antoine o. berthet (1) , raphael visoz (2) , sami chtourou (2)

NEWCOM 1st meetingJune 25, 2004

1This work was supported by France Telecom R&D, grant no. 42271470

Efficient MMSE-based Turbo-Decoding ofSpace-Time BICM over MIMO Block Fading

ISI Channel with Imperfect CSIR

Antoine O. Berthet (1), Raphael Visoz (2), Sami Chtourou (2)

(1) École Supérieure d'Électricité (SUPELEC)Wireless Communications Departmentwww.supelec.fr/ecole/radio/berthet.html

(2) France Telecom R&D, DMR/IIMwww.francetelecom.com/...



Presentation outline

• Context and motivations• Communication model• Information-theoretic limits• Joint equalization and decoding of STBICM (perfect CSIR case)• Simplified MMSE-based turbo-processing• Numerical results and discussion• Turbo principle extended to joint channel estimation,

equalization and decoding (imperfect CSIR case)• Simplified MMSE-based turbo-processing• Numerical results and discussion (cont.)• Open issues



Context and motivations

Research context. Since the last few years, space-time coding has been the scene of considerable attention and progress

• Design of efficient space-time codes• Known result: BICM offer remarkable diversity gain on ergodic

SISO fading channel space extension• STBICM with iterative decoding (ID) on ergodic MIMO fading

(flat) channel approaches the capacity Hochwald, Ten Brink, “Achieving Near-Capacity on a Multiple Antenna Channel,” IEEE

COM-51, May 2003.

• In non-ergodic scenarii (without or with ISI) excellent performance compared to other existing space-time coding schemes

Berthet, Visoz and Boutros, “Space-Time BICM versus Space-Time Trellis Code for MIMO Block Fading Multipath AWGN Channel,” IEEE ITW’03, Mar 2003.



Context and motivations (cont.)

Problem statement. when neither space, time nor frequency dimensions are orthogonalized at the transmitter, strong ISI and Multiple Antenna Interference (MAI) come as a result and have to be compensated for at the receiver

• Interleaver between the channel code and the modulator, source of design flexibility, precludes any brute force optimum joint decoding sub-optimum 2-step procedure

Most demanding task: MIMO detection• Since several iterations will be required to converge towards

optimum results, it is even more crucial to find very low-complexity algorithms to realize symbol digit detection and decoding



Context and motivations (cont.)

Contribution. Our concern is to solve the problem of ISI and MAI cancellation with polynomial (at most cubic) complexity in all system parameters, while performing as close as possible from the theoretical available benchmarks, namely the Matched-Filter Bound (MFB) and the channel outage

• Our equalizing strategy is basically inspired from the seminal papers by

Glavieux and al., “Turbo-equalization over a Frequency-Selective Channel," Int. Symp. Turbo Codes, Brest, France, 1997

Wang and Poor, “Iterative (Turbo) Soft-Interference Cancellation and Decoding for Coded CDMA,” IEEE COM-47, July 1999.

Chan, Wornell, "A Class of Block-Iterative Equalizers for InterSymbol Interference Channels: Fixed Channel Results,“ IEEE COM-49, Nov. 2001.

Space-Time generalization not so obvious interesting degree of freedom in the receiver design



Communication model

General assumptions• Point-to-point transmission• Unknown CSI at the transmitter• Perfect or imperfect CSI knowledge at the receiver• R T MIMO channel• Frequency-selective (memory M)• B-block fading channel Typical wireless mobile radio environment



Space-Time BICM

Channel code: any binary linear code with high dmin

Interleaver: bitwise interleaver before modulation Constellation: PSK or QAM per antenna Qt bits/symbol

Labeling: from Q interleaved bits to T constellation symbols

Stefanov, Duman, “Turbo-Coded Modulations for Systems with Transmit and Receive Antenna Diversity over Block Fading Channels…” IEEE JSAC, May 2001

Binarycode

BinaryInterleaver

Modulator

Modulator

RT MIMO fading ISI channel

xk ykdkc



Channel model

B-block fading channel model. Space-Time code word X X1,…,XB spans over a finite number of independent channel realizations H1,…,HB

• Fading blocks are thought as separated both in time and/or frequency and may be correlated or not.

• Model well suited to represent a slowly time-varying MIMO multipath channel where blocks may either result from frequency-hopping in TDMA systems or be identified with subcarriers in OFDM systems.

If MAI is perfectly removed (GAD assumption), the MIMO block fading channel decomposes into a virtual SISO BT-block fading channel actually assumed for designing STBICM interleaving



Channel model (cont.)

Convolutional model• Discrete-time base-band equivalent vector channel output

• Additive noise vectors i.i.d circularly symmetric complex Gaussian with covariance matrix ²I

• Channel taps are RT complex random matrix with zero-mean and mean power satisfying the normalization constraint

0

y H x wM

b b b bk k k m k

m

†

0

H H IM

b bm m

m

E diag T



Channel model (cont.)

Length-LF sliding-window model as a valid approximation of the blockwise matrix model

where we introduce the stacked vectors and the Sylvester channel matrix

y H x wb b b bk k k

1 2

1 2

1 2

x x x

y y y

w w w

b b bk k L k L M

b b bk k L k L

b b bk k L k L

TT T

TT T

TT T

0

0

H H

H

H H

b bM

b

b bM



Joint equalization and decoding

Overall MAP decoding minimum BLER

• Brute force resolution intractable due to the random interleaver which breaks the outer code structure

• Belief propagation (BP) iterative joint decoder applied on the underlying factor graph approximates the marginal pmfs

• Decision made after a fixed number of iterations

1 1ˆ arg maxPr ,..., ; ,...,c

c = c Y Y H HMAP B BC

1 1Pr ,..., ; ,...,Y Y H Hn B Bc

1 1

1 1

Pr 1 ,..., ; ,...,ˆ ln

Pr 0 ,..., ; ,...,

Y Y H H

Y Y H Hn B B

nn B B

cc sign

c



Exact BP-ID

• BP iterative joint decoder. Locally optimal results (i.e., decisions coincide with MAP) provided that the word length is large enough and the number of iterations sufficient.

• The BP iterative joint decoder relies on the definition of some computation building blocks that exchange messages in the form of pmfs on variables of interest

• For STBICM, the two computation building blocks, namely MIMO detector and outer decoder trivially inherited from the serial scheme structure

• Bitwise interleaving variable nodes are symbol digits and coded bits

• Exchanged messages have the form of binary pmfs (or equivalently logarithmic probability ratios)



Factor graph

Coded bit nodes

Symbol digit nodes

Code constraint node

Channel constraint nodes

Labeling constraint nodes

Interleaver connections

Information bit nodes



Exact BP-ID (cont.)

Exchanged messages. Define log priors on symbol digits as

• Messages from MIMO detector relative to symbol digits

• Messages from decoder relative to coded bits

,

,

,

Pr 1lnPr 0

i kli k

i k

d

d

P

1,

1,

2 1, ,2: ( ) 1 ( , ) ( , )

,det, 2 1

, ,2: ( ) 0 ( , ) ( , )

1exp ( )

ln1

exp ( )

X X

X X

y H x X

y H x X

Li k

Li k

lk m k m j n i kA k m j n i k

li k

lk m k m j n i kA k m j n i k

PL

P

: 1,

: 0

expln

exp

c

c

n

n

ln nC c n nl dec

n ln nC c n n

c

c

YL

Y



Part 1: Efficient MMSE-based joint equalization and decoding with perfect CSIR



Classical MMSE-based ID

Motivation. Simplify the exact BP iterative decoder various algorithms, all inspired from the seminal paper by Wang et al.

Classical approach. Consider antennas as distinct users• Problem formally equivalent to the one of MUD in the presence

of ISI• Inner MIMO detector block replaced by a much simpler soft-in

soft-out module, which transforms the optimal APP estimation of vector xk into a sub-optimum MMSE estimation of each vector component xt,k individually, followed by a soft-in soft-out APP demapper

El Gamal, Hammons, "A New Approach to Layered Space-Time Coding and Signal Processing," IEEE IT-47, Sept. 2001.



Novel MMSE-based ID (cont.)

Drawbacks for such approaches

1. One single-dimensional Wiener filter for each transmit antenna (computationally costly for large MIMO systems)

2. Both ISI and MAI cancellation tasks rely on the sub-optimum MMSE criterion

New strategy. Based on a 2-stage process (some kind of group detection in two dimensions)

1. Multidimensional filtering stage to remove the ISI corrupting the T-dimensional vectors xk (only one single Wiener filter)

2. Symbol digit MIMO detection stage to deal with the residual MAI




Linear front end for ISI cancellation (in T-dimensional sense). Possible criteria are conditional or unconditional MMSE (or even max SNR)

Regenerated interference: using log extrinsic ratios coming from channel decoder

MIMO detection (MAI resolution): bitwise APP computation on symbol digits. Possible criteria are MAP, MMSE and max SNR

Multidim.Wiener filter

F

MIMOdetector

(log-domain) Deinterleaver

ChannelDecoder

(log-domain)

Interleaver

InterferenceRegenerator

MMSE symb.estimator

yk yk zk

xk

ISI cancellation MAI resolutionXTR

XTR

XTR




MMSE vector symbol estimate

Tentative soft decision vector used to regenerate the ISI (in multidimensional sense) corrupting symbol xk

where E is the T(LFM)T matrix defined as

1,1

,1

exp ( )|

1 expx

xx x x

Q li i kil

k k QA li ki

E

PP

P

;x x E xk k k

1 2

†E 0 0 I 0 0T T T T T T T T T T

L L M




Projection theorem associated to stochastic matrix inner product x,y E[xy] x,y and projection space generated by

• Detailed biased multidimensional Wiener filter

• Covariance matrix structure (infinite space-time interleaving)

with the variance evaluated using the consistent estimator

11 † † † 2, ,x y y y x xF = E H H H Il l l l

2 21 1x x I I Il l lx T T T T x T Tdiag

12 †

0

1x x

Llx k k

lLT

; ;y = y Hxl lk k k




Output of the multidimensional Wiener filter. Equivalent TT MIMO fading ‘flat’ channel

Gaussian approximation on the compound residual ISI + noise term (valid for large M)

• Exact APP estimation on each symbol digit replaced by (Cholesky factorization of the spatial correlation matrix )

z G xl l lk k k

1

1

2 1 ,,2: ( ) 1

,det,

2 1 ,,2: ( ) 0

1exp ( )

ln1

exp ( )

x x

x x

z G x x

z G x x

i

i

l l l bk j i kA j i

li k

l l l bk j i kA j i

PL

P




Genie-aided decoder (GAD) assumption

• Biased multidimensional Wiener filter

Tends to the matched filter (apart from the multiplication by a TT constant matrix)

Filter output tends to the canonical flat fading AWGN channel

†x x E E

1† † 2 † †F = E H HE I E H

† † †z x w H HMFBk k k m mm



Numerical results

Design. Terminated convolutional codes with max dfree & PSK Malkamäki, “Coded Diversity on Block Fading Channels”, IEEE IT-45, Mar.

1999. Ariyavisitakul, “Turbo-Space-Time Processing to Improve Wireless Channel

Capacity”, IEEE COM-48, Aug. 2000.

Objective 1. Test the potential of the novel equalizing strategy in its simplest mode MMSE-IC ISI / MF-IC MAI

Rate-1/3 64-state NRC, 8-PSK (Gray) Quasi-static channel (B 1) Code word length N 1536 coded bits



Numerical results (cont.)

1,0E-03

1,0E-02

1,0E-01

1,0E+00

-4 -3 -2 -1 0 1 2 3 4 5 6

Eb/No (dB)

BLE

R

outage

MFB

MAP iter 0

MAP iter 1

MAP iter 5

MF-IC iter 0

MF-IC iter 1

MF-IC iter 5

MIMO 1-block 22 EQ2, 2 bpcu




1,0E-04

1,0E-03

1,0E-02

1,0E-01

1,0E+00

-4 -3 -2 -1 0 1 2 3

Eb/No (dB)

BLE

R

outage

MFB

MAP iter 0

MAP iter 1

MAP iter 5

MF-IC iter 0

MF-IC iter 1

MF-IC iter 5





1,0E-03

1,0E-02

1,0E-01

1,0E+00

-7 -6 -5 -4 -3 -2 -1 0 1

Eb/No (dB)

BLE

R

outage

MFB

MAP iter 0

MAP iter 1

MAP iter 5

MF-IC iter 0

MF-IC iter 1

MF-IC iter 5





1,0E-03

1,0E-02

1,0E-01

1,0E+00

-9 -8 -7 -6 -5 -4 -3

Eb/No (dB)

BLE

R

outage

MFB

MF-IC iter 0

MF-IC iter 1

MF-IC iter 5





Objective 2. Classical approach vs. novel approach Rate-1/2 64-state NRC, 8-PSK (Gray) Quasi-static channel (B 1) Code word length N 1536 coded bits

Objective 3. (corollary). Adaptation of the chosen criterion for MAI resolution to the system load

Rate-1/3 64-state NRC, 8-PSK (Gray) relax criterion (MMSEMF) Rate-2/3 64-state NRC, 8-PSK (Gray) upgrade criterion (MMSEMAP) Quasi-static channel (B 1) Code word length N 1536 coded bits





1,0E-04

1,0E-03

1,0E-02

1,0E-01

1,0E+00

-5 -4 -3 -2 -1 0 1 2

Eb/No (dB)

BLE

R

outage

MFB

MMSE/MAP it5

MMSE/MMSE it5

MMSE joint it5

MMSE/MF it5





1,0E-04

1,0E-03

1,0E-02

1,0E-01

1,0E+00

-3 -2 -1 0 1 2 3 4 5 6

Eb/No (dB)

BLE

R

outage

MFB

MMSE/MAP it5

MMSE/MMSE it5

MMSE joint it5

MMSE/MF it5



Part 2: Efficient MMSE-based turbo-decoding with imperfect CSIR




Additional iterative loop (channel estimation): APP-based MMSE symbol estimate, MMSE channel estimate

Multidim.Wiener filter

F

MIMOdetector

(log-domain) Deinterleaver

ChannelDecoder

(log-domain)

Interleaver

InterferenceRegenerator

MMSE symb.estimator

yk yk zk

xk

ISI cancellation MAI resolution

MMSEchannel

estimator

MMSE symb.estimator

Interleaver

H

XY

Channel estimation

APP

XTR

XTR

XTR



Numerical results

Objective 4. Test the convergence of the double loop Rate-1/3 64-state NRC, 8-PSK (Gray) 44 MIMO quasi-static (B 1) EQ4 Code word length N 3072 coded bits Ideal 424 matrix symbol pilot (0.39 dB insertion loss) or ideal 432 matrix

symbol pilot (0.51 dB insertion loss) MMSE-IC ISI / MAP or MMSE-IC MAI / MMSE channel estimation




MIMO 1-block 44 EQ4, 4 bpcu, 8.57% pilot

1,0E-03

1,0E-02

1,0E-01

1,0E+00

-6 -5 -4 -3 -2 -1 0 1 2 3

Eb/No (dB)

BLE

R

outage

MFB

Perf. it0

Perf. it5

Mism. it0

Mism. it9

ALG1 it0

ALG1 it9

ALG2 it0

ALG2 it9




MIMO 1-block 44 EQ4, 4 bpcu, 12.1% pilot

1,0E-03

1,0E-02

1,0E-01

1,0E+00

-6 -5 -4 -3 -2 -1 0 1 2 3

Eb/No (dB)

BLE

R

outage

MFB

Perf. it0

Perf. it5

Mism. it0

Mism. it9

ALG1 it0

ALG1 it9

ALG2 it0

ALG2 it9



Open research topics

• Convergence analysis of such turbo receivers• Improved turbo receivers for high loads• Design of STBICM: rate-diversity tradeoff, code universality El Gamal, Damen, “Universal Space-Time Coding,” IEEE IT-49, May 2003 Boutros, Gresset, “Turbo Coding and Decoding for Multiple Antenna Channels,” Sept. 2003. Fabregas, Caire, “Coded Modulation in the Block Fading Channels,” submitted IT, 2004

• Tight bounds on the performance limits• Debate single-carrier vs. multi-carrier transmission for 4G

antoine o. berthet (1) , raphael visoz (2) , sami chtourou (2)

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