CDMA Concept

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Chapter 8

Basic CDMA Concepts

8.1 INTRODUCTION

CDMA protocols constitute a class of protocols in which the multiple access property is

primarily achieved by means of coding. Each user is assigned a unique code sequence

used to encode the information-bearing signal. The receiver, knowing the code

sequences of the user, decodes a received signal after reception and recovers the

original data. Since the bandwidth of the code signal is chosen to be much larger than

the bandwidth of the information-bearing signal, the encoding process enlarges

(spreads) the spectrum of the signal and is therefore also known as spread-spectrum

modulation. The resulting encoded signal is also called a spread-spectrum signal, and

the CDMA protocols are often denoted as spread-spectrum multiple access (SSMA)

protocols.

It is the spectral spreading of the coded signal that gives the CDMA protocols

their multiple access capability. It is therefore important to know the techniques to

generate spread-spectrum signals and the properties of these signals.

The precise origin of spread-spectrum communications may be difficult to pin-

point because modern spread-spectrum communication is the outcome of developments

in many directions, such as high-resolution radars, direction finding, guidance,

correlation detection, matched filtering, interference rejection, jamming avoidance,

information theory, and secured communications [110].

The spread-spectrum modulation techniques were originally developed for use

in military radar and communication systems because of their resistance against

jamming signals and a low probability of detection. Only in recent years with new and


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cheap technologies emerging and a decreasing military market have the manufacturers

of spread-spectrum equipment and researchers become interested in the civilapplications.

To qualify as a spread-spectrum modulation technique, two criteria must be

fulfilled [9]:

1. The transmission bandwidth must be much larger than the information bandwidth;

2. The resulting radio-frequency bandwidth is determined by a function other than the

information being sent (so the bandwidth is independent of the information signal).

This excludes modulation techniques like FM and pulse modulation (PM).

Therefore, spread-spectrum modulation transforms an information-bearing

signal into a transmission signal with a much larger bandwidth. This transformation is

achieved by encoding the information signal with a code signal that is independent of

the data and has a much larger spectral width than the data signal. This spreads the

original signal power over a much broader bandwidth, resulting in a low(er) power

density. The ratio of transmitted bandwidth to information bandwidth is called the

processing gain PG of the spread-spectrum system,

PGB

B

t

i

= (8.1)

where Bt

is the transmission bandwidth and Bi

is the bandwidth of the information-

bearing signal.

The receiver correlates the received signal with a synchronously generated

replica of the code signal to recover the original information-bearing signal. This

implies that the receiver must know the code signal used to modulate the data.

Because of the coding and the resulting enlarged bandwidth, spread-spectrum

signals have a number of properties that differ from the properties of narrowband

signals. The most interesting from a communication systems point of view are

discussed below. Each property is briefly explained with the help of illustrations, if

necessary, by applying direct-sequence spread-spectrum techniques.

1. Multiple access capability. If multiple users transmit a spread-spectrum signal at thesame time, the receiver can still distinguish between the users, provided each user

has a unique code that has a sufficiently low cross-correlation with the other codes.

Correlating the received signal with a code signal from a certain user will then only

despread the signal of this user, while the other spread-spectrum signals will remain

spread over a large bandwidth. Thus, within the information bandwidth, the power

of the desired user is much larger than the interfering power, provided there are not

too many interferers, and the desired signal can be extracted. The multiple access

capability is illustrated in Figure 8.1. In Figure 8.1(a), two users generate a spread-

spectrum signal from their narrowband data signals. In Figure 8.1(b) both users


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transmit their spread-spectrum signals at the same time. At the receiver only the

signal of user 1 is despread and the data recovered.

1

2

1

1

2 2

1&2

(a) (b)

Figure 8.1 Principle of spread-spectrum multiple access.

2. Protection against multipath interference. In a radio channel there is not just one

path between a transmitter and receiver. Due to reflections (and refractions), a

signal is received from a number of different paths. The signals of the different

paths are all copies of the transmitted signal but with different amplitudes and

phases. Adding these signals at the receiver is constructive at some of thefrequencies and destructive at others. In the time domain, this results in a dispersed

signal. Spread-spectrum modulation can combat this multipath interference;

however, the way in which this is done depends very much on the type of

modulation used. In the next section where CDMA protocols based on different

modulation methods are discussed, we show for each protocol how multipath

interference rejection is obtained.

3. Privacy. The transmitted signal can only be despread and the data recovered if the

code is known to the receiver.

4. Interference rejection. Cross-correlating the code signal with a narrowband signal

spreads the power of the narrowband signal, thereby reducing the interfering power

in the information bandwidth. This is illustrated in Figure 8.2. The spread-spectrumsignal (s) receives a narrowband interference (i). At the receiver the spread-

spectrum signal is despread while the interference signal spreads, making it appear

as background noise compared with the despread signal.

5. Anti-jamming capability, especially narrowband jamming. This is more or less the

same as interference rejection except the interference is now willfully inflicted on

the system. It is this property together with the next one that makes spread-spectrum

modulation attractive for military applications.

6. Low probability of interception (LPI) or covert operation. Because of its low power

density, the spread-spectrum signal is difficult to detect.


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i

s i

s

Figure 8.2 Interference rejection.

There are a number of modulation techniques that generate spread-spectrum

signals. We briefly discuss the most important ones:

Direct-sequence (DS) spread-spectrum. The information-bearing signal is multiplied

directly by a fast code signal.

Frequency hopping (FH) spread-spectrum. The carrier frequency at which the

information-bearing signal is transmitted is rapidly changed according to the code

signal.

Time-hopping (TH) spread-spectrum. The information-bearing signal is not transmitted

continuously. Instead, the signal is transmitted in short bursts where the times of the

bursts are decided by the code signal.

Chirp modulation. This kind of spread-spectrum modulation is almost exclusively used

in military radars. The radar continuously transmits a low-power signal whosefrequency is (linearly) varied (swept) over a wide range.

Hybrid modulation. Two or more of the above-mentioned spread-spectrum modulation

techniques can be used together to combine the advantages and, it is hoped, to combat

their disadvantages.

In Section 8.2, the above-mentioned modulation techniques are used to obtain

the multiple access capability that we want for CDMA (SSMA) protocols. Section 8.3

presents the code sequences and the properties of these sequences in detail.

8.2 SPREAD-SPECTRUM MULTIPLE ACCESS

We can classify the SSMA or CDMA protocols in two different ways: by concept or by

modulation method. The first classification gives us two protocol groups, averaging

systems and avoidance systems. The averaging systems reduce the interference by

averaging the interference over a wide time interval. The avoidance systems reduce the

interference by avoiding it for a large part of the time.

Classifying by modulation gives us five protocols, direct-sequence (or pseudo-

noise), frequency hopping, time-hopping, protocols based on chirp modulation, and

hybrid methods. Of these, the first (DS) is an averaging spread-spectrum protocol,


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while the hybrid protocols can be averaging protocols depending on whether DS is used

as part of the hybrid method. All the other protocols are of the avoidance type. Table8.1 summarizes both ways of classification.

Table 8.1

Classifying SSMA Protocols

DS TH FH Chirp Hybrid

Averaging x x

Avoidance x x x x

In the following sections, CDMA protocols are discussed where a division has

been made that is based on the modulation technique.

8.2.1 DS

In the DS-CDMA protocols, the modulated information-bearing signal (the data signal)

is directly modulated by a digital code signal. The data signal can be either an analog or

digital signal. In most cases it will be a digital signal. What we often see in the case of a

digital signal is that the data modulation is omitted and the data signal is directly

multiplied by the code signal and the resulting signal modulates the wideband carrier. It

is from this direct multiplication that the DS-CDMA protocol gets its name.

Data

modulator

Carrier

generator

Code

generator

Data Wide-band

modulationcode

Figure 8.3 Block diagram of a DS-SSMA transmitter.

In Figure 8.3, a block diagram of a DS-CDMA transmitter is given. The binary data

signal modulates a radio frequency (RF) carrier. The modulated carrier is then

modulated by the code signal. This code signal consists of a number of code bits or

chips that can be either +1 or 1. To obtain the desired spreading of the signal, the

chip rate of the code signal must be much higher than the chip rate of the information

signal. For the code modulation various modulation techniques can be used but usually

Wideband

code

modulation

Data

modulator

Carrier

generatorCode

generator

Data


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some form of PSK such as BPSK, differential BPSK (D-BPSK), quadrature PSK

(QPSK), or MSK is employed.If we omit the data modulation and use BPSK for the code modulation, we get

the block diagram given in Figure 8.4.

Carrier

generator

Code

generator

XBinary data Wide-band

modulator

Figure 8.4 Modified block diagram of a DS-SS transmitter.

time

Data signal

Code signal

Data signal x code signal

BPSK-modulated signal

Figure 8.5 Generation of a BPSK-modulated spread-spectrum signal.

The DS-SS signal resulting from this transmitter is shown in Figure 8.5. In this figure,

ten code signals per information signal are transmitted (the code chip rate is 10 times

the information chip rate), so the processing gain is equal to 10. In practice, the

processing gain is much larger (in the order of 102

to 103).

After transmission of the signal, the receiver (seen in Figure 8.6) uses coherent

demodulation to despread the spread-spectrum signal using a locally generated code

sequence. To perform the despreading operation, the receiver must not only know the

Wideband

modulator

Carrier

generator

Code

generator

Binary data


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code sequence used to spread the signal, but the codes of the received signal and the

locally generated code must also be synchronized.This synchronization must be accomplished at the beginning of the reception

and maintained until the whole signal is received. The synchronization/tracking block

performs this operation. After despreading, a data-modulated signal results and after

demodulation the original data are recovered.

Code

generator

demodulator

Carrier

generator

Data DataCode

demodulator

Codesynchr.

/tracking

Figure 8.6 Receiver of a DS-SS signal.

In the previous section, a number of advantageous properties of spread-spectrum

signals were mentioned. The most important of those properties from the viewpoint ofCDMA protocols is multiple access capability, multipath interference rejection,

narrowband interference rejection, and, with respect to secure/private communication,

LPI. We explain these four properties in relation to DS-CDMA.

Multiple access. If multiple users use the channel at the same time, multiple DS

signals will overlap in time and frequency. At the receiver, coherent demodulation

is used to remove the code modulation. This operation concentrates the power of the

desired user in the information bandwidth. If the cross-correlation between the code

of the desired user and the code of the interfering user is small, coherent detection

will only put a small part of the power of the interfering signals into the information

bandwidth. Multipath interference. If the code sequence has an ideal autocorrelation function,

the correlation function is zero outside the interval [ Tc,Tc] where Tc is the chip

duration. This means that if the desired signal and a version that is delayed for more

than 2Tc are received, coherent demodulation treats the delayed version as an

interfering signal, putting only a small part of the power in the information

bandwidth.

Narrowband interference. The coherent detection at the receiver involves a

multiplication of the received signal by a locally generated code sequence.

Code

synchr./

tracking

Code

demodulator

Data

demodulator

Code

generatorCarrier

generator

Data


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However, as we saw at the transmitter, multiplying a narrowband signal with a

wideband code sequence spreads the spectrum of the narrowband signal so that itspower in the information bandwidth decreases by a factor equal to the processing

gain.

LPI. Because the direct sequence signal uses the whole signal spectrum all the time,

it has a very low transmitted power per hertz. This makes it very difficult to detect a

DS signal.

Apart from the above-mentioned properties, the DS-CDMA protocols have a

number of other specific properties that we can divide into advantageous (+) and

disadvantageous () behavior:

+ The generation of the coded signal is easy. It is done by simple multiplication.

+ Since only one carrier frequency has to be generated, the frequency synthesizer

(carrier generator) is simple.

+ Coherent demodulation of the spread-spectrum signal is possible.

+ No synchronization among the users is necessary.

It is difficult to acquire and maintain the synchronization of the locally generated

code signal and the received signal. Synchronization has to take place within a

fraction of the chip time.

For correct reception, the locally generated code sequence and the received code

sequence must be synchronized within a fraction of the chip time. This combined

with the nonavailability of large contiguous frequency bands practically limits thespread bandwidth to 10 to 20 MHz.

The power received from users close to the base station is much higher than that

received from users further away. Since a user continuously transmits over the

whole bandwidth, a user close to the base will constantly create a lot of interference

for users far from the base station, making their reception impossible. This near-far

effect is solved by applying a power control algorithm so that all users are received

by the base station with the same average power. However, this control proves to be

quite difficult.

8.2.2 FH

In FH-CDMA protocols, the carrier frequency of the modulated information signal is

not constant but changes periodically. During time intervals T, the carrier frequency

remains the same but after each time interval the carrier hops to another (or possibly the

same) frequency. The hopping pattern is decided by the code signal. The set of

available frequencies the carrier can attain is called the hop-set.

The frequency occupation of an FH-spread-spectrum system differs

considerably from a DS-spread-spectrum system. A DS system occupies the whole

frequency band when it transmits, whereas an FH system uses only a small part of the

bandwidth when it transmits but the location of this part differs in time.


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Suppose an FH system is transmitting in frequency band 2 during the first time

period (see Figure 8.7). A DS system transmitting in the same time period spreads itssignal power over the whole frequency band so the power transmitted in frequency band

1 will be much less than that of the FH system. However, the DS system transmits in

frequency band 1 during all time periods, while the FH system only uses this band part

of the time. On average both systems will transmit the same power in the frequency

band.

In a DS system, the narrowband interference is reduced by a factor of PG. In an

FH system however, it is the (raw) chip error rate that is reduced by PG. For strong

interference this can be a significant difference, where a single interferer may

overload a DS receiver but only cause a single chip error now and then in an FH

system (which the forward error control (FEC) scheme may easily handle).

The difference between FH-spread-spectrum and DH-spread-spectrum

frequency usage is illustrated in Figure 8.7.

frequency

time time

frequency

FH DS

Figure 8.7 Time/frequency occupancy of FH and DS signals.

The block diagram for an FH-CDMA system is given in Figure 8.8.

Figure 8.8 shows the block diagram of an FH-CDMA transmitter and receiver.

The data signal is baseband-modulated on a carrier. Several modulation techniques can

be used for this but it does not really matter which one is used for the application offrequency hopping. Usually FM modulation is used for analog signals and frequency

shift keying (FSK) modulation for digital signals. Using a fast-frequency synthesizer

controlled by the code signal, the carrier frequency is converted up to the transmission

frequency.

The inverse process takes place at the receiver. Using a locally generated code

sequence, the received signal is converted down to the baseband-modulated carrier. The

data are recovered after (baseband) demodulation. The synchronization/tracking circuit

ensures that the hopping of the locally generated carrier synchronizes to the hopping

pattern of the received carrier so that correct despreading of the signal is possible.

Frequency Frequency

Time Time


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Code

generatorCode

generator

demodulator

Data DataData

Frequency

syntheziserFrequency

syntheziser

Baseband

modulator

Up

converter

Down

converter

Synchr.

tracking

Figure 8.8 Block diagram of an FH-CDMA transmitter and receiver.

Within the FH-CDMA protocols, a distinction is made based on the hopping

rate of the carrier. If the number of hops is (much) greater than the data rate, it is called

fast-frequency-hopping (F-FH) CDMA protocol. In this case, the carrier frequency

changes a number of times during the transmission of 1 bit, so that 1 bit is transmitted

in different frequencies. If the number of hops is (much) smaller than the data rate, it is

called slow-frequency-hopping (S-FH) CDMA protocol. In this case, multiple bits are

transmitted at the same frequency.

The occupied bandwidth of the signal on one of the hopping frequencies

depends not only on the bandwidth of the information signal, but also on the shape of

the hopping signal and the hopping frequency. If the hopping frequency is much smallerthan the information bandwidth (which is the case in S-FH), then the information

bandwidth is the main factor that decides the occupied bandwidth. If however, the

hopping frequency is much greater than the information bandwidth, the pulse shape of

the hopping signal will decide the occupied bandwidth at one hopping frequency. If this

pulse shape is very abrupt (resulting in very abrupt frequency changes), the frequency

band will be very broad, limiting the number of hop frequencies. If we make sure that

the frequency changes are smooth, the frequency band at each hopping frequency will

be about 1/Th times the frequency bandwidth, where Th is equal to the hopping

frequency. We can make the frequency changes smooth by decreasing the transmitted

power before a frequency hop and increasing it again when the hopping frequency haschanged.

As was done with the DS-CDMA protocols, we discuss the properties of FH-

CDMA with respect to multiple access capability, multipath interference rejection,

narrowband interference rejection, and probability of interception.

Multiple access. It is quite easy to visualize how the F-FH and S-FH CDMA

protocols obtain their multiple access capability. In the F-FH protocol, 1 bit is

transmitted in different frequency bands. If the desired user is the only one to


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transmit in most of the frequency bands, the received power of the desired signal is

much higher than the interfering power and the signal is received correctly.In the S-FH protocol, multiple bits are transmitted at one frequency. If the

probability of other users transmitting in the same frequency band is low enough, the

desired user is received correctly most of the time. For those times that interfering

users transmit in the same frequency band, error-correcting codes are used to recover

the data transmitted during that period.

Multipath interference. In the F-FH CDMA protocol the carrier frequency changes a

number of times during the transmission of 1 bit. Thus, a particular signal frequency

is modulated and transmitted on a number of carrier frequencies. The multipath

effect is different at the different carrier frequencies. As a result, signal frequencies

that are amplified at one carrier frequency will be attenuated at another carrier

frequency and vice versa. At the receiver, the responses at the different hopping

frequencies are averaged, thus reducing the multipath interference. This is not as

effective as the multipath interference rejection in a DS-CDMA system but it still

gives quite an improvement.

Narrowband interference. Suppose a narrowband signal is interfering on one of the

hopping frequencies. If there are PG hopping frequencies (where PG is the

processing gain), the desired user will (on the average) use the hopping frequency

where the interferer is located 1/PG percent of the time. The interference is therefore

reduced by a factor PG.

LPI. The difficulty in intercepting an FH signal lies not in its low transmissionpower. During a transmission, it uses as much power per hertz as does a continuous

transmission. But the frequency at which the signal is going to be transmitted is

unknown and the duration of the transmission at a particular frequency is quite

small. Therefore, although the signal is more readily intercepted than a DS signal, it

is still a difficult task to perform.

Apart from the above-mentioned properties, FH-CDMA protocols have a number of

other specific properties that we can divide into advantageous (+) and


+ Synchronization is much easier with FH-CDMA than with DS-CDMA. With FH-CDMA, synchronization has to be within a fraction of the hop time. Since spectral

spreading is not obtained by using a very high hopping frequency but by using a

large hop-set, the hop time will be much longer than the chip time of a DS-CDMA

system. Thus, an FH-CDMA system allows a larger synchronization error.

+ The different frequency bands that an FH signal can occupy do not have to be

contiguous, because we can make the frequency synthesizer easily skip over certain

parts of the spectrum. Combined with the easier synchronization, this allows much

higher spread-spectrum bandwidths.


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+ Because FH-CDMA is an avoidance spread-spectrum system, the probability of

multiple users transmitting in the same frequency band at the same time is small. Ifa user far from the base station transmits, it is received by the base station even if

users close to the base station are transmitting, since those users are probably

transmitting at other frequencies. Thus, the near-far performance is much better than

that of DS.

+ Because of the larger possible bandwidth a FH system can employ, it offers a higher

possible reduction of narrowband interference than a DS system.

A highly sophisticated frequency synthesizer is necessary.

An abrupt change of the signal when changing frequency bands lead to an increase

in the frequency band occupied. To avoid this, the signal turned off and on when

changing frequency. Coherent demodulation is difficult because of the problems in maintaining phase

relationship during hopping.

8.2.3 TH

In the TH-CDMA protocols, the data signal is transmitted in rapid bursts at time

intervals determined by the code assigned to the user.

Data

modulator

Carrier

generator generator

demodulator

Carrier

Data DataSlow in

fast out

Data

Buffer

Code

generator

Code

generator

Fast in

slow out

Buffer

Figure 8.9 Block diagram of a TH-CDMA transmitter and receiver.

The time axis is divided into frames and each frame is divided into Mtime slots.During each frame the user will transmit in one of the M time slots. Which of the M

time slots is transmitted depends on the code signal assigned to the user. Since a user

transmits all of its data in 1, instead of M time slots, the frequency it needs for its

transmission has increased by a factor M. A block diagram of a TH-CDMA system is

given in Figure 8.9.


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Time

Frequency

Figure 8.10 Time-frequency plot of the TH-CDMA protocol.

Figure 8.10 shows the time-frequency plot of the TH-CDMA systems.

Comparing Figure 8.10 with Figure 8.7, we see that the TH-CDMA protocol uses the

whole wideband spectrum for short periods instead of parts of the spectrum all of the

time.

Following the same procedure as for the previous CDMA protocols, we discuss

the properties of TH-CDMA with respect to multiple access capability, multipath

interference rejection, narrowband interference rejection, and probability ofinterception.

Multiple access. The multiple access capability of TH-SS signals is acquired in the

same manner as that of the FH-SS signals, namely by making the probability of

users transmissions in the same frequency band at the same time small. In the case

of time hopping, all transmissions are in the same frequency band so the

probability of more than one transmission at the same time is small. This is again

achieved by assigning different codes to different users. If multiple transmissions

do occur, error-correcting codes ensure that the desired signal can still be

recovered.

If there is synchronization among the users, and the assigned codes are such that nomore than one user transmits at a particular slot, then the TH-CDMA protocol

reduces to a TDMA protocol where the slot in which a user transmits is not fixed

but changes from frame to frame.

Multipath interference. In the TH-CDMA protocol, a signal is transmitted in

reduced time. The signaling rate therefore increases and dispersion of the signal

will lead to overlap of adjacent bits much sooner. Therefore, no advantage is

gained with respect to multipath interference rejection.

Narrowband interference. A TH-CDMA signal is transmitted in reduced time. This

reduction is equal to 1/PG where PG is the processing gain. At the receiver we only


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receive an interfering signal during the reception of the desired signal. Thus, we

only receive the interfering signal 1/PG percent of the time, reducing the interferingpower by a factor PG.

LPI. With TH-CDMA, the frequency at which a user transmits is constant but the

times at which a user transmits are unknown and the durations of the transmissions

are very short. Particularly when multiple users are transmitting, this makes it

difficult for an intercepting receiver to distinguish the beginning and end of a

transmission and to decide which transmissions belong to which user.

Apart from the above-mentioned properties, the TH-CDMA protocols have a

number of other specific properties that we can divide into advantageous (+) and


+ Implementation is simpler than that of FH-CDMA protocols.

+ It is a very useful method when the transmitter is average-power limited but not

peak-power limited since the data are transmitted is short bursts at high power.

+ As with the FH-CDMA protocols, the near-far problem is much less of a problem

since TH-CDMA is an avoidance system, so most of the time a terminal far from

the base station transmits alone, and is not hindered by transmissions from stations

close by.

It takes a long time before the code is synchronized, and the time is short in which

the receiver has to perform the synchronization.

If multiple transmissions occur, a lot of data bits are lost so a good error-correctingcode and data interleaving are necessary.

8.2.4 Chirp Spread Spectrum

Although chirp spread spectrum is not yet adapted as a CDMA protocol, for the sake of

completeness a short description is given here.

f1

f2

t1 t2

T

B

Figure 8.11 Chirp modulation.

2

1

t1 t2

B

T


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A chirp spread-spectrum system spreads the bandwidth by linear frequency

modulation of the carrier. This is shown in Figure 8.11.The processing gain PG is the product of the bandwidth B over which the

frequency is varied and the duration Tof a given signal waveform:

PG BT = (8.2)

8.2.5 Hybrid Systems

The hybrid CDMA systems include all CDMA systems that employ a combination of

two or more of the above-mentioned spread-spectrum modulation techniques. If we

limit ourselves to DS, FH, and TH modulations, we have four possible hybrid systems:DS/FH, DS/TH, FH/TH, and DS/FH/TH.

The idea of the hybrid system is to combine the specific advantages of each of

the modulation techniques. If we take, for example, the combined DS/FH system, we

have the advantage of the antimultipath property of the DS system combined with the

favorable near-far operation of the FH system. Of course, the disadvantage lies in the

increased complexity of the transmitter and receiver. For illustration purposes, we give

a block diagram of a combined DS/FH CDMA transmitter in Figure 8.12.

Up

converter

Frequency

synthesizer

Code

generator

Code

generator

Code clock

Data

Figure 8.12 Hybrid DS-FH transmitter.

Up converter


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The data signal is first spread using a DS code signal. The spread signal is then

modulated on a carrier whose frequency hops according to another code sequence. Acode clock ensures a fixed relation between the two codes.

8.3 DESIGN OF PSEUDONOISE SEQUENCES

The objective of this section is to present an overview of the design and properties of

code sequences for CDMA systems. The choice of the type of code sequence for

CDMA systems is important with respect to the resistance against both multipath and

multiuser interference.

8.3.1 Basics

To combat these types of interference, two properties are very important: (1) Each code

sequence in the set must be easy to distinguish from a time-shifted version of itself, and

(2) each code sequence in the set must be easy to distinguish from (a possibly tune-

shifted version of) every other signal in the set.

The first property is important with respect to multipath propagation effects that

occur in mobile outdoor and indoor radio environments The second property plays an

important role with respect to the multiple access capability of the communications

system. In this chapter, we describe three types of code sequences: maximum length,

Gold, and kasami.

Before describing the construction of these code sequences and discussing the

correlation properties with respect to the requirements mentioned above, we present in

the next section some basic definitions of correlation functions and some information

about shift register sequences. Finally, some numerical examples of the aforementioned

code sequences are given.

Correlation functions

Primarily because system implementation is simpler, code sequences used for CDMA

communications systems are required to be periodic. If T is the period of the code

sequence denoted as X(t), then periodicity implies that X(t) = X(t+T) for all time

instants t and for each code sequence X in the set. For the code symbols ofXwe use thenotation Xm. Furthermore, we assume that the code symbols are {1,1} The distinction

between code sequences X(t) and Y(t) is measured in terms of the correlation function

defined as

r X t Y t dt X Y

T

, ( ) ( ) ( ) = +0

(8.3)

This expression is shown as the cross-correlation function if X Y and as theautocorrelation function if X = Y. Code sequence of interest are those consisting of a

number of time-limited pulses called chips. Then, the signal X(t) is written as


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X t a t iT xi

c

i

( ) ( )= =

(8.4)

where axi is the ith code symbol user of x, (t) is the basic pulse wave form, and Tc is

the time duration of the pulse, termed chip duration and

( ) ( )t iT t jT dt i jc c

Tc

= 00

if (8.5)

If the delay is taken as a multiple of the chip duration (= lTc), then (8.3) is written as

r l a a X Y xi

x

i

i

N

, ( ) =+

=

10

1

(8.6)

where

= 2

0

( )t dt

Tc

(8.7)

which equals Tc if(t) is a rectangle pulse duration Tc with amplitude.In a DS-CDMA system, each data bit is multiplied with a user-specific code

sequence. For the current data bit and the previous data bit of a user with code sequence

Y, we use the notation by0 and by

-1 , respectively.

Now consider the situation in a multipath radio environment where Xis the code

sequence of the reference user and Y is the code sequence of a interfering user (or a

delayed part of code sequence X). The length of a code sequence is denoted by Nc. In

the receiver of the reference user a partial correlation operation is performed. This

situation is shown in Figure 8.13

Now we define the following two partial correlation functions

R X t Y t dt XY ( ) ( ) ( )

= 0 (8.8)

R X t Y t dt XY

N Tc c

( ) ( ) ( )

= (8.9)

by0

by1

Nc1 I1 0X

YNc1 Nc1 00


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270

Figure 8.13 Cross-correlation of code sequence X of the reference user, and code sequence Ybeing the code sequence of an interfering user or a delayed version of the reference

code sequence.

Assuming that is a multiple of the chip duration Tc implying = lTc, these partialcorrelation functions are written as

R l a a xy xi

y

i

i

l

( ) =

=

10

1

(8.10)

R l a axy xl

y

l

l

Nc

( ) =

=

11

1

(8.11)

IfX = Y, then (8.10) and (8.11) are the partial autocorrelation functions and in the case

XY, (8.10) and (8.11) are the partial cross-correlation functions.With respect to the sign of by

0and by

1, there are two possibilities: either by

0and

by1 have the same sign or they have the opposite sign. For the first case we have the

periodic correlation function:

xy xy xy xl

y

l

m

N

l R l R l a ac

( ) ( ) ( )= + =

=

1

0

1

(8.12)

Also, xy(l) satisfies

x y c y x N l l, ,( ) ( ) = (8.13)

which implies that xy

(l) is an even function with respect to N.

If by0 and by

1 have the opposite sign, then we have an a-periodic correlation

function

xy xy xy x

i

y

i

x

i

y

i

n l

N

i

l

l R l R l a a a ac

( ) ( ) ( )= =

=

=

1 11

0

1

(8.14)

which is odd with respect to Nc, that is,

x y c y x N l l, ,( ) ( ) = (8.15)


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For analysis and comparison of code sequences it is convenient to define peakcorrelation functions. For a set of periodic sequences, the peak periodic cross-

correlation magnitude c is defined as

{ } c xy cl l N x y x y= max ( ) : , , ,0 1 (8.16)

The peak out-of-phase-periodic autocorrelation magnitude is defined as

{ } a x cl l N x= max ( ) : ,0 1 (8.17)

Now the larger ofc and a is denoted by max.

Analogously, we define the peak a-periodic cross-correlation magnitude

c and

the peak out-of-phase a-periodic autocorrelation magnitude

a , respectively

c xy cl l N x y x y=

max ( ) : , , ,0 1 (8.18)

and

a x cl l N x=

max ( ) : ,0 1 (8.19)

The larger of

c and

a is denoted as

max .

The two requirements mentioned in the introduction are now equivalently

reformulated: (1) For each sequence in the set, both the periodic out-of-phase

autocorrelation function and the a-periodic out-of-phase autocorrelation function must

be small for 1 l Nc1. (2) For each pair of sequences x and y, both the periodicautocorrelation and the a-periodic cross-correlation function must be small for all l.

Linear Shift Registers

Code sequences must have noiselike properties to meet the requirements mentioned in

the preceding section. However, because of implementation problems, the code

sequences are generated according to a periodic deterministic scheme. Periodic code

sequences having noiselike properties are called PN sequences. A proper way to

generate these code sequences is by using linear binary shift registers. An example for

such a register is presented in Figure 8.14. In this configuration, an XOR operation is

performed on the contents of register 2 and register 0 and the result is fed back to the


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272

input of register 4. The shift direction of the shift register is from left to right (4-3-2-1-

0).The register in Figure 8.14 with five sections generates a code sequence with length

Nc=251=31. We show in the next section that the feedback connections are chosen

very carefully in order to generate a code sequence with satisfactory correlation

properties. In general, the configuration of a linear binary shift register of n sections is

described by a generator polynomial, which is a binary polynomial of degree n. The

number n is the number of sections of the shift register:

{ }( )h x h x h x h x h hn n n n i( ) ... ,= + + + +

0 1

1

10 1 (8.20)

.

h(x) = x5

+ x2

+ 1

Figure 8.14 Two-tap linear binary shift register.

We use the notation used by Sarwate and Pursley [11] where h0 = hn = 1 and hi = 1 for i

0 and i n if there is a feedback connection from the ith cell. It is convenient and

conventional to represent the polynomial h(x) by a binary vector h = (h0, h1, ..., hn) and

to express this vector in octal notation. For example, the shift register in Figure 8.14 is

represented by generator polynomial h(x) = x5 + x2 +1. The binary representation of this

polynomial is 100101 and the octal representation is 45. If the sequence generated by

h(x) is denoted as u, then a circular shifted version of u is denoted as Tu where i is the

number of shifts. For instance, if u = 10011101 then Tu = l001110. Note that TNu =

T0

u = u.

8.3.2 PN Codes

Three basic classes of code sequences suitable for CDMA applications are discussed in

this section:

maximum length sequences;

Gold sequences;

Kasami sequences.

+

4 1 023


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273

Maximum length sequences

Maximum length code sequences are generated by a single linear shift register. As thename suggests, maximum length code sequences are precisely the sequences of

maximum possible period (Nc = 2"-1) from an n-stage binary shift register with linear

feedback. To generate a maximum length code sequence, the generator polynomial

must be a primitive polynomial of degree n. Before explaining the term primitive

polynomial, first the following terms are defined:

Irreducible polynomial

This is a polynomial that can not be decomposed into other polynomials. Example: The

polynomial x2

+ 2x +1 is not irreducible since x2

+ 2x +1 = (x + 1)(x +1). The

polynomial x2

+ x +1 is irreducible.

Exponent

The smallest positive integer p for which the polynomial h(x) is a divisor of (1 xp) is

called the exponent ofh(x).

Primitive polynomial

A primitive polynomial of degree n is an irreducible polynomial with exponent 2n

1.

It has been proven that the periodic autocorrelation for a maximum length

sequence u is given by

uc c

c

lN l N

l N

( )mod

mod=

=

0

1 0(8.21)

Thus, binary maximum length-sequence has a two-valued periodic autocorrelation

function.

Golomb [12] observed that if n 0 mod 4, there exists pairs of maximum length

sequences with three-valued cross-correlation functions, where the three values are

{1, t(n), t(n) 2}with

t n n

n

n

n( )

( )

( )= +

+

+

+

1 2

1 2

1

2

22

odd

even(8.22)

A cross-correlation function taking on these values is called a preferred three-valued

cross-correlation function and the corresponding pair of maximum length sequences

(polynomials) is called a preferred pair of maximum length sequences. For this

preferred pair of maximum length sequences we find

a c t n= = ( ) (8.23)


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274

Figures 8.15 to 8.17 show preferred pairs of maximum length sequences for periods 31,63, and 127, respectively.

Figure 8.15 Preferred pairs of maximum length sequences of period 31. The vertices of everytriangle form a maximal connected set.

It is clear from these figures that only very small sets of maximum length

sequences can have good periodic cross-correlation properties. For multiple access

systems, it is desirable to obtain larger sets of sequences of period Nc = 2n

1 which

have the same bound t(n) on the peak periodic cross-correlation as do themaximal connected sets. Although there are no analytical results that give the values of

the maximal a-periodic cross-correlation

c for maximum length sequences generated

by preferred pairs, Massey and Uhran [13] have obtained bounds on

c . They state that

if the maximum of the periodic cross-correlation and the periodic autocorrelation maxequals t(n), then the bound for the a-periodic cross-correlation is

c

n

n

n

n

n

n

=+ +

+ +

2 2 1

2 2 1

1

1

2

12

even

odd( )

(8.24)

We did not find a bound in the literature for out-of-phase a-periodic autocorrelation.


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275

Figure 8.16 Preferred pairs of maximum length sequences of period 63. Every pair of adjacentvertices is a maximal connected set.

Gold Sequences

One important class of periodic sequences that provides larger sets of sequences with

good periodic cross-correlation is the class of Gold sequences. A set of Gold sequences

of period N = 2n1 consists of (Nc + 2) sequences for which the maximum periodic

cross-correlation c = t(n) with t(n) given by (8.22). A set of Gold sequences isconstructed from appropriately selected maximum length sequences. Suppose a shift

register polynomial f(x) factors into h(x) h x

( ) where h(x) and h x

( ) have no factors in

common. Then the set of all sequences generated by f(x) is just the set of all sequences

of the form a b, where a is some sequence generated by h(x), b is some sequence

generated by h x

( ) , and a and b are not necessarily nonzero sequences. Now suppose

that h(x) and h x

( ) are two different primitive binary polynomials of degree n that

generate the maximum length sequences u and v, respectively, of period Nc = 2n 1. Ify

denotes a nonzero sequence generated by f(x) = h(x) h x

( ) , then either


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276

Figure 8.17 Preferred pairs of maximum length sequences of period 127. Every set of sixconsecutive vertices is a maximal connected set.

y T ui= (8.25)

or

y T vj= (8.26)

or

y T u T vi j= (8.27)

where 0 i, j Nc 1 and where, as before, Ti

u Tjv denotes the sequence whose kth

element is ui+k vj+k. From this it follows that y is some phase of some sequence in theset G(u,v) defined by

{ }G u v u v u v u Tv u T v u T vNc( , ) , , , , ,...,=

2 1 (8.28)

Note that G(u, v) contains Nc+ 2 = 2n

+ 1 sequences of period Nc.

Figure 8.18 shows a possible configuration to generate a Gold sequence of

length Nc = 63. The octal representation of the shift registers producing u and v are 141

and 163, respectively (h(x) = 1+ x5

+ x6

and h x

( ) = l + x + x4

+ x5

+ x6).


25/38


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278

Furthermore, since h x

( ) is shown to be a polynomial of degree n/2, w is a maximumlength sequence of period 2

n/21. Now consider the sequences generated by the

polynomial h(x) h x

( ) of degree 3n/2. Clearly, any such sequence must be of one of the

forms T iu, T jw or T iu Tjw, where 0 i 2n 1 and 0 j2n/2 1. Thus, any

sequence y of period 2n

1 generated by h(x) h x

( ) is one of the sequences in the set

G(u,w) defined by

{ }G u w u w u w u Tw u T w u T wn( , ) , , , , ,...,=

2 2 2 (8.31)

This set of sequences is called the small set of Kasami sequences denoted by Ks(u) inhonor of Kasami, who discovered that the correlation functions for sequences belonging

to Ks(u) take on the values in the set {1, s(n), s(n) 2} with s(n) given by (8.30).

Consequently, for the set Ks(u),

max ( )= = +s nn

1 2 2 (8.32)

Notice that max for the set Ks(u) is approximately one half of the value of max achievedby the sets discussed previously. On the other hand, Ks(u) contains only 2

n/2 = (Nc+1)1/2

sequences, while the sets of Gold code sequences contain Nc +2 sequences. An example

for a shift register configuration that produces a small set of Kasami codes of length Nc= 63 is presented in Figure 8.19. The octal representation of the shift registers

producing u and v are 103 and 15, respectively, h(x) = 1 + x + x6 = 1000011 and h x

( )

= 1 + x2

+ x3

= 1101.

Besides the small sets of Kasami sequences, there are also large sets of Kasami

sequences. Let n be even and let h(x) denote a primitive binary polynomial of degree n

that generates the maximum length sequence u. Let w = u[s(n)] denote a maximum

length sequence of period 2n/2

1 generated by the primitive polynomial h (x) of degree

n/2 and let h x

( ) denote the polynomial of degree n that generates u[t(n)].

Then, the set of sequences of period Nc generated by h(x) h(x) h x

( ) , called thelarge set of Kasami sequences and denoted by KL(u), is as follows:

1. If n = 2 mod 4, then

{ }K u G u v T w G u vL ii

n

( ) ( , ) ( , )=

=

0

2 22

UU (8.33)

where v = u[t(n)] and G(u,v) is defined in (8.28).


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279

h(x) = 1 + x + x6

h x

( ) = 1 + x2

+ x3

Figure 8.19 Shift register configuration for the small set of Kasami codes with length Nc = 63.

2. If n = 0 mod 4 then

{ }K u H u T w H u L t n i t ni

n

( ) ( ) ( )( ) ( )=

=

0

2 22

UU

( ){ }v T w j k j kn( ) : , < 0 2 0 2 113

2U (8.34)

where v(t) is the result of decimating T i(u) by t(n) and Ht(n)(u) is defined as

H u

u u v u Tv u T v

u u v u Tv u T v

u u v u Tv u T v

t n

Nc

Nc

Nc

( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( )

, , , ...,

, , , ...,

, , , ...,=

0 0 1 0

1 1 1 1

2 2 1 2

3

3

3

(8.35)

In either case, the correlation functions for KL(u) take on the values in the set {1,t(n),

t(n) 2, s(n), s(n) 2} and max = t(n). If n = 2 mod 4 then KL(u) contains 2n/2

(2n

+ 1)

sequences while ifn = 0 mod 4, KL(u) contains 2n/2(2n + 1) sequences.

An example of a shift register configuration that produces a large set of Kasami

codes of length Nc = 63 is presented in Figure 8.20. The octal representation of the shift

+

+ +

5 4 23 1 0

2 1 0


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280

registers producing the sequences u, v, and w are 103, 15, and 147, respectively, (h(x) =

1 + x + x6

, h x

( ) = 1 + x2

+ x3, and h (x) = 1 + x + x

2+ x

5+ x

6).

h x

( ) = 1 + x + x6

h(x) = 1 + x2

+ x3

h (x) = 1 + x + x2

+ x5

+ x6

Figure 8.20 Shift register configuration for the large set of Kasami codes with length Nc = 63.

Numerical Examples

Table 8.2 presents a number of examples of PN code sequences. Three types of

sequences are considered. Gold sequences (G), small-set Kasami sequences (KS), and

large-set Kasami sequences (KL). The first column denotes the code length Nc, the third

column shows the maximum number of code sequences per set, and in the fourth

column the values that periodic cross-correlation can take are given. The last three

columns show the octal representation of the polynomials describing the linear binary

shift registers used to generate the desired code sequence. Table 8.2 only shows some

examples for pseudo-random code sequences.

+

+

+

+ + +

5 42 1

03

2 1 0

5 4 3 2 1 0


29/38


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282

Figure 8.21 (a) Periodic autocorrelation and (b) cross-correlation for Gold code with code lengthNc = 127. Generator polynomials 211 and 277 (octal).

Figure 8.22 (a) a-Periodic autocorrelation and (b) cross-correlation for Gold code with codelength Nc = 127. Generator polynomials 211 and 277 (octal).

Chip delay

(a)

Cross-correlation

Chip delay

(b)

Cross-correlation

Autocorrelation

Cross-correlation

Autocorrelation

Autocorrelation

Chip delay

(b)Chip delay

(a)


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283

Figure 8.23 (a) Periodic autocorrelation and (b) cross-correlation for Gold code with Nc = 255.Generator polynomials 717 and 765 (not preferred sequences).

Figure 8.24 (a) Periodic autocorrelation and (b) cross-correlation functions for small-set Kasamicode with Nc=255. Generator polynomials 435 and 023.

Code sequences with length Nc=255 that have better correlation properties arethe Kasami sequences. Figures 8.24(a) and 8.24(b) show the autocorrelation and cross-

correlation of a small set of Kasami codes. Figures 8.25(a) and 8.25(b) show the

autocorrelation and cross-correlation of a large set of Kasami codes.

Cross-correlationAutocorrelation

Chip delay

(a)

Chip delay

(a)

Chip delay

(b)

Chip delay

(b)


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284

Figure 8.25 (a) Periodic autocorrelation and (b) cross-correlation functions for large Kasamicode with Nc = 255. Generator polynomials 435, 023, and 675.

8.3.3 Random Wave Approximation

In a multipath propagation environment such as the indoor radio environment, there is

overlap between shifted data bits of the reference user and of other users. This situation

is depicted in Figure 8.26.

This implies that the receiver suffers from interference caused by both thedesired signal and by the signals from other users. The interference power is determined

by the characteristics of the multipath channel (time delay, phase, and amplitude) and

by the correlation properties of the code sequences used.

b11

t=T b10

t=0 b1-1

b11

b10

b1-1

Figure 8.26 Overlap of bits (and code sequences) due to multipath interference.

Path 1 < j, user 1

Path 1 = j, user 1


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285

The ACF determines the amount of self-interference, while the cross-correlation

between the desired code sequence and code sequences of other users determines theamount of multiuser interference. To simplify these performance calculations, an

approximation of the code sequence characteristics is applied. The starting point for this

approximation is the expression for the correlation variance defined as

a E b R b R= +

1

1

1

0

2

( ) ( )

(8.36)

It is worth mentioning here that the interference power is related to this variance. In

(8.36), b11 and b1

0 are, respectively, the previous and the next bit with values {1,1}

having equal probability of occurrence. The functions R() and R

( ) are the partial

correlation functions. If the delay is a multiple of the chip duration ( = pTc), then theexpressions for the discrete correlation functions are

R pN

a ac

i

k

i p

i

p

( ) =

=

1

10

(8.37)

R pN

a ac

i

k

i p

i p

Nc

( ) =

= +

1

1

1

1

(8.38)

where aki

is the ith code symbol of the sequence of user k and Nc is the length of the

code sequence. To compute the variance in (8.36), we average over all possible time

delays and over all possibilities for b11 and b1

0. The time delays in a multipath

environment are obviously not multiples of the code symbol duration. However, if we

know the discrete correlation function, then the correlation for a non discrete time delay

is very easy to calculate by considering that the correlation function is linear between

two discrete time delays, as shown in Figure 8.27.

To find an expression for the variance in (8.36), we approximate the Gold and

Kasami sequences by a random code sequence consisting of Nc code symbols. For a

random code sequence, the code symbols aki = 1 and aki = 1 occur with equal

probability. Assuming that the data bits are 1 or 1 with equal probability, the variance

in (8.36) is written as

a E R R E R R= +

+

1

2

1

2

2 2

( ) ( ) ( ) ( )

(8.39)

To simplify this expression further, it is instructive to observe one chip of normalized

duration overlapped by another chip with delay . This situation is depicted in Figure8.28.


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286

TC 2TC 3TC 4TC

Figure 8.27 Part of a correlation function.

Figure 8.28 Overlap of two chips, aki

and aki-1

.

For the two chips aki and ak

j1 there are two possibilities: either they have the same sign

or they have opposite sign. Both situations occur with the same probability in case of a

random sequence. The overlap area denoted here by AO determines the contribution ofchip ak

i to the correlation function (normalized on the code length Nc). In the case of

equal bits, the overlap area, normalized on the code length Nis 1/N, while in the case of

unequal bits, the part between 0 and cancels the part between and 2, implying that

the overlap area is (12)/Nc. In terms of the overlap area:

AN

if a ac

k

i

k

i

0

11= =

(8.40)

0 1

aki

akiaki-1

2


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287

A N if a ack

i

k

i

0

11 2

=

=

Now, the expectation ofA02

is calculated by averaging over all possible delays

[ ]E AN N

dNc c c

0

2

2

2

2 2

0

11

2

1 1

2

1 2 2

3= +

=

( ) (8.41)

Now, the final simplified expression for the variance in (8.35) is

[ ]a cc

N E A N= =2

2

3 (8.42)

Before applying this approximation, we verify the approximation for a number of

practical Gold sequences and Kasami sequences. Therefore, a large number of these

code sequences has been generated, and for each combination of code sequences the

expectation of the correlation variance has been calculated by averaging over all

possible delays. The results are shown in Figures 8.29(a) to 8.29(e). To explain these

figures, we use the Gold code of length 31 as an example. The plot shows a number of

bars and a line. The line represents the approximated value for the correlation variance

given by (8.42), and each bar represents the simulated correlation variance between

two code sequences of the same length. Earlier, we found for example that it ispossible to generate 65 code sequences of length 63. For all figures, we only show 50

bars for clarity of the plot. In each plot we first observe a large peak, which is actually

the average correlation variance of the autocorrelation function. All the other bars

present the average correlation variance of cross-correlations with other codes. By

observing Figures 8.29(a) to 8.29(e), it is reasonable to conclude that the approximation

of (8.36) is rather good. To strengthen this conclusion, quantitative results are shown in

Table 8.3.Code correlation varianceCode correlation variance

Code number

(a)

Code number

(b)


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288

Figure 8.29 (a) Gold code (Nc = 31), (b) Kasami code (Nc = 31), (c) Gold code (Nc = 127), (d)

Kasami code (Nc = 255), and (e) Gold code (Nc = 511).

Table 8.3

Quantitative Comparison of Simulation Results and Approximation

for Correlation Variance for Several Practical Code Sequences

Code correlation varianceCode correlation variance

Code correlation variance

Code number

(c)Code number

(d)

Code number(e)


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289

.

8.3.4 Conclusions

In this section, a description was given of three types of pseudo-noise sequences

suitable for DS-CDMA systems. Gold codes and Kasami code sequences are especially

suitable, since it is possible to generate a relatively large number of code sequences

with bounded periodic correlation functions. The basic properties of the code sequences

were discussed and shift register configurations to generate the sequences were shown.

The periodic correlation functions are important when the desired data bit overlaps with

a previous or next data bit having the same sign. In the situation where the previous or

next overlapping bit has the opposite sign, the so-called a-periodic correlation functionis very important. For this a-periodic correlation function, well-defined bounds are

found in literature. However, by simulation, we saw that the peaks in the a-periodic

correlation function can be much larger than the bounded periodic correlation function.

Furthermore, it was shown that Gold code sequences and Kasami code

sequences cannot be generated with arbitrary length. In the first place, the length of a

code sequence can always be written as 2n l where n is an integer. This implies that

we can generate sequences with lengths 31, 63, 127, 255, and so forth. Gold sequences

cannot be generated for integer values n being a multiple of 4. This implies that we

cannot generate Gold sequences with length Nc = 255 since this would imply n = 8,

which is a multiple of 4. On the other hand, Kasami sequences cannot be generated for

odd values of n. For example, Kasami code sequences with length Nc = 127 and Nc =

511 are not possible. Code sequences with these lengths must be generated by a Gold

shift register generation.

PASCAL software was developed to generate Gold sequences and Kasami

sequences. For simplification of performance calculations, an approximation of the

correlation variance is desirable. A very simple expression for this correlation variance

results if we approximate real code sequences of length Nc by random sequences of

length Nc. This approximation has been verified by simulation and the results show that

the approximation is quite good.

Approximation

acN

=2

3

Sample Mean ms Sample Standard Deviation S

Gold code

Nc = 63

0.010582 0.010406 0.002182

Kasami code

Nc = 63

0.010582 0.0119 0.005654

Gold code

Nc = 127

0.005249 0.005553 0.000722

Kasami code

Nc = 255

0.002614 0.0025691 0.000289


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290

REFERENCES

[1] R. Prasad, CDMA for Wireless Personal Communications, Norwood, MA:

Artech House, 1996.

[2] Special issue on spread-spectrum communication, IEEE Trans. Commun., Vol.

COM-30, May 1982.

[3] M.K. Simon, J.K. Omura, R.A. Scholtz, and B.K. Levitt, Spread-spectrum

communications, Vol. I, II, III, Comp. Sci., 1985.

[4] R.A. Scholtz, The spread-spectrum concept, IEEE Trans. Commun., Vol.

COM-25, pp. 748755, August 1977.[5] D.J. Torrieri, Principles of Secure Communication Systems, Norwood, MA:

Artech House, 1985.

[6] G.R. Cooper and C.D. McGillem, Modern Communication and Spread-

Spectrum, New York: McGraw-Hill Company, 1986.

[7] S.G. Glisic and P.A. Leppanen (Eds.), Code Division Multiple Access

Communications, Boston: Kluwer Academic Publishers, 1995.

[8] A.J. Viterbi, CDMA Principles of Spread-Spectrum Communications, Reading,

MA: Addison-Wesley Publishing Company, 1995.

[9] R.C. Dixon, Spread-Spectrum Systems, New York: John Wiley & Sons, 1984.

[10] A.M. Viterbi and A.J. Viterbi, Erlang capacity of a power controlled CDMA

system, IEEE J. Selected Areas in Comm., Vol. 11, pp. 892899, August 1993.

[11] D.P. Sarwate and M.B. Pursley, Crosscorrelation properties of pseudo-random

and related sequences, Proc. IEEE, Vol. 68, No. 5, May 1980.

[12] S.W. Golomb, Shift Register Sequences, San Francisco, CA: Holden-Day, 1967.

[13] J.L. Massey and J.J. Uhran, Jr., Final report for multipath study, Contract

NASS-10786, Univ. Notre Dame, IN, 1969.

[14] R. Gold, Optimal binary sequences for spread spectrum multiplexing, IEEE

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Documents

CDMA Concept