An investigation-on-efficient-spreading-codes-for-transmitter-based-techniques-to-mitigate-mai-and-isi-in-tddcdma-downlink

An Investigation on Efficient Spreading Codes forTransmitter Based Techniques to Mitigate MAI and

ISI in TDD/CDMA DownlinkAbhijit Mitra and Cemal Ardil

Abstract—We investigate efficient spreading codes for transmitterbased techniques of code division multiple access (CDMA) systems.The channel is considered to be known at the transmitter which isusual in a time division duplex (TDD) system where the channelis assumed to be the same on uplink and downlink. For such aTDD/CDMA system, both bitwise and blockwise multiuser trans-mission schemes are taken up where complexity is transferred tothe transmitter side so that the receiver has minimum complexity.Different spreading codes are considered at the transmitter to spreadthe signal efficiently over the entire spectrum. The bit error rate (BER)curves portray the efficiency of the codes in presence of multipleaccess interference (MAI) as well as inter symbol interference (ISI).

Keywords—Code division multiple access, time division duplex,transmitter technique, precoding, pre-rake, rake, spreading code.

I. INTRODUCTION

D IRECT sequence CDMA (DS-CDMA) is an efficientwireless communication channel accessing scheme, able

to sustain many simultaneous high data-rate users [1]-[2]. Inpractical conditions, however, wireless DS-CDMA systemsface a combination of channel effects that reduce the systemeffectiveness drastically unless these impairments are takencare of. The major problems encountered here are the MAI,due to simultaneous usage of the bandwidth by many users,and, ISI, due to multipath channels. MAI and ISI are alwaysadded to the background thermal noise modeled as additivewhite Gaussian noise (AWGN). Thus, the systems utility islimited by the amount of total interference instead of thebackground noise exclusively as in other cases. In other words,the signal to interference plus noise ratio (SINR) is the limitingfactor for a mobile communications system instead of thesignal to noise ratio (SNR). Therefore, in systems applyingCDMA the two problems of equalization and signal separationhave to be solved simultaneously to increase the SINR andachieve a good performance. Multiuser detection (MUD) hasbeen studied extensively and a number of solutions have beenproposed [3]-[5]. These techniques are all receiver based andthey usually require channel estimation as well as knowledgeof all the active users spreading codes and they have consid-erable computational cost. While this is feasible for the basestation (for the uplink scheme), it contrasts with the desire

Manuscript received May 14, 2007; revised October 1, 2007.A. Mitra is with the Department of Electronics and Communication

Engineering, Indian Institute of Technology (IIT) Guwahati, India. E-Mail:[email protected].

C. Ardil is with the Azerbaijan National Academy of Aviation, Baku,Azerbaijan. E-mail: [email protected].

to keep portable units (for the downlink scheme), like mobilephones, simple and power efficient. An alternative to MUDis to use multiuser transmission scheme [6], i.e., precoding acommon transmitted signal for the service of all users usingthe information of the channel impulse response such that theISI and MAI effects are minimized before transmission inthe downlink. The extra computational cost is transferred tothe base station where power and computational resources aremore readily available. This is possible in TDD systems whereboth uplink and downlink use the same frequency. Thus thetransmitter is able to know the fast fading of the multipathchannel based on the uplink received signal and use thisknowledge for precoding on the downlink. This presumes thatthe TDD frame length is shorter than the coherence time of thechannel. If the TDD system is intended only for slowly movingterminals then longer TDD frames could also be used. Apossible scenario in which the above assumptions are satisfiedwould be a personal communication system with low mobilityusers such as pedestrians in an outdoor environment. Indoorand microcell environments are the most probable applicationareas for TDD communications [7]. A second scenario couldbe a wireless local area network (WLAN). In such a casethe indoor radio frequency (RF) channel has a small delayspread and a computer workstation environment has essentiallystationary channels. A slow variation of the channels couldbe addressed with a periodical update of the channel profileestimates in the base station.

In a multiuser transmission scheme, a DS-CDMA trans-mitter usually modulates the information signal by manyorthogonal spreading codes and in the ith receiver the receivedsignal is correlated with a replica of the same spreading codeintended for ith user. Here, even if the system is constrained tobe synchronous, the multipath nature of the channel essentiallydestroys the orthogonality between the received signals. Thus,low crosscorrelation between the desired and the interferingusers is important to reduce the MAI. Moreover, adequateautocorrelation properties are required for reliable initial syn-chronization. Large sidelobes of the autocorrelation functioncan easily lead to erroneous code synchronization decisions.Good autocorrelation properties of the spreading code resultin a better resolution of the multipath components of aspread spectrum signal. Crosscorrelation and autocorrelationproperties are connected in such a way that both cannotbe achieved simultaneously. For example, random codes ingeneral exhibit good autocorrelation properties but worse crosscorrelation than the deterministic ones. Spreading codes are a

World Academy of Science, Engineering and TechnologyInternational Journal of Electrical, Electronic Science and Engineering Vol:2 No:12, 2008

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http://waset.org/publications/10076/An-Investigation-on-Efficient-Spreading-Codes-for-Transmitter-Based-Techniques-to-Mitigate-MAI-and-ISI-in-TDD/CDMA-Downlink

d S d

d

^

^

1

K

h

Kh

1

C1...K

C1...K

Channel 1Spreading

Channel K

Linear MUD 1

Linear MUD K

Fig. 1. Linearity of CDMA downlink.

kind of pseudo random codes and can be divided into pseudo-noise (PN) codes and orthogonal codes. PN sequences aregenerated with a linear feedback shift register. The outputs ofthe shift register cells are connected through a linear functionformed by exclusive-or (XOR) logic gates into the input ofthe shift register. Some of the PN sequences are (i) maximallength m-sequence, (ii) Gold, (iii) Kasami etc. Examples ofOrthogonal codes include (i) Walsh-Hadmard (ii) modifiedWalsh-Hadamard, (iii) orthogonal Gold etc. A comparativestudy of many PN and orthogonal sequences can be foundin [8].

In this paper we concentrate on exploring some of thespreading sequences described above which can be advan-tageous in multiuser transmission for TDD/CDMA systems.For investigating the efficiency of any spreading code, weuse the asynchronous CDMA system code measurements.In particular, we want to look for certain spreading codeswith good cross-correlation properties so that they can beapplied readily to those channels with multipath problems.This would not only take care of MAI and ISI at the transmitterside, but also would void the requirement of equalizationprocess at the receiver side. To check for the effectiveness ofthe spreading codes, we consider both blockwise (e.g., jointtransmission) and bitwise (e.g., pre-rake and rake diversity)techniques. Certain correlation measurements, based on [8],are applied to find out the suitability of these sequences forthe said techniques and depending on these, we find theBER performance of the transmitted sequences with differentnumber of users in a system.

The paper is organized as follows: we briefly discuss themathematical and conceptual backgrounds of transmitter basedtechniques in Section 2, treating both blockwise and bitwisetechniques sequentially. Complexity issues of these techniquesare taken up in Section 3. Section 4 deals with the differentspreading codes and their correlation measurements. Based onthese, results are given in Section 5 and finally, we concludeby summarizing the important concepts discussed herein inSection 6.

II. TRANSMITTER BASED TECHNIQUES IN CDMA

The problems of implementing multiuser techniques inmobile receivers and the need for their removal is underlinedin the last section. The linearity of the conventional CDMAdownlink system, presented simplified in Fig. 1, brings theconcept of somehow reversing the MUD technique. Here, theaim is to transfer the complexity and the computational load to

d

d

^

^

1

K

Channel 1

Channel K

d

Precoding

Spreading

andC (Q−n)

1

CK(Q−n)

C C1 K

h h1 K

S p

Fig. 2. Linear precoding with a linear transformation.

the transmitter (BS) where weight and size is not of concernand resources, like power and space for hardware are readilyavailable while maintaining at least the same performancethat the receiver based MUD techniques provide. The mobilereceiver (MS) will be restricted to the knowledge of its ownsignature waveform. Therefore, the kth subscriber’s receivershall consist of a simple correlator or a filter matched to thespreading sequence ck, ideal for single user in an AWGNchannel and no channel estimation, adaptive equalizer orfeedback from the BS is required. In addition to that the overallcapacity of the downlink in system is increased as no trainingsequences are needed to be transmitted.

An answer to the concept posed here is to apply a lineartransformation matrix T on the transmitted vector d (the dataspreading is included in the T matrix) in order to eliminateISI and MAI, the major impairments of a CDMA system,before transmission. Under this scheme, the actual transmittedsignal is distorted before transmission in such a way that afterpassing through the radio channel, the MS yields the desireddata. Each MS should have the knowledge of the downlinkchannel impulse response and the spreading codes of everyuser to apply a joint MUD. If we take into account all mobilereceivers, then the total information required is all K downlinkchannels and signature waveforms. The transformation matrixT should be a function of the same knowledge in linearprecoding. In other words, to achieve good performance thetransmitted signals in the downlink must be jointly optimizedbased on the spreading code and the downlink channel impulseresponse of every user. The BS obviously knows the spreadingcodes of all the active users in a cell and all it needs are thedownlink channel impulse responses. The uplink channels canbe estimated by the BS but this knowledge cannot be usedfor the downlink unless the principle of reciprocity is valid.In TDD this is valid which is the cause of using TDD inprecoding. As shown in Fig. 2, the precoded transmitted signalcan be described in general with a linear transformation matrixT applied on the data. In the following subsections we classifythe realization of this linear algorithm either as blockwise orbitwise technique. Although both of them can be described byan appropriate matrix T , there are important differences whichwe discuss in the following subsections.

A. Blockwise Techniques

In blockwise algorithms, the data is precoded and transmit-ted in blocks of N data bits for each of the K users. Thismeans that transformation matrix T is applied to a block of


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NK data bits. Furthermore, it is desirable for the resultingsignal sp to retain the same length NQ as produced bythe conventional CDMA system where Q denotes the lengthof the specific spreading codes. Thus, dimensions of the Tmatrix shall be NK × NQ. Note that T can be chosenaccording to different optimization criteria and the complexityfor determining it varies from algorithm to algorithm. Ignoringthis complexity, the multiplications required per bit per userfor transmission of any blockwise technique, resulting fromsp = Td, is given as

θblock =(KN)(NQ)(KN)

KN= N2QK (1)

which shows that the multiplications required for one symboltransmission are proportional to the square of a block lengthN2 which can be excessively high for any real TDD/CDMAscheme. A not so apparent problem with the blockwisealgorithms is the fact that in a multipath environment theend bits of each block are not correctly precoded and thisdeteriorates the overall performance. Each block is treatedindependently and the ISI, between the symbols of the blockitself, is canceled. However, under the scenario of continualblock transmission each block is extended in duration due tomultipath and therefore it overlaps with the next one. Thedegree of damage (the number of symbols affected) dependson the channels delay spread L. One solution to mitigate thisproblem is to increase the block length, but this results inan increased complexity. A second solution is to neglect thenumber of affected symbols resulting in loss of capacity.

1) Joint transmission: In joint transmission (JT) [9]-[10]the algorithm employs a common signal sp of length NQwhich gives the desired data at the output of all individualMS. The received signal ek at the kth user is given as

ek = Hks + v, (2)

where channel matrix Hk = [Hi,jk ], i = 1, ..., NQ + L − 1,

j = 1, ..., NQ, and

[Hk]i,j ={

hi−jk 0 ≤ i− j ≤ L− 1

0 otherwise.(3)

In (2), v is a noise vector of length (NQ+L−1). The noiselessversion of ek can be written as ek = Hks. After arranging allK matrices Hk into a new K(NQ + W − 1) × NQ matrixH where

H = [HT1 , · · · ,HT

k , · · · ,HTK ]T (4)

and all ek, k = 1, ..., K, vectors to a total received vectore = [eT

1 , · · · , eTk , · · · , eT

K ]T , it can be concisely written as

e = Hsp. (5)

The total received signal e in the above equation cannot beobserved by a single MS. An MS can only observe ek as givenin (2). The output vectors d̂k, k = 1, ..., K, at the decisionvariable of the K users are combined to form the vector d̂ =[d̂1

T, · · · , d̂k

T, · · · , d̂K

T]T where any d̂k = [d̂1

1, · · · , d̂Nk ]T .

The kth receiver filter matched to the users spreading codecan be written as

d̂ = BT Hsp (6)

where the K(NQ+W−1)×KN diagonal matrix B is definedas

B = blockdiag(B1, · · · ,Bk, · · · ,BK), (7)

with any (NQ + L− 1)×N matrix Bk defined as

Bk = [CTk O]T ,

and O being a N × (L−1) zero matrix. The NQ×N matrixCk = [Ck]i,j , i = 1, ..., NQ, j = 1, ..., N where

[Ck]i,j ={

ci−Q(j−1)−1k for i ≤ Q(j − 1) ≤ Q

0 otherwise(8)

and cks are the transmitted CDMA codes. The objective of anyprecoding algorithm is that the output of the mobile receiveryields the transmitted data, i.e., d̂ = d. Substituting this into(6) the problem of JT takes the form of

BT Hsp = d. (9)

Matrices B, H and the vector d in (9) are known at the BSand sp is an unknown vector with length NQ. The conditionKN < NQ is a basic assumption for TDD/CDMA, and hence(9) constitutes an optimization problem, where the number ofrestrictions contained in the vector d of length KN is smallerthan the number NQ of degrees of freedom, expressed bythe vector sp. Therefore, the validity of (9) implies that ithas infinitely many solutions for sp. A constraint criterion isnecessary to be imposed to the system. It is desirable for thetransmitted vector sp to be of minimum energy and it can beachieved by standard Lagrange techniques. The solution aftersolving through Lagrange techniques is

sp = HT B(BT HHT B)−1d (10)

where the joint precoding matrix T for JT can be written as

TJT = HT B(BT HHT B)−1. (11)

Equation (11) shows that joint transmission can be consideredas a set of independent pre-rake (HT B) applied on themodified information signal given by the linear transformationof the data vector d [11].

B. Bitwise Techniques

In the bitwise techniques, the precoding realization doesnot include blocks of data to be processed. The data of userk after being spread is pre-filtered by an FIR filter of lengthP with a discrete time impulse response pk(n) as shown inFig. 3. The resulting modified signals are summed to formthe final transmitted signal sp. The filter is applied on thetransmitted waveform rather than the data symbols as in theblockwise techniques. Thus the multipath resolution affordedby the CDMA spreading is exploited. Moreover, since thefilters are applied at the chip level and the derivation ofthe algorithms are restricted to consider only a few symbols(even one), the higher computation required for data-blocksolutions is eliminated. Pre-filters also have the advantage ofnot modifying the original CDMA structure directly as it is asimple addition of an array of FIR filters to the existing BStransmission system. Furthermore, the bitwise nature of the


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d Km

d 1m

e 1(n)

e K(n)

p K (n)

p 1 (n)

y 1 (n)

y K (n)

sp

e(0) e(Q) p(P)p(0)

Q P

Σ

Fig. 3. Bitwise precoding scheme.

algorithms removes the undesirable effect of the end bock-bits as described in the previous section. The taps of the pre-filters are determined by the adopted technique. Ignoring thecomplexity of the algorithm used to determine the taps, themultiplications required now per transmitted symbol per userbitwise is given by

θbit = PQ. (12)

Comparing (1) and (12), we observe that the complexity ratioof blockwise and bitwise techniques comes as

θblock

θbit=

N2K/2P

. (13)

In a CDMA system with linear MUD the number of users thatcan be accommodated do not outnumber the spreading gainK ≤ Q. If we set as a reasonable pre-filter length P as twicethe spreading gain Q and K as Q/2, then

θblock

θbit=

N2Q/22Q

=N2

4. (14)

Clearly, for N ≥ 2 (in a realistic system, N À 2) the multipli-cations required with a blockwise implementation of precodingoutnumber the corresponding bitwise implementation by alarge number. For less complexity, the bitwise techniques likepre-rake thus has gained importance.

1) Pre-rake diversity: This technique was initially de-scribed in [12] for DS spread spectrum systems and thenextended in [13] for TDD/CDMA mobile communications.The algorithm for pre-rake origins from the diversity theoryin frequency selective channels. In a mobile environment thecombination of the received signals from diverse independentpaths or mediums can improve the system performance. Hencein the radio mobile communications it is desirable to receive asignal from diverse independent paths and then combine theirpowers. This is what a rake receiver does.

The pre-rake technique is straightforward and takes directadvantage of the fact that in TDD the channel impulseresponse can be assumed the same for the uplink and thedownlink. The idea is to transmit a number of signals that

merge to a signal with the characteristics of a rake diversitysignal when received after the multipath channel. Each oneof these transmissions should be then delayed according tothe estimated relative path delay and amplified accordingto the estimated path complex coefficient. In other words,in the downlink the BS multiplies the signal to be sent touser k by the time inverted complex conjugate of the uplinkchannel impulse response of the same user. When the signal istransmitted it is convolved with the channel impulse responseof user k. This produces a strong peak at the output ofthe channel which is equivalent to the rake receivers output.Therefore, the receiver of the MS does not need to estimatethe channel impulse response and only uses a matched filtertuned to this peak. The scenario is explained with the analogyof rake and pre-rake concept for a single user scheme in thefollowing. We begin with the SNR analysis at the output ofa rake receiver with the input signal x(n) = wkdn

kcnk with a

transmission power w2k . The signal y2 after passing from the

multipath channel and being perturbed by AWGN is

y2 =L−1∑

l=0

h(l)x(n− lTc) + v(n). (15)

The filter right after y2 is matched to the spreading code. Therake combination follows this matched filtering and we have

y3 =L−1∑

l=0

L−1∑m=0

h(l)h∗(L− 1−m)x(n− (l + m)Tc)

+L−1∑

l=0

h∗(L− 1− nTc)v(n− lTC) (16)

at the output of the rake combiner. The desired output of therake system is

∑L−1l=0 h(l)x(n− lTc) and occurs at time n =

(L− 1)Tc, (l + m = L− 1), which has a signal strength of

(L−1∑

l=0

h(l)h∗(l))2w2k. (17)

Noise adds up incoherently with power σ2. From (17), theSNR at the output of the rake receiver is

SNRrake =w2

k

σ2(L−1∑

l=0

h(l)h∗(l))2. (18)

In contrast, in a pre-rake, to make sure that the power of thesignal at the output of the pre-rake transmitter is equal to w2

k,a power scaling factor is chosen to compensate for the gainsproduced by h∗(l) and can be taken as [12]

F =1√∑L−1

l=0 h(l)h∗(l). (19)

If we think about a pre-rake combining which is similar to amultipath estimation, the output signal is

y4 = F(L−1∑

l=0

h(l − nTc)∗x(n− lTc)). (20)


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After transmission, convolution with the multipath channel andaddition of AWGN yields the output signal

y6 = F (L−1∑

l=0

L−1∑m=0

h∗(l)h(L−1−m)x(n− (l+m)Tc))+v(n).

(21)The desired signal occurs again at time n = (L − 1)Tc andhas a power equal to

(L−1∑

l=0

h(l)h∗(l))2w2kF 2. (22)

The noise at the output of the matched filter has a power equalto σ2. We replace F with the expression given above and thusthe SNR can be written as

SNRpre-rake = (L−1∑

l=0

h(l)h∗(l))2w2

k

σ2F 2 = (

L−1∑

l=0

h(l)h∗(l))w2

k

σ2.

(23)Equations (18) and (23) show that the SNR for the pre-rake system is equal to that of the rake system for a singleuser except the power scaling factor. This analysis statesthat under the assumption that the channel parameters areestimated ideally on the transmitter, the two systems havesimilar performance.

In [13] the concept of pre-rake was extended to a multiuserTDD/CDMA system. The signal for user k after spreadingis filtered by the time inverse complex conjugate impulseresponse of the kth user channel and this process is repeatedfor every user before transmission. The produced signals areappropriately scaled to maintain the power at the desired levelsand then superimposed at the antenna element. The blockdiagram of the pre-rake technique applied in a TDD/CDMAis identical with the general description of a bitwise precodingtechnique as illustrated in Fig. 3. Therefore, pre-rake has theadvantages of a bitwise approach in terms of simplicity inimplementation. Furthermore, the calculation of the pre-filter’stap coefficients don’t require any complicated algorithm. Eachpre-filter’s impulse response is the time inverse conjugated ofthe corresponding uplink channel.

The principle applied is that in the downlink the desireduser’s signal is maximal ratio combined by the channel itselfwhile other user signals are not. Under the multiuser scenario,however, the pre-rake is proved to be an insufficient techniqueunable to compensate for the multipath interference and MAIas shown in [13],[14].

III. COMPLEXITY ISSUES

The precoding techniques described in the earlier sectionrequire excessive computational cost compared to the usualconventional spreading. The complexity is similar or exceedsthe one demonstrated by the receiver based multiuser tech-niques as described in [4]. However, it is shifted to the BS,where the resources are more readily available and thus it isless critical. Table I summaries the computational cost for JTand pre-rake schemes. The criteria used are the dimensionof the matrix that needs to be inverted and the numberof multiplications per transmitted symbol. The number of

TABLE ICOMPUTATIONAL COMPLEXITY OF JT AND PRE-RAKE TECHNIQUES.

Precoding algorithm Dimension of matrix Number ofto be inverted mult. per symbol

JT KN ×KN N2QKPre-rake none LQ

multiplications are calculated after the final transformationmatrix T for the blockwise techniques, as discussed in abovesection. As expected the blockwise technique JT is moredemanding in terms of complexity compared to the bitwisepre-rake.

IV. CORRELATION MEASURES OF DIFFERENT SPREADINGSEQUENCES

In order to compare different sets of spreading sequences,we need a quantitative measure for the judgment. Therefore,we take help of some useful criteria as given in [8], that canbe used for such a purpose. These are based on correlationfunctions of the set of sequences since both the MAI andsynchronization amiability depend on the crosscorrelation be-tween the sequences and the autocorrelation functions of thesequences, respectively. There are, however, several specificcorrelation functions that can be used to characterize a givenset of the spreading sequences.

In [1], one of the first detailed investigations of the asyn-chronous DS-CDMA system performance was given. Thework obtained a bound on the SNR at the output of thecorrelation receiver for a CDMA system with hard-limiter inthe channel. The need for considering the aperiodic crosscor-relation properties of the spreading sequences is also clearlydemonstrated. Since that time, many additional results havebeen obtained which helped to clarify the role of aperiodiccorrelation in asynchronous DS-CDMA systems.

For general polyphase sequences {µ(i)n } and {µ(l)

n } of lengthN , the discrete aperiodic correlation function is defined as

ρi,k(τ)| =

1N

∑N−1−τn=0 µ

(i)n [µ(l)

n+τ ]∗ for 0 ≤ τ ≤ N − 11N

∑N−1+τn=0 µ

(i)n−τ [µ(l)

n ]∗ for N − 1 ≤ τ < 00 |τ | ≥ N

(24)when {µ(i)

n } = {µ(l)n } then (24) defines the discrete aperiodic

autocorrelation function.Another important parameter used to assess the synchro-

nization amiability of the spreading sequence {µ(i)n } is a merit

factor, or a figure of merit, which specifies the ratio of theenergy of autocorrelation function main-lobes to the energyof the autocorrelation function side-lobes in the form

Ψ =ρi(0)

2∑N−1

τ=1 |ρi(τ)|2. (25)

In DS-CDMA systems, we want to have the maximum valuesof aperiodic cross correlation functions and the maximumvalues of out-of-phase aperiodic autocorrelation functions assmall as possible, while the merit factor as large as possiblefor all of the sequences used.

The BER in a multiple access environment depends on themodulation technique used, demodulation algorithm, and the


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signal to noise power ration (SNR) available at the receiver.Pursley [2] showed that in case of a BPSK asynchronous DSCDMA sytem, it is possible to express the average SNR atthe receiver output of a correlator receiver of the ith user asa function of the average interference parameter (AIP) for theother K users of the system, and the power of AWGN presentin the channel.

A. Mean Square Correlation Measures

In order to evaluate the performance of a whole set of Mspreading sequences, the mean-square aperiodic crosscorrela-tion (MSACC) for all sequences in the set, denoted by RCC ,was introduced by [17] as a measure of the set crosscorrelationperformance, where

RCC =1

M(M − 1)

M∑

i=1

N−1∑

k=1,k 6=i

N−1∑

τ=1−N

|ρi,k(τ)|2. (26)

A similar measure known as mean-square aperiodic auto-correlation (MSAAC), denoted by RAC , was introduced forcomparing the autocorrelation performance and is given by

RAC =1M

M∑

i=1

N−1∑

τ=1−N,τ 6=0

|ρi,k(τ)|2. (27)

For DS-CDMA applications we want both parameters RCC

and RAC to be as low as possible [16], [17]. Because theseparameters characterize the whole sets of spreading sequences,it is convenient to use them as the optimization criteria in de-sign of new sequence sets. We need to find out maximum valueof aperiodic crosscorrelation functions since this parameter isvery important when the worst-case scenario is considered.

B. Optimized Codes for Pre-Rake and JT

The autocorrelation and crosscorrelation measures whichare discussed above are calculated for the following sequences:(a) maximal length, (b) Gold, (c) Walsh-Hadamard, and,(iv) modified Walsh-Hadamard [18]. The different correlationparameters for the above sequences can be found in [8]. Forour purpose, the parameters are calculated for a sequence oflength 31, for m and Gold sequences, and, of length 32, forWalsh-Hadamard and modified Walsh-Hadamard sequences.

JT is a transmitter based precoding which uses all userscodes and channel impulse response for precoding. It issimilar to joint detection which is used at mobile unit. Theadvantage of using JT transmission over pre-rake diversitycombiner technique is that it reduces the MAI which cannotbe done by pre-rake or rake receiver. So the optimized codefor JT is the one which has very low mean-square out ofphase autocorrelation (which is a must) along with a lowcrosscorrelation value. For rake receiver and pre-rake receiver,however, which is generally considered single user receiver thecode should have good autocorrelation and crosscorrelationproperties.

−5 0 5 10 15 2010

−6

10−5

10−4

10−3

10−2

10−1

100

SNR

BE

R

BER PLOT FOR 10 USERS

JT−PNJT−GOLDJT−WALSHJT−MOD−WALSH

Fig. 4. BER plots of JT for 10 users using different sequences.

−6 −4 −2 0 2 4 6 8 10 1210

−6

10−5

10−4

10−3

10−2

10−1

100

SNR

BE

R


JT−PNJT−GOLDJT−WALSHJT−MOD−WALSH

Fig. 5. BER plots of JT for 20 users using different sequences.

V. RESULTS AND DISCUSSIONS

The performance of the JT, pre-rake and rake receiversis analyzed with different codes which are discussed in theabove section, for 10 and 20 users. Simulation is done withthe following assumptions: (a) modulation scheme is simplybinary phase shift keying (BPSK), (b) system is simulated forHIPERLAN channel models (we used channel model 5 forsimulation purpose), and (c) channel estimated in uplink isexactly equal to channel in downlink, i.e., it is a TDD system.

BER plots for joint transmission for 10 users and 20 usersare shown in Figs. 4 and 5, respectively. It is clear from theplots that JT has good performance for Gold, modified Walshand m-sequence for 10 users and they are approximatelysame because these codes have good autocorrelation propertieswhereas Walsh doesn’t have that. But when the number ofusers are increased the performance of m-sequence is not asgood as Gold and modified Walsh because it has high mean


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−6 −4 −2 0 2 4 6 8 10 1210

−6

10−5

10−4

10−3

10−2

10−1

100

SNR

BE

R


PRE−RAKE−PNPRE−RAKE−GOLDPRE−RAKE−WALSHPRE−RAKE−MOD−WALSH

Fig. 6. BER plots of pre-rake for 10 users using different sequences.

−5 0 5 10 1510

−5

10−4

10−3

10−2

10−1

100

SNR

BE

R


PRE−RAKE−PNPRE−RAKE−GOLDPRE−RAKE−WALSHPRE−RAKE−MOD−WALSH

Fig. 7. BER plots of pre-rake for 20 users using different sequences.

square crosscorrelation value and maximum peaks of aperiodiccrosscorrelation than Gold and modified Walsh sequences.

Similarly BER plots for pre-rake are shown in Figs. 6 and 7.For rake receiver, these are shown in Fig. 8 and Fig. 9 for 10and 20 users as earlier. JT scheme uses all codes and channelimpulse response of all users for precoding which reducesthe multiple access interference. It is found that in case ofpre-rake, for less number of users, Gold sequence performsbetter than the all other codes but for 20 users and above theperformance of Walsh sequence is better than the others sinceWalsh codes have less mean-square crosscorrelation value.Whereas for rake receiver the performance of modified Walshand Walsh are good for 10 and 20 users, respectively, becauseWalsh codes have low mean-square correlation value than themodified Walsh sequence.

−5 0 5 10 1510

−6

10−5

10−4

10−3

10−2

10−1

SNR

BE

R


RAKE−GOLDRAKE−MOD−WALSHRAKE−WALSH

Fig. 8. BER plots of rake for 10 users using different sequences.

0 5 10 15 20 2510

−6

10−5

10−4

10−3

10−2

10−1

100

SNR

BE

R


RAKE−GOLDRAKE−MOD−WALSHRAKE−WALSH

Fig. 9. BER plots of rake for 20 users using different sequences.

VI. CONCLUSIONS

In CDMA systems, an alternative to multiuser detection isto use multiuser transmission scheme where the extra compu-tational cost is transferred to the base station where power andcomputational resources are more readily available. Here thechannel estimation at the transmitter is possible if we assumeTDD where both uplink and downlink use the same frequency.We have taken up both the blockwise and bitwise techniquesfor such multiuser transmission schemes. In particular, theperformance of joint transmission, pre-rake and rake diversitycombiners for a TDD/CDMA system is investigated with thehelp of different spreading codes. The main virtue of JT isthat it reduces the MAI effectively than pre-rake or rake, butit is more complex than the latter two algorithms. Although weassumed that the systems are synchronous, we have used themeasures of spreading codes which are used for asynchronoussystem. It is observed that optimized codes for the JT schemeare Gold and modified Walsh-Hadamard codes. On the other


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hand, for pre-rake and rake combining, the optimized codescome out to be Walsh-Hadamard codes.

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