New Jersey Institute of Technology Digital Commons @ NJIT
Dissertations Electronic Theses and Dissertations
Fall 1-31-2001
Interference suppression and diversity for CDMA systems
Xiaodong Cai New Jersey Institute of Technology
Follow this and additional works at: https://digitalcommons.njit.edu/dissertations
Part of the Electrical and Electronics Commons
Recommended Citation Cai, Xiaodong, "Interference suppression and diversity for CDMA systems" (2001). Dissertations. 457. https://digitalcommons.njit.edu/dissertations/457
This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at Digital Commons @ NJIT. It has been accepted for inclusion in Dissertations by an authorized administrator of Digital Commons @ NJIT. For more information, please contact [email protected].
Copyright Warning & Restrictions
The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material.
Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or reproduction is not to be “used for any purpose other than private study, scholarship, or research.” If a, user makes a request for, or later uses, a photocopy or reproduction for purposes in excess of “fair use” that user may be liable for copyright infringement,
This institution reserves the right to refuse to accept a copying order if, in its judgment, fulfillment of the order would involve violation of copyright law.
Please Note: The author retains the copyright while the New Jersey Institute of Technology reserves the right to distribute this thesis or dissertation
Printing note: If you do not wish to print this page, then select “Pages from: first page # to: last page #” on the print dialog screen
The Van Houten library has removed some of the personal information and all signatures from the approval page and biographical sketches of theses and dissertations in order to protect the identity of NJIT graduates and faculty.
A S AC
I E E E CE SU ESSIO A I E SI Y O C MA SYS EMS
b d n C
I co e- i isio mu i e-access (C MA sys ems ue o o -o ogo a i y o e
s ea i g co es a mu i a c a e s e esi e sig a su e s i e e e ce
om o e use s Sig a a i g ue o mu i a o aga io is a o e sou ce
o im ai me i wi e ess C MA sys ems o e se e e y im ac i g e o ma ce
I is isse a io e uce - a k mi imum mea squa e e o (MMSE ecei e
a e uce - a k mi imum a ia ce ecei e a e i es iga e o su ess i e -
e e ce; a smi i e si y is a ie o mu ica ie C MA (MC-C MA sys ems
o com a a i g; acke com i g is s u ie o o i e o i e e e ce su essio
a i e si y o C MA a om access sys ems
e e uce - a k MMSE ecei e a uses a e uce - a k es ima e co a ia ce
ma i is s u ie o im o e e e o ma ce o MMSE ecei e i C MA sys ems
I is s ow a e e uce - a k MMSE ecei e as muc e e e o ma ce a
e u - a k MMSE ecei e w e e co a ia ce ma i is es ima e y usi g a i i e
um e o a a sam es a e esi e sig a is i a ow ime sio a su s ace I
is a so emo s a e a e e uce - a k mi imum a ia ce ecei e ou e o ms
e u - a k mi imum a ia ce ecei e e o a i i y e si y u c io o e
ou u S o e u - a k a e uce - a k i ea MMSE es ima o s is e i e
o a ge e a i ea sig a mo e u e e assum io a e sig a s a oise
a e Gaussia is i u e
S ace- ime co i g a is o igi a y o ose o a ow a sys ems is
a ie o a MC-C MA sys em i o e o ge a smi i e si y o suc a
wi e a sys em Some ec iques o oi y eco e e s ace- ime co e a su ess i e e e ce a e e e o e e c a e es ima io usi g ei e i o c a e s o i o sym o s is s u ie o MC-C MA sys ems wi s ace- ime co i g
e o ma ce o C MA a om access sys ems wi acke com i i g i a i g c a e s is a a y e y com i i g e cu e e a smi e acke wi a i s
e ious a smi e co ies e ecei e o ai s a i e si y gai us a i c ease i e e e ce a oise su essio gai e e o e e i e o a e ama ica y
ec eases wi e um e o a smissio s i c easi g w ic i u im o es e sys em oug u a e uces e a e age e ay INTERFERENCE SUPPRESSION AND DIVERSITY FOR CDMA SYSTEMS
by Xiaodong Cai
A Dissertation Submitted to the Faculty of New Jersey Institute of Technology in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy of Electrical Engineering
Department of Electrical and Computer Engineering
January 2001 Copyright © 2001 by Xiaodong Cai
ALL RIGHTS RESERVED A O A AGE
I E E E CE SU ESSIO A I E SI Y O C MA SYS EMS
d n C
( Aka su isse a io A iso a e o esso o E ec ica a Com u e E gi ee i g I
o gya Ge Commi ee Mem e a e Assis a o esso o E ec ica a Com u e E gi ee i g I
ic a a a Commi ee Mem e a e o esso o E ec ica a Com u e E gi ee i g I
A e a e M aimo ic Commi e Mem e a e Associa e o esso o E ec ica a Com u e E gi ee i g I
ack Wi e s Commi ee Mem e a e Mem e o ec ica S a A & a s- esea c e a k IOG A ICA SKE C
A th r: Xiaodong Cai
r : Doctor of Philosophy
t : January 2001
Und r r d t nd Gr d t Ed t n:
• Doctor of Philosophy in Electrical Engineering, New Jersey Institute of Technology, Newark, NJ 2001
• Master of Engineering in Electrical Engineering, National University of Singapore, Singapore, 1997
• Bachelor of Science in Information and Electronic Engineering, Zhejiang University, Hangzhou, China, 1989
M j r: Electrical Engineering
bl t n nd r nt t n :
Xiaodong Cai, Yi Sun, and Ali N. Akansu, "Performance of DS-CDMA random access systems with packet combining in fading channels," to be submitted to IEEE Journal in Selected Area on Communications.
Xiaodong Cai and Ali N. Akansu, "Multicarrier CDMA systems with transmit diversity," IEEE VTC 2000, Boston, MA, Oct. 2000.
Xiaodong Cai, Hongya Ge, and Ali N. Akansu, "Reduced rank minimum variance receiver for asynchronous CDMA Systems," IEEE ICC 2000, New Orleans, LA, pp. 1030-1033, June 2000.
Xiaodong Cai and Ali N. Akansu, "A subspace method for blind channel identification in OFDM systems," IEEE ICC 2000, New Orleans, LA, pp 929-933, June 2000.
v Xiaodong Cai, Hongya Ge, and Ali N. Akansu, "Low-rank minimum variance CDMA receiver in multipath channels," IEEE ICASSP 2000, Istanbul, Turkey, pp. 2877-2880, June 2000.
Xiaodong Cai, Hongya Ge, and Ali N. Akansu, "On the conditioned signal-to-noise ratio of linear MMSE estimators," 34th Annual Conference on Information Sciences and Systems, Princeton, NJ, pp. FA2:1-5, Mar. 2000.
Kun Wang, Xiaodong Cai, and Hongya Ge, "A novel space-time rake receiver for DS-CDMA systems," 34th Annual Conference on Information Sciences and Systems, Princeton, NJ, pp. FA3:12-17, Mar. 2000.
Xiaodong Cai, Hongya Ge, and Ali N. Akansu, " Low-rank MMSE detector for synchronous DS-CDMA," 33th Asilomar Conference on Signals, Systems and Computer, Pacific Grove, CA, pp. 940-944, Oct. 1999.
Mahalingam Ramkumar, Ali N. Akansu, and Xiaodong Cai, "Floating signal constellations for multimedia steganography," IEEE ICC 2000, New Orleans, LA, pp. 249-253, June 2000.
Xiaodong Cai and Ali N. Akansu, "OFDM systems embedded training sequence in the guard intervals," submitted to ICASSP 2001.
H.H. Chen and Xiaodong Cai , "Waveform optimization for OQAM-OFDM systems by using nonlinear programming algorithms," 1997 47th IEEE Vehicular Technology Conference, Phoenix, AZ, pp. 1385-1389, May 1997.
Hsiao-Hwa Chen and Xiaodong Cai, "Optimization of transmitter and receiver filters for OQAM-OFDM systems using nonlinear programming," IEICE Transactions on Commu- nications, v E80-B n 11 Nov 1997, pp. 1680-1687. o my e o e a e s
i ACK OW E GME
I wish to express my sincere gratitude to my advisor, Dr. Ali N. Akansu, for providing a stimulating and inspiring research environment. It was his constant encouragement, guidance and support that made this pursuit stimulating and rewarding. I would like to express my appreciation to Dr. Hongya Ge, who spend much time to discuss with me on some ideas and details. I have benefited so much from her suggestions and comments. Thanks are due also to Dr. Yi Sun for his insightful discussions that lead to the research work on CDMA random access system with packet combing.
I must extend my gratitude to Dr. Richard Haddad, Dr. Alexander M. Haimovich and Dr. Jack H. Winters for serving as members of the dissertation committee and for their valuable comments. No doctoral experience would be complete without the friends that have helped shape it. I would like to thank my good friends Anil, Bin, Burak, Feihong, Minyi, Sebnem and Surong for making my stay at the laboratory enjoyable. Finally, words can never express the gratitude I feel toward my mother and father who teach me the importance of hard work and perseverance and instill in me the confidence that I could succeed at whatever I chose to do.
v A E O CO E S
Ch pt r
1 I O UC IO 1
1 1 C MA Sys ems 1
1 1 1 S-C MA 1
1 1 Mu ica ie C MA
1 Mu iuse e ec io 3
1 3 i e si y ec iques 5
1 esis O e iew
E UCE - A K MI IMUM MEA SQUA E E O ECEI E A E UCE - A K MI IMUM A IA CE ECEI E O S- C MA SYS EMS
1 e uce - a k MMSE ecei e 9
1 1 e uce - a k MMSE ecei e 11
1 e o ma ce A a ysis 1
1 3 A a i e e uce - a k MMSE ecei e ase o a Su s ace- acki g A go i m 1
1 ume ica a Simu a io esu s 19
e uce - a k Mi imum a ia ce ecei e 3
1 A ow-Com e i y Mi imum a ia ce ecei e
e uce - a k Mi imum a ia ce ecei e 31
3 Simu a io esu s 33
3 o a i i y e si y u c io o Co i io e S s o i ea MMSE Es ima o s 3
3 1 o a i i y e si y u c io o Co i io e S s o u - a k a e uce - a k MMSE Es ima o s 37
3 ume ica esu s 1
v A E O CO E S (C nt n d Ch pt r
2.4 Summary 42 3 MULTICARRIER CDMA SYSTEMS WITH TRANSMIT DIVERSITY . 45
3.1 Space-Time Coding 46 3.2 MC-CDMA with Transmit Diversity 47 3.2.1 Signal Model 48 3.2.2 Interference Suppression and Decoding 49 3.2.3 Simulation Results 52 3.3 Channel Estimation 56 3.3.1 Wide-Sense-Stationary and Uncorrelated Scattering Channel Model 56 3.3.2 Channel Estimation Using Pilot Channels 59 3.3.3 Channel Estimation Using Pilot Symbols 63 3.3.4 Simulation Results 65 3.4 Summary 71 4 PACKET-SWITCHED CDMA RANDOM ACCESS SYSTEMS WITH PACKET COMBINING 72 4.1 System Description 74 4.2 Bit Error Probability 77 4.2.1 Slotted CDMA System 77 4.2.2 Unslotted CDMA System 81 4.3 System Throughput and Delay 85 4.4 Numerical Results and Discussions 86
4.5 Summary 90
5 CONCLUSIONS AND FUTURE DIRECTIONS 95 5.1 Conclusions 95 5.2 Future Directions 97
x A E O CO E S (C nt n d
Ch pt r A E I _A E I A IO O E SECO A IA E I A I E O MSE I EQ 99 E E E CES 1 IS O A ES
bl
2.1 The Adaptive Algorithm for the Reduced-Rank MMSE Detector 20
x IS O IGU ES
r
1 SI o e MMSE e ec o s =31 K=1 S = SI o e MMSE e ec o s =31 K=1 S = (K-1 i e - e e ces S s 1 3 SI o e MMSE e ec o s =31 K=1 S = (K-1 i e - e e ces S s a e 1 1 1 1 1 3 3 5 SI o e MMSE e ec o s =15 K=1 S = (K-1 i e - e e ces S s a e s 5 5 MSE o e MMSE e ec o s =31 K=1 S = K-1 i e e e ce use s S s a e 9 9 1 1 1 11 11 MSE o e MMSE e ec o s =31 K=1 S = K-1 i e e e ce use s S s a e 9 1 11 1 3 31 7 MSE o e MMSE e ec o s =31 K=1 S = K-1 i e e e ce use s S s a e 1 17 1 19 1 3 7 e o ma ce o e a a i e e uce - a k MMSE e ec o i a y amic mu i e-access c a e e ocessi g gai is =15 e o ge i g ac o is [3 = 995 7 9 Mi imum a ia ce ecei e 31 1 Ou u SI com a iso o i e e a ks =31 K= S = (K-1 i e e e ces S s a e s 35 11 Ou u SI com a iso o i e e a ks =31 K= S = (K-1 i e e e ces S s a e 3 s 35 1 e o ma ce o e a a i e e uce - a k MMSE e ec o i a y amic mu i e-access c a e 3 13 e si y u c io o o ma i e ou u S i u S =15 M= =31 = 3
ii IS O IGU ES (C nt n d r 1 e si y u c io o o ma i e ou u S i u S = M= =31 = 3 15 e si y u c io o o ma i e ou u S i u S =15 M=1 =15 =1 1 e si y u c io o o ma i e ou u S i u S = M=1 =15 =1 3 1 A MC-C MA a smi e wi a smi i e si y 3 E e sus S o S-C MA MC-C MA wi o e a e a a wi wo a e as K=1 5 3 3 E e sus S o MC-C MA wi a smi i e si y K=1 5 3 E e sus S o MC-C MA wi a smi i e si y K=3 55 3 5 E e sus S o MC-C MA wi a smi i e si y MMSE e ca ie com i e 55 3 Mea squa e -e o o e c a e es ima o usi g i o c a e s
3 7 i e o a e o MC-C MA wi i o c a e s fdTb = 1 K=1 =
3 i e o a e o MC-C MA wi i o c a e s fdTb = 1 K= = 7
3 9 i e o a e o MC-C MA wi i o c a e s fdTb = 5 K=1 = 7
3 1 i e o a e o MC-C MA wi i o c a e s fdTb = 5 K= = 3 11 Mea squa e -e o o e c a e es ima o usi g i o sym o s
3 1 i e o a e o MC-C MA wi i o sym o s fdTb = 1 K=1 = M= 9
3 13 i e o a e o MC-C MA wi i o sym o s fdTb = 1 K= = M= 9
3 1 i e o a e o MC-C MA wi i o sym o s fdTb = 5 K=1 =9 M= 7
3 15 i e o a e o MC-C MA wi i o sym o s fdTb = 5 K= =9 M= 7 IS O IGU ES (C nt n d
r 4.1 BER versus SNR for the slotted CDMA system. a = 3/8, = 2, Processing gain = 64 in simulation. 91 4.2 BER versus SNR for the unslotted CDMA system. a = 3/16,L = 2, Processing gain = 64 in simulation. 91 4.3 BER versus normalized offered load. S = d = 2. The number of transmissions rt = 3. 92 4.4 BER versus the number of transmissions. S = 1 d = 3/8, = 2 92 4.5 Normalized throughput of the slotted CDMA system. S = d = 2. 93 4.6 Average delay of the slotted CDMA system. S = d = 2. . . 93 4.7 Normalized throughput of the unslotted CDMA system. S = d = 2 94 4.8 Average delay of the unslotted CDMA system. S = d = 2. . 94
i C A E
I O UC IO
. C MA Sys ems
I wi e ess commu ica io s mu i e access sc emes a e use o a ow ma y use s o s a e simu a eous y a i i e amou o a io s ec um eque cy i isio mu i e access ( MA ime i isio mu i e access ( MA a co e i isio mu i e access (C MA a e e ee ma o access ec iques use o s a e e a ai a e
a wi i a wi e ess commu ica io sys ems MA assig s a u ique eque cy
a o c a e o eac use O ce e c a e is assig e o o e use ca s a e
e same c a e MA sys ems i i e e a io s ec um i o ime s o s a i eac s o o y o e use is a owe o ei e a smi o ecei e I C MA sys ems a
e use s s a e e same s ec um a wi a ime s o s Eac use is assig e a s eci ic co e a ca e use o se a a e i om o e use s I ou wo k we a e
a icu a y i e es e i some ec iques o im o e e e o ma ce a ca aci y o C MA sys ems
. . S C MA
I i ec seque ce C MA ( S-C MA sys ems a a ow a sig a a co ai s a message is mu i ie y a sig a wi a e y a ge a wi sig a ca e e s ea i g sig a e s ea i g sig a is com omise o c i s a a e e i e y a seu o a om seque ce w ic is k ow o o e a smi e a ecei e
e c i a e is muc g ea e a e a a a e o e message A use s use e same ca ie eque cy a may a smi simu a eous y e ecei e e o ms a co e a io o e a io o e ec e sig a o e esi e use A o e use s sig a a ea as oise a e ou u o e co e a o e oise comi g om o e use s a e ca e mu i e access i e e e ce (MAI
C MA sys ems ca o e a e some MAI I o uc io o eac a i io a ac i e use i c ease e o e a e e o i e e e ce o e o e use s Eac use i o uces a u ique e e o i e e e ce a e e s o owe e e i s imi g sy c o i a io
e a i e o o e sig a s i e sys em a i s s eci ic c oss-co e a io wi o e
C MA sig a s e o e a ce o MAI is o u imi e a as e um e o i e -
e i g use s i c eases e equi a e oise esu s i eg a a io o e o ma ce
E e i e um e o use s is o oo a ge some use s may e ecei e a suc
ig sig a e e s a a owe owe use may e swam e ou is is e ea - a e ec use s ea e ecei e a e ecei e a ig e owe s a ose a away a
ose u e away su e a eg a a io i e o ma ce
o com a e ea - a o em owe co o is use i mos C MA sys ems
owe co o is o i e y eac ase s a io a assu es a eac mo i e use wi e ase s a io co e age a ea o i es e same sig a e e o e ase s a io
ecei e is so es e o em o a ea y use o e owe i g e ase s a io
ecei e a ow i g ou e sig a s o a away use s es i e e use o owe co o e e o ma ce a c a e ca aci y S-C MA sys ems a e imi e y e
MAI
. .2 M lt rr r C MA
e mu ica ie C MA a smi e s ea s e o igi a a a s eam o e i e e su ca ie s usi g a s ea i g co e i e eque cy omai A ac io o e sym o co es o i g o a c i o e s ea i g co e is a smi e oug a i e e ca ie I o e o e su e a eac ca ie u e goes a a i g e um e o ca ie may e g ea e a e ocessi g gai I is case e o igi a a a s eam is i s co e e i o se e a a a e s eams Eac a a e a a s eam is mo u a e o e ( ocessi g gai ca ie s Mu ica ie mo u a io ca e e o me usi g i e se isc e e ou ie a s o m (I w ic ca e im eme e e y e icie y with fast algorithms. A proper guard interval is inserted in between different data blocks to eliminate inter block interference. It has been shown [29] that the MC-
CDMA has better performance than the DS-CDMA in fading channels.
.2 M lt r t t n Multiuser detection techniques can substantially increase capacity relative to the matched filter receiver. The matched filter treats MAI the same as background Gaussian noise, whereas a multiuser detector exploits the specific structure of MAI. The optimal multiuser receiver proposed by Verdu [97] demonstrates that DS-CDMA is not fundamentally MAI limited and can be near-far resistant. The optimal detector comprises a bank of matched filters followed by a maximum-likelihood (ML) sequence detector whose decision algorithm is the Viterbi algorithm [70]. The computational complexity of the optimal detector grows exponentially with the number of users. To reduce the complexity, many suboptimal detectors have been proposed. These suboptimal detectors can be put in three categories: nonlinear detector, linear detector and a hybrid of the nonlinear and linear detectors. The nonlinear multiuser detectors include successive interference cancellation (SIC) [40, 43, 67, 100], parallel inference cancellation (PIC) [17, 50, 51, 95, 111], decision-feedback detector [20] and iterative detector [2, 64, 102]. In successive interference cancellation, the users are ordered from strongest to weakest, and are successively demodulated. The inter- ference are removed from users in that order. In parallel interference cancellation, estimated symbols from all users simultaneously regenerate and remove interference for each user. Whereas successive interference cancellation requires a nonuniform distribution of transmitted powers across users to achieve uniform performance across users, parallel interference cancellation is less sensitive to this power distribution. A decision-feedback multiuser detector is analogous to th decision-feedback equalizer for single-user channels. It consists of a linear feedforward filter followed by a feedback
oo w ic im eme s successi e i e e e ce ca ce a io a is e ee ack ma i is co s ai e o e owe - iago a so a use s a e emo u a e succes- si e y e i e a i e mu iuse e ec o is i s i e y i e a i e u o eco e s [7]
Es ima e sym o s a e ou u o e eco e a o g wi e ia i i y i o ma io is use o ca ce o a ia y ca ce i e e e ce o o e use s e e o ma ce o
e i e a i e mu iuse e ec o ca eac e si g e-use ou
e i ea mu iuse e ec o is a im o a c ass o su o ima e ec o
ecause i is ea - a esis a a is easi y im eme e e i ea mu iuse
e ec o i c u es eco e a o [5 59 9] a i ea MMSE e ec o [ 1 11 ]
A eco e a o emo es a c oss co e a io s e wee use s e e o e e imi a i g mu i e access i e e e ce eco e a o s a e a so s ow o e o ima y ea -
a esis a [5 ] owe e i a ma e a a ogous o e o- o ci g equa i a io
oise e a ceme may e a o em e MMSE e ec o [ 1 11 ] mi imi es e mea squa e -e o e wee e a smi e sym o a e ou u o e e ec o
MMSE e ec o as a so ee s ow o e ea - a esis a [ 1] As e e e o
ackg ou oise e s o e e o o as e e gies o i e e e ces i c ease o i i i y
e MMSE i ea e ec o co e ges o e eco e a i g e ec o
A com i a io o e eco e a i g e ec o a IC was co si e i [9 ] com i a io o MMSE e ec o a IC i [1 39] a com i a io o e eco -
e a i g e ec o a SIC i [19] I ese e ec o s a i ea mu iuse e ec o is usua y i s use o ge e a e i i ia sym o es ima es ese es ima es a e e use i a a a e o successi e i e e e ce ca ce e o emo e esi ua i e e e ce
om e ecei e sig a gi i g a"c ea e -u " sig a is sig a is agai i u o a i ea mu iuse e ec o gi i g a e i e se o es ima es is oce u e ca e i e a e o im o e e es ima es u e
. v r t hn
I wi e ess e i o me sig a a i g a ises ima i y om mu i a o aga io o a a smi e sig a ue o e ec io s o ysica o ec s e s e g o e
a i g sig a may e e y weak ue o es uc i e a i io o mu i a s i e
o aga io me ia Se e e a e ua io i sig a s e g makes i im ossi e o e
ecei e o e e mi e e a smi e sig a owe e e e ec s o a i g ca e su s a ia y mi iga e oug e use o i e si y ec iques ee mai o ms o i e si y a e a i io a y e oi e o a yi g eg ees i wi e ess commu ica io s sys ems em o a i e si y s ec a i e si y a s a ia i e si y
Temporal diversity is e ec i e w e e a i g is ime-se ec i e C a e co i g i co u c io wi ime i e ea i g e ec s em o a s ea i g o sym o s e e y
o i i g o i e si y Spectral diversity is e ec i e w e e a i g is eque cy- se ec i e is o m o i e si y ca e ac ica y e oi e w e e a ai a e
a wi o a smissio is a ge e oug a i i i ua mu i a com o e s ca egi o e eso e o equi a e y w e i is a ge e oug a i e e su a s o e a smissio a wi e e ie ce e ec i e y i e e e a i g
I C MA sys ems e sig a a wi is muc a ge a e co e e a wi o e c a e us C MA sys em ca ake a a age o eque cy i e si y
Spatial diversity i o es e use o mu i e a e as a ei e e ecei e e
a smi e o o e sig a s ecei e om su icie y s ace a e as wou
a e esse ia y u co e a e e e o es e ecei e e o m com i i g o se ec io a swi c i g o im o e e qua i y o e ecei e sig a
e use o mu i e a e as a e mo i e makes e emo e u i s a ge a mo e e e si e I is mo e eco omica a easi e o a mo e a e as o e ase s a io s a e a e emo e u i s o is easo a smi i e si y sc emes a e
e y a ac i e i a ac ica sys em e ea y a oac es o a smi i e si y use sig a ocessi g a e a smi e o s ea e i o ma io ac oss e a e as 6
I [1 1 9 1 77 1 7] o ogo a sig a i g is use a e a smi e ase swee i g is em oye i [35 53] so a e ecei e sig a is a as a i g sig a e e e c a e is s ow a i g e sig i ica gai o e a smi i e si y ca
e ea i e y iew is o em om a co i g e s ec i e a e a u e y om
e sig a ocessi g oi o iew ece y S ace- ime e is co i g [ 7 ] a s ace- ime ock co i g [ , 5] a e o ose o a smi i e si y Ge e a eo y
o co s uc e ec i e s ace- ime co es a e gi e i [3 3 ]
.4 h Ov rv
I is i o uc o y c a e we a e a em e o e iew e C MA sys ems mu iuse e ec io a i e si y ec iques a us ay e ackg ou o e su ec ma e ia o is o osa
C a e is a ou e e uce - a k MMSE ecei e e e uce - a k mi imum a ia ce ecei e a e o a i i y e si y o co i io e S o
i ea MMSE es ima o s I Sec io 1 e e uce - a k MMSE ecei e is i s
e e o e e e o ma ce o e e uce - a k MMSE ecei e i e ms o e
MSE a e ou u o e ecei e is a a y e i a y a a a i e e uce - a k
MMSE ecei e is e e o e ase o a su s ace acki g a go i m I Sec io we s a y e e o i g a ow-com e i y mi imum a ia ce (M C MA ecei e a e e e o a e uce - a k M ecei e I sec io 3 e o a i i y e si y
u c io o co i io e S o i ea MMSE es ima o s is s u ie ese es ima o s a e e u - a k es ima o o ai e y sam e ma i i e se (SMI me o a e
e uce - a k es ima o o ai e y e i ci a com o e i e se ma i ( CI me o
I c a e 3 MC-C MA sys ems wi a smi i e si y is s u ie e s ace- ime ock co e is use o i o uce a smi i e si y Ou em asis is u o e esig o i ea ecei e a eco es e s ace- ime co e a su esses 7 interference. Channel estimation using pilot channels or pilot symbols is studied for the multicarrier CDMA system with space-time coding. In chapter 4, the system performance of CDMA random access systems with linear receivers and packet combing in multipath fading channels is analyzed. By using packet combing, the receiver obtains a diversity gain and a interference suppression gain. Both the slotted CDMA system and unslotted CDMA system with random spreading signature are considered. The bit error rate of the MMSE receiver, decorrelator and matched filter receiver in fading channels is first calculated, and the system throughput and average delay is then analyzed. Chapter 5 contains concluding remarks and a summary of the thesis. C A E 2
E UCE A K MI IMUM MEA SQUA E E O ECEI E A E UCE A K MI IMUM A IA CE ECEI E O S C MA SYS EMS
Mi imum mea squa e e o (MMSE i e e e ce su essio me o s a e ee
o ose o S-C MA sys ems [ 1] I as ee s ow a suc sc emes o i e
o e ia y a ge e o ma ce gai s e a i e o e co e io a ma c e i e
ecei e e i MMSE ecei e i [37] mi imi es e ecei e s mea ou u e e gy (MOE w i e co s ai i g e es o se o e use o i e es o a co s a I is s ow a MOE a MMSE a e i ec y e a e a mi imi i g o e is equi a e
o mi imi i g e o e
I [7 ] i ea mu iuse e ec o s o sy c o ous C MA a e e i e wi i
e amewo k o co s ai e o imi a io [ ] I e case o a si g e co s ai
a co es o s o k ow e ge o e esi e use s co e e ge e a co s ai e o imi a io e ec o e uces o e MOE e ec o i [37] ese i ea e ec o s a e simi a i s i i o e mi imum a ia ce eam o mi g a ge e a i e si e o e ca ce e (GSC i e co e o a ay sig a ocessi g [ ] e s ea i g co e o e esi e use ays e same o e as e s ee i g ec o A e e sio o
e co s ai e o imi a io a oac o mu i a C MA c a e s was o i e i [ 9 ] I is s ow a e e o ma ce o e mi imum a ia ce ecei e wi o ima co s ai s a oac es e e o ma ce o MMSE ecei e a ig S e o ima co s ai ec o ca e ou y ma imi i g e ou u sig a owe a e
e i e e e ce is su esse usi g a mi /ma a oac
I S-C MA sys ems e um e o ac i e use s K is usua y ess a e
ocessi g gai e ce e e ec i e a k o e oise- ee sig a co a ia ce
ma i is usua y ess o muc ess a e sig a ime sio I is c a e we e o e e ow a k a u e o e C MA sig a o e e o e e uce - a k
8
MMSE ecei e a e e uce - a k mi imum a ia ce ecei e e o ec i es o
e uce - a k MMSE ecei e i c u e e uci g o e com u a io a com e i y a e amou o ai i g a a a is equi e o co a ia ce es ima io e uce -
a k ocessi g me o s i c u e e mu is age Wie e i e (MW [ 7] e c oss- s ec a me ic (CSM [ 5 ] i ci a com o e s i e se ( CI [93 9 9] eige ca ce e [31 3 ] a i e a s o ms [ ] e e ec o e um e o a a sam es i co a i ace ma i es ima io o e e uce - a k MMSE i e is s u ie i [ 9 1 ] e uce a k mu is age Wie e i e a CI e uce a k MMSE
i e a e ee a ie o C MA sys em [3 1 1] I is c a e we wi use CSM me o o e uce e a k o MMSE ecei e a mi imum a ia ce ecei e I wi
e s ow a e e uce - a k ecei e ca ou e o m u - a k ecei e w e e co a ia ce ma i is es ima e om a i i e um e o a a sam es o u e u e s a e e o ma ce o e u - a k a e uce - a k ecei e we s u y
e e si y u c io o e co i io e ou u S o e i ea MMSE es ima o s
ase o a ge e a sig a mo e
2. d d n MMSE v r
We co si e a S-C MA sys em wi K use s simu a eous y a smi i g o e a a i i e w i e Gaussia oise (AWG c a e e ecei e ase a sig a ca
e mo e e as
w e e n(t is AWG wi owe s ec a e si y a A is e ecei e sig a am i u e om use is e sym o u a io τk is e a i e e ay wi es ec
o e ecei e a (t is e o ma i e s ea i g wa e o m I is assume a
b ( } is a se o i e e e equi o a e +1 a om a ia es a a (t is 0 su o e o y o e i e a [ 7] S ea i g wa e o m k (t is e esse as
use 71 (t is a o ma i e c i wa e o m o u a io c a = I is e ocessi g gai
I is sec io we es ic ou a e io o e sy c o ous case o mo e ( 1 i w ic 7-1 = 7- = = τK = 0. It is e su icie o co si e e ecei e sig a
u i g o e sym o u a io a e ecei e sig a mo e ecomes
A asy c o ous sys em o K use s ca e iewe as equi a e o a sy c o ous sys em wi K — 1 use s [ us e esu s o is sec io a y i is co e as we
Co si e e sy c o ous mo e ( 3 Sam i g e c i -ma c e i e ou u
a c i a e we ge a 1 ec o wi i a sym o i e a
is e o ma i e sig a u e wa e o m
ec o o e a use a n is a w i e Gaussia oise ec o wi mea 0 a
co a ia ce ma i σ I (I e o es e N x i e i y ma i We ca a so e ess
( as
2. . d d n MMSE v r
Su ose e esi e use is use 1 a i ea mu iuse e ec o o emo u a i g is use s a a i i ( 5 is i e o m o a i ea i e o owe y a a imi e
e i ea MMSE e ec o mi imi es e mea -squa e e o a is gi e b
I is easi y s ow a e MMSE so u io o is
is e c oss-co e a io e wee 1 a r, a ma i C is e co a ia ce ma i o r. We ca is e ec o u - a k MMSE e ec o e co a ia ce ma i is gi e y
I ca a so e e esse i e ms o i s si gu a a ue ecom osi io
eige a ues o C i esce i g o e a U, = [ ... UK]co ai s e co es o i g
o o o ma eige ec o s; A = σ I -K a Un co ai s e — K o o o ma eige ec o s wi e eige a ue - e a ge s ace o U, is ca e e sig a s ace si ce i as e same a ge as S. e a ge o Un is ca e e oise s ace
Si ce s 1 is o ogo a o e oise s ace i is easi y s ow a e u - a k
MMSE e ec o i ( ca a so e e esse i e ms o e sig a s ace a ame e s 2 a mea -squa e e o is w i e as
I ca e see om ( 11 a e MMSE e ec o is a ec o yi g i e sig a s ace e ime sio o e sig a s ace is K, e ce we ca is e ec o a k-K
e ec o I as e same e o ma ce as e u - a k e ec o ecause e esi e use s sig a u e is o ogo a o e oise s ace We wi see a e a e a k-K
e ec o e o ms e e a e u - a k e ec o w e e co a ia ce ma i is es ima e I e o owi g eo em we e i e e o ose e uce - a k MMSE
e ec o a ies i a su s ace o e sig a s ace
h r Suppose that matrix U,. contains r(r < K) columns of U and A consists of corresponding eigenvalues, and the reduced-rank MMSE detector lies in the range space of U r , then the rank-r MMSE detector C r is given by
and the mean-squared error is found as
r f: e = [ , w w ] a c = 1 w e e mea -squa e e o is ca cu a e y
e i a i e o M S Er wi es ec o is o ai e as 13
e i g i e equa o e ec o we ge
e e we use e ac a e eige ec o s a e o o o ma e e a k- MMSE
e ec o i ( 13 o ows y su s i u i g w i ( 17 i o ( 15 we ge e mea - squa e e o i ( 1 111
a k MMSE e ec o ca a so e o ai e as o ows e o ec io ma i
o e a ge s ace o U is = U U e o ec io o e ecei e sig a o e
a ge o U is 1 = e i ea MMSE e ec o ase o 1 is c 1 = C1-1 1 w e e C 1 is e co a ia ce ma i o 1 a i is e c oss-co e a io e wee 1 a 1 I is easi y s ow a c 1 is e same as c i ( 13
Com a i g ( 1 a ( 1 we ca see a e mea -squa e e o o e
e uce - a k e ec o is o ess a a o e a k-K e ec o Si ce e sig a
o i e e e ce a io o e MMSE e ec o is gi e y SIR =1/MMSE — 1 [ 1]
e e uce - a k e ec o ca o e o m e e a e u - a k e ec o u
y ica y e K use owe s a e i e e e e esi e use may ie i a owe
ime sio a su s ace o e sig a s ace I is case i we c oose U suc a
e esi e use is i e a ge o U e e e uce - a k e ec o as e same
e o ma ce as e a k-K e ec o I e esi e use ies i e w o e sig a s ace
e e uce - a k e ec o wi e o m wo se a e a k-K e ec o o a gi e
a k we ca c oose e su s ace i w ic e e uce - a k MMSE e ec o ies suc a e oss o e e o ma ce is mi imi e e us e i e a qua i y Qi as
Qi ca e iewe as e o ma i e e e gy o use 1 o ec e o o e i ase
e MMSE i (1 ca a so e e esse as 4
e e o e gi e e a k o e e ec o e o ima a k- MMSE e ec o
is o ai e y o ci g e e ec o o ie i e su s ace s a e y e asis
co es o i g o a ges Q i o e a e o ose su s ace se ec io makes use
o e sig a u e o e esi e use is me o o c oosi g su s ace is simi a o
e c oss s ec a me ic (CSM a oac [ ] o su s ace se ec io i e co e
o a ge e a i e si e o e ca ce e
I ac ice e co a ia ce ma i C is u k ow I is es ima e om e
ecei e sig a A commo y use es ima io is e sam e co a ia ce ma i a
is e ma imum ike i oo es ima e o e co a ia ce ma i u e e Gaussia
assum io e eige ec o s a eige a ues o e es ima e co a ia ce ma i a e
i e e om ose o e ue co a ia ce ma i e MMSE e ec o is o ai e
om e es ima e eige ec o s a eige a ues We wi see a e a e e uce -
a k MMSE e ec o yi g i o e su s ace e o ms e e a o e a k-K
e ec o a e u - a k e ec o is is e ma o a a age o e e uce - a k
MMSE e ec o
2. .2 rf r n An l
I is sec io we a a y e e e o ma ce o e e uce - a k MMSE e ec o s i
e ms o e mea -squa e e o a e ou u o e e ec o s e e uce - a k
MMSE e ec o s a e o ai e om e es ima e co a ia ce ma i We i s ie y
e iew e asym o ic s a is ics o e eige a ues a eige ec o s com u e om
e sam e co a ia ce ma i W e M sam es o a a ec o r , m = 1 M}
a e a ai a e e co a ia ce ma i ca e es ima e y
e Ai a ui e o e e i eige a ue a co es o i g eige ec o com u e
om e sam e co a ia ce ma i C We e i e Δλi = A i — i a ui = ui — ui
Assumi g a a e eme s o A i 1 K} a e is i c We k ow om 15
is asym o ica y o ma wi e o mea a
is asym o ica y i e e e o {Δui i = 1 K} E eme s
a e mu ua y i e e e e a ia ce o Δλi is o =
A /M e co a ia ces o { ui i = 1 K} i e imi i g is i u io a e gi e
y [3]
e us e o e e a k- MMSE e ec o o ai e om e es ima e co a ia ce ma i as é I is a a om ec o e e i g o e es ima e eige a ues a eige ec o s A e mea -squa e e o co i io e o c is a so a a om a ia e Ou o ec i e is o ge e mea o e co i io e mea -squa e e o
e a oac is ase o a seco -o e ay o se ies e a sio o e co i io a mea -squa e e o
e mea -squa e e o co i io e o is gi e y
e seco -o e ay o se ies e a sio o MSEr a ou e oi ={ui λi i = 1 } is gi e y
w e e ec o gi is e g a ie o MSEr a o g u a oi ; fi is e i s a ia e i a i e o MSEr wi es ec o λi a oi ; is e seco a ia e i a i e o MSEr wi es ec o λi a a oi ; a e e eme s o e ec o o a ma i i a e gi e y 6
ake e ec a io o MSEr wi es ec o {Δλi ui i = 1 } we a e
w e e tr(• e o es e ace o e ma i i e a e esis e e we use e ac
a e mea s o Δλi a u i a e e o a e e eme s o {Δλi i = 1 } a e mu ua y i e e e a {Δλi i = 1 } is i e e e o { u i i = 1 }
ii a 4 ca e ou as
(i e i a io o ii a i is gi e i A e i A
2. . Ad pt v d d n MMSE v r d n S b p r n Al r th
o im eme e ow- a k MMSE e ec o we ee o es ima e e eige ec o s o e co a ia ce ma i co es o i g o e sig a s ace a e co es o i g eige a ues is ca e ac ie e y usi g si gu a a ue ecom osi io (S o eige a ue ecom osi io (E o e a a sam e co a ia ce ma i C assica
a c E a a c S a go i ms [ ] a e com u a io a y ema i g I o e o o e come is i icu y a um e o a a i e a go i ms o su s ace
acki g as ee e e o e [1 113] I [1 1] e o ec io a o ima io su s ace acki g ( AS a go i m i [113] is use o i a a i e mu iuse
e ec io e AS a go i m as ow com u a io a com e i y (O(NK)). 17
owe e i s co e ge ce s ee is e y s ow o c oose e o ima a k o e
o ose ow- a k MMSE e ec o we ee e o ogo a eige ec o s owe e
e asis o e sig a su s ace acke y AS a e o o ogo a I is wo k we use e su s ace acki g a go i m i e ow- a k a a i e i e ame
O A 1 i [ ] e su s ace acki g a go i m i O A 1 as com u a-
io a com e i y o O( K e e is a o e owe com e i y (O( K su s ace
acki g a go i m i O A 3 i [ ] owe e we o se e i simu a io s a i as e y ow co e ge ce s ee I co as e su s ace acki g a go i m i
O A 1 co e ges as i simu a io s I a C MA sys em use s e e o ea e e sys em a om y e e o e e sig a s ace c a ges We ee a as co e ge ce a go i m o ack a ia io s o e sig a s ace e su s ace acki g a go i m i O A 1 assumes a k ow sig a s ace ime sio I ca o ack e a k o
e sig a co a ia ce ma i I is wo k we com i e e a k acki g me o i
[11 ] i o e su s ace acki g a go i m i O A 1 We e ie y e iew e
a a i e a go i m o o a k a su s ace acki g
e o e co a ia ce ma i a ime t as C e i e a K ma i U wi o o o ma co um s e o owi g o ogo a i e a io [ ] ge e a es a seque ce o ma i { i
w e e U a a e e ac o s o a ski y Q ecom osi io o ma i A
Assumi g a C oes o c a ge i ime o e ca s ow [ ] a e seque ce
o ecu sio ma i { U } wi co e ge owa s e ma i o omi a eige ec o s
ikewise e seque ce o e ia gu a ma i { } wi co e ge owa s e
iago a ma i o omi a eige a ues I ou case C is e i e y C =
Ei =i i - i i w e e 1 C is u a e ecu si e y acco i g o C = 8βCt
A key s e [ ] owa s e as su s ace acki g a go i m is e o ogo a o ec io o e ac ua ecu sio ma i U o o e e ious su s ace s a e y e co um s o U _1 us we a e
w e e e = U i U a A is o ogo a o e co um s ace o U -1 e u a e equa io ( ecome
O y e as e m equi es O( 2 K o e a io s u i ca e
eg ec e wi ou a y e o ma ce e a y [ ] is esu s i e O( r2 ecu sio
o a i ec u a i g o ma i A
e as su s ace acki g a go i m co sis s o equa io s ( 31 a ( 3 We ca mo i y is a go i m o ack o e a k a e sig a s ace as o ows Su ose
a e a k is K a we ack K+1 omi a eige ec o s a eige a ues ase o e es ima e eige a ues o e ca es ima e e a k o e sig a s ace usi g i o ma io - eo e ic c i e ia suc as e Akaike i o ma io c i e io (AIC [1 3]
Su ose e es ima e a k is I K emo e e as K — co um s om ma i U I K a a ec o x o ma i U as i s as co um ec o x ca e o ai e y o ec i g e a a ec o o o o ogo a su s ace o co um s a o U e qua i y AIC is e i e as o ows
is e i e as
e es ima e o a k is gi e y e a ue o k a mi imi es e qua i y ( 35
A e e eige ec o s a co es o i g eige a ues a e es ima e we ca co s uc e o ima ow- a k MMSE e ec o Assume a e ecei e k ows e ms io sig a u e o e esi e use S i e es ima e o qua i y Qi i ( 1 is Q = l t e o ima a k- MMSE e ec o c is o ai e usi g e eige ec o s a eige a ues co es o i g o a ges ( i A yi g e e ious a a o eac o K
ow- a k e ec o s { ci i = 1 K} we ca es ima e e mea -squa e e o a
e ou u o eac ow- a k e ec o e o ima ow- a k MMSE e ec o is e o e a i g e sma es mea -squa e e o W e we es ima e e mea -squa e e o e e ec o ca o e a e ei e i e ai i g mo e o e ecisio - i ec e mo e i a y e o ose a a i e a go i m o e ow- a k MMSE e ec o is summa i e i a e I
2. .4 r l nd S l t n lt
I is sec io we o i e some simu a io e am es o emo s a e e e o ma ce o e e uce - a k MMSE e ec o e e o e i sec io 1 1 a k- MMSE
e ec o ies i e su s ace s a e y eige ec o s co es o i g o a ges
Q (Q is e i e i ( 1 We a so gi e e a a y ica esu s usi g e ec ique
e e o e i sec io 1 We use Go seque ce as e s ea i g seque ce e
esi e use is use 1 e e o ma ce measu e o simu a io is e sig a o i e -
e e ce a io (SI e sus e a k o e MMSE e ec o s Si ce e is i u io o
e ou u o e i ea MMSE e ec o is a o ima e y Gaussia [ 9] e ou u
SI a s a es easi y i o a equi a e e o o a i i y o e i e a a i s o
e esi e use SI is e i e as SIR = E {c 1 }/ a { } w e e e e ec a io is wi es ec o e a a i s o MAI s a e oise W e e co a ia ce ma i is k ow i e e sig a u es a e am i u es o a e use s a e k ow SI is 20 1 gi e y
I simu a io s e e ec a io o e a io is e ace y e ime a e agi g o e a io
I a a ysis e e o ma ce measu e is mea -squa e e o (MSE e sus e a k o e e ec o s e i u S (S is e i e as A1 /σ o e esi e use is
Example 1: Simulation of a single user system
We i s co si e e si g e use case e ocessi g gai is N = 31 e simu a e e o ma ce is o e i ig 1 e a a o e a e a e age o e
i e e e simu a io s Si ce e oise- ee sig a as a k 1 e o ma ces o a e e ec o s wi i e e a ks a e e same w e e co a ia ce ma i is k ow W e e co a ia ce ma i is es ima e we see a e a k-1 e ec o
as e es e o ma ce I we use mo e asis o e a e o e co es o i g o
e a ges Qi i = 1 N o co s uc e e ec o we ge mo e oise a e
esi e sig a a e ou u o e e ec o e e o e e e o ma ce eg a es
We ca a so see a e um e o sam es M, use o es ima e e co a ia ce ma i a ec s e e o ma ce o e a k- ( 1 e ec o o e am e w e
M = SI a e u - a k e ec o ou u is 11 1 W e M = 1 i is a ou 1
Example 2: Simulation of 10 user systems
We e co si e 1 use cases e ocessi g gai is N = 31 e a a
o e a e e a e age o e i e e e simu a io s I ig i e i e -
e e ce use s S s a e 1 is may e e case i w ic e e is o y o e use i e ce u e e e is i e -ce i e e e ces e sig a u e o e esi e use
ies i a su s ace w ose ime sio is a mos o i s e e gy is i a o e- ime sio a su s ace e e o e w e e co a ia ce ma i is es ima e e a k-1 e ec o 22
as e es e o ma ce I ig 3 e e a e i e weak i e e e ces a ou s o g i e e e ces e a k- e ec o as e es e o ma ce ig is o
e e ec owe co o case w e e i e i e e e ce use s a e e same owe as
e esi e use I is case a k-K e ec o as e es e o ma ce si ce e
sig a u e o e esi e use is i e w o e sig a s ace A o e simu a io s s ow
a e e ec o s w ose a k is g ea e a K e o m wo se a e o ima
e uce - a k e ec o
Example 3: Comparison of simulation and analytical results
I is e am e we com a e e simu a io esu s wi e a a y ica esu s
e ocessi g gai is N = 31 e e a e 1 use s i e sys em e um e o
sam es use o es ima e e co a ia ce ma i is 1 S s o i e e use s a e
c ose o e i e e i o e o make e e a ges eige a ues o e co a ia ce
ma i e i e e w ic is ecessa y i a a ysis e simu a io esu s a e e
a e age o e i e e e u s I ig 5 a ig mos o e e e gy
o e esi e use is i a ow ime sio a su s ace e ce w e e e ec o
is o ai e om e es ima e co a ia ce ma i o e simu a io esu s a
e a a y ica esu s s ow a e uce - a k e ec o as e e e o ma ce a
e a k-K e ec o u w e co a ia ce ma i is k ow a k-K as e es
e o ma ce as e ec e is s ows e a a age o e e uce - a k MMSE
e ec o w e e co a ia ce ma i is u k ow I ig 7 i e e e ces owe s
a e c ose o a o e esi e use e sig a u e o e esi e use is i e w o e
sig a s ace e e o e e a k-K e ec o as e es e o ma ce
Example Performance simulation of the adaptive reduced-rank MMSE detector i a y we use e a a i e a go i m e e o e i Sec io o simu a e e
e o ma ce o e a a i e e uce - a k e ec o i a y amic mu i e-access
c a e e simu a io esu s a e is aye i ig A t = e e a e 1 2 use s i e c a e e esi e use s S is e e a e si 1 - use s o e - use o e 3 - use o e - use A = a - use e e s
e c a e ; a t = e wo - use s e i e c a e e ocessi g gai is N = 31 e o ge i g ac o is = 995 e a a o e a e e a e age o e i e e e simu a io s e i s 1 i e a io s a e i e ai i g mo e a e es a e i e ecisio i ec e mo e e e e ious i s a e use o es ima e e mea -squa e e o We see a e o ima e uce - a k e ec o as a o ima e a a age o e e a k-K e ec o e a a i e a go i m as a as co e ge ce s ee
2.2 d d n M n r n v r
I is sec io we co si e e e uce - a k mi imum a ia ce (M ecei e e a a age o mi imum a ia ce ecei e e a i e o e MMSE ecei e is a e
M ecei e ca e im eme e i y e M ecei e o y ee s k ow e sig a u e a e imi g o e esi e use I s e o ma ce is c ose o e MMSE
ecei e I a a i e im eme a io o e o ima mi imum a ia ce ecei e [9 ]
e o ima co s ai ec o is i icu o ack u e mo e i com e mu i a c a e s e e is a ase am igui y i e o ima co s ai ec o e e o e
e a smi e a a s ou e i e e ia y e co e e ase am igui y ca
e eso e y i e e ia eco i g I is sec io we o ose a AKE ecei e
o owe y a equa gai com i e e im u se es o se o e i e i eac i ge is o ai e y e mi imum a ia ce c i e io e oise a e ou u o e AKE
ecei e is a o ima e y w i e e a smi e a a a e i e e ia y e co e
us we ca use a sim e equa gai com i e o co ec a e e e gy o e esi e use E e y i ge o e AKE ecei e is im eme e a a i e y wi e same s uc u e as a GSC A su s ace acke acks e sig a s ace o e a a i e
ow- a c o e GSC ase o e acke sig a s ace e e y i ge o e AKE 24
r 2. SI o e MMSE e ec o s =31 K=1 S =
r 2.2 SI o e MMSE e ec o s =31 K=1 S = (K-1 i e - e e ces S s 1 igu e 3 SI o e MMSE e ec o s =31 K=1 S = (K-1 i e - e e ces S s a e 1 1 1 1 1 3 3
igu e SI o e MMSE e ec o s =15 K=1 S = (K-1 i e - e e ces S s a e s 26
r 2. MSE o e MMSE e ec o s =31 K=1 S = K-1 i e - e e ce use s S s a e 9 9 1 1 1 11 11
r 2.6 MSE o e MMSE e ec o s =31 K=1 S = K-1 i e - e e ce use s S s a e 9 1 11 1 3 31 r 2. MSE o e MMSE e ec o s =31 K=1 S = K-1 i e - e e ce use s S s a e 1 17 1 19 1 3
r 2.8 e o ma ce o e a a i e e uce - a k MMSE e ec o i a y amic mu i e-access c a e e ocessi g gai is =15 e o ge i g ac o is = 995 28
ecei e c ooses a su s ace o e sig a s ace o o m e e uce - a k ecei e
Si ce we ee o y o e su s ace acke o a e i ge s a co s ai ec o s a e i e e com u a io com e i y o e o ose ecei e is muc owe a
a o e mi imum a ia ce ecei e wi e o ima co s ai s Simu a io s
emo s a e a e e o ma ce o e o ose ecei e is a mos e same as
a o e mi imum a ia ce ecei e wi e o ima co s ai s W e e co a ia ce ma i is es ima e e o ima e uce - a k ecei e ou e o ms e
u - a k ecei e
2.2. A C pl x t M n r n v r
We co si e a S-C MA sys em wi K use s simu a eous y a smi i g oug
ei es ec i e mu i a c a e s wi a i i e w i e Gaussia oise (AWG
e a smi e sig a ue o e k use is gi e y
w e e A is e sig a am i u e is e sym o u a io τk is e a i e e ay wi
es ec o e ecei e a (t is e o ma i e s ea i g wa e o m gi e i (
e k use s sig a o aga es oug a mu i a c a e wi e com e im u se es o se (t A e ecei e e ecei e sig a is i s i e e y a c i ma c e i e a e sam e a e c i a e us im u se es o se o e
a e isc e e- ime c a e
w e e is e e g o e c a e im u se
e sam e o e sig a com o e c i o e kth r
o maki g a ecisio o e sym o o e esi e use we co si e a
ec o y[ ] E C + co es o i g o e o se a io i e a e 29 w e e [ ] e o es e a ges i ege a is sma e a x As i [ ] e
e o e e acyc ic e s i o e a o a TR e o e e acyc ic ig s i o e a o
o o ec o s o e g + us o a ec o
e o e n a ica io s o ese o e a o s esu i g i e a ig s i s y es ec i e y
ec o ue o e l th use is
e o a sig a ec o is gi e y
w e e u is a com e AWG ec o wi co a ia ce a - 1
A i ea ecei e is a co e a o w a o uces e o owi g s a is ic o e
sym o z[n] = [n] e mi imum a ia ce a oac se ec s e co e a o w y mi imi i g e ou u owe E{ [ ]} su ec o a se o co s ai s [ ]
is e a a co a ia ce ma i C is a ma i w ose ows s eci y e co s ai s f is e co s ai ec o As s ow i [ ] e o ima so u io o is o em is wo = veu(c --icH)-if .
Su ose a e esi e use is use 1 e x (N + co s ai ma i C is
e o ima ec o f is ou as e eige ec o o C ; 1 C co es o i g o
e mi imum eige a ue [9 ] I a a i e im eme a io e o ima ec o f is i icu o ack I [ ] ec o f is c ose as f = [1 ] y oi g so e 30
ecei e co ec s e sig a e e gy i e i s a u isca s e e e gy i o e
a s o e oi a e e e gy iu t l [57] o ose a eco e a i g AKE
ecei e e im u se es o se o e i e i e i i ge o e AKE ecei e is o ai e y a o e co s ai e o imi a io wi e ec o i = ei w e e ei is e u i ec o wi a e eme s s e ce 1 a e i osi io e ou u s
om e i ge s o e AKE ecei e a e co e e y com i e e com i i g
ec o is ou as e i ci a eige ec o o e co a ia ce ma i o e ou u o e AKE ecei e I is o ice a e e a e ase am igui ies i e o ima
ec o f i sa sa is ecei e [9 ] a i e com i g ec o i iu s eco e a i g
AKE ecei e [57] e e o e a smi e a a s ou e i e e ia y e co e
o e uce e com e i y o e ecei e u e we o ose a sim e equa gai com i e a e iu s eco e a i g AKE ecei e i com i a io wi i e e ia e co i g/ eco i g i s we iscuss e o owi g ac
Fact: e oise a e ou u o e AKE ecei e is a o ima e y w i e
e ec o [ ] E C e o e e oise a e ou u o e AKE ecei e e a (C - i i c -1 --i -1 co a ia ce ma i o v is = (C C -1 Su ose - Y
a e e is a ma i A suc a C AC = I e Rv = σ A om e e a io s
a CC ACC = CC a CC i I, we a e A I. us v is a o ima e y w i e
e o es ec o [ ] E C as e ou u o e AKE ecei e Su ose a
e e is o esi ua i e e e ce i [ ] e o imum ecisio a ia e [9 ] o e
i e e ia y e co e a a is U[n] = [ — 1] 11 7 1 [ ] Si ce oise is a o ima e y w i e e ecisio a ia e ca e o ai e om a equa gai com i e I is gi e
y U[n] = [ — 1] [ ] I ac ice e esi ua i e e e ce may o e eg igi e
e e e ess we s i use is sim e com i e We wi see a e i simu a io s a
is ow-com e i y ecei e as a mos e same e o ma ce as sa sa is mi imum
a ia ce ecei e wi o ima co s ai s 31
Figure 2.9 Mi imum a ia ce ecei e
2.2.2 Reduced-Rank Minimum Variance Receiver
e mi imum a ia ce ecei e ca e im eme e i a a i io e o m e me a ge e a i e si e o e ca ce e (GSC [ ] as s ow i ig 9 e ec o wee i e i i ge i e u e a c ca e e esse as w ci = C (CC - ei ocki g ma i B i e owe a c is c ose o sa is y C = a o e as ime sio s o ( + q) . e o ima a a i e weig s w ai ca e ou as [ ]
is e co a ia ce ma i o e owe a c a a a
is e c oss-co e a io e wee e owe a c a a a ou u o e i i ge i e u e a c
e co a ia ce ma i R b ca a so e e esse i e ms o i s si gu a a ue
ecom osi io
( e e s o use s e ays mi ( K mi (3K + 1 a ges eige -
a ues o R b i esce i g o e a U = [u ... up] co ai s e co es o i g o o o ma eige ec o s; 11 n = σ I -D a Ur, co ai s e — o o o ma 2 eige ec o s wi e eige a ue a e a ge s ace o U is ca e e sig a s ace
e a ge o Ur is ca e e oise s ace
e u - a k so u io i ( is a ec o i e sig a s ace e e uce -
a k so u io o wag is a ec o i a su s ace o e sig a s ace Su ose wai is i e a ge o ma i U r w e e U,. co ai s co um s o e ma i U a e
iago a ma i A co ai s co es o i g eige a ues e w ai is gi e y
w e e is e m co um o e ma i
U . o a gi e a k o mi imi e e ou u owe e o ima r, c ooses
eige ec o s co es o i g o a ges a ues o Q im W e y a y i a e k ow e ou u owe o e e uce - a k ecei e ca o e ess a a o
e u - a k ecei e e e o e a y e uce - a k ecei e e o ms wo se a e
u - a k ecei e I a ac ica sys em e co a ia ce ma i y a e c oss-
co e a io y i a e es ima e e es ima es a e
W e e ecei e is o ai e om e es ima e
co a ia ce ma i a c oss-co e a io simu a io s emo s a e a e a k-
ecei e a ways ou e o ms e u - a k ecei e Si ce e es ima e sig a s ace
a oise s ace a e i e e wi e ue o es e e uce - a k ecei e wi e
a k ess a D may a e e e e o ma ce a e a k- ecei e is is a so
e i ie i simu a io s e e o e we ca c oose a o e su s ace o e e y i ge
suc a e e uce - a k ecei e ac ie es e es e o ma ce A i ui i e way
o c oosi g e su s ace is o se ec e o e suc a e squa e o e ou u is
mi imi e owe e e e uce - a k ecei e o ai e usi g is me o as owe
sig a o i e e e ce a io (SI a e u - a k ecei e i simu a io s We us
o ose a o e me o o c oosi g e uce - a k ecei e as o ows o e e y
a k (1 D) , we ca ge a o ima wa Su ose {u m m E I} is e
se o e eige ec o s a r, c ooses Ca cu a e e qua i ies 33
e e e uce - a k w ai is e o e a as e sma es
a k suc a Q r/Q ts , w e e t, is a es o a is c ose o 1 is me o a oi s usi g e eige ec o s a a e c ose o e oise s ace I simu a io s e
e uce - a k ecei e a is c ose usi g is me o e o ms a eas as we as
e a k- ecei e
e ecu si e eas -squa es ( S a go i m ca e use o e weig a a a io o e u - a k ecei e o im eme e e uce - a k ecei e we
ee o es ima e e eige ec o s o e co a ia ce ma i co es o i g o e sig a s ace a e co es o i g eige a ues e e we use e su s ace acki g a go i m i [ ] o ack e eige ec o s a eige a ues o e co a ia ce ma i
w e e /3 is e o ge i g ac o
e a go i m i [ ] ca o ack e a k o e sig a co a ia ce ma i I a
C MA sys em use s ea e o e e e sys em a om y e e o e e sig a s ace c a ges We ee o ack e a ia io s o e sig a s ace e a k acki g me o i [11 ] is com i e i o e su s ace acki g a go i m e c oss- co e a io ca e u a e ecu si e y acco i g c
2.2. S l t n lt
I is sec io simu a io esu s a e ese e o emo s a e e e o ma ce o
e o ose a go i m e e o ma ce measu e o simu a io s is e a e age
SI o ai e y i e e e u s e i u S o e esi e use is
e ocessi g gai is N = 31 e s ea i g seque ces a e e Go seque ces
Mu i a c a e s a e ee a s E e y a is a om y ge e a e om a com e
Gaussia is i u io e ays a e a so a om y ge e a e C a e s a e ays a e
i e i e e y u e ou u SI e sus e a k o e ecei e o e equa owe case a e ea - a case a e is aye i ig 1 ig 11 es ec i e y We o se e a e o ose ow-com e i y ecei e as a mos e same e o ma ce 3 as sa sa is s mi imum a ia ce ecei e wi e o ima co s ai s W e e co a ia ce ma i is k ow e uce - a k ecei e s ca o ou e o m e u - a k
ecei e owe e w e e co a ia ce ma i is es ima e e o ima e uce -
a k ecei e as a ge SI a e u - a k ecei e o e am e i equa owe case is aye i ig 1 e ou u SI o e a k-15 ecei e is a ge a a o e u - a k ecei e w e M = e easo is e ai e as o ows
W e e co a ia ce ma i is k ow e oise s ace is a so k ow e oise s ace is o ogo a o e c oss-co e a io ec o us e u - a k ecei e is i
e sig a s ace e e o e e u - a k ecei e as e same e o ma ce as e
a k- ecei e owe e w e e co a ia ce ma i is es ima e e es ima e
oise s ace is o o ogo a o e c oss-co e a io ec o a ymo e As a esu
e u - a k ecei e as a com o e i e oise s ace e e is mo e oise a
e ou u o e u - a k ecei e a a o e e uce - a k ecei e e e o e i s ou u SI eg a es e simu a io esu s o e a a i e e sio o e
o ose e uce - a k a u - a k mi imum a ia ce ecei e s a e emo s a e i ig 1 e S a go i m is use o e u - a k ecei e I e uce - a k
ecei e e es o o su s ace se ec io is s = 99 A t = e e a e eig use s i e c a e S s o a e use s a e A t = wo 3 - use s a o e - use e e e c a e ; a t = e - use wo 3 - use s a wo - use s e i e c a e We see e a a age o e e uce - a k
ecei e o e e u - a k ecei e Figure 2.10 Ou u SI com a iso o i e e a ks =31 K= S = (K-1 i e e e ces S s a e s
Figure 2.11 Ou u SI com a iso o i e e a ks =31 K= S = (K-1 i e e e ces S s a e 3 s 6
r 2. 2 e o ma ce o e a a i e e uce - a k MMSE e ec o i a y amic mu i e-access c a e
2. r b b l t n t n t n f C nd t n d S f n r MMSE E t t r
o u e u e s a e e o ma ce o e e uce - a k ecei e s e e o e i
as wo sec io s we s u y e o a i i y e si y u c io o e ou u S o
i ea MMSE es ima o s w e e co a ia ce ma i is es ima e A e a e o em is o e ec a k ow sig a wi a om ase i e ese ce o com e Gaussia
oise usi g a a a i e a ay e o imum e ec o was gi e i [ 1] e o a-
i i y e si y u c io o S a e ou u o e e ec o a is o ai e usi g
e sam e co a ia ce ma i was e i e y ee et al [73] a a uma a [33]
W e e u e yi g oise co a ia ce ma i is o u - a k e uce - a k e ec o s
[ ] o i e e o ma ce a a age o e e u - a k a oac
2. . r b b l t n t n t n f C nd t n d S f ll n nd d d n MMSE E t t r
Co si e a ge e a i ea a a mo e [ 7] gi e y
a om a ame e s a n is a 1 Gaussia oise ec o wi e o mea a co a ia ce ma i o- 1 Su ose a a ea i a io o 1 is o e es ima e h a
a ia ce o 1 (say ? a e assume o e k ow O e a ame e s a e assume
o e uisa ce a ame e s o i e e e ces o 1 e ma i a e a ia ce o
uisa ce a ame e s a oise a e assume o e u k ow o e es ima o is
a a mo e is o e use i igi a commu ica io s o e am e i a mu iuse commu ica io sys em wi i ea mo u a io e e e i o ma io - ea i g a a o p use s a e e mo u a e wa e o m e sig a o use 1 is o i e es a o e s a e i e e e ces e e ecei e sig a ca e mo e e wi a o e a a mo e
o co e ie ce o a a ysis we u e assume a e e eme s o a e i e e e Gaussia a om a ia es wi e o mea a a e a ia ce o eac e eme is o ecessa y e same U e e Gaussia assum io s e i ea
MMSE es ima o is ac ua y a ue MMSE es ima o e i e weig s , a yie e i ea MMSE es ima o o 1 a e gi e y
w e e is e co a ia ce ma i o x. e es ima e o [ e ou u
S is gi e y 8
e o ima e ec o a e ec s sig a 1 is w = i [73] w e e is e co a ia ce ma i o i e e e ces us oise I ca e s ow a e weig ec o o e o ima e ec o is o o io a o a o e MMSE es ima o e e o e
e ou u S o e o ima e ec o is e same as a o e MMSE es ima o
owe e w e e weig ec o s a e o ai e om e es ima e co a ia ce ma i we wi see a e e si y u c io s o e ou u S s a e i e e
o ma y a ica io s e co a ia ce ma i is u k ow e e o e es ima e co a ia ce ma i is use i ca cu a i g e weig ec o w e us assume a M i e e e a a s a s o s { 1 a e o se e U e e Gaussia assum io
e ma imum- ike i oo es ima e o e co a ia ce is e sam e co a ia ce ma i
a is gi e y
us e weig ec o is ou as
is me o o ca cu a i g e weig ec o is ca e e sam e ma i i e se
(SMI me o o e a e weig ec o w is a a om ec o e ou u S co i io e o W is
e co i io e S is u e ou e y e ma imum ac ie a e S e esse i ( 9 We o ma i e e co i io e S wi es ec o i s u e ou
e o e is o ma i e S y ρ e o e
We o ice a p as e same o mu a as e o ma i e ou u S o e e ec o ase o e SMI me o i [73] ecause e a a a e a Gaussia is i u io e e si y o p is gi e y [73]
us e e si y o ρs is ou as
Su s i u e ( 53 i o ( 5 we a e
U ike e o ma i e S o e o ima e ec o i [73] e o ma i e S o
e MMSE es ima o e e s o e ma imum ac ie a e S I [73] i is ou
a a eas M = — 3 sam es o a a a e ee e o e e ec o o mai ai a a e age ou u S oss o e e a 3 Si ce e e ec a io o ρs is a
y e geome ic u c io e e is o c ose - o m o e um e o sam es equi e
o e MMSE es ima o o ac ie e a a e age e o ma ce e e owe e gi e
e ma imum ac ie a e S e g o e a a ec o a e e o ma ce
oss e a i e o e ma imum ac ie a e S o e ca com u e e um e o e sam es y usi g ume ica i eg a io We ca a so a o ima e y ca cu a e e
um e o sam es as o ows W e N > e u c io p(ρ as o e a o y o e ma imum oi o e i e a ( 1 I ca e ou as
W e N = e u c io p(ρ as a 40 ma imum oi a = (M — 1 /( S I e ma imum oi is a = 5 e
o a i i y a ρs is g ea e a 5 is a o ima e y equa o 5 We ca i
a M = — 3 + ( — 1 so a p(ρ ac ie es ma imum a ue a =ρ 5
is is a use u " u e-o - um " equi eme o e um e o a a sam es o e es ima o s e o ma ce oss o e ess a 3 o e a e um e o a a sam es is o o io a o e ma imum ou u S a e e g o e a a
ec o
W e is es ima e usi g sam e co a ia ce ma i i ( 5 we e o m e S o e es ima e co a ia ce ma i . e e uce - a k MMSE es ima o s a e co s uc e om e es ima e eige ec o s a eige a ues W e p i ci a eige a ues a e i e e ese eige a ues a ei co es o i g eige ec o s a e asym o ic Gaussia is i u io s [ ] ei mea a co a ia ce ca e ou i [ ] owe e i is i icu o e i e e e si y o e ou u S o e
e uce - a k es ima o s om e is i u io s o e eige a ues a eige ec o s
We co si e e e uce - a k es ima o usi g p es ima e eige ec o s co es o i g
o e p a ges eige a ues w ic is gi e y
is me o o ca cu a i g e weig ec o is ca e e i ci a com o e i e se
( CI me o We wi gi e a asym o ic o mu a o e CI es ima o ase o
e o mu a we ge e asym o ic e si y o e ou u S
Su ose a we a e a ec o
I is k ow a as M ∞ w e e --1-- e o es co e ge ce i o a i i y e ce we a e a . e e o e — co e ges o e e o ec o i o a i i y Si ce e ou u S is a co i uous u c io o e weig
ec o we a e S — S I ge e a e co e ge ce o e i e e ce o wo 4
a om seque ces o e o i o a i i y oes ecessa i y im y a ei e si ies co e ge owe e i simu a io we o se e a e e si y u c io s o e ou u
S o e es ima o s usi g a o e wo o mu a a e a mos same I is easy o ge
e eo e ic e si y o e ou u S o e es ima o W
e es ima o i ( 59 ca e o ai e as o ows A y e i ea
a s o m = U o e x 1 a a ec o x, we ge a p x 1 ec o t = x.
ase o e a s o me a a t, we ca use e SMI me o o ge e es ima o
e i ea a s o m ese es e Gaussia is i u io o e a a us e
o a i i y e si y u c io o e o ma i e ou u S o es ima o w is e same u c io as i (11 wi e a ame e e ace y p. Si ce e e si y o ou u S o es ima o w is a o ima e y e same as a o es ima o as
M ∞ we ge a asym o ic e si y o e o ma i e ou u S o e CI es ima o
2. .2 r l lt
Co si e a case i w ic e co um s o ma i H a e Go seque ces (s ea i g seque ces use i i ec seque ce s ea -s ec um co e- i isio mu i e-access
eo e ic cu es a simu a io cu es o e o e ou u S a e s ow i
ig 13 ig 1 ig 15 a ig 1 I ese igu es so i i e is eo e ic cu e as i e is simu a io cu e a o i e is simu a io o CI es ima o usi g asym o ic o mu a W e = 31 p = M = e o a i i y e si y
u c io s a e is aye i ig 13 a ig 1 o S =15 a S =
es ec i e y S is e i e as σ1 /σ e i e e e ces a e e same owe as
e esi e sig a Simu a e e si y u c io s a e o ai e om e is og am o
1 i e e e u s We o se e a e CI es ima o s usi g e e ac o mu a a usi g e asym o ic o mu a a e a mos e same e si y cu e Com a i g
ig 13 wi ig 1 we see a e es ima o ee s mo e a a sam es o 42
a e e same o ma i e ou u S w e e i u S is ig e om ig
13 a ig 1 we a so see a wi muc ig e o a i i y e CI me o yie s ig e ou u S a SMI me o Equi a e y o ac ie e e same e e o e o ma ce e CI me o ee s ess um e o a a sam es a e SMI me o o e am e i e case i ig 13 we ca use e " u e o um " i sec io o ge M 1 o e SMI es ima o a M t 1 o e CI es ima o o ac ie e a e o ma ce wi i 3 o e ma imum ou u S W e M is a ge a p is c ose o e e o ma ce ga e wee e SMI es ima o a e CI es ima o ecomes sma e is is emo s a e i ig 15 a ig 1
2.4 S r
I is c a e we s u y e e uce - a k MMSE a mi imum a ia ce C MA
ecei e s I is emo s a e a e e uce - a k MMSE ecei e ou e o ms e co e io a u - a k MMSE ecei e w e e esi e sig a is i a ow- ime sio a su s ace a e co a ia ce ma i is es ima e e mi imum a ia ce ecei e ca e i y im eme e usi g e s uc u e o ge e a i e si e o e ca ce e
e o ose ow-com e i y mi imum a ia ce ecei e as a mos e same
e o ma ce as e ig -com e i y o ima mi imum a ia ce ecei e e
e uce - a k mi imum a ia ce ecei e agai ge e e e e o ma ce com a e wi e u - a k mi imum a ia ce ecei e o u e e i y a e e uce - a k
ecei e oes a e a a age o e e u - a k ecei e we s u y e o a i i y
e si y u c io o e co i io e S o i e MMSE es ima o s U e e
Gaussia assum io we e i e e o e u - a k MMSE es ima o ase o
e sam e ma i i e se me o e o e asym o ic e uce - a k MMSE es ima o ase o e i ci a com o e i e se me o is a so o ai om
ose s we co c u e a e e uce - a k es ima o s o ou e o m e u - a k es ima o 4
r 2. e si y u c io o o ma i e ou u S i u S =15 M= =31 =
r 2. 4 e si y u c io o o ma i e ou u S i u S = M= =31 = r 2. e si y u c io o o ma i e ou u S i u S =15 M=1 =15 =1
r 2. 6 e si y u c io o o ma i e ou u S i u S = M=1 =15 =1 C A E MU ICA IE C MA SYS EMS WI A SMI I E SI Y
A e a i e si y is a ac ica e ec i e ec ique o e uci g e e ime a e ec s i wi e ess a i g c a e s e c assica a e a i e si y a uses mu i e a e as a e ecei e i c eases e cos si e a owe o e emo e u i s I is mo e easi e a eco omica o a e mu i e a e as a e ase s a io a e
a e emo e u i s ece y a smi i e si y as ee s u ie o com a e
a i g c a e s
I [1 1 9] i ea i e i g is i o uce a e a smi e so a e wa e o m a e e y a smi a e a is o ogo a o eac o e A e ecei e
ue o e o ogo a i y amo g sig a s om i e e a e as a o ima com i e ca e use o co ec a e e e gy o m i e e a e as A o ogo a sig a i g
o a smi i e si y i C MA sys em is s u ie i [1 ] e ay a smi i e si y
a is a s ecia case o o ogo a i e i g is s u ie i [77 1 7] A i ea o
o i ea equa i e s ou e use a e ecei e i e e ay i e si y sc eme
I [35 53] ase swee i g is use a e a smi e so a e ecei e sig a is a as a i g sig a e e e c a e is s ow a i g Com i e wi co i g
is ec ique a s e s e s ace i e si y o ime i e si y A ese ec iques a oac e a smi i e si y om a sig a ocessi g oi o iew S ace- ime co es [ 7 5] com i e sig a ocessi g a e ecei e wi co i g ec iques
o i es sig i ica gai o e e i e si y gai i o uce y sig a ocessi g a
e a smi e
Mu ica ie C MA [3 ] as ee o ose o e wi e a mu iuse sys ems
I is s ow [3 ] a MC-C MA ca e ec i e y com i e a e ecei e sig a e e gy sca e e i e eque cy omai w e eas S-C MA ca o a ways em oy e e e gy sca e e i e ime omai e e o e MC-C MA as e e e o ma ce i eque cy-se ec i e a i g c a e a e S-C MA Si ce eac su ca ie i
4 46
MC-C MA u e goes a a i g we ca a u a y com i e e s ace- ime co i g
wi MC-C MA o ge a smi i e si y o a wi e a sys em
. Sp C d n
S ace- ime e is co i g is o ose i [ 7 ] I is emo s a e a s eci ic s ace- ime e is co es esig e o - a smi a e as e o m e eme y we i s ow- a i g c a e e i o me owe e w e e um e o a smi a e as is
i e e eco i g com e i y o s ace- ime e is co es i c eases e o e ia y wi
a smissio a e I [1 5] o ogo a ock co es a e o ose o a ow a
a i g c a e s I was s ow a e s ace- ime ock co es ca ac ie e e ma imum i e si y o e o a gi e um e o a smi a ecei e a e as a i s e co i g a eco i g sc eme as e y i e com e i y e ge e a eo y o co s uc i g s ace- ime co es o SK mo u a io is gi e i [3 ] o eco e
e s ace- ime co es e ecei e ee s e c a e s a e i o ma io owe e a o e ami y o e s ace- ime co es ame u i a y s ace- ime mo u a io [3 ]
e o ms e y we e e oug e ecei e as o k ow e ge o e c a e s a e i o ma io A s ace- ime co e is e i e as [3 ]
f n t n 3 1 A s ace- ime co e C o si e M co sis s o a ( n M e o co o co e C a a s a ia a se a ma s eac co ewo ec o C E C o a 71 ma ices w ose e ies a e a ea a geme o ose o C e s ace- ime co e C is sai o e i ea i o C a a e i ea
Su ose a e e a e t a smi a e as e s a a a se ma s
o e ma i 47 w e e ci is e co e sym o assig e o a smi i a ime t.
Su ose a e sym o a a e o e co ewo s is Y e e co e sym o s a e ma e y e mo u a o i o co s e a io oi s om e isc e e com e -
a ue sig a i g co s e a io a e f y→Ω e e mo u a o ma i g u c io
e s = f (c) is e ase a e sio o e co ewo s as a smi e oug e c a e Su ose a e a k o e ma i B f (c)— f (e) is a e eige a ues o e ma i A = a e i i w e e c a e a e a y ai o is i c co ewo s
e we a e e esig c i e ia o s ace- ime co es [ 7]
1. Rank Criterion: Ma imi e e a k o e a ai s o is i c co ewo s o
ac ie e e ma imum i e si y
2. Product Distance Criterion: Ma imi e e co i g a a age
o e a ai s o is i c co ewo s
Si ce e eco i g me o o e ock s ace- ime co es is e y sim e we wi use em o e MC-C MA sys em We a e a icu a y i e es e i e ock s ace- ime co es o a smissio usi g wo a ou a smi a e as w ic a e
3.2 MC CDMA with Transmit Diversity
A MC-C MA a smi e wi s ace- ime co i g is s ow i ig 3 1 We assume
a e e a e wo a smi a e as a e ocessi g gai N is equa o e
um e o ca ie s e sim es s ace- ime ock co e i [1 5] is use o e
wo a smi a e a case e ou u s o e s ace- ime e co e a e co ie o 48
r . A MC-C MA a smi e wi a smi i e si y
i e e ca ie s e i o e i e e ca ie is mu i ie y a c i o e s ea i g co e I e se isc e e ou ie a s o m (I is use o im eme mu ica ie mo u a io A e e cyc ic e i is a e e sig a is a smi e om o e o e a e as A e ecei e e sig a is i s co e e o ase a sig a A e
e o io o e sig a co es o i g o e e i is emo e isc e e ou ie
a s o m ( is e o me o e sig a sam es
.2. S n l M d l
Assume a e e g o e cyc ic e i is o ge a e e g o e c a e im u se es o se e e e is o i e ock i e e e ce (I I I is su icie o co si e e ecei e sig a i wo co secu i e ocks say ock a ock 1 A e
is e o me e a a a nth ca ie i ock a ock 1 ca e w i e as 4 w e e K is e um e o ac i e use s sk [ ] is e nth c i o e th use s s ea i g co e A is e am i u e o e th use s sig a [n] a i [ ] a e a i i e w i e
Gaussia oise wi a ia ce 2 a o [ ] a [n] a e c a e es o se om wo
a smi a e as o e ecei e a e nth ca ie We assume a e c a e is
e s ow a i g c a e a is e c a e es o ses a e e same i ock a
.2.2 Int rf r n S ppr n nd d n
I e e is o y o e use i e sys em e ma imum ike i oo eco e is sim y a ma imum a io com i e [ 5] owe e w e e e a e mo e a o e use s i e sys em i is i icu o em oy a ma imum ike i oo eco e ecause e ecei e
as o k ow e ge o e s ea i g co es o a e ac i e use s We s a co si e ou sc emes a e ec e i o ma io ea i g i s o e esi e use w i e su essi g o e use s i e e e ce ese ou sc emes a e ma imum a io com i e (M C 0 o ogo a i y es o i g com i e (O C mi imum mea squa e e o com i e
(MMSEC a mi imum mea squa e e o mu iuse e ec o (MMSEMU
1 M x r t b n r
e ou u s o e M C a e gi e y
I ca e s ow a
w e e 1 a /1 a e i e e e ce om e o e use s a a 1 a e Gaussia
oise I is see om (3 13 a (3 1 a M C co e e y com i e e sig a s
om wo a smi a e as e ecisio s o wo i s a e
Orth n l t r t r n b n r
e o ogo a i y amo g e sig a s o i e e use s is os a e e a s- mi e sig a asses oug e c a e I e o ogo a i y ca e es o e e i e e e ce ca e com e e y e imi a e e i e se o ma i 9-1 ca e ou as
I e ma i is si gu a a sue oi e se o 1-1 ca e ou Su ose a e ma i 1 is o si gu a e ou u s o e O C a e gi e y O C ca ce s a e i e e e ce i e a ces e oise W e e c a e es o ses a a ca ie a e sma e S a e ou u o O C wi e e y ow
3 Minimum mean square error combiner:
I MMSEC a MMSE es ima e o e sig a o e esi e use a eac ca ie is i s o ai e e es ima es o e sig a is e co e a e wi e s ea i g co e o e esi e use o o ai e ecisio s a is ic e weig s w oo [ ] a w 1 [ ]
a mi imi e e mea squa e e o
e ou as
Simi a y e weig s w 1 [n] a w11 [ ] a mi imi e e mea squa e e o 2
MMSEC ies o es o e e o ogo a i y as muc as ossi e u o o e a ce
e oise as i O C I ee s e k ow e ge o e oise a ia ce
Minimum mean square error multiuser detector:
I a o e ee sc emes e s uc u e o e o e use s s ea i g co es is o e o e y e ecei e o su ess e i e e e ce MMSEMU uses is s uc u e
o ac ie e e e e o ma ce MMSEMU i s e weig ma i W o mi imi e e mea squa e e o
ma i ca e es ima e usi g a ai a e a a We ca see a e com e i y o
e MMSEMU is muc ig e a e o e ee sc emes ecause i ee s o
i e a ma i
I a ese sc emes e ecei e ee s o k ow e c a e s a e i o ma io
I ac ice eac a e a ca em oy a i o c a e e ecei e uses e i o
c a e o es ima e e c a e s a e A e a i e y some i o sym o s ca e
i se e i e use s a smi e sig a s e i o sym o s e a e e ecei e o
es ima e e c a e
.2. S l t n lt
Simu a io s emo s a e e e o ma ce o e MC-C MA wi a smi i e si y
i a ow i k mu i a a i g c a e Wa s - a ama co es a e c ose as e
s ea i g co es ocessi g gai is N = 3 e a i g c a e as 3 i e e e
a s a i s mu i a i e si y o i e is e o e ia e e ay s ea is T =
w e e 7 is e c i u a io o e S-C MA a as e same a wi as
e MC-C MA We assume a e ecei e k ow e c a e e ec y ig 3 s ows e i e o a e o e S-C MA MC-C MA wi si g e a smi a e a a wi wo a smi a e as e S-C MA sys em uses a ee i ge AKE
ecei e wi ma imum a io com i e e MC-C MA sys ems use ma imum a io com i e s e um e o use s is 1 I is see a e MC-C MA wi a smi
i e si y as e es e o ma ce ig 3 3 a ig 3 com a e e i e o a e o
MC-C MA sys ems wi i e e com i g sc emes MMSE com i e as e same
E as MMSE mu iuse e ec o w e K=3 a as s ig y ig e E a
MMSEMU w e K=1 ecause MMSEMU as muc ig e com e i y a
MMSEC MMSEC is e e e i a ac ica sys em I ig 3 5 e e o ma ce o e MC-C MA sys ems wi a wi ou a smi i e si y is com a e e
MMSE com i e is use I is see agai a e a smi i e si y im o e e sys em e o ma ce o ma e ow ma y use s a e i e sys em r .2 BER versus SNR for DS-CDMA, MC-CDMA with one antenna and with two antennas, K=10
r . BER versus SNR for MC-CDMA with transmit diversity, K=10 55
r .4 BER versus SNR for MC-CDMA with transmit diversity, K=32
r . BER versus SNR for MC-CDMA with transmit diversity, MMSE per carrier combiner 6
. Ch nn l E t t n
In the receiver design in section 3.2, the channel state information is assumed to be known. In practice, the receiver has to estimate the channel response. The reference signal is needed for the receiver to estimate the channel. To provide with the reference signal for the receiver, the transmitter can transmit pilot signals. In a
CDMA system, the pilot signal can be transmitted using a particular spreading code, that is the pilot signal is transmitted by pilot channel. In downlink, the common pilot channel can be used by all the mobile users. The pilot signal can also be time-multiplexed [11, 12, 56] with a user's data and spread by the user's spreading code [23, 55]. In this case, each user uses its particular pilot symbols to estimate the channel. Since the pilot symbols are not transmitted continuously, the receiver has to interpolate the estimated channel to do demodulation. In next sections, after briefly introduce the wide-sense-stationary and uncorrelated scattering (WSSUS) channel model for the wireless communication channel, we shall study the performance of the MC-CDMA system with space-time coding when the channel is estimated using either pilot channels or pilot symbols.
. . W d S n St t n r nd Un rr l t d S tt r n Ch nn l M d l In wireless communication systems, the received signal experiences significant power fluctuation due to fading. Signal fading is caused by multipath propagation in the form of scattering, reflection, and refraction. The propagation path or paths change with the movement of the mobile unit and/or the movement of its surroundings in the propagation environment. A fading multipath channel is generally characterized as a linear, time-varying system having an impulse response (τ; t) which is a wide-sense stationary random in the t-variable. By assuming that the multipath signals propagating through the channel at different delays are uncorrelated, the channel is modeled as a wide-sense 57 s a io a y u co e a e sca e i g o WSSUS c a e [ 7 ] W e e e a e a
a ge um e o sca e s i e c a e a co i u e o e sig a a e ecei e as is e case i io os e ic o o os e ic sig a o aga io e ce a imi
eo em ca e a ie I is case e ime- a ia im u se es o se (τ; t is a com e - a ue Gaussia a om ocess i e t a ia e I e ocess is e o- mea e e e e o e o e c a e im u se es o se a a y ime i s a as a ay eig o a i i y is i u io a e ase is u i o m y is i u e i e i e a ( 7 ime a ia io s i e c a e im u se ca e c a ac e i e y e au oco e a io u c io o (τ; t as
Si ce e sca e i g a wo i e e e ays is u co e a e we a e
e y ica au oco e a io u c io o mo i e commu ica io c a e is gi e by 1421
w e e (x is e e o -o e esse u c io o e i s ki fd is o e
eque cy I we e At = e esu i g au oco e a io u c io is sim y e a e age owe ou u o e c a e as a u c io o e ime e ay
is ca e e e ay owe s ec um o e mu i a i e si y o i e
ime a ia io s i e c a e im u se es o se o eque cy es o se esu i eque cy s ea i g ge e a y ca e o e s ea i g o e sig a a smi e
oug e c a e Mu i a o aga io esu s i s ea i g e a smi e sig a i ime Co seque y a a i g mu i a c a e may e ge e a y c a ac-
e i e as a ou y s ea c a e i ime a eque cy A ou y s ea c a e may e c a ac e i e y e sca e i g u c io S(τ;λ w ic is gi e y e ou ie 8
a s o m o M A i e A a ia e a is
Sca e i g u c io is a measu e o e owe s ec um o e c a e a e ay a eque cy o se A om e sca e i g u c io we o ai e e ay owe s ec um o e c a e y sim y a e agi g S(τ;λ o e A i e
Simi a y e o e owe s ec um is
e a ge o a ues o e w ic e e ay owe s ec um (7 is o e o is e i e as e mu i a s ea o e c a e e c a e co e e ce a wi a is e i e as e eci oca o e mu i a s ea i e h = 1/ m h o i es us wi a measu e o e wi o e eque cy a o e w ic e a i g is ig y co e a e Simi a y e a ge o a ues o e w ic e o e owe s ec um
Sc(λ is o e o is e i e as e o e s ea Bd o e c a e e a ue o
e o e s ea Bd o i es a measu e o ow a i y e c a e im u se a ies i ime e c a e co e e ce ime T h is e i e as e eci oca o e o e
W e e a wi W o e a smi e sig a is muc sma e a e co e e ce a wi o e c a e i e W co a e eque cy com o e s i
e a smi e sig a u e go e same a e ua io a ase s i i a smissio
oug e c a e Suc a c a e is ca e fr n -n n l t v o a f d n
A eque cy- o se ec i e a i g c a e as a ime- a yi g mu i ica i e e ec o
e a smi e sig a W e e a smi e sig a as a a wi W g ea e
a e co e e ce a wi co o e c a e e eque cy com o e s o
e a smi e sig a wi eque cy se a a io e cee i g co a e su ec e o
i e e gai s a ase s i I suc a case e c a e is sai o e fr n -
l t v W e W Bcoh, e mu i a com o e s i e c a e es o se
a a e se a a e i e ay y a eas 1/W a e eso a e I is case i we use
e sam i g eo em o e ese e eso a e ecei e sig a com o e s e
ime- a yi g c a e es o se ca e e ese e as[7 ]
w e e hl (t is e com e - a ue c a e gai o e mu i a com o e a
is e um e o eso a e mu i a com o e s is gi e y
e a gai s Mt } a e mo e e as wi e-se se s a io a y mu ua y u co e a e
a om ocesses
. .2 Ch nn l E t t n U n l t Ch nn l
I IS-95 a C MA e e is i o c a e i e ow i k e ecei e a mo i e ca use e i o c a e o es ima e e c a e s a e a o co e e emo - u a io I e MC-C MA sys em wi a smi i e si y eac a smi a e a ca a so uses a i o c a e as i IS-95 a C MA o e a e e ecei e o es ima e e c a e e o e e c a e i a io co es o a smi a e a a
a smi a e a 1 as 5p a s a e k a s i e e i e se ou ie a s o m o
e s ea i g co e o use a e co e o e i o c a e o a e a i es ec-
i e y e §k a e e e co e ec o s a a a cyc ic e i o e g o e s ea i g co es sik a s i e a smi e sig a is e su e osi io o e i o sig a a K use s sig a e a smi e sig a s i ock a ock + 1 a
a smi a e a a e gi e y 60
e a smi e sig a s i ock a ock +1 a a smi a e a 1 a e gi e
y
Assume a e c a e is s ow a i g so a e c a e im u se es o se i
wo co secu i e a a ock is esse ia y e same e o e e im u se es o se o e c a e om a smi a e a i i = 1 i ock a ock + 1 as
ecei e sig a ec o s i
ock a ock + 1 a e emo i g e sig a co es o i g o e cyc ic e i is gi e y
a e w i e Gaussia oise a ma i o is gi e y
a ma i 1 is e i e i a simi a ma e e i e ma i C o as
a e i e ma i C i a simi a way as Cpo . e ecei e sig a ec o i (3 33 ca a so e e esse as 61
are signals of K users which are considered as the interference to the pilot signal when the receiver estimates the channel.
Then, we have
The receiver uses these 4Q + 2 blocks of data to estimated the channel.
A. MMSE channel estimator The MMSE channel estimator for channel coefficients h[n] is given by
where R = E(rr ) is the covariance matrix of r and p = E(rhH(n)) is the crosscor- relation between the data vector and the channel coefficients. To calculate R and p, the receiver needs the knowledge of the all the spreading codes of the active users, the amplitudes of the users' signal, the autocorrelation function and the multipath intensity profile. While the MMSE channel estimator is optimal linear estimator that minimizes the mean squared error between the channel coefficients and the estimate of the channel, it needs to invert the covariance matrix of size which requires much computation.
B. LSE channel channel estimator LSE channel estimator first obtains instantaneous estimates of the channel coeffi- cients using least square error criterion, then use a linear filter to smooth the instan- taneous estimates of the channel coefficients. The instantaneous estimate of the 62 channel is given by
Since the receiver knows the spreading codes of the pilot channels, the matrix can be calculated off-line. Therefore, to obtain an instantaneous estimate of the channel, the receiver only need to multiply the received data vector by a 2L x 2N matrix. If the channel autocorrelation function, or equivalently, the
Doppler spectrum known, the optimal MMSE linear filter to smooth the instan- taneous estimates the Wiener filter that has a frequency response equal to the square root of the Doppler spectrum. To reduce the delay of the channel estimation, a FIR MMSE filter can be used instead of the optimal Wiener filter, which can be obtained as follows. Denote the ith element estimates are available, we define a vector We can use the channel autocorrelation function to calculate the covariance matrix of vector h , Rh, and the crosscorrelation between h [n and h , ph . Then the FIR
In general, the Doppler spectrum is not known, or it may even change with time. The best knowledge of the Doppler spectrum is that is a lowpass spectrum with a maximum Doppler frequency fd Therefore, we can use an ideal low pass filter with a cut-off frequency equal to or greater than fd as the filter to smooth the instantaneous estimate of the channel. The nth tap of impulse response of the ideal lowpass filter given by
the delay and memory, the lowpass filter can be truncated to a FIR filter. 6
. . Ch nn l E t t n U n l t S b l
I we use e i o c a e o es ima e e c a e s a e eac a e a ee s o e s ea i g co e W e e um e o a smi a e as i c eases e ecei e ee s mo e s ea i g co es w ic e uces e um e o co es a ai a e o e use s
u e mo e w e e ase s a io uses a smi eam o me o e uce e i e -
e e ce e wee e use s a i e e oca io s e use s a i e e oca io s s ou
e assig e i e e s ea i g co es o e i o c a e s w ic u e e uce e
um e o s ea i g co es a ai a e a imi e um e o use s i a ce is
o em ca e a oi e i eac mo i e uses ime mu i e e i o sym o s o es ima e
e c a e
Su ose a i e e y M a a ocks wo ocks o e i o sym o s a e i se e e i o sig a is u mo u a e s ea i g co e Assume a e esi e use is use 1 e a smi e sig a s a a e a i e i o a a ocks o use 1 a e gi e y
e a smi e sig a s a a e a 1 i e i o a a ocks a e gi e y
e i e a ma i 1 i e same ma e as C i (3 35 e ecei e sig a is gi e
y 64 where I(2nM) and I(2nM+1) are interference users' signals, v(2nM) and v(2nM+1)
are white Gaussian noise. Suppose that 4Q data blocks corresponding to the pilot signals, r[2(n + M]
1 block. The MMSE channel estimator can be found if the channel autocorrelation function, multipath intensity profile, all the users' codes and transmitted power and the noise variance are known. The MMSE channel estimator should invert a Q x Q matrix, which needs too much computation for a practical system. Thus, as in the previous section, we can first use least squared error criterion to obtain the instantaneous channel estimates, then smooth the instantaneous estimates to reduce the variance of the estimate errors.
As in (3.40), the LSE estimate of the channel is given by
Since the Doppler spectrum is usually not known, the optimal smoothing filter is difficult to find. We then can use a ideal lowpass linear filter to interpolate the instantaneous channel estimates to obtain final channel estimates. The nth tap of impulse response of the ideal interpolating filter for h[nM + i], i = 2, ... , M — 1 blocks given by
where is the duration of a data block. 6
. .4 S l t n lt
In th t n, l t n r lt t p r th t p rf r n nd r
d ff r nt h nn l nd t n h n th r p l t h nn l r p l t b l d t
t t th h nn l. In l t n, t p th WSSUS h nn l n r t d b
n th M nt C rl th d [ 4]. h d l pr d n f r l d tr b t d n
th rd nt rv l h l n th d t b 4 f th d t bl . p th
h v th v r n th v r r d rr r f th h nn l t t h n
p l t h nn l r d. All th r h v th p r. f n th r t f th
p r f p l t h nn l nd th p r f th d t = Ap 2 A 2 In . .6
= 0d f r fd b = 0.00 nd = 6d f r fd b = 0.00 . W th t h h
p r f th p l t h nn l n d d f r th h nn l t t r t nt n d
p rf r n h n th ppl r fr n l r . In . . , . .8, . .
nd . . 0, th b t rr r r t nd r d ff r nt h nn l nd t n r h n. It
b rv d th t p rf r n d r d l htl h n th h nn l t t d. . .
d n tr t v r r d rr r f th h nn l t t h n p l t b l r
d. C p r d th th t t r n p l t h nn l , th h nn l t t r n
p l t b l n d h h r p r t p n t th l n b r f th n t nt n
h nn l t t v l bl t th th h nn l t t . Wh n p r f ll th
r p l t b l r r d, nt rf r n l v l l r d. h r f r , h nn l
t t rr r l r h n th ppl r fr n h h. t rr r r t f th
t f r d ff r nt n b r f r h n fd b = 0.0 r d n tr t d n . . 2
nd . . . S n th h nn l t t rr r ll, th E l htl l r r
h n th t t d h nn l r d. In . . 4 nd . . , E h n f r fd b = 0.00 . In th , nt rf r n d r d th p rf r n f th h nn l
t t r, p ll h n th n b r f th t v r l r . h r f r , b t
rr r r t n th t t d h nn l h l r r th n th d l . r .6 M n r d rr r f th h nn l t t r n p l t h nn l .
r . t rr r r t f MC C MA th p l t h nn l . fdTb = 0.00 , K= 0, =0d . 6
r .8 t rr r r t f MC C MA th p l t h nn l . fdTb = 0.00 , K=20, =0d .
r . t rr r r t f MC C MA th p l t h nn l . fdTb = 0.00 , K= 0, =6d . 68
r . 0 t rr r r t f MC C MA th p l t h nn l . =6d .
r . M n r d rr r f th h nn l t t r n p l t b l . 6
r . 2 t rr r r t f MC C MA th p l t b l . fdTb = 0.00 , K= 0, =6d , M=4
r . t rr r r t f MC C MA th p l t b l =6d , M=4 0
r . 4 t rr r r t f MC C MA th p l t b l . fdTb = 0.00 , K= 0, = d , M=2
r . t rr r r t f MC C MA th p l t b l . fdTb = 0.00 , K=20, = d , M=2 71
3.4 Summary
In this chapter, we apply the block space-time codes that is originally proposed for a narrow-band system to wideband multicarrier CDMA systems. Our emphasis is on designing receiver that can jointly decode the space-time codes and suppress multiple access interference. Among the proposed four receivers, MMSE combiner is the best trade-off between the performance and the complexity. The channel estimation using pilot channels and pilot symbols is studied for the MC-CDMA with space-time coding. While the channel estimator using pilot channels has better performance, it is not suitable for a system with many transmitted antennas or with transmit beamformer. On the other hand, since the channel estimator using pilot symbols does not using extra channels, more spreading codes are available for mobile users, thereby more users can be accommodated in a cell. However, in a fading channel with relative large Doppler frequency, a sufficient number of pilot symbols is required for estimating the channel, which reduces the frequency efficiency. C A E 4
ACKE SWI C E C MA A OM ACCESS SYS EMS WI ACKE COM I I G
r t n d d v n lt pl ( S C MA h b n nv t t d t pr v d p t lt pl nd h h d t r t n r l n t n [ 2].
In r nd p t t h d C MA t , t r r r n lt n l tr n t d t p t ( th rr r r t h l n th r A O A r nd
t , f t r r tr n n r, ll th p t r d tr d.
h r f r , C MA r nd t h v th p t nt l f r pr v n n th
p t f A O A. h p rf r n f th C MA r nd t
n l z d n [ 2] th th pt n th t th lt pl nt rf r n (MAI
th d n nt f rr r . h thr hp t n l f th C MA r nd
t n dd t v h t G n n (AWG h nn l r pr nt d
n [ 6, 66, , ]. It h n th t th C MA t th rr r rr t n d n h th r l htl b tt r thr hp t p rf r n p r d t lt h nn l n rr b nd A O A t th th t t l b nd dth [ 6]. h C MA r nd t t d d n [ 6, 66, , ] pl t h d f lt r r v r th t l t th r nt rf r n ppr n p b l t , th r f r , th r thr hp t l t d.
ntl , n r d tt nt n h b n p d t C MA r nd t th
lt r d t t n [6 , , 4]. It h n th t lt r d t t n n f ntl
pr v th t thr hp t.
A t t r p t r t (A Q h r nl d n n
t n t th f db h nn l [ 06]. In th p r nd t p I h br d A Q
h , p t n rr r th t t b r tr n tt d r d rd d nd r pl d b th r p . In th t p II h br d A Q h , p t th t t b r tr n tt d
r n t d rd d, b t r b n d th th r r p t d p . C d b n [ ,
4 ] nd d v r t b n [ 06] r t nl d p t b n h . In
2
d b n th p t r n t n t d t f r d rd fr n r n l l n r nd l -r t d In d v r t b n p t r b n d t th b t l v l th nd v d l b t fr lt pl d nt l p f p t r b n d t r t n l p t [1 5] t b n h b n ppl d t C MA r nd
t t pr v th t p rf r n [ 5 9 7 99] Av r d v r t
b n r n l z d f r C MA t th nv l t n l d n [7 ] In [9] b th d v r t b n n nd d b n n r n l z d f r C MA r nd
t th t nd th f r rd rr r rr t n ( EC n AWG h nn l In [
5] l r b nd nd n pp r b nd f th thr hp t f th C MA r nd
t th d v r t b n n f d n h nn l r pr nt d h t b l t
f th C MA r nd t th d v r t b n nv t t d n [99]
h p t b n h pr v th p rf r n b t th nn t ff t v l
ppr th nt rf r n n th t h d f lt r tp t r d th np t t th b n r In [ 1 3 ] pt lt r d t t r nd l n r lt r d t t r th t ll th p f th tr n tt d p t r pr p d h b t
rr r r t ( E nd th n t r p rf r n r n l z d f r AWG h nn l
In th r t d th p rf r n f th S-C MA r nd
t th l n r lt r r v r nd d v r t b n n f d n h nn l O r p rf r n n l p rf r d f r l r t th h r n r nd
pr d n n W th t th v r rr v l r t f th tr ff nd th pr n n t nd t nf n t b t th r r t f x d r t ppr h
d f r n l z n th Erl n p t f d ff r nt t l tr ff t [ 1 ] In l r C MA t n h h th n b r f th t v r K nd th pr n
n tends to infinity and their ratio is fixed, it was shown [15, 98] that the output signal to noise ratio (SNR) converges to a deterministic limit in probability. While performance analysis for a CDMA random access system of finite size with diversity combing is very difficult (if possible), the asymptotic analysis for a large system is 4 tr t bl rth r r th pt t r lt n pr d t th b h v r f t
th d r t z nd n n n ht nt th t p rf r n fr th pt t r lt h l r t r nt r t d n h r r p rh p r r l v nt t f t r r l t W h ll n l z b th l tt d nd n l tt d
C MA r nd t In n r l n l f n l tt d C MA t
pl t d b th lt r nt rf r n xp r n b p t v r
nt n l d t n hr n p t rr v l nd d p rt r v r n l r t n tt r t l tt d r n l tt d th tp t S f l n r r v r
nv r t d t r n t l t h r f r n p t th n l f l tt d nd
n l tt d t n n fr r If th r v r b n th rr nt r tr n -
tt d p t th ll t pr v tr n tt d p th b t rr r r t ( E dr t ll d r th th n b r f tr n n n r n S pp th t th r v r b n J d nt l p f th d r d r p t C p r d t th r v r th t d rd ll th p t f l n tr n n t d v r t n pl
n n r d nt rf r n nd n ppr n n f J. E h r tr n n h
r nd d l If th d l l n r th n th h r nt t f th f d n h nn l
h r tr n tt d p t nd r nd p nd nt f d n h h pr v d d v r t
n In n r l th nt rf r n r nf r t n b t t h r tr n n f th d r d r p t r n rr l t d nd th n r l n rr l t d h r f r
n h r ntl b n th d r d r n l b t v r t th nt rf r n
nd n h h pr v d th nt rf r n nd n ppr n n h p t
pr b b l t n r th th n b r f tr n n n r n h h n t rn pr v th t thr hp t
4. S t r pt n
W n d r S-C MA r nd t n t n f n l b t t n
nd t t l f M b l r l r h r n r t d t p t nd tr n t
v r n d b nd r l h nn l t th b t t n E h r r nd n t r n th pr n n f N h p p r b t E nt ll th h nn l pr t l A O A E h r n b n th r n f th t
p r t n d r n t n d r b l d In th r n t n d th
r tr n t n l rr v n p t A r n d r d t b n b l d
h n t pr v l tr n tt d p t n t f ll r v d b th b
t t n nd r tr n n r t d W h ll n d r b th th l tt d t
nd th n l tt d t th f x d p t l n th In l tt d t h r
n th r n t n d tr n t n l rr v n p t n th f r t l t ft r th p t rr v l Wh n th r nt r th b l d t r tr n t th p t n th n xt l t th pr b b l t pr . In n n l tt d t th r n th r n t n
d p n r v n n p t tr n t t d t l If r b l d
t r tr n t th p t ft r r nd d l W th t p t nt n
ff nt rr r d t t n p b l t th t th b t t n n d t t ll th rr r p t h f db h nn l d t b rr r-fr r pl t f n l
th t th d t r n t n d d n n f r rd rr r rr t n ( EC
d th h th rr r d t t n d h ld b d h h t nr l t b t t t xt nd th n l n th r t th t th EC r th
t th EC t p bl t r tr n t p t th d ff r nt d rd
h r v r b n th p t t th d l v l n t p -II h br d A Q [ 5]
In th r th t th b l d r tr n t p t d nt l t th pr v tr n tt d p t h r v r pr th r v d d t n h tr n n t th b t l v l h r v r h t t pr th r v d p t On th t t p th tp t f th d t t r nd b n th n
( pt l r b- pt l t t d n t t t h th r t p ll th r n l r v d d t n h tr n n nd d j ntl d t t n b d n th 6 d t h l t r th d n d r r nd h h r p t t n pl x t b t
b bl t t l r b t rr r pr b b l t
In n r l th p t rr v l h v t d - t t pr b b l t d tr - b t n [7 ] In th r th t th p t rr v l d tr b t n
n th rr v l r t A W d f n th ff r d tr ff l d G th v r n b r f rr v n p t n p t d r t n p G = λ p h r f r th pr b b l t th t x tl r tr n t n p t d r t n
W r h r nt r t d n l r t n h h h v G —+ nd G I = h l r t nt ll h nf n t ff r d tr ff l d nd b nd dth b t th ff r d tr ff l d n r l z d b th pr n n f x d In l tt d
t t h n [ 3] th t th n b r f r K tr n tt n n p t d r t n ( l n b t d r t n nf n t nd K/ nv r t n pr b b l t
A h r t pr f f ll S n th n b r f r K n th
t r nd n v r bl th n G n th n K th f
nd p nd nt n r nd v r bl th n G = th W f
r b r K/ nv r t n pr b b l t →∞ Unl n f n t
t n h h th nt rf r n v r nt n d ff r nt tr n n th ff t f th nt rf r n t l n r r v r n l r t nt ll th n ll th tr n n h h f l t t th p rf r n n l On d ff lt t n l z th p rf r n f th n l tt d C MA p t n t r th t th nt rf r n n
n p t d r t n h n n d t r nd l rr v l nd d p rt r In n
n l tt d t W n l h th t th n b r f th t v r K n b t d r t n n r l z d b th pr n n l nv r t n pr b b l t
W n d r b t d r t n fr t t t + Tb f th d r r K 1 r
rr v d n th d r t n (t — p t — p + b] l v th t K2 r rr v d n th d r t n (t — p + Tb, t] t n th t nd K3 r rr v n th t 77
n th b t d r t n h n b r f t v r n th p rt l r b t d r t n
K = K + K3 - Kl It tr htf r rd t h th t KI nv r t n pr b b l t →∞ h r f r t r l t v t h r t r z th ff t f th
nt rf r n f r h l r n l tt d t
4.2 t Err r r b b l t
W h ll t d th p rf r n f MMSE r v r d rr l t r nd t h d f lt r r v r f r b th l tt d nd n l tt d C MA r nd t n lt p th f d n h nn l h r v r t l z th t t t f ll th r v d p t n d ff r nt tr n n
4.2. Sl tt d C MA S t
S pp th t th d r d r f l d t tr n t p t n — 1 tr n n nd
tr n tt n p t f t th t t th rr nt l t W n d r n b t d r t n f th p t S pl n th tp t f th h p- t h d f lt r t th h p r t bt n x 1 d t v t r f r th jth ( j 1 tr n n f th p t
SK d l t n d; th b (j n l- pr b bl +1 r nd v r bl W th t r 1 th d r d r h nf r-
t n b t r th n h tr n n h b t
1 r d t b n rr l t d h r n bl pt n h n 8 th r tr n n pr b b l t n th n xt p t d r t n v r ll In th
h n t r b th f l n tr n n th pr b b l t th t th t
r r tr n t th b t n th p t d r t n n l bl
th pr d n n t r f r k. It l nt r r nd l n r t d fr th t -1A/I IA } th l pr b b l t s l,l = L r th h ft d r pl f s . pl f th n l th pt n n [ ] th t s , 1 = L — 1 r nd p nd nt th h th r All th h th pt n nr l t th n l r lt nd r th pt n f t th l t n r lt n th
h ft d ll n l r t th h ft n pr v d n h r nd n
v n th h th r d r pl t n l(j th h nn l n f r p th 1 f r k n th j th tr n n h h d t b n rr l t d If th r nd d l f r tr n n l r r th n th h r nt t f th f d n h nn l th
pt n r n bl v r n pr t l t th r tr n n d l
n t b l r n h th t th h nn l ff nt n d ff r nt tr n n
r n rr l t d v rth l t pl f th n l t ll th t th
r n rr l t d An l b d n th rr l t d h nn l ff nt p bl b t t ll n t b p r d n th r In r l nv r n nt th t a(j)l n - f- ht l z r - n b t n pl x b G n t t n nd b l r nd v r bl h pl t d h l h d tr b t n W l th t th d l - pr d f th h nn l ll p r d t th b l t th t nt r-
b l- nt rf r n (ISI n b n l t d n(j pl x h t G n n
th v r n σ
r th j nt d t t n p rp t J d t v t r n ( t bt n
W f r t n d r th n n r d rr r (MMSE r v r It ll
n n [ 1] th t th MMSE r v r f r th j th tr n n
r rr l t n b t n b 1 nd (j h tp t f th MMSE r v r f r th j th tr n n
h r I (j th nt rf r n pl th n It h n [ 9 ] th t I (j
G n h n f I (j z r nd th v r n
h r v r b n tp t f th MMSE r v r f r tr n n t f r th d n v r bl z f r b 1 It n b h n th t th th pt l ht f th
b n r f r z(j 1/d(j h r f r th d n v r bl
OI n pr b b l t —+ h r th n l t n t th t n
h r f r th d n v r bl n ( nv r t l t z n pr b b l t
E nv r t l t
P n., n pr b b l t [7 ]
h r
Wh n th v r n f a l (j) r d ff r nt n v l t E n th f r l
n [ 5] In th r th t h h nn l n h th v r n nd
h ll ( 9 t l l t p t pr b b l t
W n l d j nt MMSE d t t n b d n ll th d t r v d n J tr n n U n th n l d l n ( 3 bt n th MMSE r v r
bl d n l tr t n b h n th t
It b rv d th t th j nt d t t r t ll v l nt t th p r t d t t r
th th pt l b n r S n nl h v t p th tp t f nd v d l d t t r n p r t d t t n n d l r f r p r t d t t n h th p r t d t t n th th pt l b n r pr f rr d n pr t l t
h lt p th d rr l t n d t t r pr p d n [11 ] f n th n t r
tr x n th j th tr n n th p d - nv r f th n t r tr x SW. Wh n S(j) h f ll l n r n
r h r nt r t d n r 1 t th f r t tp t f th d rr l t r 8
h r n1 (j G n nd t v r n tr x (j) th f r t L x L b-
U n n MMSE b n r t b n th tp t f
nd I G n th z r n nd v r n
W n ( 9 t v l t b t rr r r t f r th d rr l t r
Wh n th r v r th t h d f lt r th n x r t b n r t
tr htf r rd t t th f ll n r lt f r l r t [ ] h d n v r bl z nv r t z* n pr b b l t
ntr l l t th r I G n d tr b t d h r f r E n b l l t d b n ( 9
4.2.2 Un l tt d C MA S t
In n l tt d C MA r nd t r n tr n t t n t S pp th t th r v r n th t n f th d r d r nd th r r K(j) r tr n t n n b t d r t n th r nd d l A n[91] th t t b h p n hr n t th n l tr t bl h pl f h p t h d 82
f lt r tp t f r N x 1 d t v t r -
h r b -1 (j), b2 (j) r th t n t v b l f th th r h h v rl p
th r 1 n n b t d r t n akl (j) th h nn l n d f n d b f r n l tt d
t l (j nd v (j) r d t r n d b th pr d n n t r s l (j) nd th d l r l t v t r 1 If d E [ N) d n t th r l t v d l n t r f n b r f h p f th h r th r p t t r 1 th n l (j h t f r t d
l nt t b th l t d l nt f s l (j) nd th r t z r S l rl v l (j h th f r t d l nt z r nd th l t N — d l nt t b th f r t N — d l nt
S1 1(j) h SI h v d b r 1 n th d t fr th jth tr n n v n
A th t th d l pr d f th lt p th h nn l v r ll p r d t th pr n n h n n l r t h r KIN = N, Kσ h r
3 n [91] b t th l t n SI f r 1 f r n hr n G n h nn l n b xt nd d t th n hr n lt p th h nn l A n [91] th p r l 8 d tr b t n f th d l f th d ff r nt r r l t v t th d r d r d t nv r t f x d d tr b t n G(r h r th d l d r l t v t r 1 v n b d = [τ ] h p r l d tr b t n f th p r f th r d t
nv r t f x d d tr b t n (p
h r
and
h r Ep nd E d n t th xp t t n th r p t t th p r d tr b t n (
nd th d l d tr b t n G(τ r p t v l I( =1+ β nd 1 7- x n nd t r f n t n th t 1 f r x nd th r h l t n t (x x t nd n n l f f n t n (x 0.
r f r t nd r th pt n th t 11 l = 1, . . . , L r nd p nd nt r nd n fr h r A n [ ] h v
ff t f th d l pr d h n th v r n f n l nt f tr x S (j th
th t f th l nt f tr x S1 1 n [91] h n th p r f th
nt rf r n r h r r th th p r f th r n th n l d l
n [91] ll n x tl th t p t pr v h r 3 n [91] n h
Aft r th r v r b n th tp t f MMSE d t t r f r J tr n n
f th p t n th pt l b n r th SI 1 nv r t 84
n pr b b l t S n th nt rf r n nd n t th tp t f MMSE r v r
G n n ( 9 t l l t b t rr r r t
h ff t v n t r tr x f z N x ( K(j — 1 f r th j th tr n n
A n th n hr n th d rr l t r
f th nv r x t h nt rf r n r pl t l
l n t d th v r n tr x f th G n n
1 th n v r n „ 1 th f r t L x L b-bl th pt n th t th n t r n f th d ff r nt lt p th p n nt
r nd p nd nt t tr htf r rd t xt nd h r 3 3 n [91] b t th SI
f d rr l t r n n hr n AWG h nn l t n hr n lt p th h nn l
In lt p th h nn l
h r f r SI 1 (j nv r t
Aft r b n tp t f th d rr l t r f r J tr n n h v SI 1
It tr htf r rd t h th t th t h d f l r r v r n th n hr n
lt p th h nn l h th pt t p rf r n n th n hr n
lt p th t t n [ ] ll b th r nd n t r r d th
ff t v nt rf r n f p rt l r r t th tp t f th t h d f lt r nl r l t d t t p r nd h n th n t d th t r l t v d l v r n f n t t th t th pr d n n t r h G ld n h h h v
p l r rr l t n pr p rt th r rr l t n n th n hr n r t p ll l th n n th n hr n h r f r th pt t r lt f r th
t h d f lt r h r n t ppl bl t h t 8
4. S t hr hp t nd l
In th t n t d th thr hp t nd d l f th l tt d nd n l tt d
C MA r nd t S n b th th ff r d l d nd b nd dth nf n t
n r l z d th ff r d l d b th pr n n N. h thr hp t h h d f n d th th v r n b r f p t f ll tr n tt d n p t d r t n l n r l z d b th pr n n
In th C MA r nd t th p t b n n th b t rr r r t d r n th th n b r f tr n n n r n h p t pr b b l t d ff r nt f r th p t th d ff r nt n b r f tr n n W
th t th l n th f th p t Lp . S pp th t th p t f l n J — 1 tr n n th n th p t pr b b l t n th th tr n n v n b
h p t f l r pr b b l t n th th tr n n th pf( = 1 — p (
h n nd t n l p t pr b b l t ft r J tr n n n b f nd
n t (t th n b r f p t th t r tr n tt d th th t n th rr nt p t d r t n A n S t n III, th b t rr r r t nv r t d t r n t l t n l r t Und r th nd t n t h n [ 3] th t
(t n l tt d t n r nd v r bl th th r t
h r G(1 th n rr v l r t nd Nj (t), J = 1 r t ll nd p nd nt
In n n l tt d t d n t Nit th n b r f p t th t f l n th th tr n n S n th n rr v n p t r n f1 n r nd v r bl th r t G(1 pf (1 W th t th d l b t n t n t v 86 tr n n r t ll nd p nd nt r nd v r bl th n xp n nt l d tr - b t n r h r [ ] n pr ft r r nd d l th
xp n nt l d tr b t n t ll n pr h r f r n n n l tt d t th n b r f p t th t r tr n tt d th nd t n p t d r t n
n r nd v r bl th r t G( nd n n th t N (t), J =
1 r nd p nd nt n r nd v r bl th th n v n n (
h ff r d l d n b xpr d
h n r l z d thr hp t v n b
h n r l z d thr hp t b
h d l d f n d th v r n b r f tr n n f p t It v n
4.4 r l lt nd n
In th t n pr nt l t n nd n l r lt t h th p rf r n
f b th l tt d nd n l tt d C MA r nd t W th t th r v r h th n l d f th h nn l t t nf r t n nd d l f ll th
r In pr t l t h nn l t t nd th d l n b t t d th r bl ndl r b n tr n n n v r h nn l t t n t f th 7
p f th r In l t n th n b r f p th f th h nn l L All th p th f d ff r nt r r nd p nd nt pl x G n r nd v r bl th th
v r n h h nn l n h tr n n nd p nd nt h p t l n th
p = 1
1 nd h th b t rr r r t f l tt d nd n l tt d C MA
t f r d ff r nt S W pl t th E f 1 nd p nd nt r n n h h
pr d n n t r r nd p nd ntl n r t d In l t n th pr d n
n t r t th nd p th th h ft d r pl f th r n l pr d n n t r ;
h r n n l th t th pr d n n t r t d ff r nt p th r
nd p nd nt r 1 nd n th t E n l t n pr d
r nd th pt t l t Wh n th pr n n n r t xp t d th t th pr d r nd th pt t l t b r n rr In AWG
h nn l t h n [ 1] th t MMSE r v r nv r t th d rr l t r h n
S t nd t nf n t v r t b rv d n 1 nd th t MMSE r v r h b tt r p rf r n v n h n S v r h h h n b xpl n d
f ll C n d r th n l d l f r th n hr n C MA n ( h
ff t v n t r f r k n jth tr n n s (j ak(j). A S t nd t
nf n t th MMSE r v r nv r t v t r th t rth n l t th r n
p f th ff t v n t r f th nt rf r n r h d n n f th
p K — 1 If akl,l = 1, . . . , L r ll l th pt t SI f th MMSE r v r (1 — a)SNR h n 1 On th th r h nd th pt t SI f th
lt p th d rr l t r (1 —α S h n αL < 1 h r f r th MMSE r v r h ppr x t 10log(1 α α d dv nt v r th d rr l t r r v r h n S
h h h l r n l n n b dr n f r th n l tt d C MA t W
l fr 1 nd th t th b t rr r r t ft r thr tr n n
h l th n th t ft r n tr n n f r ll th l n r r v r 3 pl t b t rr r r t tt n d f r d ff r nt n r l z d ff r d l d Wh n f n th 88
l tt d C MA t nd A n th n l tt d C MA t th d rr l t r d n t x t h d rr l t r n t t bl f r th t th d r t
ff r d l d n lt p th h nn l Wh n ff r d l d v r h h MMSE r v r h l t th b t rr r r t th t h d f lt r r v r In h h ff r d l d r th r n ff nt d r f fr d f r th MMSE r v r t ppr th nt rf r n h r f r MMSE r v r t nd t h v th p rf r n th t h d f lt r r v r h th b t rr r r t v r th n b r f tr n n It n th t th b t rr r r t d r l n rl th th n b r
f tr n n n r n
h n r l z d thr hp t nd v r d l f r l tt d C MA t
h n n 5 nd h thr hp t nd v r d l f n rr b nd
A O A r l pl tt d n th f r In th A O A t th t th r n n h r f r th p t n b f ll tr n tt d f th r n
ll n h C MA t th MMSE r v r nd p t b n n h th b t p rf r n It thr hp t h h h r th n A O A t f r ll th ff r d tr ff l d Wh n th n r l z d ff r d l d l r ( th C MA t
n MMSE r v r b t th t p t b n n h l t th thr hp t
th t th p t b n v r h n th n r l z d ff r d l d
n r t thr hp t d r dr t ll Wh n th n r l z d ff r d l d
h h th MMSE r v r th t p t b n n d n t h v ff nt d r
f fr d t ff t v l ppr th nt rf r n h p t pr b b l t d r v r f t th r p t t th n r f th n r l z d ff r d l d h n th n r l z d ff r d l d r t th n n v r f th r v r b n J p t t t J f ld nt rf r n nd n ppr n h r f r v n h n th n r l z d ff r d l d v r h h ( 1 th r v r th th p t b n n
t ll n ppr th nt rf r n th th n b r f p t tr n n n r n
h th r n h th t th p t b n n h h h thr hp t h n 8 n r l z d ff r d l d h h If th t p t b n th thr hp t f th t pl n MMSE r v r nd t h d f lt r t nd t b th h n n r l z d ff r d l d t nd t nf n t h b b rv d n 3 th b t rr r r t f th MMSE r v r nd t h d f lt r t nd t b th
h n th n r l z d ff r d l d v r l r h thr hp t f th t th
t h d f lt r nd th t p t b n h l r th n th A O A t
h t ntr d t th b rv t n [1 ] th t th C MA r nd t
th th t h d f lt r r v r h l t th thr hp t th A O A
t h d t th f ll n r n r t ff t f dd t v n n t
n d r d n [1 ] h n f l tr n n r d t b d nl b th lt pl - nt rf r n S nd f r rd rr r rr t n d d
n [1 ] It b rv d [1 ] th t th bl rr r rr t n p b l t n r th
ff t v thr hp t n r nt l t r h x ft r h h f rth r d n r d th ff t v thr hp t In th t n d r d h r f th rr r
rr t n d th ff t v thr hp t n b pr v d n ll n d r th f d n h nn l n h h th p t pr b b l t h l r th n n th
AWG h nn l h n S th In th t th v r d l f th
t th p t b n h ll r th n th t f th t th t p t
b n h b th th p t b n th p t pr b b l t
n r th th n b r f tr n n If n p t b n th p t pr b b l t th n tt r h n t th p t tr n tt d h n r l z d thr hp t nd v r d l f r n n l tt d C MA t h n
n 7 nd S l rl n th l tt d C MA t p t b n n
pr v th p rf r n f n n l tt d C MA t 0
4. S r
h t p rf r n f th C MA r nd t n lt p th f d n
h nn l r n l z d f r l r t n h h th ff r d l d nd th pr n
n t nd t nf n t b t th r r t f x d h l n r MMSE lt r r v r h h b tt r p rf r n th n th t h d f lt r n l r r v r v r
th t p t b n n h n th n r l z d ff r d l d r t r th n n n
l tt d t nd r t r th n h lf n n l tt d t l n r MMSE r v r
nn t ff t v l ppr th lt pl - nt rf r n ; th th thr hp t d r t z r n h h ff r d l d r n W th p t b n n th r v r n t nl t d v r t n n f d n h nn l b t l bt n n nt rf r n
nd n ppr n n W th th n b r f tr n n n r th p t
pr b b l t n r v n h n th ff r d l d v r l r h r f r p t b n pr v th t p rf r n f r ll th ff r d l d Unl
n th C MA t th t p t b n n th thr hp t f C MA t
th p t b n t nd t f n t v l h n th n r l z d ff r d l d v r l r h C MA t th MMSE r v r nd p t b n h h h h r thr hp t th n th A O A t f r ll th ff r d l d
r 4. E v r S f r th l tt d C MA t = 3/ L = r n n N = n l t n
r 4.2 E v r S f r th n l tt d C MA t = 3/1 = r n n N = n l t n 2
r 4. BER versus normalized offered load. S = d = 2. The number of transmissions rt = 3.
r 4.4 BER versus the number of transmissions. S = 1 d = 3/8, = 2.
r 4. r l z d thr hp t f th l tt d C MA t S = d =
r 4.6 Av r d l f th l tt d C MA t S = d = 4
r 4. r l z d thr hp t f th n l tt d C MA t S = d =
r 4.8 Av r d l f th n l tt d C MA t S = d = C A E
CO C USIO S A U U E I EC IO S
. C n l n
h d rt t n nv t t t t hn n l nt rf r n ppr n
t hn nd d v r t t hn t pr v th t p rf r n f C MA
t Sp f ll n nt rf r n ppr n t hn t d th r d d-
r n MMSE r v r nd r d d-r n n v r n r v r f r S-C MA
t In d v r t t hn t d th MC-C MA t th tr n t d v r t nd p t C MA r nd t th p t b n n
In Ch pt r f r t d v l p r d d-r n MMSE r v r f r S-C MA
t Wh n th v r n tr x f th r v d n l n n t h n th t r d d-r n MMSE r v r h r p rf r n p r d th th f ll- r n MMSE r v r v r h n th v r n tr x t t d fr n f n t n b r f d t pl r n l nd l t n h th t th r d d- r n MMSE r v r th t h pr p r nv l nd nv t r tp rf r th f ll-r n r v r p ll h n th d r d n l n l d n n l
b p nd th p r f d ff r nt r r d ff r nt An d pt v r d d-r n
MMSE r v r th n d v l p d b d n b p tr n l r th C p r d
th th S f ll-r n d pt v r v r th d pt v r d d-r n MMSE r v r h l r r tp t SI b t h h r pl x t W th n nv t t th r d d- r n n v r n r v r th t n b bl ndl pl nt d h n v r n r v r n b pl nt d n th tr t r n r l z d d l b
n l r h l t n d n tr t th t th r d d-r n n v r n r v r tp rf r th f ll-r n n v r n r v r f rth r nd r t nd th r n h th r d d-r n MMSE r v r h b tt r p rf r n t d th pr b b l t d n t f n t n f th tp t S f l n r MMSE t t r b d
n n r l l n r n l d l h pdf f tp t S f f ll-r n MMSE t t r
6 th t d r t nv r f th v r n tr x d r v d An pt t pdf f th r d d-r n MMSE t t r n pr n pl p n nt nv r f th v r n
tr x l d r v d r th pdf th dv nt f th r d d-r n
MMSE t t r
In h pt r 3 th lt rr r C MA t th tr n t d v r t t d d
h l n r bl p -t d h h r n ll pr p d f r n rr b nd
t ppl d t d b nd MC-C MA t W th n pr p d f r h t j ntl d d th p -t d nd ppr lt pl nt rf r n
h f r h r x r t b n r rth n l r rt n b n r
MMSE b n r nd MMSE lt r d t t r It h n th t th MMSE
b n r th b t tr d ff b t n th p rf r n nd th pl x t Ch nn l
t t n n p l t h nn l p l t b l r th n t d d f r th lt rr r
C MA t Wh l th h nn l t t r n p l t h nn l h b tt r p rf r n t r d th n b r f pr d n d v l bl f r b l r th r b r d th n b r f r n ll
In h pt r 3 nv t t th C MA r nd t th p t
b n n n f d n h nn l h p rf r n f b th th l tt d C MA t
nd n l tt d C MA t th r nd pr d n n t r n l z d h
n l b d n l r t n h h th ff r d l d nd th pr n n t nd t nf n t b t th r r t f x d In h l r t t r l t v l t
h r t r th ff t f lt pl - nt rf r n W f r t n l z th b t rr r r t
f th MMSE r v r d rr l t r nd t h d f lt r r v r n f d n h nn l
h p t th t f l n tr n n n t d rd d; th r v r b n
ll th d t f th p t fr d ff r nt tr n n d n th r v r bt n nt rf r n ppr n n nd d v r t n h nt rf r n
ppr n n d t th f t th t n h r tr n n f th p t th nt rf r n n r ll n rr l t d S n th f d n nd p nd nt n h r tr n n d v r t n bt n d b p t b n n It h n th t th b t rr r r t d r th th n b r f tr n n n r n W th n
n l z th t thr hp t nd v r d l r th n l f r b th th
l tt d C MA nd n l tt d C MA t t n th t lt r d t t n nd p t b n n b t nt ll pr v th p rf r n f C MA r nd
t
.2 t r r t n
pl nt r d d-r n MMSE r v r r r d d-r n n v r n r v r b p tr r th t n tr b th th n l p nd nv l
t d th th b f th n l p r r d h b p l r th
h ld h v r n bl pl x t nd nv r n p d In th l t n
b rv d th t th AS l r th [113] nd O A 3 l r th [ ] h th
rd r f pl x t S d pt v f lt r b t th r nv r n v r l On th th r h nd th r b p tr n l r th [1 ] h v h l r r p - t t n pl x t v l p n ff nt b p tr n l r th th pr t l
pl x t ll b v r nt r t n nd h ll n n r r h d r t n
In h pt r 3 ppl th p -t d n t d b nd t lt rr r
C MA t M t f th p -t d n h th t th f d n
h nn l n t fr n l t v Alth h h p -t d n l r ll
n fr n l t v f d n h nn l th r n t pt l f r h h nn l A
pl p -t d n [5 ] h b n pr p d f r lt p th h nn l Sp -t
d n th t n f ll xpl t th d v r t pr v d d b fr n - l t v f d n
h nn l ll b fr tf l r r h r
In th C MA r nd t th p t b n n t d d n h pt r
d d n t n d n W b n th p t t th b t l v l Wh n d n
ppl d t th tr n tt d d t b n th p t t d l v l ll h v b tt r 8 performance than combing the packets at the bit level. Therefore, the research on packet combing, decoding and multiuser detection for CDMA random access system is worthy to be pursued. A E I A
E I A IO O E SECO A IA E I A I E O MSE I EQ. 2.26
In this appendix, we derive H j and F in Eq. 2.26. Let's denote the last two terms
We first derive the first and second partial derivatives of M1. The gradient of M1 along u is given by
Then the Hessian matrix of Ml, Hl , is given by
1
are columns of matrix X and matrices are defined as
Here P is a matrix whose jth column is vector p and other columns are zero vectors. M1 can also be expressed as
h f r t p rt l d r v t v f M1 th r p t t λ v n b
Then the second partial derivative of M1 with respect to is found as
It is easily shown that the second term in the above equation is equal to zero and Thus, we have
We next determine the derivatives of M2. M2 can also be expressed as
The gradient of M2 along Il is given by 1 1
It n fr (37 th t h v And bt n d
h r th th l n f tr x W p( p h nd d r v t v f M th r p t t λ t p nt v n b E E E CES
1 S M Al t "A pl tr n t d v r t t hn f r r l - n t n " IEEE Journal on Select Areas in Communications, v l 1 pp 1 51-1 5 O t 199
Al x nd r M C d A A n t rf r nd C S hl l "It r t v lt r nt rf r n r d t n rb C MA " IEEE Trans. Commun., v l 7 pp 1 -1 15 l 1999
3 W And r n "A pt t th r f r pr n p l p n nt n l " Annals of Mathematical Statistics, v l 3 pp 1 -1 19 3
A Ann l nd K h r v "An l f n l tt d d r t- n pr d p tr lt pl n t r th p t b n " Electronics Letters, v l 33 pp 1 73-1 7 S pt 1997
5 A Ann l nd K h r v " hr hp t p rf r n f l tt d S/C MA A O A th p t b n v r n r l z d f d n h nn l " Electronics Letters, v l 33 pp 1195-1197 l 1997
A ll "Ch r t r z t n f r nd l t -v r nt l n r h nn l " IEEE Trans. Commun. Syst., v l CS-11 pp 3 -393 19 3
7 C rr nd A Gl v x " r pt rr r rr t n d n nd d d n rb -C d " IEEE Trans. Comm, v l COM- pp 1 1- 1 71 O t 199
rt nd G ll r Data Networks. En l d Cl ff r nt - ll 199
9 A M Y l A G ll v r nd K h r v "M x -l l h d d d n nd d b n f r S/SSMA l tt d A O A " IEEE Trans. Commun., v l 5 pp 1 -1 1 1997
1 zz S U ll nd W nt r "Ad pt v nt nn rr n b- p t hn n b l r d nv r n nt th fl t f d n nd CCI " n IEEE 49th Vehicular Technology Conference, pp 5 -5 M 1999
11 K C v r "An n l f p l t b l t d d l t n f r l h f d n h nn l " IEEE Trans. Veh. Technol., v l pp - 93 v 1991
1 K C v r " l t b l t d d l t n nd d ff r nt l d t t n n f d n nd d l pr d " IEEE Trans. Commun., v l 3 pp - 1 l 1995
02 0
13 Ch "C d b n n — A x -l l h d d d n ppr h f r b n n n rb tr r n b r f n p t " IEEE Trans. Commun., v l 33 pp 3 5-393 M 19 5
1 G M Cr h n "S ppr n f lt pl nt rf r n n S- C MA t n W n r f lt r n nd p r ll l n ll t n " Proc. IEE Commun., v l 1 3 pp - 3 A 199
15 C nd S nl " n r lt r r v r ff t v nt rf r n ff t v b nd dth nd r p t " IEEE Trans. Inform. Theory, v l 5 pp 1- 57 M r 1999
1 W d Gr f nd S hn rt " rf r n p r n f l tt d A O A S/SSMA n t r nd lt h nn l n rr -b nd l tt d A O A n t r " IEEE Trans. Commun., v l pp 5 -55 Apr 199
17 v l r M K S n nd ph l "I pr v d p r ll l nt rf r n n ll t n f r C MA " IEEE Trans. Commun., v l pp 5 - b 199
1 E M l n A nn nd Gr t "A Q - t r t n b d d pt v S f r r l t n l nd fr n tr n " IEEE Trans. Signal Processing, v l pp 91 -9 Apr 199
19 A l- ll n " rr l t n d n-f db d t t r f r n hr n d -d v n lt pl - h nn l " IEEE Trans. Commun., v l 1 pp 5- 9 b 1993
A l- ll n "A f l f lt r d n-f db d t t r f r n hr n d -d v n lt pl - h nn l " IEEE Trans. Commun., v l 3 pp 1- 3 b/M r h/Apr l 1995
1 Ed lb t M nd G K nn n "Cr t r f r pt - n l- d t t n th r f r rr " J. Am. Stat. Assoc., pp 199- 5 n 19
Ev n nd " n r lt r r v r f r lt p th f d n h nn l " IEEE Trans. Inform. Theory, v l pp 59- 7 S pt
3 nt "An ff nt AKE r v r r h t t r th p l t n l n ll t n f r d nl n n t n n S-C MA nd r r l n t r " IEEE Trans. Commun., v l 7 pp 3- 7 n 1999
S G ld t n nd I S d " d d-r n d pt v f lt r n " IEEE Trans. Signal Processing, v l 5 p 9 9 b 1997 04
5 S G ld t n nd I S d "S b p l t n f r p rt ll d pt v n r rr pr n " IEEE Trans. Aerosp. Electron. Syst., v l 33 pp 539- 5 3 Apr 1997
S G ld t n nd I S d "S b p l t n f r p rt ll d pt v n r rr pr n " IEEE Transactions on Aerospace and Electronic Systems, v l 33 pp 539-5 Apr l 1997
7 S G ld t n I. S d nd . S h rf "A lt t r pr nt t n f th W n r f lt r b d n rth n l pr j t n " IEEE Trans. Inform. Theory, v l pp 9 3- 959 v 199
G G l b nd C n Matrix Computations. h hn p n Un v r t r 199
9 G nd S " rf r n f A n hr n Orth n l M lt rr r C MA S t n r n -S l t v d n Ch nn l " IEEE Trans. Commun., v l 7 pp 1 -1 9 l 1999
3 A M v h " h n n l r d pt v r d r b n n l th d " IEEE Trans. Aerosp. Electron. Syst., v l 3 pp 53 -5 Apr 199
31 A M v h nd Y r- "An n n l nt rf r n n l r " IEEE Trans. Signal Processing, v l 39 pp 7 - n 1991
3 A n nd E G l "On th h r f Sp - C d f r SK M d l t n " IEEE Trans. Inform. Theory, v l pp 5 -5 M r
33 C n r "An lt rn t d r v t n f th d tr b t n f th nd - t n d n l-t -n r t n " IEEE Trans. Antennas and Propagation, v l A -3 pp 3- M r 19
3 S r nd r d " n nd rf r n f M lt rr r C MA S t n r n -S l t v l h d n Ch nn l " IEEE Trans. Vehicular Technology, v l pp 15 -159 S pt 1999
35 A r Ad h nd j "C b n d ff t f ph p n tr n tt r d v r t nd h nn l d n " IEEE Trans. Vehicular Technology, v l 1 p 17 17 M 199
3 M h ld nd M rz tt "Un t r p -t d l t n f r lt pl - nt nn n t n n l h fl t f d n " IEEE Trans. Inform. Theory, v l pp 5 3-5 M r
37 M n U M dh nd S rd " l nd lt r d t t n " IEEE Trans. Inform. Theory, v l 1 pp 9 -9 l 1995 0
3 M n nd S G ld t n "Ad pt v r d d-r n r d l rr l t n l r th f r S-C MA nt rf r n ppr n " n 32nd Asilomar Conf. Signals, Syst. Comput., ( f Gr v nd CA pp 11 -111 v b r 199
39 A t-M d n nd K Ch "MMSE/ IC lt r d t t n f r S/C MA t th nt r- nd ntr - ll nt rf r n " IEEE Trans. Commun., v l 7 pp 91- 99 b 1999
A C nd t f "S v nt rf r n n ll t n f r lt r n hr n S/C MA d t t r n lt p th f d n l n " IEEE Trans. Commun., v l pp 3 -391 M r h 199
1 r n "S pr p rt f th Erl n l f n t n " The Bell System Technical Journal, v l 53 pp 5 5-551 M r 197
W C Microwave Mobile Communications. Y r W l 197
3 A h n n nd S Sv n n "M lt t nt rf r n n ll t n n lt -r t S/C MA n b l r d h nn l " n IEEE Vehicular Technology Conference, (Atl nt GA pp - 7 M 199
hn n nd E d n Arr Signal Processing: Concepts and Techniques. En l d Cl ff r nt - ll 1993
5 S K ll l "An l f t p II h br d A Q h th d b n n " IEEE Trans. Commun., v l 3 pp 1133-1137 A 199
M K v h nd A r b ll " h t t t l p rf r n f th MUSIC nd th M n - r l r th n r lv n pl n v n n " IEEE
Trans. Acoustics Speech and Signal Processing, v l ASS - 3 pp 331- 3 Apr 19
7 S K Fundamentals of Statistical Signal Processing: Estimation Theory. En l d Cl ff r nt - ll 1993
I K r t n nd W ft " p dl d pt v n ll n f nt rf r n " n High Resolution Methods in Underwater Acoustics (M v t nd G nv n d pp - 9 Spr n r- rl Y r 1991
9 I K r t n nd W ft "Ad pt v d t t n n l r n ppr x - t n t d t tr x " IEEE Trans. Aerosp. Electron. Syst., v l 3 pp 55- 7 n 199
5 K hn I M t r nd S p th "An d pt v n l r f h nn l nt rf r n f r pr d- p tr lt pl - - n t n n t r n p r l n " IEEE J. Select. Areas Commun., v l pp 91- 99 M 199 06
51 K hn I M t r nd S p th "C b n t n f n d pt v rr nt nn nd n l r f nt rf r n f r d r t- n pr d- p tr lt pl - t " IEEE J. Select. Areas Commun., v l pp 75- M 199
5 S K r nd S nd " h d t -r t p t n t n f r ll l r n t r n C MA l r th nd p rf r n " IEEE J. Select. Areas Commun., v l 17 pp 7 - 9 M r 1999
53 W Y K nd M tz " n nd n l f tr n tt r d v r t n nt nt n l fr n ff t f r r l n t n " IEEE Trans. Vehicular Technology, v l pp 71- 1 v 1997
5 E nd nd A lr j " r n t d v r t h f r h nn l th nt r b l nt rf r n " n Proc. ICC 2000, ( Orl n nd USA pp 3 7-311 n
55 n "Opt l r pt n p rf r n b nd nd t ff r t n l f r f r n - t d h r nt C MA n t n th ppl t n " IEEE Trans. Commun., v l 7 pp 15 3-1591 O t 1999
5 C - nd K h r " l t b l d d h r nt M r SK n fr n - l t v f t l h f d n h nn l " IEEE Trans. Commun., v l pp 5 - n 199
57 nd K "A d rr l t n AKE r v r f r C MA n t n v r fr n - l t v f d n h nn l " IEEE Trans. Commun., v l 7 pp 1 3 -1 5 l 1999
5 p nd S rd " n r lt r d t t r f r n hr n d - d v n lt pl - h nn l " IEEE Trans. Inform. Theory, v l 35 pp 1 3-13 n 19 9
59 p nd S rd " r-f r r t n f lt r d t t r n n hr n h nn l " IEEE Trans. Commun., v l 3 pp 9 -5 Apr IEEE r n C n
U M dh " l nd d pt v nt rf r n ppr n f r th n r-f r r t nt t n nd d d l t n f d r t- n C MA n l " IEEE Trans. Signal Proc., v l 5 pp 1 -11 n 1997
1 U M dh nd M n "MMSE nt rf r n ppr n f r d r t- n pr d p tr C MA " IEEE Trans. Commun., v l pp 317 - 31 199
M tr nd A M rr n "Erl n p t nd n f r ppr x t n f r h r d nb ff r d r r " IEEE/ACM Trans. Networking, v l pp 55 -57 199 1 7
3 U M tr j r nd K M W r n "St b l t f C MA d t n t r th f x d nd d pt v MMSE r v r " n Proc. 33rd Asilomar Conference on Signals, Systems and Computers, ( f Gr v CA pp 197- 1 O t 1999
M M h r " rb -b d lt r d t t n " Proc. 1997 Int. Symp. on Inf. Th., l 1997
5 M n n " t l tr n n p rf r n n f d n d p r v d v r t h nn l " IEEE Trans. Commun., v l 1 p 3339 n 1973
K M rr nd S hn rt " t thr hp t n l tt d A O A S/SSMA r d t th r nd n t r n " IEEE Trans. Commun., v l pp 1 3-1 3 l 199
7 t l nd ltz n ""An l f pl v nt rf r n n l- l t n t hn f r pr d- p tr lt pl - t " " IEEE Journal of Selected Areas in Communications, v l 1 pp 79 - 7 n 199
C h A M v h A b S G ld t n nd I S d " d d-r n S A p rf r n n l " IEEE Trans. Aerosp. Electron. Syst., v l 3 pp - 7 Apr
9 r nd S rd " r b b l t f rr r n MMSE lt r d t t n " IEEE Trans. Inform. Theory, v l 3 pp - 71 M 1997
7 G r Digital Communications. M Gr - ll 1995
71 p j " rf r n n l f l tt d A O A/C MA t th d pt v MMSE r v r " IEICE Trans. Fundamentals, v l E - pp 5- 9 1997
7 h dh r " rf r n n l f r nd p t- t h d d d v n lt pl t " IEEE Trans. Commun., v l 9 pp 95-9 n 19 1
73 I d M ll tt nd r nn n " p d nv r n r t n d pt v rr " IEEE Trans. Aerospace Electron. Syst., v l AES-1 pp 53- 3 v 197
7 S nd -Y W n " rf r n f C MA l tt d A O A lt pl th lt r d t t n " n Proc. IEEE Wireless Commun. and Network. Conf. (WCNC'99), ( Orl n nd A pp 39- 3 1999
75 S t O d Y z t M K t nd A O " hr hp t n l f S/SSMA n l tt d A O A t th f x d p t l n th " IEEE J. Select. Areas Commun., v l 1 p 75 -75 199 08
7 S h d rf nd W ll "A n tr n d pt z t n ppr h t M lt r d t t n " IEEE Trans. Signal Processing, v l 5 pp 5 - n 1997
77 S h dr nd W nt r " n l n h f r pr v n th rr r p rf r n f fr n -d v n -d pl x ( tr n n t n tr n tt r nt nn d v r t " Int. J. Wire. Inform. Net., v l 1 p 1 9-59 199
7 S S nd S W r "A d v r t b n n S/C MA t th nv l t n l n d n nd t rb d d n " IEEE Trans. Vehicular Technology, v l pp 3 -31 M 1995
79 St r nd A b " hr hp t p rf r n f n n l tt d d r t- n SSMA p t r d n t r " IEEE Trans. Commun., v l 37 pp 1 - 3 A 19 9
Str b h " - n Ad pt v lt r " IEEE Trans. Signal Processing, v l pp 93 - 9 7 1995
1 Y S n " t r d v r t f r nd l tt d C MA n t r " n Proc. 33rd Asilomar Conference on Signals, Systems and Computers, ( f Gr v nd CA pp 1 -1 1 O t 1999
Y S n "M lt r d t t n n n t r d v r t f r r nd p t- t h d C MA n t r " n Proc. 34th Conference on Information Science and Systems, ( r n t n nd pp A3-1 M r
3 Y S n " t r d v r t f r nd p t- t h d C MA n t r - p rt I: lt r d t t n " Submitted to IEEE Trans. Signal Processing, n
Y S n " t r d v r t f r nd p t- t h d C MA n t r pt lt r d t t n " Submitted to IEEE Trans. Signal Processing, n
5 r h f r h n nd A C ld rb n "Sp - l C d fr Orth n l n " IEEE Trans. Inform. Theory, v l 5 pp 1 5 -1 7 l 1999
r h A b S h dr nd A C ld rb n "Sp - C d f r h t t W r l C n t n rf r n Cr t r n n th r n f Ch nn l E t t n Err r M b l t nd M lt pl th " IEEE Trans. Commun., v l 7 pp 199- b 1999
7 r h S h dr nd A C ld rb n "Sp - C d f r h t t W r l C n t n rf r n Cr t r n nd C d C n tr t n " IEEE Trans. Inform. Theory, v l pp 7 -7 5 M r 199 109
M K t n "Inv r f lt r n r t r f r C MA t " IEEE Trans. Signal Processing, v l 5 pp 1 -11 n 1997
9 M K t n nd G G nn "Opt l d rr l t n r v r f r S-C MA t n l pr n fr r " IEEE Trans. Sig. Proc., v l pp 3 -3 5 199
9 M K t n nd " rf r n n l f n v r n C MA r v r " IEEE Trans. Signal Processing, v l pp 3 1 -3 v 199
91 K nd C "Eff t v nt rf r n nd ff t v b nd dth f l n r lt r r v r n A n hr n C MA t " IEEE Trans. Inform. Theory, v l pp 1 -1 7 l
9 ft I K r t n nd K r n " t - d pt v d t t n f n l " IEEE Trans. Aerosp. Electron. Syst., v l 19 pp 313-31 M r h 19 3
93 ft K r n nd I K r t n " t d pt v n l t t n b n l r v l d p t n f d t tr x " Proc. IEEE, v l 7 pp - 5 n 19
9 M K r n "A t t ppr h t th d n nd n l f pt SK r v r f r n r l z d d v r t n t n v r l h f d n h nn l " IEEE Trans. corn., v l 7 pp 13 5-1375 S pt 1999
95 M K r n nd A zh n "M lt t d t t n f r n hr n d -d v n lt pl - n t n " IEEE Trans. Commun., v l 3 pp 5 5-519 Apr l 199
9 M K r n nd A zh n " r- pt d t t n n n hr n d -d v n lt pl - t " IEEE Trans. Commun., v l 39 pp 5- 3 M 1991
97 S rd "M n pr b b l t f rr r f r n hr n G n lt pl - h nn l " IEEE Trans. Inform. Theory, v l I -3 pp 5-9 n 19
9 S rd nd S Sh "Sp tr l ff n f C MA th r nd pr d n " IEEE Trans. Inform. Theory, v l 5 pp - M r 1999
99 j r nd K M W r n "On St b l t f S-C MA d t n t r pl n r tr n n th r " n Proceeding of the 38th Conference on Decision and Control, ( h n x Ar z n pp 35 - 35 9 1999 11
1 A t rb " r l -r t nv l t n d f r x th r t l p rf r n f pr d- p tr lt pl - t " IEEE Journal on Selected Areas in Communications, v l pp 1 - 9 M 199
1 1 W n nd r " l nd lt r d t t n A b p ppr h " IEEE Trans. Inform. Theory, v l pp 77- 91 M r 199
1 W n nd r "It r t v ( rb ft nt rf r n n ll t n nd d d n f r d d C MA " IEEE Trans. Commun., v l 7 pp 1 - 1 1 l 1999
1 3 M W x nd K l th " t t n f n l b nf r t n th r t r t r " IEEE Trans. Acoust. Speech Signal Processing, v l ASS -33 pp 3 7-39 Apr 19 5
1 W r d " v r t f r d r t- n pr d p tr t n lt pl tr n t nt nn " n Proc. IEEE ICC'93, pp 1775-1779 M 1993
1 5 S W r "Ad pt v r t rr r ntr l thr h th f d v r t b n nd j r t -l d d n n h br d-A Q pr t l " IEEE Trans. Commun., v l 39 pp 3 -3 5 M r 1991 1 S W r Error Control Systems for Digital Communication and Storage. En l d Cl ff r nt - ll 1995
1 7 W nt r " h d v r t n f tr n t d v r t n r l t th l h f d n " IEEE Trans. Vehicular Technology, v l 7 pp 119- 1 3 b 199
1 A W ttn b n "A n b nd dth ff nt tr n t nt nn d l t n d v r t h f r l n r d t l d l t n " n Proc. IEEE ICC'93, pp 1 3 -1 3 M 1993
1 9 G W W rn ll nd M r tt "Eff nt n l pr n t hn f r xpl t n tr n t nt nn d v r t n f d n h nn l " IEEE Trans. Signal Processing, v l 5 pp 191- 5 n 1997
11 Sh rt nd C K hf rth "A f l f b pt d t t r f r h r nt lt r n t n " IEEE J. Select. Areas Commun., v l pp 3- 9 M 199
111 G W n - nd S h r "Ad pt v lt t p r ll l nt rf r n n ll t n f r C MA " IEEE J. Select. Areas Commun., v l 17 pp 1 15-1 7 O t 1999
11 Y n "An xt n n f th AS d l r th t b th r n nd b p tr n " IEEE Signal Processing Letters, v l pp 179-1 S pt 1995 111
113 Y n " r j t n ppr x t n b p tr n " IEEE Trans. Signal Processing, v l pp 95-1 7 n 1995 11 K -W Y p nd -S "Eff nt l t n f d t l tr n n v r WSSUS h nn l " IEEE Trans. Commun., v l 3 pp 9 7- 913 1995 115 h n E K Ch n nd C "O tp t MAI d tr b t n f MMSE lt r r v r n S-C MA t " submitted for publi- cation. 11 v n r nd r d "S b pt l lt r d t t r f r fr n - l t v l h f d n n hr n C MA h nn l " IEEE Trans. Commun., v l 3 pp 15 -157 br r /M r h/Apr l 1995