`
`Addison-Wesley Wireless CommunicationsSeries
`
`
`Principlesof
`Spread
`Spectrum
`Communication
`
`Andrew J. Viterbi
`
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`

`

`Principles of
`Spread Spectrum
`Communication
`
`Andrew J. Viterbi
`
`A
`vv
`ADDISON-WESLEY PUBLISHING COMPANY
`Reading, Massachusetts - Menlo Park, California . New York . Don Mills, Ontario
`Wokingham, England . Amsterdam - Bonn . Sydney - Singapore - Tokyo - Madrid
`San Juan - Paris . Seoul . Milan . Mexico City . Taipei
`
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`

`

`Manyofthe designations used by manufacturers andsellers to distinguish their
`products are claimed as trademarks. Wherethose designations appearin this book
`and Addison-Wesley was awareof a trademark claim, the designations have been
`printed in initial caps orall caps.
`The publisheroffers discounts on this book when ordered in quantity for special
`sales. For more information please contact:
`Corporate & Professional Publishing Group
`Addison-Wesley Publishing Company
`One Jacob Way
`Reading, Massachusetts 01867
`
`Library of Congress Cataloging-in-Publication Data
`Viterbi, Andrew J.
`CDMA:principles of spread spectrum communication / Andrew J. Viterbi.
`p. cm.
`Includes bibliographical references and index.
`ISBN 0-201-63374-4
`1. Code division multiple access.I. Title.
`TK5103.45.V57 1995
`321.3845—dc20
`
`94-23800
`CIP
`
`Copyright © 1995 by Addison-Wesley Publishing Company
`All rights reserved. No part of this publication may be reproduced, stored ina
`retrieval system, or transmitted, in any form, or by any means,electronic, mechan-
`ical, photocopying, recording, or otherwise, without the prior consent of the pub-
`lisher. Printed in the United States of America. Published simultaneously in Can-
`ada.
`
`Text design by Wilson Graphics & Design (Kenneth J. Wilson)
`
`ISBN 0-201-63374-4
`Text printed on recycled and acid-free paper.
`123456789 10 MA 979695
`First Printing, April 1995
`
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`

`

`CONTENTS
`
`List of Figures and Tables xiii
`Preface xvii
`
`INTRODUCTION
`
`1.1 Definition and Purpose 1
`1.2 Basic Limitations of the Conventional Approach 2
`1.3 Spread Spectrum Principles 4
`1.4 Organization of the Text 8
`
`RANDOM AND PSEUDORANDOMSIGNAL
`GENERATION
`
`2.1 Purpose 11
`2.2 Pseudorandom Sequences 12
`2.2.1 Maximal Length Linear Shift Register Sequences 12
`2.2.2 Randomness Properties of MLSR Sequences 19
`2.2.3 Conclusion 22
`2.3 Generating Pseudorandom Signals (Pseudonoise) from
`Pseudorandom Sequences 23
`2.3.1 First- and Second-OrderStatistics of Demodulator Output
`in Multiple Access Interference 26
`2.3.2 Statistics for QPSK Modulation by Pseudorandom
`Sequences 29
`2.3.3 Examples 31
`2.3.4 Bound for Bandlimited Spectrum 33
`2.4 Error Probability for BPSK or QPSK with Constant Signals in
`Additive Gaussian Noise and Interference 34
`Appendix 2A: Optimum ReceiverFilter for Bandlimited Spectrum 37
`
`SYNCHRONIZATION OF PSEUDORANDOMSIGNALS
`
`3.1 Purpose 39
`3.2 Acquisition of Pseudorandom Signal Timing 39
`3.2.1 Hypothesis Testing for BPSK Spreading 40
`
`vii
`
`[rrr
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`viii
`
`Contents
`
`3.2.2 Hypothesis Testing for QPSK Spreading 44
`3.2.3 Effect of Frequency Error 45
`3.2.4 Additional Degradation When N Is Much Less Than One
`Period 48
`
`3:3
`
`3.4
`
`Detection and False Alarm Probabilities 48
`3.3.1 Fixed Signals in Gaussian Noise (L = 1) 49
`3.3.2 Fixed Signals in Gaussian Noise with Postdetection
`Integration (L > 1) 50
`3.3.3 Rayleigh Fading Signals (L = 1) 51
`The Search Procedure and Acquisition Time 52
`3.4.1 Single-Pass Serial Search (Simplified) 53
`3.4.2 Single-Pass Serial Search (Complete) 56
`3.4.3 Multiple Dwell Serial Search 58
`Time Tracking of Pseudorandom Signals 60
`3.5.1 Early—Late Gate MeasurementStatistics 61
`3.5.2 Time Tracking Loop 63
`Carrier Synchronization 67
`Appendix 3A: Likelihood Functions and Probability Expressions 68
`3A.1 Bayes and Neyman-—Pearson Hypothesis Testing 68
`3A.2 Coherent Reception in Additive White Gaussian Noise 69
`3A.3 Noncoherent Reception in AWGNfor Unfaded Signals 70
`3A.4 Noncoherent Reception of Multiple Independent
`Observations of Unfaded Signals in AWGN 72
`3A.5 Noncoherent Reception of Rayleigh-Faded Signals in
`AWGN 74
`
`3.0
`
`3.6
`
`MODULATION AND DEMODULATIONOF SPREAD
`SPECTRUM SIGNALS IN MULTIPATH AND MULTIPLE
`ACCESS INTERFERENCE
`
`~ 41
`
`4.2
`
`Purpose 77
`Chernoff and Bhattacharyya Bounds 77
`4.2.1 Bounds for Gaussian Noise Channel 79
`4.2.2 Chernoff Bound for Time-Synchronous Multiple Access
`Interference with BPSK Spreading 80
`4.2.3 Chernoff Bound for Time-Synchronous Multiple Access
`Interference with QPSK Spreading 82
`4.2.4 Improving the Chernoff Bound by a Factor of 2 83
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`Contents
`
`ix
`
`4.3 Multipath Propagation: Signal Structure and Exploitation 84
`44 Pilot-Aided Coherent Multipath Demodulation 87
`4.4.1 Chernoff Bounds on Error Probability for Coherent
`Demodulation with Known Path Parameters 92
`4.4.2 Rayleigh and Rician Fading Multipath Components 93
`4.5 Noncoherent Reception 96
`4.5.1 Quasi-optimum Noncoherent Multipath Reception for
`M-ary Orthogonal Modulation 97
`4.5.2 Performance Bounds 105
`4.6 Search Performance for Noncoherent Orthogonal M-ary
`Demodulators 108
`
`4.7 Power Measurementand Control for Noncoherent Orthogonal
`M-ary Demodulators 113
`4.7.1 Power Control Loop Performance 116
`4.7.2 Power Control Implications 118
`Appendix 4A: Chernoff Bound with Imperfect Parameter
`Estimates 120
`
`5 CODING AND INTERLEAVING
`
`5.1 Purpose 123
`5.2 Interleaving to Achieve Diversity 123
`5.3 Forward Error Control Coding— Another Meansto Exploit
`Redundancy 126
`5.3.1 Convolutional Code Structure 127
`5.3.2 Maximum Likelihood Decoder—Viterbi Algorithm 132
`5.3.3 Generalization of the Preceding Example 139
`5.4 Convolutional Code Performance Evaluation 140
`5.4.1 Error Probability for Tailed-off Block 140
`5.4.2 Bit Error Probability 142
`5.4.3 Generalizations of Error Probability Computation 143
`5.4.4 Catastrophic Codes 149
`5.4.5 Generalization to Arbitrary Memoryless Channels —
`Coherent and Noncoherent 151
`5.4.6 Error Boundsfor Binary-Input, Output-Symmetric
`Channels with Integer Metrics 152
`5.5 A Near-Optimal Class of Codes for Coherent Spread Spectrum
`Multiple Access 155
`5.5.1 Implementation 155
`
`hppaEETees
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`x
`
`Contents
`
`5.6
`
`5.5.2 Decoder Implementation 157
`5.5.3 Generating Function and Performance 159
`5.5.4 Performance Comparison and Applicability 164
`Orthogonal Convolutional Codes for Noncoherent Demodulation
`of Rayleigh Fading Signals 167
`5.6.1 Implementation 167
`5.6.2 Performance for L-Path Rayleigh Fading 168
`5.6.3 Conclusions and Caveats 171
`Appendix 5A: Improved Bounds for Symmetric Memoryless
`Channels and the AWGN Channel 173
`Appendix 5B: Upper Bound on Free Distance of Rate 1/n
`Convolutional Codes 176
`
`CAPACITY, COVERAGE, AND CONTROL OF SPREAD
`SPECTRUM MULTIPLE ACCESS NETWORKS
`
`6.1
`
`General 179
`
`6.2
`
`6.3
`
`6.4
`
`6.5
`
`6.6
`
`Reverse Link Power Control 182
`Multiple Cell Pilot Tracking and Soft Handoff 183
`Other-Cell Interference 185
`6.4.1 Propagation Model 185
`6.4.2 Single-Cell Reception—Hard Handoff 186
`6.4.3 Soft Handoff Reception by the Better of the Two Nearest
`Cells 189
`6.4.4 Soft Handoff Reception by the Best of Multiple Cells 193
`Cell Coverage Issues with Hard and Soft Handoff 196
`6.5.1 Hard Handoff 196
`6.5.2 Soft Handoff 198
`Erlang Capacity of Reverse Links 199
`6.6.1 Erlang Capacity for Conventional Assigned-Slot Multiple
`Access 199
`6.6.2 Spread Spectrum Multiple Access Outage—Single Cell and
`Perfect Power Control 203
`6.6.3 Outage with Multiple-Cell Interference 207
`6.6.4 Outage with Imperfect Power Control 208
`6.6.5 An Approximate Explicit Formula for Capacity with
`Imperfect Power Control 212
`6.6.6 Designing for Minimum Transmitted Power 214
`6.6.7 Capacity Requirementsfor Initial Accesses 215
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`Contents
`
`xi
`
`6.7. Erlang Capacity of Forward Links 218
`6.7.1 Forward Link Power Allocation 218
`6.7.2 Soft Handoff Impact on Forward Link 222
`6.7.3 Orthogonal Signals for Same-Cell Users 224
`Interference Reduction with Multisectored and Distributed
`Antennas 227
`
`6.8
`
`6.9
`
`Interference Cancellation 229
`
`6.10 Epilogue 232
`
`References and Bibliography 235
`
`Index 239
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`

`xvill
`
`Preface
`
`In Chapters 2 to 5, this book covers all aspects x spreadee
`transmission over a physical multiple-access channe iene 8 ie .
`hronization, modulation, and error-correcting coding Si
`ace
`re
`ionals. Chapter 6 relates these physical layer
`sequence spread spectrum signals.
`P
`-
`Ee
`.
`alae cower
`functions to link and network layer properties involving cent
`i
`age, Erlang capacity, and network control. Tis ounlne is oe in
`bringing together several wide-ranging technical disciplines, pate y cov-
`ered in this sequence and in one text. However,the presentation is well
`integrated by a numberof unifying threads. First, the entire text is de-
`voted to the concept of universal frequency reuse by multiple agers of
`multiple cells. Also, two fundamental techniques are used in a Wane of
`different forms throughout the text. The first is the finite-state machine
`representation of both deterministic and random sequences; the secondis
`the use of simple, elegant upper bounds on the probabilities of a wide
`range of events related to system performance.
`However, given the focus on simultaneous wideband transmission for
`all users over a common frequency spectrum, the text purposely omits
`two important application areas: narrowband modulation and coding
`methods, including multipointsignal constellations andtrellis codes; and
`frequency hopped multiple access, where modulation waveforms are in-
`stantaneously narrowbandoverthe duration of each hop.It also generally
`avoids digressions into principles of information theory. In short, al-
`though the material covered through Chapter 5 mostly also applies to
`narrowbanddigital transmission systems, the book mainly covers topics
`that apply to wideband spread spectrum multiple access.
`Three motivating forces drove me to write this book.It began with my
`three decades of teaching within the University of California system.
`There, keeping with the healthy trend in communication engineering
`courses,I tried to make theory continually morepertinent to applications.
`tary commissionfor the Marconi
`
`demonstration, and standardization 0
`the
`code-division multiple access (CDMA) system. Adopted in 1993 by
`Femunication Industry Association, the CDMA standard ise is
`€ embodimentofmanyoftheprinciplesPresented in this text. Although
`this book is not meant solely for this Purpose, it doe
`justi
`manyof the techniques containedin the standard. | a oe a
`that my goal is to present t
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`

`Pilot-Alded Coherent Multipath Demodulation
`
`87
`
`The pilot sequence can be searched by the h
`ypothesis testing device of
`Figure 3.1 with time iGelay) hypotheses separated by a fraction of a chi
`T., However, once the first strong componentis found, the entire mere
`window forall components can be limited to typically a few tens of chip
`times, representing the total delay dispersion of the multipath propaga-
`ton. The pilot pseudorandom sequenceis unmodulated, and thecarrier
`frequency is assumedto be accurately tracked. Thus, the number of chips
`used for estimation can be madeaslarge as desired, limited only by the
`rate of change of amplitude and phase.Also,unlikethelast chapter where
`the initial acquisition search ended whenthecorrect hypothesis was de-
`tected, the search here will not end. Onceapath is detected and verified,
`the search continues indefinitely, since new multipath componentswill
`appear and old ones disappear frequently, particularly for users in mo-
`tion. Once found, the component sequence timing mustbe tracked by an
`early—late gate, bothto refine the time estimate and to adjustfor distance
`and velocity of users in motion.
`Wewill explore this mechanization morefully. However,wefirst note
`that whereas the multipath propagation modelof Figure 4.1 has long been
`accepted in the communication theory literature, it has been traditionally
`associated with a static receiver, in which it was assumedthat each of the
`components (and even their number, L) remained at a constant delay,
`although their amplitudes and phases might vary. Employing a receiver
`that takes a static number of paths, in place of the varying numberas-
`sumed here, complicates the form of the optimum receiver: L mustgener-
`ally be taken to be larger than if only the currently active path delays are
`being demodulated. Also, witha static receiver, motion causes a transition
`from one delay path to another with possible discontinuity of amplitude
`and phase.
`In the next section we explore the optimum pilot-aided demodulator
`based on tracking each multipath component.In the following subsection,
`We consider its performance.
`
`4.4 Pilot-Aided Coherent Multipath
`Demodulation
`A pilot sequence for determining multipath component characteristics 1S
`Welljustified for one-to-manytransmission channels, such as the forward
`(down-) link from a base station to multiple users. This is because the
`Samepilot Sequence is shared amongthe k,, users controlled by that base
`Station. For the same reason, the energy devotedto the pilot canbe cea
`ae that devoted to the individual users. Thus, if X(t) given m i, fe
`received signal for the kth user, let Xo(t) be the unmodulated p
`
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`Modulation and Demodulation ofSpread Spectrum Signals
`iodu!
`
`88
`
`af (0)
`
`biG(k,) *
`
`Multipath
`Propagation
`
`‘
`x X (0+X,(7)
`
`
`
`Figure 4.2 Multiuser (base station) modulator and multipath channel.
`
`signal, so that x,(0) = 1 for all n. Also, we assumethat the pilot’s pseudo-
`random sequenceis shared byall users by multiplying thepilot pseudo
`random (+ 1) Sequence with all the user-specific sequences (Figure 4.2),
`Hence, the received signal containing k,, users and a pilot sequence, all
`originating from a common base station, will be
`
`ky
`
`k=]
`
`Here, X(t) is given by (4.24) for k = 1,2,...,k,, but Xo(f) is further
`weed byAo,the additional gain allotted to the pilot signal.
`’
`s pornFigure 4.2,a(0) and a‘2(0) are the pilot’sQPSKspread
`€quence. The users’ sequences are the product® of those of the P!
`
`* Thereason for multi
`:
`-
`eapapify
`€ particular b Piving the user Sequence by the pilot sequenceis to identify
`ase station thatis handlingthecall.
`
`the use
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`

`Pilot-Aided Coherent Multipath Demodutlation
`and of the user-specific sequences b(k) and bk). Thatis
`
`89
`
`an(k) = af(0)bM(k),
`a) = AQ, k=12..,
`
`4.25
`
`Furthermore, the timing ofall individual usersis lockedto thatof the pilot
`sequence, so that the multipath delays need only be searched on the pilot
`sequence.
`The optimum demodulator structure for L multipath propagation
`paths (as assumed in Figure 4.1) is known as a Rake receiver [Price and
`Green, 1958]. It wasfirst implementedin static form in the late 1950s. This
`is shown in Figure 4.3 for the kth user. Figure 4.3a consists of the parallel
`combination of L elements, one of which is shown in Figure 4.3b. Each
`multipath component demodulatoris called a “finger’’ of the rake. The
`pilot sequence tracking loop of a particular demodulatoris started by
`the timing delay estimation of a given path, as determined by the
`pilot's pseudorandom sequencesearcher. This is then used to remove the
`pilot QPSK spreading, giving rise to the quadrature outputs (Figure
`4.3):
`
`VE. [Ap + x,(K)DP(Kae cos , + v®,
`VE. [Ap + x,(K)DQ(k)]ay sin be + v.
`
`Ay is the pilot gain, and v® and v©) are the contributions of all other
`(uncorrelated) multipath components as well as those ofall otherusers.
`From this the relative path values a, cos ¢; and asin ¢, can be estimated
`by simply averaging over an arbitrary numberof chips, N,. This number
`should be as large as possible without exceedingthe period over which ay
`and ¢, remain relatively constant.
`The optimum (maximum likelihood) demodulator forms the weighted,
`phase-adjusted, and delay-adjusted sum of the L components. This
`amounts to taking the inner product of the modulated received I and Q
`‘omponents with the I and Q unmodulated component magnitudeesti-
`mates @cos be and &sin de. The result for the nth chip of the ¢th path,
`after multiplication by the quadrature-user-specific pseudorandom se-
`ences as shown in Figure 4.3b, is
`
`nk) = VE, x,(k)@ecre cos(he — $e)
`ae +&e(v fs a + vOsin dy):
`
`(4.26)
`
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`

`
`
`
`
`Y¥(k)
`
`23H8aw
`
`n
`
`(a) L-PathDemodulator
`
`tipath propagation. (a)L-pathdemodulator.
`
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` & &sQ:®
`
`D 38c
`
`& QS
`
`sQ:a S
`
`o®
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`

`
`
`
`Pilot
`
`
`From ae
`Sequence
`
`
`
`
`-p>| (Early—Late Gate)
`
`
`Matched
`‘
`:
`‘om
`Fillers:
`Searcher
`ee9
`al?
`(0).an%
`(0)
`b,(2) (0)
`Y, (kK)
`
`
`
`
`
`
`Despreading—FYE.[Ag+xp(k) bp(®) (K)]ez,sin Jv (2)
`
`a
`
`
`
`
`
`Pilot
`Sequence
`
`a,(") (0),a,{) (0
`
`~~
`VE[Aptxn(h) by") (k)]a, cos @+v,(")
`bl) (K)
`
`
`
`Figure 4.3 (b) Each of L parallel demodulators (Rake fingers) for kth user.
`
`(b) Each of L Parallel Demodulators
`(Rake Fingers) for kth User
`
`
`
`
`
`
`
`UOKDINDOWEgYLodyinyyHUBJBYODPEpPly-lojlg
`
`L6
`
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`

`92
`
`Oo
`
`Modulation andDemodulation ofSpreadSpectrum Signals
`Summing overthe N chips over which x,,(k) is constant (+ 1), we have
`1) = ENE, ade c08(he — be)
`a + d&,[cos 3, y J) + sin de SY),
`(4.27)
`
`u
`
`ame
`
`Thus,
`
`FLY(k) lxq(8) = —1 = — NINE, avdie cos(e ~ &)],
`with a change of sign if x,(k) = +1, and
`VarlY(k)] = N@3o/2,
`
`(4.28a)
`
`(4.28b)
`
`whereI, is given in (4.16).
`Weproceed to obtain Chernoff boundson the error probability using
`the methodsof Section 4.2.
`
`4.4.1 Chernoff Bounds on Error Probability for Coherent
`Demodulation with Known Path Parameters
`Initially, conditioning on known amplitudes a, and phases op, we obtain
`the Chernoff bound,
`
`€=1
`
`e=1
`
`e=1
`
`L
`
`L
`
`oe
`
`P,(a, @;k) = Pr B Yk) > 01 a, @, x(k) = — |
`< We (ex|» 5 rae| | a, &, x(k) = -1)
`= sunexp |-pNYVE.(k) 5 cette COS(e — de) + p?N » cal
`NE.{k) |S Ap, COS(dh, — aa|
`
`> lo
`€=1
`
`= exp{— a (4.29)
`
`
`
`g neglect the inaccuracy in the amplitude and phaseestimates, taking
`If w
`e = Pe, & = ap, we obtain
`
`7
`
`P5(k) < exp |- 5 cANEA/a
`L
`a i exp[—a¢NE.(k)/Tol
`
`e=1
`
`(4.30)
`
`(perfect estimates).
`
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`Pilot-Aided Coherent Multipath Demodulation
`
`93
`
`Further, it is shown in Appendix 4A thatif we do not assume exact phase
`and amplitude
`her estimates based on N, unmodulated
`i
`estimates, but rat
`i
`chips of a pilot whose chip energy is AGE.(see Figure 4.3), the error proba-
`bility is bounded by
`
`= &xpl= a@NE.(h)/In)
`P,(k) < a1=[NAN] (4.31)
`
`Generally, if the paths are knownandthetotal received energy perchip is
`E.(k), then we may normalize the relative path gains so that
`L
`
`az= 1.
`
`€=1
`
`Thus, for fixed amplitude and phase multipath, the performance bound
`with perfect estimates, (4.30), is the same as for a single-componentsignal,
`if energy is taken as the sum of the componentenergies. The explanation
`is simple: When the multipath amplitudes and phases are known, the
`optimal receiver operates as a matchedfilter to the combination of the
`transmitter filter and the (multipath) channel.
`
`4.4.2 Rayleigh and Rician Fading Multipath Components
`Now we no longer assume constant amplitude. Welet the multipath com-
`ponent amplitudes be random variables, mutually independent because
`we assume that each path’s attenuation is unrelated to thatofall others.
`Then the error probability for perfect estimates becomes
`
`I exp(—a2NE./T)
`P, =E[P,(a,,..., @)] <e|
`E
`L
`= |] Elexp(-a7E,/Io)) 4 [] Ze4 2.
`€=1
`f=2
`
`€=1
`
`(4.32)
`
`Here, E, 4 NE, is the N-chip symbol energy, and the expectations are wa
`tespect to the random variables a,. We drop the user index k for conve-
`Nience. We also assume perfect estimates, although by scaling all Ze by the
`denominatorof (4.31), we mayalso obtain a boundfor imperfect estimates.
`If each component is the combination of many reflections arriving at
`nearly the same delay but with random phases,wecan take the aeae
`be Rayleigh-distributed. Then the probability density function oe
`Dacre
`ig
`(4.33a)
`
`pla) =
`
`2
`Oe
`
`f
`
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`Modulation and Demoaulation of Spread Spectrum Signals
`
`94
`
`Or, letting Be = a3, we obtain the chi-squared density,
`e~B/o
`7
`oF
`
`/
`
`B>0,
`
`p(B) =
`
`(4.33b)
`
`3
`3 = ElBe] = Ela’.
`here
`Thus,for Rayleigh-distributed attenuations,
`Ze= Ele-PO]=| 1 exp| F (Fo 1) |ap
`-_
`(4.34)
`1 + o3E,/]y
`
`-B(E
`= 4
`—BeE./To = — — =e 24
`
`=
`
`Letting
`
`this can be written as
`
`E,, = BeE, = o7E,,
`
`Ze =— (Rayleigh fading component).
`1+ E,/Ip
`
`(4.35)
`
`If the componentis the combination of a specular componentanda Ray-
`leigh component, the probability density function of a, becomesRician.
`Its square B, becomes noncentral chi-squared,
`
`e7 (Be sr yo / a7
`
`P(Be) = gl I(2V VeBe/2).
`
`(4.36)
`
`Then
`
`Le — Ele~PeEs/10)
`Sale
`
`Ye + B(1 + o2E
`
`J
`
`Co €
`
`|e [AAAAEM (222) ap./ot
`(4.37)
`:
`(=
`YeE,/Ty
`)
`(Rician fading component).
`> aqnapeexoeee
`PPOED “TF 046/Iy
`ote that this reduces to the Rayleigh fading result (4.34) when Ye~ s
`andto t0 the known amplitude and phase result when o7= 0.
`equal average strength, so an L multipath componentsareall Rayleig
`f
`=o forall £,
`
`Not
`
`i
`
`,
`
`Supposethat th
`
`Ho
`
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`Pllot-Aided Coherent Multipath Demodulation
`
`95
`
`and therefore, for each component,
`
`Bes = o1E, = o7E =s
`
`s*
`
`Then,letting the random variable
`
`L
`7 >, ate, = > BeE,,
`€=1
`
`it is easily shown (see Appendix 3A.5) that since the individual fading
`variables are all independent,
`
`xb = le x/Es
`
`me EE
`
`(4.38)
`
`which is Lth-order chi-squared. It follows from (4.34) that, in this case,
`
`PLZ = Z
`ese Ul
`
`&
`
`‘
`
`= ae =
`
`:
`1 + (o°E,/Ip)
`
`| aa| 4,39
`1 + (E,/Ip) ot
`
`—=
`
`.
`
`.
`
`We may rewrite (4.39) as
`
`where
`
`Pp < exp[—In(1/Z)],
`
`In(1/Z) = LIn{1 + (E,/Ip)].
`
`(4.40)
`
`From (4.40) we obtain Figure 4.4: a plot of the ratio® of the total average
`symbol energy-to-interference density LE, /Iy over that required for an
`unfaded Gaussian channelto achieve a given exponent value, In(1/Z).
`Note from (4.9) or (4.32) thatfor the latter channel, In(1/Z) = E./I). Thus,
`this is the average excess energy (in decibels) required bythis degraded
`channel to achieve the same performance as for an unfaded signal in
`additive Gaussian noise.
`
`oe
`this ratio is actually
`* All quantities are in decibels and henceare logarithmic functions. Thus,
`ired for the
`excess energy, in decibels, required for the faded channel over that requ
`unfaded AWGNchannel.
`
`
`
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`
`
`
`
`
`
`
`
`Exponent In (1/Z) (dB)
`
`14AY|TT
`
`
`
`PesSeeae
`
`az=
`Zz
`g<°oaa
`&c
`
`25a &ocw
`
`i a8b
`
`sw &&s<
`
`96
`
`Modulation and Demodulation ofSpreadSpectrum Signals
`
`i, "
`
`Figure 4.4 Required excess energy (dB) for L equal-strength multipath fading
`relative to unfaded coherent AWGN.
`
`Note that as L — ~ (so that each component's average energy Ee)
`butLE,is finite), the bound approaches
`
`P, <= eTLEs/To
`
`so that the excess energy approaches zero. This shows that with an
`asymptotically large number of independent Rayleigh components,per-
`formance approaches that of unfaded propagation. This is an extreme
`and unrealistic example of the beneficial effect of independentdiversity
`components. We shall return to these results in Chapter 5 when we
`consider interleaving, with delay, to produce more independent com:
`ponents.
`
`
`
`
`
`
`4.5 Noncoherent Reception
`Transmissionof a Pilot is very valuable for initial acquisitionand time
`
`tracking. “ is also valuable for obtaining good amplitudean has
`oe makingPossible quasi-optimum coherent reception and
`Wsaf
`lt
`ve idesof multipath components. Unfortunately,itisa
`
`Aeaffordable, particularly on the
`ma
`
`SAN from eachof the multiple access user:
` 5
`use
`powereon settingin each individual
`
`EOWEE 18 greater than the data-modulated
`=
`
`
`
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`
`
`83
`
`o
`
`Multiple Cell Pilot Tracking andSoftHandoff
`gation may be estimated a priori to lie between 3 and 7d
`B, according to
`teanalyses in Chapters 4 and 5. However, conditions wil]
`vary according
`the multipath fading environment, Particularly if man
`y pathsare in-
`volved. Thus, as noted in Section 4.7, it is useful to add a Powercontrol
`mechanism. called eo cures eS. adjusts the desired E,/Ip level
`sccording t0 the individual user's €rror
`rate measured at
`the base
`gation. This then guarantees a given error rate per coded voice frame or
`message packet (typicallyset at or below 1%). However, the resulting
`Elly parameter, which is already a log-normal random variable—
`or normal in decibels—because of power control inaccuracy, will have
`greater variability, manifested as a larger standard deviation of its
`normally distributed decibel measure. Thus, while Section 4.7 arrives
`ata typical standard deviation for the closed-loop system between 1.1
`and 1.5 dB, the standard deviation caused by the outer loop variations
`is of the same order of magnitude. Hence,
`the combination of these
`two independent components leads to an estimate of total standard
`deviation on the order of 1.5 to 2.1 dB. It has been measured experimen-
`lally [Viterbi and Padovani, 1992; Padovani, 1994] to be between 1.5
`and 2.5 dB. We shall assess the effect of variability on capacity in Sec-
`tion 6.6.
`
`63 Multiple Cell Pilot Tracking and Soft Handoff
`The forward link for each cell or sector generally employs a pilot modu-
`lated only by the cell-specific, or sector-specific, pseudorandom sequence,
`added or multiplexed with the voice or data traffic. This is described in
`Chapter 4 and shownin Figure 4.2. The pilot provides for time reference
`and phase and amplitude tracking. It also can be used to identify newly
`allable pilots in adjacent cells or sectors. Specifically, while a user
`S tracking the pilot of a particular cell, it can be searching for pilots
`of adjacent cells (using -the searching mechanism of its multipath rake
`“elver). To make this simple and practical, all pilot pseudoran-
`'M sequences can use the same maximum length generator sequenc®,
`ih
`different initial vectors and hence timing offsets. The relative
`‘i Pottsets of pilots for neighboringcells and sectors are either sn
`Plori or broadcastto all users of the given cell or sector on a separa
`
`atro]|
`Section 5.3.3) the forward
`link
`ae, Performance. One simple methodis to puncture (see
`unctured symbols to un-
`Oded fea eneduently(e.g., one symbol in 12) and dedicate the P
`d in rate (e-8-, by the
`factoree of commands. The punctured codeis then reduce
`y degraded.
`one in 12 symbols is punctured).Its performance is slight!
`
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`184
`
`Capacity, Coverage, and Control of Spread Spectrum Multiple Access Networks
`
`CDMA channel, employing its own pseudorandom sequence or time-
`offset.
`Once a newpilot is detected by the searcher and found to have suffj-
`cient signal strength (usually relative to the first pilot already being
`tracked), the mobile will signal this event to its original base station.
`This in turn will notify the switching center, which enables the second
`cell’s base station to both send and receive the sametraffic to and from
`the given mobile. This process is called soft handoff. For forward link
`transmission to the mobile, the Rake demodulator (Figure 4.3) demod-
`ulates both cells’ transmission in two fingers of the rake and combines
`them coherently, with appropriate delay adjustments, just as is done
`for time-separated multipath components. For the reverse link, nor-
`mally each base station demodulates and decodeseach frame or packet
`independently. Thus, it is up to the switching center to arbitrate be-
`tween the two base stations’ decoded frames.? Soft handoff operation
`has many advantages. Qualitatively,
`transition of a mobile between
`cells is much smoother: The second cell can be broughtinto use gradu-
`ally, starting early in the transition of a mobile from onecell to its
`neighbor cell. Similarly, when thefirst cell’s signal is so weakrelative
`to the second that it cannot be demodulated and decoded correctly, it
`will be dropped either in response to the mobile’s pilot strength mea-
`surement or by action of thefirst cell. Moreover, for any given frame,
`the bettercell’s decision will generally be used, with no need to enable a
`new cell or disable an old oneasin classical “hard” handoff. In fact, to
`avoid frequent handoffs on the boundary between cells (which require
`excessive control signaling), systems with hard handoff only enable
`a second cell when its signal strength is considerably above (c.g,
`6 dB) that of the first cell. This further degrades performance on the
`boundary.
`Most importantly, however, soft handoff considerably increases both
`the capacity of a heavily loaded multicellular system and the coverage
`(area size) of each individualcell in a lightly loaded system. Weshall
`demonstratethis quantitatively, following Viterbi, Viterbi, Gilhousen, and
`Zehavi [1994]. It is first necessary to determine the mutual interference
`amongcells of a multicellular system.
`
`* Generally, each frame is provided with an error-detecting code (consisting of a moderate
`number,¢, of check bits at thetail end of the frame) which allows detection of one or more
`errors with probability on the order of 1~2-« [Wolf et al., 1982].
`
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`Electrical Engineering/Telecommunications
`CDMA
`Principles of Spread Spectrum Communication
`
`Spread spectrum multiple access communication, known commercially as CDMA
`(Code Division Multiple Access), is a driving technology behind the rapidly advancing
`personal communications industry. Its greater bandwidth efficiency and multiple
`access capabilities makeit the leading technology for relieving spectrum congestion
`caused by the explosion in popularity of cellular mobile and fixed wireless telephones
`and wireless data terminals.
`CDMA hasbeen adopted by the Telecommunications Industry Association
`(TIA) as a wireless standard. As an electrical or communications engineer, you
`must acquire a thorough grasp of CDMA fundamentals in orderto develop systems,
`products, and services for this demanding but rewarding market.
`Written by a leaderin the creation of CDMA and an internationally recognized
`authority on wireless digital communication, this book gives you the technical
`information you need.It presents the fundamentals of digital communications and
`covers all aspects of commercial direct-sequence spread spectrum technology,
`incorporating both physical-level principles and network concepts. You will find
`detailed information on signal generation, synchronization, modulation, and
`coding of direct-sequence spread spectrum signals. In addition, the book shows
`how these physical layer functionsrelate to link and network properties involving
`cellular coverage, Erlang capacity, and network control.
`With this book,you will attain a deeper understanding of personal commu-
`nications system concepts and will be better equipped to develop systems and
`products at the forefront of the personal wireless communications market.
`Andrew J. Viterbiis a pioneerof wireless digital communications technology.
`Heis best known asthe creator of the digital decoding technique usedin direct-
`broadcastsatellite television receivers and in wireless cellular telephones, as
`well as numerousother applications. He is co-founder, Chief Technical Officer,
`and Vice Chairman of QUALCOMMIncorporated, developer of mobile satellite
`and wireless land communication systems employing CDMA technology.
`Dr. Viterbi has received numerous awards, including the Christopher Columbus
`Medal, the IEEE Alexander Graham Bell Award, the MarconiInternational
`Fellowship Award, the IEEE Information Society Shannon Lecturer Award, and
`awards from the NEC C&C Foundation and the Eduard Rhein Foundation.
`
`eeeea]
`
`Cover photo © Hewlett-Packard Compam
`Cover design by Simone R.