Multiantenna Channels : Capacity, Codin g

and Signa l Processin g

This page intentionally left blank

DIMACS Series i n Discret e Mathematic s

and Theoretica l Compute r Scienc e

Volume 6 2

Multiantenna Channels : Capacity, Codin g

and Signa l Processin g DIMACS Worksho p

Signal Processin g fo r Wireles s Transmissio n October 7-9 , 200 2

DIMACS Cente r

Gerard J . Foschin i Sergio Verd u

Editors

Center fo r Discret e Mathematic s and Theoretica l Compute r Scienc e

A consortium o f Rutgers University , Princeto n University , AT&T Labs-Research, Bel l Labs (Lucen t Technologies) , NEC Laboratories America , an d Telcordi a Technologie s

(with partner s a t Avaya Labs , IB M Research, an d Microsof t Research )

American Mathematica l Societ y

https://doi.org/10.1090/dimacs/062

This DIMAC S volum e present s th e proceeding s fro m th e worksho p Signa l Processin g for Wireles s Transmissio n hel d a t th e DIMAC S Center , Rutger s University , Octobe r 7-9 , 2002.

2000 Mathematics Subject Classification. Primar y 94A05 , 94A13 , 94A14 , 94A15 , 94A24 , 94A40, 94B99 , 15A52 .

Library o f Congres s Cataloging-in-Publicatio n D a t a

DIMACS Worksho p Signa l Processin g fo r Wireles s Transmissio n (200 2 : Rutger s University ) Multiantenna channel s : capacity , codin g an d signa l processin g : DIMAC S Worksho p Signa l

Processing fo r Wireles s Transmission , Octobe r 7-9 , 200 2 / Gerar d J . Foschini , Sergi o Verdu , editors.

p. cm . — (DIMAC S serie s i n discret e mathematic s an d theoretica l compute r scienc e ; v. 62 ) Includes bibliographica l references . ISBN 0-8218-3407- X (alk . paper ) 1. Signa l processing—Congresses . 2 . Wireles s communicatio n systems—Congresses . I . Fos -

chini, Gerar d J. , 1940 - II . Verdu , Sergio , 1958 - III . Title . IV . Series .

TK5102.9.D58 200 2 621.382/2—dc22 200305774 6

Copying an d reprinting . Materia l i n thi s boo k ma y b e reproduce d b y an y mean s fo r edu -cational an d scientifi c purpose s withou t fe e o r permissio n wit h th e exceptio n o f reproductio n b y services tha t collec t fee s fo r deliver y o f document s an d provide d tha t th e customar y acknowledg -ment o f th e sourc e i s given . Thi s consen t doe s no t exten d t o othe r kind s o f copyin g fo r genera l distribution, fo r advertisin g o r promotiona l purposes , o r fo r resale . Request s fo r permissio n fo r commercial us e o f materia l shoul d b e addresse d t o th e Acquisition s Department , America n Math -ematical Society , 20 1 Charle s Street , Providence , Rhod e Islan d 02904-2294 , USA . Request s ca n also b e mad e b y e-mai l t o reprint-permission@ams.org .

Excluded fro m thes e provision s i s materia l i n article s fo r whic h th e autho r hold s copyright . I n such cases , request s fo r permissio n t o us e o r reprin t shoul d b e addresse d directl y t o th e author(s) . (Copyright ownershi p i s indicate d i n th e notic e i n th e lowe r right-han d corne r o f th e first pag e o f each article. )

© 200 3 b y th e America n Mathematica l Society . Al l right s reserved . The America n Mathematica l Societ y retain s al l right s

except thos e grante d t o th e Unite d State s Government . Printed i n th e Unite d State s o f America .

@ Th e pape r use d i n thi s boo k i s acid-fre e an d fall s withi n th e guideline s established t o ensur e permanenc e an d durability .

Visit th e AM S hom e pag e a t http://www.ams.org /

10 9 8 7 6 5 4 3 2 1 0 8 0 7 0 6 0 5 0 4 0 3

Contents

Foreword vi i

Preface i x

Part I . Capacit y o f Multiantenn a Channel s

Broadband MIM O channe l mode l fo r realisti c capacit y an d syste m performance evaluation s HAO XU , DMITR Y CHIZHIK , HOWAR D HUANG , AN D REINALD O

VALENZUELA 3

Bandwidth-power tradeof f o f multi-antenna system s i n the low-powe r regim e ANTONIA M . TULINO , ANGE L LOZANO , AN D SERGI O VERD U 1 5

Distribution o f MIM O capacit y i n th e presenc e o f correlate d signal s an d interferers: A (no t so ) larg e N analysi s ARIS L . MOUSTAKAS , STEVE N H . SIMON , AN D ANIRVA N M .

SENGUPTA 4 3

Optimality o f beamformin g i n multipl e transmitte r multipl e receive r communication system s wit h partia l channe l knowledg e STEVEN H . SIMO N AN D ARI S L . MOUSTAKA S 5 7

Part II . Capacit y o f Broadcas t Channel s an d Dirty-Pape r Codin g

Duality, dirt y pape r coding , an d capacit y fo r multiuse r wireles s channel s NLHAR JLNDAL , SRIRA M VLSHWANATH , SYE D JAFAR , AN D ANDRE A

GOLDSMITH 7 1

On th e capacit y o f th e multipl e antenn a broadcas t channe l DAVID T S E AN D PRAMO D VISWANAT H 8 7

Capacity bound s fo r Gaussia n vecto r broadcas t channel s S. VISHWANATH , G . KRAMER , S . SHAMAI , S . JAFAR , AN D

A. GOLDSMIT H 10 7

Writing o n dirt y tap e wit h LDP C code s GIUSEPPE CAIR E AN D SHLOM O SHAMA I (SHITZ ) 12 3

Dirty pape r coding : Perturbin g of f th e infinit e dimensiona l lattic e limi t GERARD J . FOSCHIN I AN D ALVAR O H . DIA Z 14 1

vi CONTENT S

Part III . Signa l Processin g fo r Multiantenn a Channel s

Maximum-likelihood decodin g an d intege r least-squares : Th e expecte d complexity BABAK HASSIB I AN D HARI S VIKAL O 16 1

Slowing th e time-fluctuatin g MIM O channe l DMITRY CHIZHI K 19 3

A spacetime architectura l superstructur e enablin g efficien t multipl e antenn a communication G. J . FOSCHIN I AN D M . SELLATHURA I 21 3

Space-time codin g wit h iterativ e receive r interface s Ezio BIGLIERI , ALESSANDR O NORDIO , AN D GIORGI O TARICC O 23 3

Diversity orde r o f space-tim e bloc k code s i n inter-symbo l interferenc e multiple-access channel s S. N . DIGGAVI , N . AL-DHAHIR , AN D A . R . CALDERBAN K 24 7

Pilot assiste d estimatio n o f MIM O fadin g channe l respons e an d achievabl e data rate s DRAGAN SAMARDZIJ A AN D NARAYA N MANDAYA M 25 5

Part IV . Networkin g Capacit y

Challenges i n UW B signalin g fo r adho c networkin g YOUNES SOUILM I AN D RAYMON D KNOP P 27 1

Efficient multiho p broadcas t fo r wideban d system s IVANA MARI C AN D RO Y YATE S 285

Foreword

A worksho p o n Signa l Processin g fo r Wireles s Transmissio n wa s hel d a t Rut -gers Universit y o n Octobe r 7-9 , 2002 . W e woul d lik e t o expres s ou r appreciatio n to Gerar d Foschin i an d Sergi o Verdi i fo r thei r effort s t o organiz e an d pla n thi s successful conference .

The worksho p wa s par t o f th e Specia l Focu s o n Computationa l Informatio n Theory an d Coding . W e exten d ou r thank s t o Rober t Calderbank , Chri s Rose , Amin Shokrollahi , Emin a Soljanin , an d Sergi o Verdu fo r thei r wor k a s special focu s organizers.

The worksho p brough t togethe r theoretician s an d practitioner s workin g o n wireless communications , information , an d codin g theor y fro m a variet y o f per -spectives. Th e mai n theme s o f th e worksho p include d capacit y o f multiantenn a channels an d o f vector broadcas t channels , "dirty-paper " coding , signa l processing , and ad hoc networking in wideband channels . Thes e are all major theme s in curren t research i n physical-laye r desig n fo r wireles s communication .

DIMACS gratefull y acknowledge s th e generou s suppor t tha t make s thes e pro -grams possible . Th e Nationa l Scienc e Foundation ; th e Ne w Jerse y Commissio n o n Science an d Technology ; DIMACS ' partner s a t Rutgers , Princeton , AT& T Labs -Research, Bel l Labs , NE C Laboratorie s America , an d Telcordi a Technologies ; an d its affiliate d partner s a t Avay a Labs , IB M Research , an d Microsof t Researc h hav e generously supporte d th e specia l focus .

Fred S . Robert s Director

Robert Tarja n Co-Director fo r Princeto n

This page intentionally left blank

Preface

The DIMAC S Worksho p o n Signa l Processin g fo r Wireles s Transmissio n wa s held a t Rutger s Universit y o n Octobe r 7-9 , 2002 , unde r th e auspice s o f th e DIMACS Specia l Focu s o n Computationa l Informatio n Theor y an d Coding . Twenty-six invite d presentation s wer e delivere d ( http://dimacs.rutgers.edu/ Workshops/Wireless/) b y leadin g researcher s i n th e fields o f wireles s communi -cations, informatio n an d codin g theory . Worksho p attendee s include d researcher s from institution s i n Nort h America , Europe , th e Middl e Eas t an d Asia . Throug h the agenc y o f DIMACS, we were abl e t o suppor t th e participatio n o f a substantia l number o f students. I n the true spiri t o f a workshop, there was considerable interac -tion among participants, accentuate d b y a sense of excitement ove r the presentatio n of fast-breaking results .

Several force s ar e coalescin g t o mak e thi s a n excitin g tim e i n th e field o f physical-layer desig n fo r wireles s communication : th e relentles s advanc e i n VLS I technology, th e recen t breakthrough s i n signa l processin g fo r multiantenn a an d multiuser systems , an d the increased pressur e fo r efficien t utilizatio n o f scarce spec-tral resources . Thes e force s mak e information-theoreti c limit s an d th e mean s o f approaching the m increasingl y relevan t fo r emergin g wireles s communicatio n sys -tems. Thi s volum e give s a snapsho t o f th e rang e o f challenge s tha t ar e currentl y garnering a grea t dea l o f attentio n fro m th e researc h community .

The first grou p o f contribution s o n "Capacit y o f Multiantenn a Channels " fol -lows in the lin e o f information-theoretic researc h pioneere d a t Bel l Labs i n the mi d 1990s. Th e contributio n b y Xu , Chizhik , Huan g an d Valenzuel a add s realis m t o the modeling of multiantenna channel s by incorporating a number o f key effects no t captured i n th e canonica l model . Eve n thoug h muc h o f the earl y emphasi s o n th e information-theoretic analysi s o f multiantenna channel s was on high signal-to-nois e ratio (SNR ) contexts , many practical embodiments, particularl y i n cellular systems , operate a t lo w receive d energ y pe r bit . Th e pape r b y Tulino , Lozan o an d Verdi i considers the bandwidth-powe r tradeof f i n the lo w SNR regime . Th e surprisin g rel -evance of large random matri x method s to systems with smal l numbers o f antenna s is illustrated i n the pape r b y Moustakas, Simo n an d Sengupta , eve n with correlate d channel coefficients . I n anothe r departur e fro m th e canonica l setting , Simo n an d Moustakas analyz e th e impac t o f channel informatio n a t th e transmitte r arra y an d determine unde r wha t condition s beamformin g i s optimal .

The secon d grou p o f paper s i s devote d t o th e capacit y o f vecto r broadcas t channels an d it s relationshi p wit h th e proble m o f "dirty-pape r coding" . I n dirty -paper coding , introduce d b y Cost a i n 198 3 building upo n earlie r work , i n additio n to th e backgroun d noise , a n interferenc e componen t i s presen t whic h i s know n a t the transmitte r bu t no t a t th e receiver . Dirty-pape r codin g i s especially relevan t t o

ix

x PREFAC E

downlink communication , wher e th e bas e statio n know s th e channel s an d therefor e knows th e multiuse r interferenc e affectin g eac h transmission . Althoug h th e sum -capacity ha s bee n solve d recently , determinatio n o f th e entir e capacit y regio n o f th e vector broadcas t channe l remain s a n ope n problem . Importan t advance s toward s its solutio n wer e announce d a t th e worksho p an d reporte d i n th e pape r b y Jindal , Vishwanath, Jafa r an d Goldsmith ; th e pape r b y Ts e an d Viswanath ; a s wel l a s th e one b y Vishwanath , Kramer , Shamai , Jafa r an d Goldsmith . Th e remainin g issu e t o be settle d i n orde r t o clai m tha t th e regio n pu t fort h i n thos e paper s i s th e actua l capacity regio n i s th e questio n o f optimalit y o f Gaussia n codebooks .

The constructiv e counterpar t t o th e capacit y o f dirty-pape r codin g i s at tract in g considerable research . Cair e an d Shama i conside r th e applicatio n o f low-densit y parity chec k code s an d pulse-amplitud e modulatio n i n th e desig n o f system s tha t approach th e fundamenta l limit s whe n th e interferenc e i s know n a t th e transmitte r only causally . Afte r a tutoria l presentatio n o f dirty-pape r coding , Foschin i an d Diaz explor e wha t ca n b e achieve d wit h bot h one-dimensiona l lattice s an d i n th e asymptote o f high-dimensiona l lattices .

The thir d par t o f th e volum e i s devote d t o signa l processing . Th e analysi s o f the averag e computationa l complexit y b y Hassib i an d Vikal o o f th e near-optima l sphere-decoding algorith m show s th e considerabl e promis e o f thi s technique , whic h has application s beyon d combatin g multiuser/mul t iantenna interference . A metho d to lowe r th e signa l processin g complexit y i n channel s wit h rapi d fluctuation s i s presented i n th e contributio n b y Chizhik . Thi s make s th e gain s promise d b y information-theoretic result s approachabl e eve n i n situation s previousl y though t to b e problematic . Foschin i an d Sellathura i sho w ho w t o arrang e a signa l i n space -time s o a s t o achiev e capacit y wit h one-dimensiona l codec s whe n ther e i s onl y on e receive antenna . Th e techniqu e i s also show n t o b e effectiv e i n approachin g capacit y when th e numbe r o f transmi t antenna s i s muc h large r tha n th e numbe r o f receiv e antennas. Th e us e o f iterativ e receptio n i n conjunctio n wit h space-tim e code s i s explored i n th e pape r b y Biglieri , Nordi o an d Taricco . Space-tim e bloc k code s fo r channels tha t incorporat e multiuser , intersymbo l an d mult iantenn a interferenc e ar e considered b y Diggavi , Al-Dhahi r an d Calderbank , wh o deriv e a simpl e formul a fo r the diversit y order . Mos t o f th e paper s i n thi s field assum e perfec t channe l knowl -edge a t th e receiver . Samardzij a an d Mandaya m explor e th e effec t o f imperfec t channel estimatio n o n achievabl e da t a rates .

The las t grou p o f paper s i n th e volum e explore s issue s relate d t o a d ho c net -working i n wideban d channels . Souilm i an d Knop p examin e th e rate s achievabl e b y flash signalin g i n ultrawideban d channel s whe n onl y channe l statistic s ar e know n a t the receiver . Mari e an d Yate s pu t fort h th e "accumulativ e broadcast " strateg y i n multihop environment s wher e th e objectiv e i s to minimiz e tota l t ransmit te d energy .

It i s a pleasure t o acknowledg e th e exper t guidanc e o f Professor Fre d S . Roberts , director o f DIM ACS. H e generousl y provide d hi s hel p an d advic e durin g th e organi -zation o f th e worksho p an d th e preparatio n o f thi s volume . W e ar e als o gratefu l t o Ms. Shirle y Hil l o f th e America n Mathematica l Societ y fo r he r diligen t processin g of th e content s o f thi s book . Finally , i t i s a pleasur e t o than k al l th e author s fo r their outstandin g effort s tha t mad e thi s volum e a reality .

Gerard J . Foschin i an d Sergi o Verdi i

This page intentionally left blank

Titles i n Thi s Serie s

62 Gerar d J . Foschin i an d Sergi o Verdu , Editors , Multiantenn a Channels : Capacity ,

Coding an d Signa l Processin g

61 M . F . Janowitz , F.-J . Lapointe , F . R . McMorris , B . Mirkin , an d F . S . Roberts ,

Editors, Bioconsensu s

60 Saugat a Bas u an d Laurean o Gonzalez-Vega , Editors , Algorithmi c an d Quantitativ e

Real Algebrai c Geometr y

59 Michae l H . Goldwasser , Davi d S . Johnson , an d Catherin e C . M c G e o c h , Editors , Data Structures , Nea r Neighbo r Searches , an d Methodology : Fift h an d Sixt h DIMAC S

Implementation Challenge s

58 Simo n Thomas , Editor , Se t Theory : Th e Hajna l Conferenc e

57 Eugen e C . Freude r an d Richar d J . Wallace , Editors , Constrain t Programmin g an d Large Scal e Discret e Optimizatio n

56 Alexande r Bar g an d Simo n Litsyn , Editors , Code s an d Associatio n Scheme s 55 Ding-Zh u D u , Pano s M . Pardalos , an d Ji e Wang , Editors , Discret e Mathematica l

Problems wit h Medica l Application s

54 Eri k Winfre e an d Davi d K . Gifford , Editors , DN A Base d Computer s V 53 Nathanie l Dean , D . Fran k Hsu , an d R . Ravi , Editors , Robus t Communicatio n

Networks: Interconnectio n an d Survivabilit y

52 Sangutheva r Rajasekaran , Pano s Pardalos , an d D . Fran k Hsu , Editors , Mobil e

Networks an d Computin g

51 Pierr e Hansen , Patric k Fowler , an d Maoli n Zheng , Editors , Discret e Mathematica l

Chemistry

50 Jame s M . Abel l o an d Jeffre y Scot t Vitter , Editors , Externa l Memor y Algorithm s

49 Ronal d L . Graham , Ja n Kratochvil , Jarosla v Nesetf i l , an d Fre d S . Roberts ,

Editors, Contemporar y Trend s i n Discret e Mathematic s

48 Harve y Rubi n an d Davi d Harla n Wood , Editors , DN A Base d Computer s II I

47 Marti n Farach-Colton , Fre d S . Roberts , Marti n Vingron , an d Michae l

Waterman, Editors , Mathematica l Suppor t fo r Molecula r Biolog y

46 Peng-Ju n Wan , Ding-Zh u D u , an d Pano s M . Pardalos , Editors , Multichanne l

Optical Networks : Theor y an d Practic e

45 Mario s Mavronicolas , Michae l Merritt , an d Ni r Shavit , Editors , Network s i n

Distributed Computin g

44 Laur a F . Landwebe r an d Eri c B . Baum , Editors , DN A Base d Computer s I I

43 Pano s Pardalos , Sangutheva r Rajasekaran , an d Jos e Rol im , Editors ,

Randomization Method s i n Algorith m Desig n

42 Ding-Zh u D u an d Fran k K . Hwang , Editors , Advance s i n Switchin g Network s

41 Davi d Aldou s an d Jame s Propp , Editors , Microsurvey s i n Discret e Probabilit y

40 Pano s M . Pardalo s an d Dingzh u D u , Editors , Networ k Design : Connectivit y an d

Facilities Locatio n

39 Pau l W . B e a m e an d Samue l R Buss , Editors , Proo f Complexit y an d Feasibl e

Arithmetics

38 Rebecc a N . Wrigh t an d Pete r G . N e u m a n n , Editors , Networ k Threat s

37 Bori s Mirkin , F . R . McMorris , Fre d S . Roberts , an d Andre y Rzhetsky , Editors ,

Mathematical Hierarchie s an d Biolog y

36 Josep h G . Rosenste in , Debora h S . Franzblau , an d Fre d S . Roberts , Editors ,

Discrete Mathematic s i n th e School s

35 Dingzh u D u , Ju n Gu , an d Pano s M . Pardalos , Editors , Satisfiabilit y Problem : Theory an d Application s 34 Nathanie l Dean , Editor , Africa n American s i n Mathematic s

TITLES I N THI S SERIE S

33 Rav i B . Boppan a an d Jame s F . Lynch , Editors , Logi c an d Rando m Structure s

32 Jean-Charle s Gregoire , Gerar d J . Holzmann , an d Doro n A . Peled , Editors , Th e SPIN Verificatio n Syste m

31 Nei l Immerma n an d Phokio n G . Kolaitis , Editors , Descriptiv e Complexit y an d

Finite Model s

30 Sandee p N . Bhatt , Editor , Paralle l Algorithms : Thir d DIMAC S Implementatio n

Challenge

29 Doro n A . Peled , Vaugha n R . Pratt , an d Gerar d J . Holzmann , Editors , Partia l

Order Method s i n Verificatio n

28 Larr y Finkelstei n an d Wil l ia m M . Kantor , Editors , Group s an d Computatio n I I

27 Richar d J . Lipto n an d Eri c B . Baum , Editors , DN A Base d Computer s

26 Davi d S . Johnso n an d Michae l A . Trick , Editors , Cliques , Coloring , an d

Satisfiability: Secon d DIMAC S Implementatio n Challeng e

25 Gilber t Baumslag , Davi d Epstein , Rober t Gilman , Hamis h Short , an d Charle s

Sims, Editors , Geometri c an d Computationa l Perspective s o n Infinit e Group s

24 Loui s J . Billera , Curti s Greene , Rodic a Simion , an d Richar d P . Stanley , Editors , Formal Powe r Serie s an d Algebrai c Combinatorics/Serie s Formelle s e t Combinatoir e Algebrique, 199 4

23 Pano s M . Pardalos , Davi d I . Shalloway , an d Guolian g Xue , Editors , Globa l

Minimization o f Nonconve x Energ y Functions : Molecula r Conformatio n an d Protei n Foldin g

22 Pano s M . Pardalos , Maurici o G . C . Resende , an d K . G . Ramakrishnan , Editors ,

Parallel Processin g o f Discret e Optimizatio n Problem s

21 D . Fran k Hsu , Arnol d L . Rosenberg , an d Dominiqu e Sotteau , Editors ,

Interconnection Network s an d Mappin g an d Schedulin g Paralle l Computation s

20 Wil l ia m Cook , Laszl o Lovasz , an d Pau l Seymour , Editors , Combinatoria l

Optimization

19 Ingema r J . Cox , Pierr e Hansen , an d Bel a Julesz , Editors , Partitionin g Dat a Set s

18 Gu y E . Blel loch , K . Man i Chandy , an d Sures h Jagannathan , Editors ,

Specification o f Paralle l Algorithm s

17 Eri c Sve n Ristad , Editor , Languag e Computation s

16 Pano s M . Pardalo s an d Henr y Wolkowicz , Editors , Quadrati c Assignmen t an d

Related Problem s

15 Nathanie l D e a n an d Gregor y E . Shannon , Editors , Computationa l Suppor t fo r

Discrete Mathematic s

14 Rober t Calderbank , G . Davi d Forney , Jr. , an d Nade r Moayeri , Editors , Codin g

and Quantization : DIMACS/IEE E Worksho p

13 Jin-Y i Cai , Editor , Advance s i n Computationa l Complexit y Theor y

12 Davi d S . Johnso n an d Catherin e C . McGeoch , Editors , Networ k Flow s an d

Matching: Firs t DIMAC S Implementatio n Challeng e

11 Larr y Finkelstei n an d Wil l ia m M . Kantor , Editors , Group s an d Computatio n

10 Joe l Friedman , Editor , Expandin g Graph s

9 Wil l ia m T . Trotter , Editor , Plana r Graph s

8 S imo n Gindikin , Editor , Mathematica l Method s o f Analysi s o f Biopolyme r Sequence s

7 Lyl e A . M c G e o c h an d Danie l D . Sleator , Editors , On-Lin e Algorithm s

For a complet e lis t o f t i t le s i n thi s series , visi t th e AMS Bookstor e a t w w w . a m s . o r g / b o o k s t o r e / .