEQUENCEISESTABLISHED

187

%18

8IEST(STEPS)=SYMBOLS(S,1);


R-97-1004 December 1997

189

N=STEPS-1;

190

whileN

>0,

191

S=SURVIVOR(S,N+1);

192

IEST(N)=SYMBOLS(S,1);

193

N=N-1;

194

end

195

196

%THE

ESTIMATEIS

NOWFOUND

FROMTHEFORMULA:

197

%IEST(n)=j*rx_burst(n)*rx_burst(n-1)*IEST(n-1)

198

%THE

FORMULAIS

REWRITTENAS:

199

%rx_burst(n)=IEST(n)/(j*rx_burst(n-1)*IEST(n-1))

200

%FOR

INITIALIZATIONTHE

FOLLOWINGISUSED:

201

%IEST(0)=1og

rx_burst(0)=1

202

%20

3rx_burst(1)=IEST(1)/(j*1*1);

204

forn

=2:STEPS,

205

rx_burst(n)=IEST(n)/(j*rx_burst(n-1)*IEST(n-1));

206

end

207

208

%rx_burstIS

POLAR(-1

AND

1),THISTRANSFORMSIT

TO

209

%BINARY

FORM(0

AND1).

210

%21

1rx_burst=(rx_burst+1)./2;

Sour

ceco

deC

.17:

viterbi_init.m

1function[

SYMBOLS,

PREVIOUS,NEXT,START,STOPS]=viterbi_init(Lh)

2%

VITERBI_INIT:

3%

Thisfunctionreturnsthetableswhichareusedbythe

4%

viterbidemodulatorwhichisimplementedintheGSMsim

5%

package.

6%

7%

SYNTAX:

[SYMBOLS,PREVIOUS,NEXT,START,STOPS]

8%

=9

%viterbi_init(Lh)

10%

11%

INPUT:

Lh:

Thelengthofthechannelimpulseresponse

12%

minusone.

13%

14%

OUTPUT:

SYMBOLS:

StatenumbertoMSK-symbolsmappingtable.

15%

PREVIOUS:Thisstatetolegalpreviousstatemappingtable.

16%

NEXT:

Thisstatetolegalnextstatemappingtable.

17%

START:

Thestartstateoftheviterbialgorithm.

18%

STOPS:

Thesetoflegalstopstatesfortheviterbi

19%

algorithm.

20%

21%

GLOBAL:

None

22%

23%

SUB_FUNC:make_symbols,make_previous,make_next,make_start,make_stops

24%

25%

WARNINGS:None

26%

27%

TEST:

Verifiedthatthefunctionactuallyrunsthesubfunctions.

28%

29%

AUTHOR:

JanH.


30%

EMAIL:


31%

32%

$Id:viterbi_init.m,v1.41998/02/1210:52:15aneksExp$

33 34SYMBOLS=

make_symbols(Lh);

35PREVIOUS=

make_previous(SYMBOLS);

36NEXT

=make_next(SYMBOLS);

37START

=make_start(Lh,SYMBOLS);

38STOPS

=make_stops(Lh,SYMBOLS);


R-97-1004 December 1997

Sour

ceco

deC

.18:

DeMUX.m

1function[rx_data]

=DeMUX(rx_burst)

2 3%DeMUX:

This

piceof

codedoes

thedemultiplexingofthe

received

4%

GSM

burst.

5%

6%SYNTAX:

[rx_data]

=DeMUX(rx_burst)

7%

8%INPUT:

ESTIMAE:Anentire148

bitGSM

burst.The

formatis

expected

9%

tobe:

10%

11%

[TAIL|

DATA

|CTRL

|TRAINING|CTRL

|DATA|

TAIL]

12%

[3

|57

|1

|26

|1

|57

|3

]13

%14

%OUTPUT:

15%

rx_data:Thecontentsof

thedatafieldsin

thereceivedburst.

16%

17%WARNINGS:None.

18%

19%AUTHOR:

Jan

H.Mikkelsen/

ArneNorre

Ekstrøm

20%EMAIL:


21%

22%$Id:

DeMUX.m,v1.31997/11/1812:46:18aneksExp

$23 24

rx_data=[rx_burst(4:60),

rx_burst(89:145)];

Sour

ceco

deC

.19:

deinterleave.m

1function[

rx_enc]

=deinterleave(rx_data_matrix)

2%

3%

deinterleave:

4%

Thisfunctiondoesdeinterleavingofde-multiplexedGSM

5%

informationbursts,eg.114sequentialbitsasextracted

6%

froma

GSMburst.Theinputis8x114bit,andtheoutput

7%

isa

single456bitinformationblock,asdeinterleavedfromthe

8%

input.

9%

10%

SYNTAX:

[rx_enc]=deinterleave(rx_data_matrix)

11%

12%

INPUT:

rx_data_matrix:

13%

The’latest’8instancesofrx_data,whichare114bit

14%

long,andmustbestoredintherowsofrx_data_matrix.If

15%

theburstsinthematrixarenumberedastheysre

16%

received,theburstinrowonehasnumberone,etc.

17%

18%

OUTPUT:

rx_enc:

19%

A456bitdatablock,asdemultiplexedfromthe8input

20%

bursts.

21%

22%

WARNINGS:Observethatnotall8x114bitsarecontainedinthe

output.

23%

24%

TEST(S):

interleave->deinterleave=0Errors.

25%

26%

AUTHOR:

JanH.


27%

EMAIL:


28%

29%

$Id:deinterleave.m,v1.41997/11/2011:12:27aneksExp$

30rx_enc(1)=rx_data_matrix(1,1);
































R-97-1004 December 1997








































100

rx_enc(71)=rx_data_matrix(7,22);

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R-97-1004 December 1997

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Sour

ceco

deC

.20:

channel_dec.m

1function[rx_block,FLAG_SS,PARITY_CHK]=channel_dec(rx_enc)

2%

3%

channel_dec:

4%

5%

SYNTAX:

[rx_block,FLAG_SS,PARITY_CHK]=channel_dec(rx_enc)

6%

7%

INPUT:

rx_enc

A456bitslongvectorcontaningtheencoded

8%

datasequenceasestimatedbytheSOVA.The

9%

formatofthesequencymustbeaccordingto

10%

theGSM05.03encodingscheme

11%

12%

OUTPUT:

rx_block

A260bitslongvectorcontaningthefinal

13%

estimatedinformationdatasequence.

14%

15%

FLAG_SSIndicationofcorrectstopstate.Flagisset

16%

to’1’ifanerrorhasoccuredhere.

17%

18%

PARITY_CHKThe3paritycheckbitinsertedinthe

19%

transmitter.

20%

21%

SUB_FUNC:

None

22%

23%

WARNINGS:

None

24%

25%

TEST(S):

Operationtestedinconjunctionwiththechannel_enc.m

26%

module.Operationprovedtobecorrect.

27%

28%

AUTHOR:

JanH.


29%

EMAIL:


30%

31%

$Id:channel_dec.m,v1.81998/02/1210:53:13aneksExp$

32 33L

=length(rx_enc);

34 35%

TESTINPUT

DATA

36%

37if

L~=456

38disp(’’)

39disp(’Inputdatasequencesizeviolation.Programterminated.’)

40disp(’’)

41break;

42end

43 44%

SEPARATEDATAIN

CLASSI,c1,ANDCLASSEII,c2,BITS

45%

CLASSI

BITSARE

DECODEDWHILECLASSIIARELEFT

46%

UNCHANGED

47%

48 49c1

=rx_enc(1:378);

50c2

=rx_enc(379:L);

51 52%

INITIALIZEVARIOUSMATRIXES

53%

54%

REMEMBERTHEVA

DECODEROPERATESONDI-BITS

55%

HENCEONLY

378/2=

189STATETRANSITIONSOCCURE

56%

57 58START_STATE=

1;

59END_STATE=

1;

60


R-97-1004 December 1997

61STATE=

zeros(16,189);

62METRIC=

zeros(16,2);

63 64NEXT=

zeros(16,2);

65zeroin=

1;

66onein=

9;

67forn

=1:2:15,

68NEXT(n,:)=

[zeroinonein];

69NEXT(n+1,:)=

NEXT(n,:);

70zeroin

=zeroin

+1;

71onein

=onein+

1;

72end

73 74PREVIOUS=zeros(16,2);

75offset=

0;

76forn

=1:8,

77PREVIOUS(n,:)=

[n+offsetn+offset+1];

78offset

=offset

+1;

79end

80PREVIOUS=[

PREVIOUS(1:8,:);

PREVIOUS(1:8,:)];

81 82%SETUP

OFDIBIT

DECODERTABLE.THE

BINARYDIBITSARE

83%HERE

REPRESENTEDUSINGDECIMALNUMBER,I.E.THE

DIBIT

84%00

IS

REPRESENTEDAS

0ANDTHE

DIBIT11

AS

385

%86

%THE

TABELIS

SETUPSO

THATTHE

CALLDIBIT(X,Y)RETURNS

87%THE

DIBITSYMBOL

RESULTINGFROM

ASTATETRANSITIONFROM

88%STATE

XTOSTATE

Y89

%90 91

DIBIT=

[0

NaN

NaNNaN

NaNNaN

NaNNaN

3NaNNaN

NaNNaN

NaNNaN

NaN;

923

NaN

NaNNaN

NaNNaN

NaNNaN

0NaNNaN

NaNNaN

NaNNaN

NaN;

93NaN

3NaNNaN

NaNNaN

NaNNaN

NaN

0NaN

NaNNaN

NaNNaN

NaN;

94NaN

0NaNNaN

NaNNaN

NaNNaN

NaN

3NaN

NaNNaN

NaNNaN

NaN;

95NaNNaN

0NaN

NaNNaN

NaNNaN

NaN

NaN

3NaNNaN

NaNNaN

NaN;

96NaNNaN

3NaN

NaNNaN

NaNNaN

NaN

NaN

0NaNNaN

NaNNaN

NaN;

97NaNNaN

NaN

3NaNNaN

NaNNaN

NaN

NaNNaN

0NaN

NaNNaN

NaN;

98NaNNaN

NaN

0NaNNaN

NaNNaN

NaN

NaNNaN

3NaN

NaNNaN

NaN;

99NaNNaN

NaNNaN

1NaN

NaNNaN

NaN

NaNNaN

NaN

2NaNNaN

NaN;

100

NaNNaN

NaNNaN

2NaN

NaNNaN

NaN

NaNNaN

NaN

1NaNNaN

NaN;

101

NaNNaN

NaNNaN

NaN

2NaNNaN

NaN

NaNNaN

NaNNaN

1NaN

NaN;

102

NaNNaN

NaNNaN

NaN

1NaNNaN

NaN

NaNNaN

NaNNaN

2NaN

NaN;

103

NaNNaN

NaNNaN

NaNNaN

1NaN

NaN

NaNNaN

NaNNaN

NaN

2NaN;

104

NaNNaN

NaNNaN

NaNNaN

2NaN

NaN

NaNNaN

NaNNaN

NaN

1NaN;

105

NaNNaN

NaNNaN

NaNNaN

NaN

2NaN

NaNNaN

NaNNaN

NaNNaN

1;

106

NaNNaN

NaNNaN

NaNNaN

NaN

1NaN

NaNNaN

NaNNaN

NaNNaN

2];

107

108

%SETUP

OFBIT

DECODERTABLE.

109

%THE

TABELIS

SETUPSO

THATTHE

CALLBIT(X,Y)RETURNS

110

%THE

DECODEDBIT

RESULTINGFROMA

STATETRANSITIONFROM

111

%STATE

XTOSTATE

Y11

2%

113

114

BIT=

[0NaN

NaN

NaNNaN

NaNNaN

NaN

1NaNNaN

NaNNaN

NaN

NaNNaN;

115

0NaN

NaN

NaNNaN

NaNNaN

NaN

1NaNNaN

NaNNaN

NaN

NaNNaN;

116

NaN

0NaN

NaNNaN

NaNNaN

NaNNaN

1NaN

NaNNaN

NaN

NaNNaN;

117

NaN

0NaN

NaNNaN

NaNNaN

NaNNaN

1NaN

NaNNaN

NaN

NaNNaN;

118

NaNNaN

0NaNNaN

NaNNaN

NaNNaN

NaN

1NaNNaN

NaN

NaNNaN;

119

NaNNaN

0NaNNaN

NaNNaN

NaNNaN

NaN

1NaNNaN

NaN

NaNNaN;

120

NaNNaN

NaN

0NaN

NaNNaN

NaNNaN

NaNNaN

1NaN

NaN

NaNNaN;

121

NaNNaN

NaN

0NaN

NaNNaN

NaNNaN

NaNNaN

1NaN

NaN

NaNNaN;

122

NaNNaN

NaN

NaN

0NaNNaN

NaNNaN

NaNNaN

NaN

1NaN

NaNNaN;

123

NaNNaN

NaN

NaN

0NaNNaN

NaNNaN

NaNNaN

NaN

1NaN

NaNNaN;

124

NaNNaN

NaN

NaNNaN

0NaN

NaNNaN

NaNNaN

NaNNaN

1NaNNaN;

125

NaN

NaN

NaNNaNNaN

0NaNNaNNaNNaNNaNNaNNaN

1NaNNaN;

126

NaN

NaN

NaNNaNNaNNaN


1NaN;

127

NaN

NaN

NaNNaNNaNNaN


1NaN;

128

NaN

NaN

NaNNaNNaNNaNNaN


1;

129

NaN

NaN

NaNNaNNaNNaNNaN


1];

130

131

%STARTUPMETRIKCALCULATIONS.

132

%13

3%

THISIS

TO

REDUCETHENUMBEROFCALCULATIONSREQUIRED

134

%AND

ITIT

RUNONLY

FORTHEFIRST4DIBITPAIRS

135

%13

613

7VISITED_STATES=START_STATE;

138

for

n=0:3,

139

140

rx_DIBITXy=

c1(2*n+1);

141

rx_DIBITxY=

c1(2*n+1+1);

142

143

for

k=

1:length(VISITED_STATES),

144

145

PRESENT_STATE=

VISITED_STATES(k);

146

147

next_state_0=

NEXT(PRESENT_STATE,1);

148

next_state_1=

NEXT(PRESENT_STATE,2);

149

150

symbol_0=

DIBIT(PRESENT_STATE,next_state_0);

151

symbol_1=

DIBIT(PRESENT_STATE,next_state_1);

152

153

ifsymbol_0==

015

4LAMBDA=

xor(rx_DIBITXy,0)+xor(rx_DIBITxY,0);

155

end

156

ifsymbol_0==

115

7LAMBDA=


158

end

159

ifsymbol_0==

216

0LAMBDA=


161

end

162

ifsymbol_0==

316

3LAMBDA=


164

end

165

166

METRIC(next_state_0,2)=METRIC(PRESENT_STATE,1)+LAMBDA;

167

168

ifsymbol_1==

016

9LAMBDA=


170

end

171

ifsymbol_1==

117

2LAMBDA=


173

end

174

ifsymbol_1==

217

5LAMBDA=


176

end

177

ifsymbol_1==

317

8LAMBDA=


179

end

180

181

METRIC(next_state_1,2)=METRIC(PRESENT_STATE,1)+LAMBDA;

182

STATE([next_state_0,next_state_1],n+1)=PRESENT_STATE;

183

184

ifk

==

118

5PROCESSED=

[next_state_0next_state_1];

186

else

187

PROCESSED=

[PROCESSEDnext_state_0next_state_1];

188

end


R-97-1004 December 1997

189

end

190

191

VISITED_STATES=PROCESSED;

192

METRIC(:,1)=

METRIC(:,2);

193

METRIC(:,2)=

0;

194

end

195

196

197

%STARTINGTHE

SECTIONWHEREALL

STATESARE

RUNTHROUGH

198

%IN

THE

METRICCALCULATIONS.THIS

GOESON

FORTHE

199

%REMAININGDIBITSRECEIVED

200

%20

120

2forn

=4:188,

203

204

rx_DIBITXy=

c1(2*n+

1);

205

rx_DIBITxY=

c1(2*n+

1+1);

206

207

for

k=1:16,

208

209

prev_state_1=PREVIOUS(k,1);

210

prev_state_2=PREVIOUS(k,2);

211

212

symbol_1=

DIBIT(prev_state_1,k);

213

symbol_2=

DIBIT(prev_state_2,k);

214

215

if

symbol_1==0

216

LAMBDA_1=


217

end

218

if

symbol_1==1

219

LAMBDA_1=


220

end

221

if

symbol_1==2

222

LAMBDA_1=


223

end

224

if

symbol_1==3

225

LAMBDA_1=


226

end

227

228

if

symbol_2==0

229

LAMBDA_2=


230

end

231

if

symbol_2==1

232

LAMBDA_2=


233

end

234

if

symbol_2==2

235

LAMBDA_2=


236

end

237

if

symbol_2==3

238

LAMBDA_2=


239

end

240

241

METRIC_1=

METRIC(prev_state_1,1)+

LAMBDA_1;

242

METRIC_2=

METRIC(prev_state_2,1)+

LAMBDA_2;

243

244

if

METRIC_1<

METRIC_2

245

METRIC(k,2)=METRIC_1;

246

STATE(k,n+1)=

prev_state_1;

247

else

248

METRIC(k,2)=METRIC_2;

249

STATE(k,n+1)=

prev_state_2;

250

end

251

end

252

253

METRIC(:,1)=METRIC(:,2);

254

METRIC(:,2)=0;

255

256

end

257

258

%STARTINGBACKTRACKINGTODETERMINETHEMOST

259

%PROBABLESTATETRANSITIONSEQUENCE

260

%26

126

2STATE_SEQ=

zeros(1,189);

263

264

[STOP_METRIC,STOP_STATE]=min(METRIC(:,1));

265

266

if

STOP_STATE==END_STATE

267

FLAG_SS=

0;

268

else

269

FLAG_SS=

1;

270

end

271

272

STATE_SEQ(189)=

STOP_STATE;

273

274

for

n=

188:-1:1,

275

STATE_SEQ(n)=

STATE(STATE_SEQ(n+1),n+1);

276

end

277

278

STATE_SEQ=

[START_STATESTATE_SEQ];

279

280

%RESOLVINGTHECORRESPONDINGBITSEQUENCS

281

%28

228

3for

n=

1:length(STATE_SEQ)-1,

284

DECONV_DATA(n)=

BIT(STATE_SEQ(n),STATE_SEQ(n+1));

285

end

286

287

%SEPARATINGTHEDATAACCORDINGTOTHEENCODING

288

%RESULTINGFROMTHE

TRANSMITTER.

289

%29

029

1DATA_Ia=

DECONV_DATA(1:50);

292

PARITY_CHK=

DECONV_DATA(51:53);

293

DATA_Ib=

DECONV_DATA(54:185);

294

TAIL_BITS=

DECONV_DATA(186:189);

295

296

rx_block=

[DATA_IaDATA_Ibc2];


R-97-1004 December 1997

Sour

ceco

deC

.21:

channel_simulator.m

1function[r

]=

channel_simulator(I,Q,OSR)

2%CHANNEL_SIMULATOR:

3%

This

functionisintendedas

an

skeletonforchannel

4%

simulatorimplementations,and

isnot

to

beconsidderd

5%

as

an

actualchannelsimulator.Itdoes

howeverprovide

6%

amean

formakingthe

GSMsimpackageproducedetection

7%

errors.Substitutethis

functionwithuserdefined

8%

functions.

9%

10%SYNTAX:

channel_simulator(I,Q,OSR)

11%

12%INPUT:

I:

The

inphasesignalas

producedby

themodulator.

13%

Q:

The

quadraturesignalas

itis

producedby

the

14%

modulator.

15%

OSR:

The

oversamplingratio,

definedasf_s/r_b.This

16%

parameteris

notused

in

theincudedchannel_simulator

17%

function,but

ispassed

tothe

functionforfuture

18%

use.

19%

20%OUTPUT:

r:

The

receivedsignal,as

predictedbythe

channel

21%

simulator.

22%

23%WARNINGS:Do

not

usethis

functionfor

scientificpurposes.

24%

25%AUTHOR:

Jan

H.

Mikkelsen/

Arne

NorreEkstrøm

26%EMAIL:


27%

28%$Id:

channel_simulator.m,v1.6

1998/02/1210:56:13aneksExp

$29 30

%THE

CHANNELSIMULATORINCLUDEDIN

THEGSMsimPACKAGEONLY

ADD

31%NOISE,

ANDSHOULD_NOT_

BEUSED

FORSCIENTIFICPURPOSES.

32%

33%SUBSTITUTETHE

NEXTLINES

WITHA

LINECONTAININGA

CHANNELSIMULATION.

34%HERE

WE

SIMPLYADDNOISE

OFVARIANCEVar

TOTHE

MODULATEDSIGNAL.NOTE

35%THAT

THISNOISE

ISONLY

BANDLIMITEDBY

THE

SAMPLERATE.

36%

37Var=0.02;

38FACTOR=sqrt(Var);

39samples=length(I);

40random=randn(1,2*samples);

41r=I

+j.*Q+

random(1:samples).*FACTOR;

42r=r

+random(samples+1:2*samples).*FACTOR.*j;

Sour

ceco

deC

.22:

GSMsim_demo.m

1function[

]=


2%

GSMSIM_DEMO:

3%

ThisfunctiondemonstratesthefunctionoftheGSMsim

4%

package.Usethisfileasastartingpointforbuilding

5%

yourown

simulations.

6%

7%

SYNTAX:


8%

9%

INPUT:

LOOPS:

Thenumberofloopsthatthedemoistorun,

10%

eachloopcontain10burst.

11%

Lh:


12%

minusone.

13%

14%

OUTPUT:

None,but

onscreen.

15%

16%

WARNINGS:Do

notexpectthisexampletobemorethanexactlythat,

17%

an

example.ThisexampleisNOTscientificallycorrect.

18%

19%

AUTHOR:

JanH.


20%

EMAIL:


21%

22%

$Id:GSMsim_demo.m,v1.151998/10/0110:19:04hmiExp$

23 24tTotal=clock;

25 26%

THEREHAS

NOTBEEN

ANYERRORS,YET...

27%

28B_ERRS=0;

29 30%

gsm_setMUST

BERUNPRIORTOANYSIMULATIONS,SINCEITDOESSETUP

31%

OF

VALUESNEEDEDFOROPERATIONOFTHEPACKAGE.

32%

33gsm_set;

34 35%

PREPARETHE

TABLESNEEDEDBYTHEVITERBIALGORITHM.

36%

37[

SYMBOLS,

PREVIOUS,NEXT,START,STOPS]=viterbi_init(Lh);

38 39%

THISIS

THE

SIMULATIONLOOP,OVERTHEBURSTS

40%

41A_Loop=0;

42for

Loop=1:LOOPS

43 44%

GETTHE

TIME

45%

46t0=clock;

47 48for

n=1:10;

49%

GETDATA

FORA

BURST

50%

51tx_data=

data_gen(INIT_L);

52 53%

THISIS

ALLTHATISNEEDEDFORMODULATINGAGSMBUST,INTHEFORMAT

54%

USEDIN

GSMsim.THECALLINCLUDESGENERATIONANDMODULATTIONOFDATA.

55%

56[

burst,

I,

Q]

=gsm_mod(Tb,OSR,BT,tx_data,TRAINING);

57 58%

ATTHIS

POINTWERUNTHECHANNELSIMULATION.NOTE,THATTHECHANNEL

59%

INCLUDESTRANSMITTERFORNT-END,ANDRECEIVERFRONT-END.THECHANNEL

60%

SELECTIONIS

BYNATUREINCLUDEDINTHERECEIVERFRONT-END.


R-97-1004 December 1997

61%

THECHANNEL

SIMULATORINCLUDEDIN

THE

GSMsimPACKAGEONLYADD

62%

NOISE,AND

SHOULD_NOT_BE

USEDFOR

SCIENTIFICPURPOSES.

63%

64%r=channel_simulator(I,Q,OSR);

65r

=I+

j*Q;

66 67%

RUNTHE

MATCHEDFILTER,IT

ISRESPONSIBLEFOR

FILTERINGSYNCRONIZATION

68%

ANDRETRIEVALOF

THE

CHANNELCHARACTERISTICS.

69%

70[Y,

Rhh]=

mafi(r,Lh,T_SEQ,OSR);

71 72%

HAVINGPREPAREDTHE

PRECALCULATABLEPARTOF

THEVITERBI

73%

ALGORITHM,ITIS

CALLEDPASSINGTHE

OBTAINEDINFORMATIONALONG

WITH

74%

THERECEIVEDSIGNAL,

ANDTHE

ESTIMATEDAUTOCORRELATIONFUNCTION.

75%

76rx_burst=

viterbi_detector(SYMBOLS,NEXT,PREVIOUS,START,STOPS,Y,Rhh);

77 78%

RUNTHE

DeMUX

79%

80rx_data=DeMUX(rx_burst);

81 82%

COUNTTHE

ERRORS

83%

84B_ERRS=B_ERRS+sum(xor(tx_data,rx_data));

85 86end

87 88%

FIND

THELOOPTIME

89%

90elapsed=etime(clock,t0);

91 92%

FIND

AVERAGELOOPTIME

93%

94A_Loop=(A_Loop+elapsed)/2;

95 96%

FIND

REMAININGTIME

97%

98Remain

=(LOOPS-Loop)*A_Loop;

99 100

%UPDATETHE

DISPLAY

101

%10

2fprintf(1,’\r’);

103

fprintf(1,’Loop:%d,

AverageLoopTime:

%2.1fseconds’,Loop,A_Loop);

104

fprintf(1,’,Remaining:%2.1fseconds’,Remain);

105

106

end

107

108

Ttime=etime(clock,tTotal);

109

BURSTS=LOOPS*10;

110

fprintf(1,’\n%dBurstsprocessedin%6.1f

Seconds.\n’,BURSTS,Ttime);

111

fprintf(1,’Used%2.1fsecondsper

burst\n’,Ttime/BURSTS);

112

fprintf(1,’Therewere%d

Bit-Errors\n’,B_ERRS);

113

BER=(B_ERRS*100)/(BURSTS*148);

114

fprintf(1,’Thisequals%2.1fPercentofthe

checkedbits.\n’,BER);

Sour

ceco

deC

.23:

GSMsim_demo_2.m

1function[]

=GSMsim_demo_2(NumberOfBlocks,Lh,LogName)

2%

GSMSIM_DEMO:

3%

ThisdemonstratesthefunctionoftheGSMsim

4%

package.Usethisfileasastartingpointforbuilding

5%

yourown

simulations.

6%

7%

SYNTAX:

GSMsim_demo_2(NumberOfBlocks,Lh,logname)

8%

9%

INPUT:

NumberOfBlocks:

10%

ThenumberofGSMcodeblockstoprocess,ablock

11%

correspondstofourGSMbursts.

12%

13%

Lh:


14%

minusone.

15%

LogName:

16%

Thebasenameofthefiletowhichthesimulationlogis

17%

tobewritten.Thesimulationlogishandyfor

18%

evaluatingtheconvergenceogasimulation.

19%

20%

OUTPUT:

Toa

file

called:logname.NumberOfBlocks.Lh

21%

Simulationstatisticsareconstantlyechoedtothescreenfor

22%

easyreference.

23%

24%

WARNINGS:Donot

expectthisexampletobemorethanexactlythat,

25%

anexample.ThisexampleisNOTscientificallycorrect.

26%

27%

AUTHOR:


28%

EMAIL:


29%

30%

$Id:GSMsim_demo_2.m,v1.61998/10/0110:18:47hmiExp$

31 32%

Thisis

an

aidfor

thefinalscreenreport

33%

34tTotal=clock;

35 36%

Createthe

nameof

thelogfileforfuturereference.

37%

38LogFile=[LogName’_’

num2str(NumberOfBlocks,’%9d’)’_’];

39LogFile=[LogFilenum2str(Lh,’%3d’)’.sim’];

40 41%

Printheaderto

thelogfile,abortiffileallreadyexist.

42%

43fid=fopen(LogFile,’r’);

44if

fid==-1

45LogFID=fopen(LogFile,’w’);

46fprintf(LogFID,’%%GSMsim_demo_2-simulationlog.\n’);

47fprintf(LogFID,’%%\n’);

48fprintf(LogFID,’%%Settings:

NumberOfBlocks=%d\n’,NumberOfBlocks);

49fprintf(LogFID,’%%

Lh=%d\n’,Lh);


51fprintf(LogFID,’%%BlockNumber’);

52fprintf(LogFID,’%%B_ERRS_IaB_ERRS_IbB_ERRS_IIB_ERRS_II_CHEAT\n’);


54fclose(LogFID);

55else

56error(’Thelogfileallreadyexists,abortingsimulation...’);

57end

58 59%

Therehas,

notyet,beenobservedanyerrors.

60%


R-97-1004 December 1997

61B_ERRS_Ia=0;

62B_ERRS_Ib=0;

63B_ERRS_II=0;

64B_ERRS_II_CHEAT=0;

65 66%gsm_set

MUSTBE

RUNPRIOR

TOANY

SIMULATIONS,SINCE

ITDOES

SETUP

67%OF

VALUESNEEDED

FOROPERATIONOF

THEPACKAGE.

68%

69gsm_set;

70 71%PREPARE

THETABLESNEEDED

BYTHE

VITERBIALGORITHM.

72%

73[SYMBOLS

,PREVIOUS,

NEXT

,START

,STOPS

]=

viterbi_init(Lh);

74 75%We

need

toinitializethe

interleavingroutines,forthat

we

needan

so

76%called

firstburstfor

theinterleaver,thisburst

willnot

befully

77%received.Nor

willbit

errorsbe

checked,hencethereis

no

reasonfor

78%encodingit...

79%

80tx_enc1=round(rand(1,456));

81 82%Now

we

needa

tx_data_matrixto

startthe

deinterleaverthus

getdata

83%for

aburst.Bit

errorswillbe

checkedforin

this

block.

84%

85tx_block2=data_gen(260);

86 87%Do

channelcodingof

data

88%

89tx_enc2=channel_enc(tx_block2);

90 91%Interleavedata

92%

93tx_data_matrix=interleave(tx_enc1,tx_enc2);

94 95%Time

goesby,

andnew

becomeold,

thusswapbefore

entryof

loop.

96%

97tx_enc1=tx_enc2;

98tx_block1=tx_block2;

99 100

%Transmitand

receiveburst

101

%10

2rx_data_matrix1=tx_data_matrix;

103

104

%Sliding

averagetimereportaid.

105

%10

6A_Loop=0;

107

108

forN=2:NumberOfBlocks+1,

109

110

%Time

reportaid.

111

%11

2t0=clock;

113

114

%Get

datafor

anewdatablock,numbertwo

isthe

latest.

115

%11

6tx_block2=data_gen(260);

117

118

%Do

channelcodingof

data

119

%12

0tx_enc2=channel_enc(tx_block2);

121

122

%tx_data_mnatrixcontainsdata

forfour

burst,generatedfromtwo

blocks.

123

%12

4tx_data_matrix=interleave(tx_enc1,tx_enc2);

125

126

for

n=1:4,

127

128

%THISIS

ALLTHATISNEEDEDFORMODULATINGAGSMBUST,INTHE

FORMAT

129

%USEDIN

GSMsim.THECALLINCLUDESGENERATIONANDMODULATTIONOFDATA.

130

%13

1[

tx_burst,I

,Q]=

gsm_mod(Tb,OSR,BT,tx_data_matrix(n,:),TRAINING);

132

133

%ATTHIS

POINTWERUNTHECHANNELSIMULATION.NOTE,THATTHECHANNEL

134

%INCLUDESTRANSMITTERFORNT-END,ANDRECEIVERFRONT-END.THECHANNEL

135

%SELECTIONIS

BYNATUREINCLUDEDINTHERECEIVERFRONT-END.

136

%THECHANNELSIMULATORINCLUDEDINTHEGSMsimPACKAGEONLYADDS

137

%NOISE,ANDSHOULD_NOT_BEUSEDFORSCIENTIFICPURPOSES.

138

%13

9r=channel_simulator(I,Q,OSR);

140

141

%RUNTHE

MATCHEDFILTER,ITISRESPONSIBLEFORFILTERINGSYNCRONIZATION

142

%ANDRETRIEVALOFTHECHANNELCHARACTERISTICS.

143

%14

4[Y,Rhh]

=mafi(r,Lh,T_SEQ,OSR);

145

146

%HAVINGPREPAREDTHEPRECALCULATABLEPARTOFTHEVITERBI

147

%ALGORITHM,IT

ISCALLEDPASSINGTHEOBTAINEDINFORMATIONALONGWITH

148

%THERECEIVEDSIGNAL,ANDTHEESTIMATEDAUTOCORRELATIONFUNCTION.

149

%15

0rx_burst=

viterbi_detector(SYMBOLS,NEXT,PREVIOUS,START,STOPS,Y,Rhh);

151

152

%RUNTHE

DeMUX

153

%15

4rx_data_matrix2(n,:)=DeMUX(rx_burst);

155

156

end

157

158

%Thisis

forbypassingthechannel,uncommenttouse

159

%16

0%

rx_data_matrix2=tx_data_matrix;

161

162

%A

blockis

regeneratedusingeightbursts.

163

%16

4rx_enc=deinterleave([rx_data_matrix1;rx_data_matrix2]);

165

166

%A

goodcheat/trickistousealltheencodedbitsforestimatingatype

167

%IIBER.

Thisestimateis100%statisticallycorrect!!!

168

%16

9B_ERRS_II_CHEAT_NEW=sum(xor(tx_enc1,rx_enc));

170

171

%Dochannel

decoding

172

%17

3rx_block=channel_dec(rx_enc);

174

175

%Counterrors

176

%17

7B_ERRS_ALL=xor(rx_block,tx_block1);

178

B_ERRS_Ia_NEW=sum(B_ERRS_ALL(1:50));

179

B_ERRS_Ib_NEW=sum(B_ERRS_ALL(51:182));

180

B_ERRS_II_NEW=sum(B_ERRS_ALL(183:260));

181

182

%Updatethe

logfile.

183

%18

4LogFID=fopen(LogFile,’a’);

185

fprintf(LogFID,’%d%d’,N-1,B_ERRS_Ia_NEW);

186

fprintf(LogFID,’%d%d’,B_ERRS_Ib_NEW,B_ERRS_II_NEW);

187

fprintf(LogFID,’%d\n’,B_ERRS_II_CHEAT_NEW);

188

fclose(LogFID);


R-97-1004 December 1997

189

190

%Sum

theerrors

191

%19

2B_ERRS_Ia=B_ERRS_Ia+B_ERRS_Ia_NEW;

193

B_ERRS_Ib=B_ERRS_Ib+B_ERRS_Ib_NEW;

194

B_ERRS_II=B_ERRS_II+B_ERRS_II_NEW;

195

B_ERRS_II_CHEAT=B_ERRS_II_CHEAT+B_ERRS_II_CHEAT_NEW;

196

197

%Time

goesby,

andnew

becomeold,thus

swapfor

nextloop.

198

%19

9rx_data_matrix1=rx_data_matrix2;

200

tx_enc1=tx_enc2;

201

tx_block1=tx_block2;

202

203

%Find

theloop

time

204

%20

5elapsed=etime(clock,t0);

206

207

%Find

averagelooptime

208

%20

9A_Loop=(A_Loop+elapsed)/2;

210

211

%FIND

REMAININGTIME

212

%21

3Remain

=(NumberOfBlocks+1-N)*A_Loop;

214

215

%UPDATETHE

DISPLAY

216

%21

7fprintf(1,’\r’);

218

fprintf(1,’Block:%d,

AverageBlockTime:

%2.1fseconds’,N-1,A_Loop);

219

fprintf(1,’,Remaining:%2.1fseconds’,Remain);

220

221

end

222

223

Ttime=etime(clock,tTotal);

224

BURSTS=NumberOfBlocks*4;

225

226

%Find

BER.

227

%22

8TypeIaBits=NumberOfBlocks*50;

229

TypeIaBER=100*B_ERRS_Ia/TypeIaBits;

230

TypeIbBits=NumberOfBlocks*132;

231

TypeIbBER=100*B_ERRS_Ib/TypeIbBits;

232

TypeIIBits=NumberOfBlocks*78;

233

TypeIIBER=100*B_ERRS_II/TypeIIBits;

234

TypeIIBitsCHEAT=NumberOfBlocks*456;

235

TypeIIBER_CHEAT=100*B_ERRS_II_CHEAT/TypeIIBitsCHEAT;

236

237

fprintf(1,’\n%dBurstsprocessedin%6.1f

Seconds.\n’,BURSTS,Ttime);

238

fprintf(1,’Used%2.1fsecondsper

burst\n’,Ttime/BURSTS);

239

fprintf(1,’\n’);

240

fprintf(1,’TypeIaBER:

%3.2f\n’,TypeIaBER);

241

fprintf(1,’TypeIbBER:

%3.2f\n’,TypeIbBER);

242

fprintf(1,’TypeIIBER:

%3.2f\n’,TypeIIBER);

243

fprintf(1,’TypeIIBER-CHEAT:%3.2f\n’,TypeIIBER_CHEAT);

Sour

ceco

deC

.24:

gsm_set.m

1%

GSM_SET:

Thisscriptinitializesthevaluesneededbythe

2%

GSMsimpackage,andmustrunbeforthepackagetowork.

3%

4%

SYNTAX:

gsm_set

5%

6%

INPUT:

None

7%

OUTPUT:

Configurationvariablescreatedinmemory,theseare:

8%

Tb(=3.692e-6)

9%

BT(=0.3)

10%

OSR(=4)

11%

SEED(=931316785)

12%

INIT_L(=260)

13%

14%

SUB_FUN:

None

15%

16%

WARNINGS:Valuescanbeclearedbyotherfunctions,andthusthisscript

17%

shouldbererunineachsimulation.

18%

Therandomnumbergeneratorissettoastandardseedvalue

19%

withinthisscript.Thiscausestherandomnumbersgenerated

20%

matlabtofollowastandardpattern.

21%

22%

AUTHOR:


23%

EMAIL:


24%

25%

$Id:gsm_set.m,v1.111997/09/2211:38:19aneksExp$

26 27%

GSM05.05

PARAMETERS

28%

29Tb

=3.692e-6;

30BT

=0.3;

31OSR

=4;

32 33%

INITIALIZETHERANDOMNUMBERGENERATOR.

34%

BY

USINGTHESAME

SEEDVALUEINEVERYSIMULATION,WEGETTHESAME

35%

SIMULATIONDATA,ANDTHUSSIMULATIONRESULTSMAYBEREPRODUCED.

36%

37SEED

=931316785;

38rand(’seed’,SEED);

39 40%

THENUMBER

OFBITS

GENERATEDBYTHEDATAGENERATOR.(data_gen)

41%

42INIT_L=

114;

43 44%

SETUPTHE

TRAININGSEQUENCEUSEDFORBUILDINGBURSTS

45%

46TRAINING=

[0

01

00

10

11

100

00

10

00

10

01

011

1];

47 48%

CONSTRUCTTHEMSK

MAPPEDTRAININGSEQUENCEUSINGTRAINING.

49%

50T_SEQ=

T_SEQ_gen(TRAINING);


R-97-1004 December 1997

Sour

ceco

deC

.25:

T_SEQ_gen.m

1functionT_SEQ=

T_SEQ_gen(TRAINING)

2%

3%T_SEQ_GEN:

4%

This

functiongeneratestheMSK-mappedversionof

the

5%


inthe

GSMsimpackage.

6%

7%SYNTAX:

T_SEQ

=T_SEQ_gen(TRAINING)

8%

9%INPUT:

TRAINING:The

trainingsequencerepresentedas

bits.(0’s

and1’s)

10%

11%OUTPUT:

T_SEQ:A

MSK-mappedrepresentationof

the26

bitslong

12%

trainingsequence.

13%

14%SUB_FUNC:None

15%

16%WARNINGS:First

MSKsymbolis

set

to1.

Thismay

be

aproblem!!!

17%

18%TEST(S):

Result

isverifiedagainstthose

reportedby95gr870T

19%

20%AUTOR:

Arne

NorreEkstrøm/

JanH.

Mikkelsen

21%EMAIL:

[email protected]/

[email protected]

22%

23%$Id:

T_SEQ_gen.m,v1.5

1998/02/1210:59:07aneksExp$

24 25%TEST

TO

SEEWETHERTHE

LENGTHOF

IcIS

CORRECT.

26%IF

NOT,

THENABORT...

27%

28iflength(TRAINING)~=

26

29error(’TRAININGisnot

of

length26,terminating.’);

30end

31 32%MAKE

APOLARVERSIONOF

TRAINING

33TRAININGPol=(2.*TRAINING)-1;

34 35%DO

DIFFERENTIALENCODINGOFTHE

BITS

36%

37forn=2:length(TRAININGPol)

38a(n)=TRAININGPol(n)*TRAININGPol(n-1);

39end

40 41%DO

GMSK

MAPPINGOFPOLAR

a(n)

42%

43%THIS

IS

ACHOICE,AND

IT

MAYBE

WRONG!!!!!!

44T_SEQ(1)=1;

45forn=2:length(TRAININGPol)

46T_SEQ(n)=j*a(n)*T_SEQ(n-1);

47end

Sour

ceco

deC

.26:

GSMsim_config.m

1%

Thisscript

addsthepathsneededfortheGSMsimpackageto

2%

run

correctly.If

youchangethestructureofthedirectories

3%

withinthe

GSMsimpackagethenyouneedtoeditthisscript.

4%

Thisscript

shouldbeexecutedwhilestandinginthedirectory

5%

GSMtop/config.

6%

7%

AUTOR:


8%

EMAIL:


9%

10%

$Id:GSMsim_config.m,v1.51998/02/1211:00:32aneksExp$

11 12%

We

shouldhavethisscriptinGSMtop/config,nowgotoGSMtop

13cd

..

;14 15

%Findout

whereGSMtopislocatedonthedisk...

16GSMtop=pwd;

17 18%

Now

thatwe

havegottheinformationweneedforsettingupthepath,

19%

thenlets

setit

up.

20path(path,[GSMtop’/config’]);

21path(path,[GSMtop’/examples’]);

22path(path,[GSMtop’/utils’]);

23path(path,[GSMtop’/src/modulator’]);

24path(path,[GSMtop’/src/demodulator’]);

25 26%

Justto

make

thisfoolproof,re-entertheconfigdirectory

27cd

config;


R-97-1004 December 1997

Sour

ceco

deC

.27:

make_interleave_m.m

1%MAKE-INTERLEAVE-M:

2%

As

thename

indicates,thistinymatlab

scriptdoesconstruction

3%

of

theinterleave.m-function.

4%

5%SYNTAX:

make_interleave_m

6%

7%INPUT:

None.

8%

9%OUTPUT:

To

interleave.tmp

10%

11%WARNINGS:An

existingfilewill

beoverwritten.

12%

13%AUTHOR:

Arne

NorreEkstrøm/

JanH.Mikkelsen

14%EMAIL:

[email protected]/

[email protected]

15%

16%$Id:

make_interleave_m.m,v1.4

1997/12/1813:27:27aneksExp$

17 18Blocks=1;

19BitsInBurst=113;

20 21out=fopen(’interleave.tmp’,’w’);

22 23forT=0:3,

24for

t=0:BitsInBurst,

25b=mod((57*mod(T,4)+t*32+196*mod(t,2)),456);

26B=floor((T-mod(b,8))/4);

27fprintf(out,’tx_data_matrix(%d,%d)=tx_enc%d(%d);\n’,T+1,t+1,B+1,b+1);

28end

29end

30fclose(out);

Sour

ceco

deC

.28:

make_deinterleave_m.m

1%

MAKE-DEINTERLEAVE-M:

2%

Asthe

nameindicates,thistinymatlabscriptdoesconstruction

3%

ofthe

deinterleave.m-function.

4%

5%

SYNTAX:

make_deinterleave_m

6%

7%

INPUT:

None.

8%

9%

OUTPUT:

Todeinterleave.tmp

10%

11%

WARNINGS:Anexistingfilewillbeoverwritten.

12%

13%

AUTHOR:


14%

EMAIL:


15%

16%

$Id:make_deinterleave_m.m,v1.41997/12/1813:26:54aneksExp$

17 18BitsInBlock=455;

19 20out=fopen(’deinterleave.tmp’,’w’);

21 22B=0;

23 24for

b=0:BitsInBlock,

25R=4*B+mod(b,8);

26r=2*mod((49*b),57)+floor(mod(b,8)/4);

27fprintf(out,’rx_enc(%d)=rx_data_matrix(%d,%d);\n’,b+1,R+1,r+1);

28end

29 30fclose(out);


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