Synthesis Lectures on Communications
`
`© SYNTHESIS
`COLLECTION OF TECHNOLOGY
`
`Code Division Multiple
`Access (CDMA)
`
`1
`
`APPLE 1022
`Apple v. Ericsson
`IPR2022-00343
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`APPLE 1022
`Apple v. Ericsson
`IPR2022-00343
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`1
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`

`Code Division Multiple Access
`Code Division Multiple Access
`(CDMA)
`(CDMA)
`
`2
`
`

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`Code(cid:2)Division(cid:2)Multiple(cid:2)Access(cid:2)(CDMA)(cid:2)
`R.(cid:2)Michael(cid:2)Buehrer
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`A(cid:2)Publication(cid:2)in(cid:2)the(cid:2)(cid:55)(cid:84)(cid:86)(cid:77)(cid:82)(cid:75)(cid:73)(cid:86)(cid:2)series
`SYNTHESIS(cid:1)LECTURES(cid:1)ON(cid:1)COMMUNICATIONS(cid:1)#2
`
`Lecture #2
`Series Editor: William Tranter, Virginia Tech
`
`Series ISSN: 1932-1244 print
`Series ISSN: 1932-1708
`electronic
`
`First Edition
`10 9 8 7 6 5 4 3 2 1
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`3
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`

`

`Code Division Multiple Access
`(CDMA)
`
`R. Michael Buehrer
`Virginia Polytechnic Institute and State University,
`Blacksburg, Virginia, USA
`
`SYNTHESIS LECTURES ON COMMUNICATIONS #2
`
`Morgan Claypool Publishers
`
`4
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`

`

`iv
`
`ABSTRACT
`This book covers the basic aspects of Code Division Multiple Access or CDMA. It begins
`with an introduction to the basic ideas behind fixed and random access systems in order to
`demonstrate the difference between CDMA and the more widely understood TDMA,
`FDMA or CSMA. Secondly, a review of basic spread spectrum techniques is presented which
`are used in CDMA systems including direct sequence, frequency-hopping, and time-hopping
`approaches. The basic concept of CDMA is presented, followed by the four basic principles
`of CDMA systems that impact their performance: interference averaging, universal frequen-
`cy reuse, soft handoff, and statistical multiplexing. The focus of the discussion will then shift
`to applications. The most common application of CDMA currently is cellular systems. A
`detailed discussion on cellular voice systems based on CDMA, specifically IS-95, is present-
`ed. The capacity of such systems will be examined as well as performance enhancement tech-
`niques such as coding and spatial filtering. Also discussed are Third Generation CDMA cel-
`lular systems and how they differ from Second Generation systems. A second application of
`CDMA that is covered is spread spectrum packet radio networks. Finally, there is an exami-
`nation of multi-user detection and interference cancellation and how such techniques impact
`CDMA networks. This book should be of interest and value to engineers, advanced students,
`and researchers in communications.
`
`KEYWORDS
`CDMA, Multiple Access, Spread Spectrum, Multiuser Detection, TDMA, FDMA, Packet
`Radio Networks
`
`5
`
`

`

`This book is dedicated to those who patiently waited for me to finish: My wife Andrea and
`our children, Faith, JoHannah, Noah, Gabrielle and Ruth.
`
`6
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`

`

`vi
`
`Contents
`
`1. Multiuser Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
`1.1 Conflict-Free Medium Access Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
`1.1.1 Time Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
`1.1.2
`Frequency Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
`1.1.3 Code Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
`1.1.4 Traffic Engineering and Trunking Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 8
`1.1.5
`Frequency Reuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
`1.2 Contention-Based Medium Access Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
`1.2.1 ALOHA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
`1.2.2 Carrier Sense Multiple Access and Carrier Sense Multiple
`Access/Collision Avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
`1.2.3 Other Random Access Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
`1.3 Multiple Access with Spread Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
`1.4
`Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
`
`2.
`
`2.3
`
`Spread Spectrum Techniques for Code Division Multiple Access . . . . . . . . . . . . . . . . 23
`2.1
`Forms of Code Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
`2.2 Direct Sequence Code Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
`2.2.1
`Power Spectral Density of Direct Sequence Spread Spectrum . . . . . . . . 27
`2.2.2 Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
`Frequency Hopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
`2.3.1
`Slow Versus Fast Hopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
`2.3.2
`Power Spectral Density of Frequency-Hopped
`Spread Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
`2.3.3 Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
`2.4 Time Hopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
`2.5 Link Performance of Direct Sequence Spread Spectrum in Code
`Division Multiple Access. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
`2.5.1 Additive White Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
`2.5.2 Multipath Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
`2.5.3
`Impact of Bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
`
`7
`
`

`

`CONTENTS vii
`
`2.6 Multiple Access Performance of Direct Sequence Code
`Division Multiple Access. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56
`2.6.1 Gaussian Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
`2.6.2
`Improved Gaussian Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
`2.7 Link Performance of Frequency-Hopped Spread Spectrum . . . . . . . . . . . . . . . . . . 64
`2.8 Multiple Access Performance of Frequency-Hopped
`Code Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
`Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
`
`2.9
`
`Cellular Code Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
`3.1
`Principles of Cellular Code Division Multiple Access . . . . . . . . . . . . . . . . . . . . . . . 73
`3.1.1
`Interference Averaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
`3.1.2
`Frequency Reuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
`3.1.3
`Soft Hand-Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
`3.1.4
`Statistical Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
`3.2 Code Division Multiple Access System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 83
`3.3 Capacity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85
`3.3.1 Comparison of Multiple Access Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 85
`3.3.2
`Second-Order Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
`3.3.3 Capacity–Coverage Trade-Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
`3.3.4 Erlang Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
`3.4 Radio Resource Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
`3.4.1
`Power Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .100
`3.4.2 Mobile-Assisted Soft Hand-Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
`3.4.3 Admission Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
`3.4.4 Load Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
`Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110
`
`3.5
`
`Spread Spectrum Packet Radio Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
`4.1 Code Assignment Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
`4.1.1 Common-Transmitter Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
`4.1.2 Receiver-Transmitter Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
`4.2 Channel Access Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
`4.3 Direct Sequence Packet Radio Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
`4.4
`Frequency-Hopped Packet Radio Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
`4.4.1
`Perfect Side Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
`4.4.2 No Side Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
`Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .124
`
`4.5
`
`3.
`
`4.
`
`8
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`

`

`viii CONTENTS
`5. Multiuser Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127
`5.1
`System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
`5.2 Optimal Multiuser Reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
`5.3 Linear Sub-Optimal Multiuser Reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
`5.3.1 The Decorrelating Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
`5.3.2 Linear Minimum Mean Squared Error Receiver . . . . . . . . . . . . . . . . . . . 137
`5.4 Non-Linear Sub-Optimal Receivers: Decision Feedback . . . . . . . . . . . . . . . . . . . 137
`5.4.1 Decorrelating Decision Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
`5.4.2
`Successive Interference Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
`5.4.3
`Parallel Interference Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
`5.4.4 Multistage Receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
`5.5 A Comparison of Sub-Optimal Multiuser Receivers . . . . . . . . . . . . . . . . . . . . . . . 156
`5.5.1 AWGN Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
`5.5.2 Near-Far Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
`5.5.3 Rayleigh Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
`5.5.4 Timing Estimation Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
`5.6 Application Example: IS-95. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .162
`5.6.1
`Parallel Interference Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
`5.6.2
`Performance in an Additive White Gaussian Noise Channel . . . . . . . . 167
`5.6.3 Multipath Fading and Rake Reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
`5.6.4 Voice activity, power control, and coding . . . . . . . . . . . . . . . . . . . . . . . . . . 168
`5.6.5 Out-of-Cell Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
`Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
`
`5.7
`
`9
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`

`ix
`
`Preface
`
`The objective of this book is to provide the reader with a concise introduction to the use
`of spread spectrum waveforms in multiple user systems, often termed code division multiple
`access or CDMA. The book has been an outgrowth of course notes presented in a graduate-
`level course on spread spectrum communications. This book should provide sufficient material
`to cover CDMA systems within a graduate-level course on spread spectrum, advanced digital
`communication, or multiple access. The text should also be useful for working engineers who
`desire a basic understanding of the fundamental concepts underlying CDMA.
`The reader of this book is expected to have a fundamental understanding of digital com-
`munications and some understanding of wireless systems in general. Additionally, readers are
`assumed to be generally familiar with basic stochastic processes, detection theory, and commu-
`nication theory. The book builds on these fundamentals by explaining how spread spectrum
`systems differ from standard digital communication systems and, more importantly, how spread
`spectrum waveforms can be used as a means of channelization in a multiple user scenario.
`The book covers the basic aspects of CDMA. In Chapter 1, the basic ideas behind
`conflict-free and contention-based systems are introduced to demonstrate the difference be-
`tween CDMA and more widely understood orthogonal access techniques such as time division
`multiple access and frequency division multiple access. Additionally, random access schemes
`such as carrier sense multiple access are examined.
`In Chapter 2, basic spread spectrum techniques that are used in CDMA systems are
`reviewed, including direct sequence spread spectrum, frequency-hopped spread spectrum, and
`time-hopping approaches. Both the link performance of such waveforms (in additive white
`Gaussian noise channels and fading channels) as well as the multiple access performance are
`examined. Special emphasis is given to fading channels since spread spectrum is more advanta-
`geous in these channels.
`Once the basic concept of CDMA is presented, Chapter 3 focuses on cellular CDMA
`systems. Specifically, four basic principles of cellular CDMA systems are presented, and their
`impact on the performance of CDMA is explained. These four basic concepts include interfer-
`ence averaging, universal frequency reuse, soft hand-off, and statistical multiplexing. While the
`discussion is general, the CDMA cellular standard IS-95 is often used as an example. Addi-
`tionally, important CDMA system functions (often termed radio resource management tech-
`niques), such as power control, mobile-assisted hand-off, load control, and admission control, are
`
`10
`
`

`

`x PREFACE
`examined. Finally, the capacity of CDMA cellular systems on both the uplink and downlink is
`derived, emphasizing the differences between the links.
`Spread spectrum waveforms are used not only in fixed access techniques such as in cellular
`systems, but also for multiple access in packet radio networks (PRNs). Chapter 4 discusses
`spread spectrum based PRNs emphasizing the differences between PRNs and their better
`known cellular counterparts. A primary emphasis is on spreading code assignment techniques,
`which is crucial in non-centralized systems.
`Finally, Chapter 5 focuses on multiuser detection. A primary limitation of CDMA link
`performance and system capacity is in-cell multiple access interference (MAI). Multiuser de-
`tection is one means of mitigating MAI on the uplink of CDMA systems. The discussion of
`multiuser detection algorithms is broken down into two basic categories: linear techniques and
`non-linear techniques. Linear techniques discussed include the decorrelating detector and the
`minimum mean square error detector. Among the non-linear approaches examined, parallel in-
`terference cancellation and successive interference cancellation are the most prominent. Finally,
`all these techniques are compared, the benefits and detriments of each approach are mentioned,
`and the application of multiuser detection to the IS-95 cellular standard is examined.
`I would like to acknowledge the many students who helped make this book possible.
`First, I would like to thank all of the students who have taken my spread spectrum course for
`their comments and input. I would also like to specifically thank several graduate students who
`helped with various plots and simulations including (but certainly not limited to) Ihsan Akbar,
`Dan Hibbard, Jihad Ibrahim, Nishant Kumar, Rekha Menon, and Swaroop Venkatesh as well
`as former colleagues at Bell Labs, especially Steve Nicoloso and Rob Soni for their assistance
`in Section 5.6. I also want to thank Lori Hughes for her many hours of editing that (or is it
`“which”?) greatly improved the initial manuscript.
`
`11
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`

`1
`
`C H A P T E R 1
`Multiuser Communications
`
`All communication systems that support multiple users must have a set of protocols to allow
`these multiple users to share a common access medium. This single-access medium may be
`explicitly shared or broken up into smaller pieces, termed channels, that must also be shared.
`A logical channel can be defined as some fraction of the available access medium that is used
`by a particular transmit/receive pair. The system may contain only a single channel or tens of
`channels. However, in either case, the number of possible transmit/receive pairs in the system
`typically far outweighs the number of channels that are available. Thus, communication systems
`must have some mechanism for sharing the available channels among active transmit/receive
`pairs. This mechanism is termed multiple access control or sometimes medium access. Many meth-
`ods exist for providing multiple access, and we will briefly examine the major techniques in
`this chapter. However, the focus of this book is one specific multiple access technique termed
`code division multiple access or CDMA, which is inherently associated with spread spectrum
`communication techniques. Since spread spectrum was developed as a military technology,
`CDMA techniques traditionally have been limited to military systems [1]. However, since the
`early 1990s, CDMA has been heavily investigated for commercial systems. Of particular note is
`the success that CDMA has experienced in commercial cellular systems. The first commercial
`CDMA standard, IS-95, pioneered by Qualcomm, Inc., was one of the three major second
`generation cellular standards and led to a third generation of cellular systems that was domi-
`nated by CDMA techniques (at least for voice services). However, before we discuss CDMA
`in detail, we must first discuss the more general concept of multiple access.
`Two basic classes of multiple access are illustrated in Figure 1.1 [2]: contention-based
`techniques and conflict-free techniques. Conflict-free multiple access involves some type of
`reservation scheme in which the resources are divided into multiple channels. These channels are
`then reserved (through some other mechanism) for use by transmit/receive pairs for the duration
`of their communication. On the other hand, contention-based multiple access techniques allow
`no reservation. Instead, users must contend for the system resources whenever communication
`takes place. Such systems typically use the entire access medium as a single channel, although
`multi-channel versions are certainly possible. Both types of systems have several variations and
`
`12
`
`

`

`2 CODE DIVISION MULTIPLE ACCESS (CDMA)
`
`Multiple access
`techniques
`
`Contention-based
`
`Conflict-free
`
`Random
`access
`
`ALOHA,
`CSMA,
`CSMA/CA,
`RTS/CTS,
`etc.
`
`Collision
`resolution
`
`TREE,
`WINDOW,
`etc.
`
`FIGURE 1.1: Multiple access techniques.
`
`TDMA,
`CDMA,
`FDMA,
`Token Bus,
`etc.
`
`provide benefits for different types of traffic. We will now discuss the two major classes of
`multiple access.
`
`CONFLICT-FREE MEDIUM ACCESS CONTROL
`1.1
`As mentioned previously, contention-free (or conflict-free) multiple access involves the division
`of system resources (i.e., the access medium) into fixed channels, which are then reserved
`by transmit/receive pairs for communication. In this way, users are guaranteed a channel for
`the duration of their communication. This type of multiple access is particularly beneficial for
`applications that require continuous, regular access to a channel, such as voice or video. However,
`for bursty data sources, such a scheme is inefficient because the channel is very often unused
`while it is reserved. The main difference between the types of contention-free multiple access is
`in how the channels are defined. In time division multiple access (TDMA), channels are defined
`according to time slots. In frequency division multiple access (FDMA), channels are defined
`according to frequency bands, and in CDMA, channels are defined not by time or frequency
`but by a spread spectrum parameter known as a spreading code. We will briefly review each type.
`
`13
`
`

`

`MULTIUSER COMMUNICATIONS 3
`
`1.1.1 Time Division Multiple Access
`TDMA systems define channels according to time slot. In other words, system time is defined as
`a series of repeating, fixed-time intervals (often called frames) that are further divided into a fixed
`number of smaller time periods called slots. When a transmit/receive pair is given permission
`to communicate, it is assigned a specific time slot in which to do so. Every time frame, each
`transmit/receive pair may communicate during its slot. An example is given in Figure 1.2 for
`four time slots. Typically, all users are given an opportunity to transmit once during a frame.
`Thus, the total frame is made up of K user slots and K guard times where K is the number
`of transmitters actively accessing the medium or equivalently the number of channels. Guard
`times are inserted to prevent collisions due to imperfect synchronization. The user throughput
`is a function of the overall system transmission rate and the number of time slots available (i.e.,
`the fraction of time they are permitted to transmit).
`
`User 1
`
`User 2
`
`User 3
`
`User 4
`
`Rx
`
`User
`1
`
`User
`2
`
`User
`3
`
`User
`4
`
`User
`1
`
`User
`2
`
`Time
`
`FIGURE 1.2: Example of a four-user TDMA system.
`
`Guard time
`
`14
`
`

`

`4 CODE DIVISION MULTIPLE ACCESS (CDMA)
`The example in Figure 1.2 demonstrates a centralized system in which multiple users
`communicate to a single receiver.1 A decentralized system can also use TDMA, but providing
`strict time synchronization in a large, decentralized system can be very challenging. Additionally,
`the example given shows only one side of the communication (mobile to base station) and
`inherently assumes frequency division duplex (FDD) operation in which the channels from the
`centralized transmitter to the distributed receivers occur on a different frequency channel. This
`second band is also divided into time slots for transmission to the separate users. However,
`TDMA systems can also use time division duplex (TDD) in which time is broken into two
`consecutive frames; the first time frame is used for uplink (or downlink) transmission, and the
`second time frame is used for downlink (or uplink) transmission.
`In a pure TDMA system, each transmitter occupies the entire bandwidth when transmit-
`ting. The system bit rate RS
`b is the rate at which each user transmits when accessing the channel.
`Ignoring guard times, the data rate per user is Rb = (RS
`b )/K , where K is the number of time
`slots per frame. If guard times are included, the relationship is a little more complicated. The
`time allocated per channel is simply equal to (Tf /K ) − Tg where Tf is the frame duration, K
`(cid:3)
`(cid:2)
`is the number of time slots (i.e., channels), and Tg is the guard time. The data rate per channel
`is equal to the number of bits transmitted per user divided by the frame duration. Thus,
`− Tg
`Tf
`− Tg
`Tf
`Clearly, we wish to have a small guard time to improve the efficiency of the system. How-
`ever, practical considerations limit the minimum size of Tg . The bandwidth of the system is
`proportional to the system data rate:
`
`Rb =
`= R S
`b
`K
`
`Tf
`K
`
`R S
`b
`
`R S
`b
`
`(1.1)
`
`b
`
`α
`
`BS ∝ R S
`k
`where k is the number of bits per symbol and α is a constant related to the filtering, pulse shape,
`and modulation scheme.
`There are advantages and disadvantages of TDMA as compared to other multiple ac-
`cess schemes. One advantage of the scheme is that it requires only a single radio frequency/
`intermediate frequency (RF/IF) section since all channels have the same frequency character-
`istics. Another advantage of TDMA is the ease with which variable data rates and asymmetric
`
`(1.2)
`
`1Note that the transmission from distributed users to a single receiver is typically referred to as the uplink while
`transmission from the centralized transmitter to the distributed receivers is termed the downlink.
`
`15
`
`

`

`MULTIUSER COMMUNICATIONS 5
`links are accommodated. Variable data rates can be assigned by simply assigning multiple time
`slots to a single transmit/receive pair. Asymmetric links can be accommodated by changing the
`relative duration of uplink and downlink time slots. The relationship between the user-specific
`data rate and the overall system data rate is further illustrated in the following example.
`
`Example 1.1. A TDMA system is to be designed with ten channels and a guard time of 50μs.
`If quadrature phase shift keying (QPSK) modulation is used, what system symbol rate is needed
`to achieve a data rate of 200kbps with a frame duration 10ms?
`
`Solution: The frame duration Tf
`is 10ms. Due to guard time, the total time available for
`transmission is 10ms − 10 ∗ 50μs = 9.5ms. The transmission time per channel is thus
`= 0.95ms
`9.5ms
`10
`
`(1.3)
`
`(1.4)
`
`(1.5)
`
`The required system data rate is then
`
`RS
`b
`
`Alternatively, from (1.1),
`
`= 10ms ∗ 200kbps
`
`0.95ms
`
`= 2.105Mbps
`
`= Rb
`− Tg
`
`1K
`
`Tf
`
`RS
`b
`
`= 200 kbps
`0.1 − 0.005
`= 2.105 Mbps
`Using QPSK (two bits per symbol), the symbol rate needed is 2.105/2 = 1.05Msps.
`
`1.1.2 Frequency Division Multiple Access
`The second major type of contention-free multiple access is FDMA in which channels are
`defined according to frequency allocation. Thus, all transmitters are active simultaneously but
`occupy different segments of the RF spectrum as illustrated in Figure 1.3. In an FDMA system,
`the bandwidth per user is simply related to the data rate and modulation scheme used. The total
`bandwidth of the system is BS = K ∗ B where K is the number of channels and B = α(Rb /k)
`(cid:5)
`is the bandwidth per channel ignoring guard bands. With guard bands, we have
`B + Bg
`
`BS = K ∗(cid:4)
`
`(1.6)
`
`where Bg is the size of the guard band.
`The efficiency of TDMA and FDMA are essentially the same, with slight differences
`depending on the guard times/bands required. Both techniques are referred to as orthogonal
`
`16
`
`

`

`6 CODE DIVISION MULTIPLE ACCESS (CDMA)
`
`FIGURE 1.3: Example of three-channel FDMA system.
`
`multiple access techniques since, ideally, there is no interference between channels. An advantage
`of FDMA over TDMA is the substantial reduction in the required symbol rate. Another
`advantage of the FDMA is that no tight synchronism between users is required and strict
`isolation between channels is relatively easy to maintain with properly designed filters and
`tuners. However, disadvantages include the fact that with a larger number of channels the IF
`filter (used to select the channel of interest) must be fairly narrow and allocating variable data
`rates requires multiple receive filters.
`
`1.1.3 Code Division Multiple Access
`As we have seen from the previous two sections, a key to contention-free multiple access is the
`definition of orthogonal channels. Orthogonal channels are channels in which a system user can
`communicate without causing interference to another user. The orthogonality can be created
`either in the time domain or in the frequency domain. In TDMA, users simply transmit at
`different times, thus maintaining orthogonality in the time domain. In FDMA, users transmit
`in different frequency bands, which creates orthogonality in the frequency domain since receivers
`can filter out unwanted frequency bands. In reality, the channels in these access techniques are
`
`17
`
`

`

`MULTIUSER COMMUNICATIONS 7
`not truly orthogonal due to imperfect filters or imperfect time synchronization, but the cross-
`channel interference is very small.
`In CDMA systems, channels are defined not by time or frequency but by code. Spread
`spectrum systems (as we will see in more detail in Chapter 2) rely on pseudo-random waveforms
`termed spreading codes to create noise-like transmissions. If users can be given different codes
`that have low cross-correlation properties, channels can be defined by those codes. To better
`(cid:6)
`understand this, let us consider an FDMA system with two channels. Assuming a linear
`modulation scheme, the transmit signals from two distinct users can be written as
`(cid:6)
`s 1 (t) =
`2P1b1 (t) cos (ω1t + θ1)
`2P2b2 (t) cos (ω2t + θ2)
`s 2 (t) =
`where Pi, bi (t), ωi, and θi are the transmit power, data signal, transmit frequency, and random
`phase offset for the ith user, respectively. Now consider the received signal (normalized so that
`the desired signal is received at maximum power) at user 1:
`r1 (t) = s 1 (t) +
`P LRs 2 (t) + n (t)
`where P LR is the relative path loss between transmitter 2 and receiver 1 and n (t) is additive
`white Gaussian noise (AWGN). Now, assuming square pulses for simplicity, the output of the
`matched filter receiver at user 1 for an arbitrary symbol period is
`r1 (t) cos (ω1t + θ1) dt
`Z = 1
`T
`0
`where T is the data symbol period and we have examined the first symbol period. Provided
`that |ω1 − ω2| (cid:4) T, the signal s 2(t) will produce no response to the filter matched to signal
`s 1(t). Thus, we can say that the channels are orthogonal. We can write similar equations for
`TDMA where the channels are defined by a time slot. However, in CDMA, the channels are
`defined by spreading codes. For example, with direct sequence CDMA (DS-CDMA), the two
`signals can be defined by
`
`(cid:6)
`
`(cid:7)
`
`T
`
`(1.7a)
`(1.7b)
`
`(1.8)
`
`(1.9)
`
`(cid:6)
`(cid:6)
`2P1a1 (t) b1(t) cos (ω1t + θ1)
`s 1(t) =
`2P2a2 (t) b2(t) cos (ω1t + θ2)
`s 2(t) =
`where a1(t) and a2(t) are spreading codes that define the