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
Top Related