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The book is an introduction to CDMA communication, and emphasizes the role this technology played in the development of wireless communication and cellular mobile radio systems that have arisen in the past decade.

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Meet the Author

KAMIL SH. ZIGANGIROV received his PhD from the Institute of Radio Engineering and Electronics at the USSR Academy of Sciences in 1966. Since then, he has been a visiting scientist at MIT in Cambridge, Massachusetts, at Napoli University in Napoli, Italy, and at the University of Notre Dame, Notre Dame, Indiana. He is currently a professor in the Department of Information Technology at Lund University in Lund, Sweden.

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Theory of Code Division Multiple Access Communication

By Kamil Sh. Zigangirov

John Wiley & Sons

Copyright © 2004 Institute of Electrical and Electronics Engineers
All right reserved.

ISBN: 0-471-45712-4

Chapter One


The subject of this book is code division multiple access (CDMA) communications. A major application of CDMA is wireless communication including mobile radio. In this chapter we introduce the basic concepts of mobile radio systems, including cellular concepts, consider the general structure of a cellular system, and study different principles of multiple-access (time, frequency, and code division) and spread spectrum concepts.

This chapter begins with an overview of the principles of cellular radio systems. Next, given the focus on simultaneous wideband transmission of all users over a common frequency spectrum, we consider direct-sequence CDMA systems, frequency-hopped CDMA systems, and pulse position-hopped CDMA systems. The chapter concludes with a description of this book. The book is devoted to the analysis of different aspects of CDMA communication. Given the rapid and continuing growth of cellular radio systems throughout the world, CDMA digital cellular radio systems will be the widest-deployed form of spread spectrum systems for voice and data communication. It is a major technology of the twenty-first century.


A cellular radio system provides a wireless connection to the public telephone network for any user location within the radio range of the system. The term mobile has traditionally been used to classify a radio terminal that can be moved during communication. Cellular systems accommodate a large number of mobile units over a large area within a limited frequency spectrum. There are several types of radio transmission systems. We consider only full duplex systems. These are communication systems that allow simultaneous two-way communication. Transmission and reception for a full duplex system are typically on two different channels, so the user may constantly transmit while receiving signals from another user.

Figure 1.1 shows a basic cellular system that consists of mobiles, base stations, and a switching center. Each mobile communicates via radio with one or more base stations. A call from a user can be transferred from one base station to another during the call. The process of transferring is called handoff.

Each mobile contains a transceiver (transmitter and receiver), an antenna, and control circuitry. The base stations consist of several transmitters and receivers, which simultaneously handle full duplex communications and generally have towers that support several transmitting and receiving antennas. The base station connects the simultaneous mobile calls via telephone lines, microwave links, or fiber-optic cables to the switching center. The switching center coordinates the activity of all of the base stations and connects the entire cellular system to the public telephone network.

The channels used for transmission from the base station to the mobiles are called forward or downlink channels, and the channels used for transmission from the mobiles to the base station are called reverse or uplink channels. The two channels responsible for call initiation and service request are the forward control channel and reverse control channel.

Once a call is in progress, the switching center adjusts the transmitted power of the mobile (this process is called power control) and changes the channel of the mobile and base station (handoff) to maintain call quality as the mobile moves in and out of range of a given base station.

The cellular concept was a major breakthrough in solving the problem of spectral congestion. It offered high system capacity with a limited spectrum allocation. In a modern conventional mobile radio communication system, each base station is allocated a portion of the total number of channels available to the entire system and nearby base stations are assigned different groups of channels so that all the available channels are assigned to a relatively small number of neighboring base stations. Neighboring base stations are assigned different groups of channels so that interference between the users in different cells is small.

The idealized allocation of cellular channels is illustrated in Figure 1.2, in which the cells are shown as contiguous hexagons. Cells labeled with the same number use the same group of channels. The same channels are never reused in contiguous cells but may be reused by noncontiguous cells. The [kappa] cells that collectively use the complete set of available frequencies is called a cluster. In Figure 1.2, a cell cluster is outlined in bold and replicated over the coverage area. Two cells that employ the same allocation, and hence can interfere with each other, are separated by more than one cell diameter.

The factor [kappa] is called the cluster size and is typically equal to 3, 4, 7, or 12. To maximize the capacity over a given coverage area we have to choose the smallest possible value of [kappa]. The factor 1/[kappa] is called the frequency reuse factor of a cellular system. In Figure 1.2 the cluster size is equal to 7, and the frequency reuse factor is equal to 1/7.


The American analog technology standard, known as Advanced Mobile Phone Service (AMPS), employs frequency modulation and occupies a 30-kHz frequency slot for each voice channel. Suppose that a total of 25-MHz bandwidth is allocated to a particular cellular radio communication system with cluster size 7. How many channels per cell does the system provide?


Allocation of 12.5 MHz each for forward and reverse links provides a little more than 400 channels in each direction for the total system, and correspondingly a little less than 60 per cell.

The other-cell interference can be reduced by employing sectored antennas at the base station, with each sector using different frequency bands. However, using sectored antennas does not increase the number of slots and consequently the frequency reuse factor is not increased.

A multiple access system that is more tolerant to interference can be designed by using digital modulation techniques at the transmitter (including both source coding and channel error-correcting coding) and the corresponding signal processing techniques at the receiver.


Multiple access schemes are used to allow many mobile users to share simultaneously a common bandwidth. As mentioned above, a full duplex communication system typically provides two distinct bands of frequencies (channels) for every user. The forward band provides traffic from the base station to the mobile, and the reverse band provides traffic from the mobile to the base station. Therefore, any duplex channel actually consists of two simplex channels.

Frequency division multiple access (FDMA) and time division multiple access (TDMA) are the two major access techniques used to share the available bandwidth in a conventional mobile radio communication systems.

Frequency division multiple access assigns individual channels (frequency bands) to individual users. It can be seen from Figure 1.3 that each user is allocated a unique frequency band. These bands are assigned on demand to users who request service. During the period of the call, no other user can share the same frequency band. The bandwidths of FDMA channels are relatively narrow (25-30 kHz) as each channel supports only one call per carrier. That is, FDMA is usually implemented in narrowband systems. If an FDMA channel is not in use (for example, during pauses in telephone conversation) it sits idle and cannot be used by other users to increase the system capacity.

Time division multiple access systems divide the transmission time into time slots, and in each slot only one user is allowed to either transmit or receive. It can be seen from Figure 1.4 that each user occupies cyclically repeating wording, so a channel may be thought of as a particular time slot that reoccurs at slot locations in every frame. Unlike in FDMA systems, which can accommodate analog frequency modulation (FM), digital data and digital modulation must be used with TDMA.

TDMA shares a single carrier frequency with several users, where each user makes use of nonoverlapping time slots. Analogously to FDMA, if a channel is not in use, then the corresponding time slots sit idle and cannot be used by other users. Data transmission for users of a TDMA system is not continuous but occurs in bursts. Because of burst transmission, synchronization overhead is required in TDMA systems. In addition, guard slots are necessary to separate users. Generally, the complexity of TDMA mobile systems is higher compared with FDMA systems.


The global system for mobile communications (GSM) utilizes the frequency band 935-960 MHz for the forward link and frequency range 890-915 MHz for the reverse link. Each 25-MHz band is broken into radio channels of 200 kHz. Each radio channel consists of eight time slots. If no guard band is assumed, find the number of simultaneous users that can be accommodated in GSM. How many users can be accommodated if a guard band of 100 kHz is provided at the upper and the lower end of the GSM spectrum?


The number of simultaneous users that can be accommodated in GSM in the first case is equal to

25 · [10.sup.6]/(200 · [10.sup.3])/8 = 1000

In the second case the number of simultaneous users is equal to 992.

Each user of a conventional multiple access system, based on the FDMA or the TDMA principle, is supplied with certain resources, such as frequency or time slots, or both, which are disjoint from those of any other user. In this system, the multiple access channel reduces to a multiplicity of single point-to-point channels. The transmission rate in each channel is limited only by the bandwidth and time allocated to it, the channel degradation caused by background noise, multipath fading, and shadowing effects.

Viterbi pointed out that this solution suffers from three weaknesses. The first weakness is that it assumes that all users transmit continuously. However, in a two-person conversation, the percentage of time that a speaker is active, that is, talking, ranges from 35% to 50%. In TDMA or FDMA systems, reallocation of the channel for such brief periods requires rapid circuit switching between the two users, which is practically impossible.

The second weakness is the relatively low frequency reuse factor of FDMA and TDMA. As we can see from Example 1.1 the frequency reuse factor 1/7 reduces the number of channels per cell in AMPS from 400 to less than 60.

Using antenna sectorization (Fig. 1.5) for reducing interference does not increase system capacity. As an example, a cell site with a three-sectored antenna has an interference that is approximately one-third of the interference received by an omnidirectional antenna. Even with this technique, the interference power received at a given base station from reused channels in other cells is only about 18 dB below the signal power received from the desired user of the same channel in the given cell. Reuse factors as large as 1/4 and even 1/3 have been considered and even used, but decreasing the distance between interfering cells increases the other-cell interference to the point of unacceptable signal quality.

A third source of performance degradation, which is common to all multiple access systems, particularly in terrestrial environments, is fading. Fading is caused by interference between two or more versions of the transmitted signal that arrive at the receiver at slightly different time. This phenomenon is particularly severe when each channel is allocated a narrow bandwidth, as for FDMA systems.


A completely different approach, realized in CDMA systems, does not attempt to allocate disjoint frequency or time resources to each user. Instead the system allocates all resources to all active users.

In direct sequence (DS) CDMA systems, the narrowband message signal is multiplied by a very large-bandwidth signal called the spreading signal. All users in a DS CDMA system use the same carrier frequency and may transmit simultaneously. Each user has its own spreading signal, which is approximately orthogonal to the spreading signals of all other users. The receiver performs a correlation operation to detect the message addressed to a given user. The signals from other users appear as noise due to decorrelation. For detecting the message signal, the receiver requires the spreading signal used by the transmitter. Each user operates independently with no knowledge of the other users (uncoordinated transmission).

Potentially, CDMA systems provide a larger radio channel capacity than FDMA and TDMA systems. The radio channel capacity (not to be confused with Shannon's channel capacity, see Chapter 8) can be defined as the maximum number [K.sub.0] of simultaneous users that can be provided in a fixed frequency band. Radio channel capacity is a measure of the spectrum efficiency of a wireless system. This parameter is determined by the required signal-to-noise ratio at the input of the receiver and by the channel bandwidth W.

To explain the principle of DS CDMA let us consider a simple example. Suppose that two users, user 1 and user 2, located the same distance from the base station, wish to send the information (or data) sequences [u.sup.(1)] = [u.sup.(1).sub.0], [u.sup.(1).sub.1], [u.sup.(1).sub.2], [u.sup.(1).sub.3] = 1, -1, -1, 1 and [u.sup.(2)] = [u.sup.(2).sub.0], [u.sup.(2).sub.1], [u.sup.(2).sub.2], [u.sup.(2).sub.3] = -1, 1, -1, -1, respectively, to the base station. First, user 1 maps the data sequence [u.sup.(1)] into the data signal [u.sup.(1)](t), and user 2 maps [u.sup.(2)] into the data signal [u.sup.(2)](t), such that the real number 1 corresponds to a positive rectangular pulse of unit amplitude and duration T, and the real number -1 corresponds to a negative rectangular pulse of the same amplitude and same duration (Fig. 1.6a). Then both users synchronously transmit the data signals over the multiple access adding channel. Because each pulse corresponds to the transmission of one bit, the transmission rate R = 1/T (bit/s) for each user and the overall rate is 2/T (bit/s).


Excerpted from Theory of Code Division Multiple Access Communication by Kamil Sh. Zigangirov Copyright © 2004 by Institute of Electrical and Electronics Engineers . Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

Preface ix

1 Introduction to Cellular Mobile Radio Communication 1

2 Introduction to Spread Spectrum Communication Systems 36

3 Reception of Spread Spectrum Signals in AWGN Channels 86

4 Forward Error Control Coding in Spread Spectrum Systems 137

5 CDMA Communication on Fading Channels 186

6 Pseudorandom Signal Generation 229

7 Synchronization of Pseudorandom Signals 255

8 Information-Theoretical Aspects of CDMA Communications 300

9 CDMA Cellular Networks 342

Appendix A: Analysis of the Moments of the Decision Statistics for the FH CDMA Communication System 385

Bibliography 390

Index 395

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