SPACESPACE--TIME CODING AND SIGNAL PROCESSINGTIME CODING AND SIGNAL PROCESSING

SpaceSpace--Time Fading ….Time Fading ….

z)10

log 1

0h(

t,z

Angle Spread d = 5, Doppler Spread fd = 200 Hz

SpaceSpace--Time Coded ModulationTime Coded Modulation

InformationSource

ReceiverSpace-Time Encoder

For each input symbol, the space-time encoder chooses the t ll ti i t t i lt li lt l t it f hconstellation points to simultaneouslysimultaneously transmit from each

antenna so that codingcoding and diversitydiversity gains are maximizedmaximized To prove this result, we perform error rate analysisTo prove this result, we perform error rate analysis To prove this result, we perform error rate analysisTo prove this result, we perform error rate analysis

SpaceSpace--Time Coding: The ModelTime Coding: The Model

N transmit and M receive antennas N transmit and M receive antennas Input energy divided equally among transmit antenna and is

denoted by (per transmit antenna)y (p ) The overall channel is made up of NM slowly varyingslowly varying spatial

sub-channels, each with AWGN with variance E h b h l i R l i h f di ( l i li Each sub-channel is Rayleigh fading (same analysis applies to Rician fading too)

At any time interval N signals are transmitted simultaneouslysimultaneously At any time interval, N signals are transmitted simultaneouslysimultaneously, one from each transmit antenna

The sub-channels undergo independentindependent fading The fade coefficients are assumed to be fixedfixed during a slot

and independentindependent from slot to another

STC: The ModelSTC: The Model

ih l] )( ,),( ),( [

:VectorCode dTransmitte T

N21 lclclclc

:Matrix Channel

11211 N

21

22221

MNMM

NH

noiseGaussian :)( . )( :Vector Signal Received

21

ll l

MNMM

ncHr

STC: Probability of Error AnalysisSTC: Probability of Error Analysis

,, , codeword dTransmitte

21

cccC L

-exp-exp)(Pr

knowledge CSIperfect with decoding ML assuming :y probabiliterror Pairwise ~

2~

2~

2~

CHHCCHHCCHHCHCC ss ddEdEQ

)(,

,exp,4

exp),2

( Pr

2~~2

s00

CCHHCHC

CHHCCHHCCHHCHCC

F

d

ddN

dN

Q

d4EΓh

)(-)()(-)(

T~

*

2

1 1

~~

111

hhCCAhM

M

j

L

lNNjNj

N

lclclclc

, , ,

and 4EΓ where, ,

~*

~~

T21oss

1

CCBCCBCCA

hhCCAh jNjjjjj

j N

STC: Probability of Error AnalysisSTC: Probability of Error Analysis

~

codeword decoded theand codeword

ed transmittebetween thmatrix error theis matrix L x N The

CC

B

LcLccccc

~~~

~

11

~

11

~

11 2211

LcLccccc

LcLccccc

NNNNNN

~~~

222222

2211

2211

B

NNNNNN

STC: Probability of Error AnalysisSTC: Probability of Error Analysis

i elorthonormaisanddiagwhereU as written becan &Hermitian is matrix NxN The

*

*

UΛΛUBBA

of rseigenvecto theare Uof columns theand ,

i.e.l,orthonorma isand,,,diag where, U*

21

N

AIUU

UΛΛU

λ

have will then we,Let 2

*~

2

*

dM NM

jj

ΛCC

hU

by the vector randomGaussian a gmultiplyin that Note

λ,

*

1 11

d

j

j iiji

jjj

h

ΛCC

matrixcovariancesamewith theRVGaussian ain resultsmatrix unitary

2

*

NM N

jU

)(H|C~CPr 1s

2

1 1s .Γ

1

λ.Γ

i

ijiM

j

N

iiji

ee Mj

STC: Probability of Error AnalysisSTC: Probability of Error Analysis

ijij 22 a haseach wherei.i.d., are variablesrandom The

2

PDF lexponentia i.e. freedom, of degrees 2on with distributi

otherwise. 0 and 0for ~ efij

MN

ijij

2

1P

get to of PDFover average error, ofy probabilit calculate To

r

i i

21

1 se

thebe,, ,andmatrix theofrank thebe N rLet Γ.1

1P

A

rMMr

r

21

P

SNR)high (at Then . of seigenvalue nonzero

A

rMs

ii

1eP

STC: Design CriteriaSTC: Design Criteria

Rank Criterion:Rank Criterion: To achieve the maximum diversity NM,Rank Criterion: Rank Criterion: To achieve the maximum diversity NM, the codeword difference matrix B(C1,C2) has to be full rank for any two codewords C1 and C2. If B(C1,C2) has a

i i k h di i i hi d Thminimum rank r, then a diversity rM is achieved. The diversity order corresponds to the slope of the error rate vs SNR curve (on a log-log scale) at high SNRrate vs. SNR curve (on a log log scale) at high SNR

Determinant Criterion:Determinant Criterion: The minimum (over all possibleDeterminant Criterion:Determinant Criterion: The minimum (over all possible codewords) product of the r non-zero eigenvalues of the codeword difference matrix is called the coding gain

hi h t h i t l hift th twhich represents a horizontal shift on the error rate vs. SNR curve and is to be maximized

SpaceSpace--Time Block CodingTime Block Coding

Definition : A space-time block code (STBC) is an array with columns representing time slots and rows representing t it ttransmit antennas

The rate (in symbols per channel use) of an STBC is defined as the no. of independent information symbols transmitted p yduring each STBC codeword divided by its time duration

The diversity order achieved by an information symbol is given by the minimum rank of the codeword difference matrixgiven by the minimum rank of the codeword difference matrix over all possible choices of this symbol irrespective of other symbols

By definition of matrix rank diversity order can’t exceed the By definition of matrix rank, diversity order can t exceed the minimum of the no. of transmit antennas and no. of time slots

The Alamouti STBC

xx 1hCode over two consecutiveb l d h l 12 xx

21 - xx

1

2h

symbols and assume channelis fixed over these 2 symbols

21

212212212212

122111

nxhxhrnxhxhr

nxhxhr

212212212212 nxhxhrnxhxhr

11211

nxhhr

(1)

*2

1*2

1

12

21

2

1

nxHrnxhhr

Achieves diversity order (1) nxHr 2 like delay diversity but at lower decoding complexity

Alamouti STBC (Cont’d)( )

REMARK:

The equivalent channel matrix in (1) is orthogonal, hencet h d filt i ML ti l d d l th 2 b lmatched filter is ML optimal and decouples the 2 symbols

IhhHHHH 22

21

The Alamouti code is a 2x2 complex orthogonal design where the elements on the main diagonal aredesign where the elements on the main diagonal are complex conjugates and the elements on the anti-diagonal are negative complex conjugates. This g g p j gSTBC has rate 1 and both symbols achieve diversity order of 2

Alamouti STBC Decodingg

~

~22 nxhh

nHxHHrHr

diversityorder 2~

2

21

ndnxh

nxhh

22h variancehas andmean zero Gaussian, still is ~n

22

22hfactor by improved h

hSNR

h

Decoding of Alamouti STBC for 2 RXDecoding of Alamouti STBC for 2 RX

1H

1r~ 1c

1c1r

c

2

121 rr

HHr **~

2H

2r~ 2c2c2r

2H

The Alamouti STBC is the optimum 2-TX STBC for 1 RX only. For more than 1 RX, it still achieves full diversity but it suffers capacity loss and we can design codes with higher coding gain (e.g. Golden code)

AlamoutiAlamouti STBC Full Diversity ProofSTBC Full Diversity Proof

Exercise : Use MATLAB to calculate the coding gain of the Alamouti STBC. Does it vary with constellation size ?

Why is Matched Filter ML for Why is Matched Filter ML for AlamoutiAlamouti STBCSTBC

Space-time matched filter achieves ML detector performance with decoupled detection and linear complexity (in the number ofdecoupled detection and linear complexity (in the number of transmit antennas) where each symbol achieves a spatial diversity order of 2 with 1 receive antenna assuming independent

ti l h l d f t h l k l d t th ispatial channels and perfect channel knowledge at the receiver and without channel knowledge at transmitter

Summaryy

Advantages of Alamouti STBCd• Maximum diversity (2nd order)

• Rate 1 (since 2 information symbols in 2 time slots)=> full-rate (under restriction of no constellation expansion)rate (under restriction of no constellation expansion)• Open loop (no need for channel knowledge at TX)• Low ML decoding complexity (linear)Low ML decoding complexity (linear)

Drawback: (more on this later)Cannot be extended to more than 2 transmit antennas forcomplex signal constellations without rate loss (i.e. rate <1) orsacrificing simple linear decoding complexity or constellationexpansion

Other STBC ExamplesOther STBC Examples

Pure spatial multiplexing (BLAST) : 4 TX, 1 time slot, rate 4, diversity 1 for all symbols

1xy y

3

2

1

xx

Hybrid STBC : 4 TX, 2 time slots, rate 3, diversity 1 for 4 symbols and diversity 2 for 2 remaining symbols

4x

symbols and diversity 2 for 2 remaining symbols

Question : How about ?

**21 xx

Question : How about ?

43

12

xxxx

2

*331 xxxx

65 xx

*

144*2 xxxx

Orthogonal Design for N > 2Orthogonal Design for N > 2

For N=2, we studied the Alamouti code but is there a rate 1rate 1STBC with decoupled linear processing for more than two p p gantennas (N >2)N >2) ?

Answer: theory of generalized orthogonal designstheory of generalized orthogonal designs Complex constellations: NONO Complex constellations: NONO Real constellations: YESYES

Rate 1Rate 1 codes with decoupled linear processing for arbitraryarbitraryb f t it t d l t ll tinumber of transmit antennas and real constellations

Rate 1/2Rate 1/2 codes with decoupled linear processing for arbitraryarbitrary number of transmit antennas and complex yy pconstellations

Rate 3/4Rate 3/4 codes with decoupled linear processing for N=33and N=44 transmit antennas and complex constellationsand N 44 transmit antennas and complex constellations

Orthogonal STBC for N > 2 ….Orthogonal STBC for N > 2 ….

Example (Example (OctonionOctonion):): Complex constellation, rate=3/4, 4 transmit antennas (N=4)transmit antennas (N=4)

210 0bbbb

**2

*0

*1

210

1

0 0 bbbbb

0*1

*2

1*0

*2

2

1

00

bbbbbb

b

Diversity order of 4 prove it !

0120 bbb

Diversity order of 4, prove it !

Interference Cancellation with Interference Cancellation with AlamoutiAlamouti STBCSTBCBurst 2

InformationSource

Space-TimeBl k E d

Terminal 1Burst 1

Source Block Encoder

Burst 2

Terminal 1Information

c1

Interference Cancellationand

ML Decision

B t 1

InformationSource

Space-Time Block Encoder

Terminal 2Informationc2

Terminal 2

Burst 1

KK users, NN transmit antennas per user. ClassicalClassical IC techniques need NN((KK 1) 11) 1 i i f f KK 11NN((KK--1) +11) +1 receive antennas to suppress interference from KK--11 co-channel users (each user employing spatial multiplexing)

Exploit code structurecode structure to suppress interference using only KK receive antennas Assumption: full synchronizationfull synchronization between terminalsantennas Assumption: full synchronizationfull synchronization between terminals

Increases system capacitycapacity (uplink) (uplink) or or data rate (downlink)data rate (downlink)

Two User Alamouti STBCTwo User Alamouti STBC

antennas receive 2With

1111 ncGHGHr

2222

Alamoutiblockis:~nsGHr

HncH tor)(DecorrelaForcing Zero

Alamoutiblock is : HncH

111

111 ˆˆGH

)(g

ncrr

22222 ˆˆGH nsrr

Zero Forcing IC with STBCZero Forcing IC with STBC

0~ 121

1111 GGIHGH

- ~ and ~

~0

11

12221

211

112

122

GHHGGHGGHH

IHHGGH

~~

. ~00~

~~

2

1

2

1

2

11

12

121

nn

sc

GH

rr

rr

IHHGGI

structure Alamouti same thehave and orthogonal are ~ and ~ GH

i lidd t t whitestill are ~ and ~ noise

and property) group tivemultiplica to(due

21 nnNote : this scheme is NOT ML and achieves diversity order of 2

caseuser -singlein asanddetect can sc

ZFIC PerformanceZFIC Performance

FER Performance of 8-PSK with STBC and Zero ForcingInterference Cancellation

10-1

100

rror

Rat

e

10-3

10-2

Fram

e E

10-4

10 3

STBC( 2 Tx, 2 Rx) + ZFIC, SIR = 0 dBSTBC( 2 Tx, 1 Rx)

10 15 20 25 3010-6

10-5

( , )STBC( 2 Tx, 2 Rx) , No Interference

SNR per Rx Antenna (dB)

10 15 20 25 30

Differential Differential AlamoutiAlamouti STBC for FlatSTBC for Flat--Fading ChannelsFading Channels

T li i t t i i i l h d f h l ti ti To eliminate training signal overhead for channel estimation, use non-coherent detection techniques such as differential encoding/decoding

In absence of noise, Alamouti STBC is given by :

)()(12

21

12

21

12

21 kHXxxxx

hhhh

yyyy

kY

If channel is fixed over 2 consecutive codewords

)()1()()1()()( kUkYkUkHXkHXkY

Given information symbols (u1,u2), differential STBC encoding/decoding rules are

Exercise : re-derive this expression in the presence of AWGN to prove the 3dB SNR loss

)()1()( kUkXkX

2)()( kuku 2

12

21 )1(/)()1()()()()(

)(

kYkYkYkukukuku

kU

AlamoutiAlamouti--OFDM Across Time or Frequency OFDM Across Time or Frequency

SpaceAcross 2 adjacent OFDM symbols (at same tone) for slowly time-varying

Time

slowly time varying highly frequency selective channels

Space Across 2 adjacent tones (within same OFDM symbol) for fast time-varying Channels with low delay spread

Frequency

y p

SummarySummary : Why Space: Why Space--Time Coding ?Time Coding ?D li k i b ttl k f t i t i i• Downlink is bottleneck for asymmetric transmission scenarios (e.g. Internet browsing & downloading)

• Signal fading is a major impairment on wireless links

• Antenna diversity is effective against signal fadingAntenna diversity is effective against signal fading

• Receive diversity improves downlink performance but i i ti d t f t i lincreases size, power consumption, and cost of terminals

• Transmit diversity at the base station keeps terminal simple and doesn’t require CSI at transmitter (open loop)

•Alamouti STBC adopted in several wireless standardsAlamouti STBC adopted in several wireless standards (CDMA-2000, W-CDMA, WiMAX (802.16), WiFi (802.11n), LTE)

Some Design IssuesSome Design Issues

For delay-sensitive applications, achieving high diversity takes precedence over high throughput to minimize ARQ retransmissions

For delay-tolerant applications, use antennas for spatial multiplexing. Diversity gains can be realized inmultiplexing. Diversity gains can be realized in frequency (multipath diversity) and/or time (ARQ)

High-mobility conditions favor use of shorter blocks, lower carrier frequencies and non-coherent receiverlower carrier frequencies, and non-coherent receiver techniques

As no. of transmit and receive antennas increases, ti l lti l i i d ti l di it dspatial multiplexing gain and spatial diversity order

increase but so does cost and complexity (more critical for user terminal than base station)

Maximizing coding gain more important than maximizing diversity gain at low SNR and vice versa

Part 3 : STC for Broadband ChannelsPart 3 : STC for Broadband ChannelsPart 3 : STC for Broadband ChannelsPart 3 : STC for Broadband Channels

S Ti C di St t Space-Time Coding Structure

Equalization for Space Time Codes Equalization for Space-Time Codes

Channel Estimation for Multiple Transmit Channel Estimation for Multiple-Transmit-Antenna Broadband Systems

Interference Cancellation in a Multi-User Broadband Environment

SpaceSpace--Time Coding onTime Coding onSpaceSpace Time Coding on Time Coding on Broadband ChannelsBroadband Channels

QAM/PSK

Transmitter ReceiverQAM/PSKEncoder

InformationSource

SpaceTime

EncoderPrefilter Equalizer

Encoder QAM/PSKEncoder

ChannelChannelEstimationEqualizer critical for operation

of terminal for broadband transmissions

EDGE Transmission ModelEDGE Transmission Model

• Frame structure identical to GSM ( 577sec slot time, 3.69sec symbol( , yduration )

• EDGE uses 8-PSK modulation to achieve higher spectral efficiency

• Linearized GMSK pulse shaping reduces adjacent channelinterference but introduces additional ISI

• Signaling over 200KHz channels causes frequency-selective fading

• 2 channels modeled as FIR filters with memory (for i=1 2))(Dh • 2 channels modeled as FIR filters with memory (for i=1,2)

• Channel impulse response can be assumed constant during the burst(quasi-static fading) since coherence time >> burst duration

)(Dhi

(quasi static fading) since coherence time >> burst duration

AlamoutiAlamouti STBC for ISI ChannelsSTBC for ISI ChannelsAlamoutiAlamouti STBC for ISI ChannelsSTBC for ISI Channels

3 STBC schemes proposed for frequency-selective channels

All 3 schemes implement Alamouti orthogonali li ith i ti f d i tsignaling either in time or frequency domain at a

block not symbol level

Aim at realizing multi-path diversity gains in addition to spatial diversity gainsaddition to spatial diversity gains

3 STBC Schemes for3 STBC Schemes for3 STBC Schemes for 3 STBC Schemes for FrequencyFrequency--Selective ChannelsSelective Channels

1) Orthogonal Frequency Division Multiplexed Space-Time Block-Coding (OFDM-STBC)Space-Time Block-Coding (OFDM-STBC)

2) Single-Carrier Frequency-Domain-2) Single Carrier Frequency DomainEqualized Space-Time Block-Coding (SC FDE-STBC)

3) Time-Reversal Space-Time Block-Coding (TR-STBC)

Common FeaturesCommon Features

1) All schemes assume channel fixed over 2consecutive blocksconsecutive blocks

2) All schemes assume a guard sequence to2) All schemes assume a guard sequence to eliminate inter-block interference

3) All schemes process pairs of received blocks

4) All schemes assume channel known at receiverreceiver

Why SC FDEWhy SC FDE--STBC ?STBC ?

Has lower sensitivity to frequency offsets and lower peak-to-average ratio (PAR) than OFDM-STBC because it is a single carrier schemebecause it is a single-carrier scheme

Low computational complexity due to use of FFT Low computational complexity due to use of FFT

SC FDE has been accepted as a transmission SC FDE has been accepted as a transmission mode (in addition to OFDM) in LTE Uplink

Summaryy

For ISI Channels, the Alamouti scheme should beimplemented at a block not symbol level (as in flat-fadingcase) in order to realize multipath diversity (in addition tocase) in order to realize multipath diversity (in addition tothe 2nd order spatial diversity). There are at least 3 waysof doing this in the time domain (called time-reversalof doing this in the time domain (called time reversalspace-time block coding (TR-STBC) or in the frequency-domain using single-carrier FDE or using multi-carrierg g g(OFDM) transmission. In the sequel, single carrier FDE-STBC will be described

SC FDESC FDE--STBCSTBC

FFT Linear Combiner

)(ky

)1( kIFFT SlicerFDE

)1( ky

• FFT and linearly combine pairs of receivedFFT and linearly combine pairs of received

blocks to eliminate inter-antenna interference

• Proceed as in 1 TX FDE Complex single tap equalizer per subchannel Complex single-tap equalizer per subchannel

IFFT averages out frequency nulls

Decisions made in time domain

The Alamouti SC-FDE Scheme for ISI Channels

))((2 Nnx )(1 nxCPN N )(ky

))((1 Nnx )(2 nxCPN N

FFTRemoveCP

y

)1( kyN N

FDEIFFTSBS)(ˆ)(ˆ kxkx

)(y

FDEIFFTSBS)()( 21 kxkx

ENCODING RULE

Th)(Xbi""f

N)length (ofblock ed transmittk theof symbol n theDenote(k)

thth

Then).(Xby i"" antenna from

)()( index time)(2

)1(1

(k)

1,2ii

nxnx Nkk

n

tiNd lthd t)(h

,....4,2,01-0,1,..Nnfor

)()(

)()( )(

1)1(

2

21

knxnx

nxnx

Nkk

N

get weblocks,input theof DFT theTaking

operation.N-modulothedenotes N)( where

f

4201-0,1,..Nmfor

)(

)( bin frequency

)()1(

)(2

)1(1

kmXmX

mXmXkk

kk

levelblock at the scheme Alamouti theiswhich

,....4,2,0)( )(1

)(2 kmXmX

SC FDESC FDE--STBCSTBC

NN

)(1 nx)mod)((2 Nnx CP

NN

)(2 nx)mod)((1 Nnx CP

n = 0,1,…., N-1)(

denotes complex conjugation

Implement Alamouti structure at a block not symbol level).( denotes complex conjugation

Input-Output Relationshipp p p

)()(2

)(2

)(1

)(1

)( zxHxHy jjjjjj

(j)2

(j)1

2211

prefix)cyclicofusetheto(duematricescirculant NN are H and H where

y

prefix)cyclicofuse the to(due

diagonal:matrix :

)(2

)(2

)(1

)(1

FFTQQQH

QQHjj

jj

g22 QQ

Receiver Operationsp

:FFT )1 )()(

2)(

2)(

1)(

1)()( jjjjjjj ZXXQyY

ZXY

:blocks of pairs ng2)Processi(k)(k)(k)

Z-Z

XX

Y-Y

Y )1k(

(k)

(k)2

(k)1

12

211)(k

(k)

blocks econsecutiv 2over fixed assumed are matrices channel 2 the where

Receiver Operations

Z~X0~filter matched timespaceApply 3)

(k)(k)22)(Y k

i f ihNfih ld

Z~Z

XX

0

0~~ (k)

2

1(k)2

12

22

1

21)(

2

)(1 YY

YY

k

decoupled are blocks

ninformatio twotheNow,.ofity orthogonal todue

21:Z~~~

2,1:Z~ ~ (k))(2)(

(k)i

)(22

21

)(

iXY

iXYkk

ki

ki

STBC-FDE SISOin as equalized becan which

2,1:Z

2

i iXY ii

:)(Z~)()(~)(Y~ binfrequency is (k)i

)(2(k)i mmmXmm k

i

SummarySummarySummarySummary

Time-domain received blocks

1,:)()(22

)(11

)( kkjnxHxHy jjjj

After FFT

1,:)()(22

)(11

)( kkjNXXY jjjj

Alamouti structure

,2211 j

)()( )(2

)1(1 mXmX kk )()( )(

1)1(

2 mXmX kk

For m=0 1 N 1 and k = 0 2 4For m=0,1,…, N-1 and k = 0,2,4,…..

SummarySummary Process 2 blocks :

)()()( kkk NXY

)1(

)(

)(2

)(1

*1

*2

21)1(

)(

kkk NN

XX

YY

Space-time matched filter combining :

NXY (1) Space time matched filter combining :

NXYZ ~022

22

21*

FDE :

NXYZ0 2

22

1

))/1()()(/(1)( 22 SNRiiiiiW ))/1(),(),(/(1)( 21 SNRiiiiiW

10 Ni

Diversity GainsDiversity GainsDiversity GainsDiversity Gains

100

EDGE TU Channel, 8−PSK Modulation,N=64

• Same total power as 1 TX

10−1

MMSE−FDE (1 TX) MMSE−FDE + STBC (2 TX)

power as 1 TX10

−2

it E

rror

Rat

e

• Diversity gains clear from

10−4

10−3B

it E

increased slope at high SNR

5 10 15 20 2510

−5

10−4

Eb/No (dB)Eb/No (dB)

hChannel EstimationChannel Estimation

h2

s2Training

y

2

1h zAWGN

s1Training AWGN

Receiver uses knowledge of t i i b l t j i tl

ZShZhh

SSY

1

21training symbols to jointly estimate two unknown channel impulse responsesY

SS

SSSSSSSS

YSSSh

h

*

*1

1

**2

*11

*1*1*

2

)(ˆSSSSS 22212

Ideally, S1 and S2 should be uncorrelated and each has impulse-like auto-correlation

Effect of Channel Estimation on SC FDEEffect of Channel Estimation on SC FDE--STBCSTBC

100

EDGE TU Channel, 8−PSK Modulation,N=64

• Length-26 PRUS

training sequence10

−1

Training Sequences are PRUS of length 26

training sequence

L t

10−2

ror

Rate

• Least squares

channel estimation 10−3B

it E

rror

Perfect Channel KnowledgeEstimated Channel

• Loss = 1-1.5 dB10

−4

5 10 15 20 2510

−5

Eb/No (dB)

Differential SpaceDifferential Space--Time Transmission for ISI ChannelsTime Transmission for ISI ChannelsDifferential SpaceDifferential Space Time Transmission for ISI ChannelsTime Transmission for ISI Channels

Differential transmission eliminates training sequence overhead g q

Performance gap from coherent < 3dB when channel estimation effects are taken into accountestimation effects are taken into account

Alternative to blind techniques (require temporal and/or spatial q ( q p pover-sampling with second-order statistics)

Problem : design differential STC for ISI channels Problem : design differential STC for ISI channels

Previous Work :Differential STBC for flat channels (Tarokh ’00)Coherent STBC for ISI channels (Liu’99, Lindskog’00)

AssumptionsAssumptionsAssumptionsAssumptions

Focus on 2 TX 1RX (extensions straightforward) Each channel is FIR filter with taps Channels fixed over 2 consecutive blocks

1 Channels fixed over 2 consecutive blocks Transmission format

GP P

Guard sequence eliminates inter-block interference

P P

Data DataGuard Guard sequence eliminates inter block interference

Differential Differential AlamoutiAlamouti STBC for ISI ChannelsSTBC for ISI Channels

With OFDM the differential STBC scheme for flat channels With OFDM, the differential STBC scheme for flat channels just described can be applied to tone for 2 consecutive OFDM blocks (assuming channel is slowly time-varying;

thm

otherwise it should be applied across 2 consecutive tones within SAME OFDM symbol). Choice depends on coherence time/bandwidth of the channel

Assumption : For OFDM-Alamouti, channel assumed fixed over 2 consecutive OFDM symbols (or subcarriers). For diff ti l OFDM Al ti h l d fi d 4differential OFDM-Alamouti, channel assumed fixed over 4consecutive OFDM symbols (or subcarriers) – more stringent

)()()()(

)()()()(

)()()()(

12

21

12

21

12

21

mXmXmXmX

mHmHmHmH

mYmYmYmY

)()()()()()()()( 11 mUmYmUmXmHmXmHmY kkkkk

ExampleExample

QPSK modulation

HIPERLAN channel : flat power delay profile8 HIPERLAN channel : , flat power delay profile

EDGE channel : , correlated taps

8

3 , p

Observation : performance approximately 3 dB i f i t h t d t ti ( i f t

3

3 dB inferior to coherent detection (assuming perfect channel knowledge for coherent) – why ? Hint : derive differential encoding/decoding rule in presence of AWGN

ExampleExample

10−1

HiperLan/II channels

coherent

EDGE channels

coherentdifferential

10−2

10−1 coherent

differential

10−1

differential

10−3

Pb

10−3

10−2

Pb

2 4 6 8 10 12 14 16 18 20

10−4

SNR (dB)

5 10 15 20 25

10

SNR (dB)

HIPERLAN Channel EDGE Channel

MultiMulti--User EnvironmentUser Environment

Two STBC users in same cell sharing same time slot Double system capacity by separating the 2 users at Double system capacity by separating the 2 users at

base station using MUD and 2RX For K users (each with 2 TX), we need K receive

t t b t tiantennas at base station

InformationSource

Space-TimeEncoder

Multi-user Detection

InformationSource

Space-TimeEncoder

Joint SCJoint SC--FDE Equalization, Decoding & FDE Equalization, Decoding & Interference Cancellation for AlamoutiInterference Cancellation for Alamouti STBCSTBCInterference Cancellation for AlamoutiInterference Cancellation for Alamouti--STBCSTBC

With 2 users and 2 RX, we have (each sub-block in the overall channel matrix has the same structure as in single-user Alamouti combined with SC-FDE that we studied before)

NXY

Interference Cancellation (decorrelator)

2

1

2

1

NN

SX

YY

ss

xx

Interference Cancellation (decorrelator)

111

11

~0~ NXYIZ xsx

Key observation : equivalent channel matrices have Alamouti orthogonal structure hence decoding proceeds as in 1 user case

22

12

~0 NSYIZ sxs

orthogonal structure, hence, decoding proceeds as in 1-user case with full diversity gain

Joint Equalization & Interference CancellationJoint Equalization & Interference CancellationJoint Equalization & Interference CancellationJoint Equalization & Interference Cancellation

Using 2 TX

FDE STBC dFDE-STBC and

2 RX at base station,

full spatial and

multi-path diversity

gains are achieved

for both usersf

SummarySummary

Space-time codes enjoy rich algebraic structureth t h ld b l it d t h fthat should be exploited to enhance performance and reduce complexity of receiver signal processing functions including channelprocessing functions including channel estimation, equalization and multi-user detection

3-layer receiver : inter-user, inter-antenna, and inter-symbol interference cancellation

Benefits more significant for broadband channels (multi path in addition to spatial diversity gains)(multi-path in addition to spatial diversity gains)

Some Design IssuesSome Design Issues

For delay-sensitive applications, achieving high diversity takes precedence over high throughput to minimize ARQ retransmissions

For delay-tolerant applications, use antennas for spatial multiplexing. Diversity gains can be realized inmultiplexing. Diversity gains can be realized in frequency (multipath diversity) and/or time (ARQ)

High-mobility conditions favor use of shorter blocks, lower carrier frequencies and non-coherent receiverlower carrier frequencies, and non-coherent receiver techniques

As no. of transmit and receive antennas increases, ti l lti l i i d ti l di it dspatial multiplexing gain and spatial diversity order

increase but so does cost and complexity (more critical for user terminal than base station)

Maximizing coding gain more important than maximizing diversity gain at low SNR and vice versa

References on STC DesignReferences on STC DesignReferences on STC DesignReferences on STC Design

V. Tarokh, N. Seshadri and A.R. Calderbank, “Space-Time Codes for High Data Rate Wireless Communications :Codes for High Data Rate Wireless Communications : Performance Criterion and Code Construction", IEEE Transactions on Information Theory,p. 744-765, March1998

V. Tarokh, H. Jafarkhani and A.R. Calderbank,”Space-Time Block Codes from Orthogonal Designs”, IEEE Transactions on Information Theory p 1456-1467 July 1999on Information Theory, p. 1456-1467, July 1999

V. Tarokh and H. Jafarkhani,"A Differential Detection Scheme for Transmit Diversity”, IEEE Journal on Selected Areas in Communications, p. 1169 -1174, July 2000

S. Alamouti, "A Simple Transmit Diversity Technique for Wireless Communications" IEEE Journal on Selected AreasWireless Communications , IEEE Journal on Selected Areas in Communications, p. 1451-1458,October 1998

STC for Narrowband ChannelsSTC for Narrowband Channels

A. Naguib, N. Seshadri, and A.R. Calderbank, “Increasing Data Rate over Wireless Channels", IEEE Signal , gProcessing Magazine, May 2000, p. 76-92

A. Naguib, V. Tarokh, N. Seshadri, and A.R. Calderbank, "A S Ti C di M d f Hi h D t R t Wi lSpace-Time Coding Modem for High-Data-Rate Wireless Communications", IEEE Journal on Selected Areas in Communications, p.1459-1477, October 1998

A.F. Naguib , N. Seshadri and A.R. Calderbank, "Applications of Space-Time Block Codes and Interference Suppression for High Capacity and High Data Rate WirelessSuppression for High Capacity and High Data Rate Wireless Systems", Asilomar Conference on Signals,Systems and Computers,Oct. 1998,p.1803 -1810

References on STC EqualizationReferences on STC Equalization

N. Al-Dhahir and A.H. Sayed, ``The Finite-Length Multi-Input Multi-Output MMSE-DFE'', IEEE Transactions on Signal Processing, p. 2921-2936, October 2000

N. Al-Dhahir, ``FIR Channel-Shortening Equalizers for MIMO ISI Channels'', IEEE Transactions on Communications, pages 213-218, February 2001

N. Al-Dhahir, ``Single-Carrier Frequency-Domain Equalization for Space-Time Block-Coded Transmissions over Frequency-Selective Fading Channels'', IEEE Communications Letters, pages 304-306, July 2001

W. Younis and N. Al-Dhahir, ``Joint Prefiltering an MLSE Equalization for Space-Time-Coded Transmission for EDGE'', IEEE Transactions on Vehicular Technology, p. 144-154, January 2002

W. Younis, N. Al-Dhahir, and A.H. Sayed, ``Adaptive Frequency-Domain f S C C SSEqualization of Space-Time Block-Coded Transmissions'', ICASSP, May

2002.

References on STC EqualizationReferences on STC Equalization

C. Fragouli, N. Al-Dhahir, S.N. Diggavi, and W. Turin, ``Prefiltered Space-Time M--BCJR Equalizer for Frequency-Selective Channels'', IEEE Transactions on Communications May 2002IEEE Transactions on Communications, May 2002

N. Al-Dhahir, ``Overview and Comparison of Equalization Schemes for Space-Time-Coded Signals with Application to EDGE'', IEEE Transactions on Signal Processing October 2002Transactions on Signal Processing, October 2002

G. Bauch and N. Al-Dhahir, ``Iterative Equalization and Decoding with Channel Shortening Filters for Space-Time Coded Modulation'', VTC'00 Fall p 1575 1582 September 2000Fall, p. 1575-1582, September 2000

S. Diggavi, N. Al-Dhahir, A. Stamoulis, and A.R. Calderbank,``Differential Space-Time Block Coding for Frequency-Selective Channels'' IEEE Communications Letters June 2002Selective Channels , IEEE Communications Letters, June 2002

N. Al-Dhahir, M. Uysal, and C.N. Georghiades, `'Three Space-Time Block-Coding Schemes for Frequency-Selective Fading Channels with Application to EDGE'' VTC p 1834 1838 October 2001Application to EDGE , VTC, p. 1834-1838, October 2001

STC for Broadband WirelessSTC for Broadband Wireless

E. Lindskog and A. Paulraj, “A Transmit Diversity Scheme for Delay Spread Channels",ICC 2000for Delay Spread Channels ,ICC 2000

Z. Liu, G. Giannakis, A. Scaglione and S. Barbarossa, “Decoding and Equalization of Unknown Multipath Channels Based on Block Precoding and Transmit Antenna Diversity"Based on Block Precoding and Transmit-Antenna Diversity , Asilomar Conf on Signals, Systems, and Computers, 1999, p. 1557-1561N Al Dh hi C F li A St li W Y i d A R N. Al-Dhahir, C. Fragouli, A. Stamoulis, W. Younis, and A.R. Calderbank, ``Space-Time Coding for Broadband Wireless Transmission'', IEEE Communications Magazine, S t b 2002September 2002

A. Stamoulis, N. Al-Dhahir, and A.R. Calderbank ``Further Results on Interference Cancellation for Space-Time Block-pCoded Systems'', Asilomar 2001

STC for Broadband WirelessSTC for Broadband Wireless

A. Stamoulis and N. Al-Dhahir, ``802.11 Network Throughput Gains due to Space-Time Block Codes'', in proceedings of CISS March 2002proceedings of CISS, March 2002

C. Fragouli, N. Al-Dhahir, and W. Turin, ``Reduced-Complexity Training Schemes for Multiple-Antenna p y g pBroadband Transmissions'', In WCNC, March 2002

C. Fragouli, N. Al-Dhahir, and W. Turin, ``Finite-Alphabet Constant Amplitude Training Sequence for Multiple AntennaConstant-Amplitude Training Sequence for Multiple-Antenna Broadband Transmissions'', ICC, April 2002