ELEC6014 RCNSs: Advanced Topic Series S Chen
ELEC6014 RCNSs: Advanced Topic Seminar
Adaptive Space-Time Shift Keying BasedMultiple-Input Multiple-Output Systems
Professor Sheng Chen
School of Electronics and Computer Science
University of Southampton
Southampton SO17 1BJ, UK
E-mail: [email protected]
Acknowledgements: Shinya Sugiura, Lajos Hanzo, Peichang Zhang
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ELEC6014 RCNSs: Advanced Topic Series S Chen
MIMO Landscape
• MIMO: exploits space and time dimensions ⇒ diversity and multiplexing gains
• Vertical Bell Lab layered space-time (V-BLAST)
– Offers high multiplexing gain at high decoding complexity owing to inter-channelinterference (ICI)
• Orthogonal space-time block codes (OSTBCs)
– Maximum diversity gain at expense of bandwidth efficiency
• Linear dispersion codes (LDCs)
– Flexible tradeoff between diversity and multiplexing gains
• Spatial modulation (SM) and space-shift keying (SSK)
– Mainly multiplexing gain, can achieve receive diversity– No ICI ⇒ low-complexity single-antenna ML detection
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ELEC6014 RCNSs: Advanced Topic Series S Chen
V-BLAST
• BLAST-type architecture: exploits spatial dimension for multiplexing gain ⇒high rate
• Inter-antenna interference or inter-channel interference ⇒ prohibitively highcomplexity for ML detection
• Assuming NR ≥ NT , NT symbols are mapped to NT transmit antennas fortransmission in tn = 1 time slot
S/P
...
1
2
NT...
1
NR
2
Det
ectio
n
... ...
N
2
1
P/S
T
3
ELEC6014 RCNSs: Advanced Topic Series S Chen
V-BLAST (2)
...
1
2
NT
...
1
NR
2
Det
ectio
n
... ...
N
2
1
P/S
S
S/P
Pre
codi
ng
1
2
NS
...
• In general, maximum spatial multiplexing order: NS = min{NT , NR}
• NS symbols are mapped to NT transmit antennas by precoding for transmissionin tn = 1 time slot
• For L-PSK or L-QAM, normalised throughput per time slot
R = Ns · log2(L) [bits/symbol]
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ELEC6014 RCNSs: Advanced Topic Series S Chen
OSTBCs
• Space-time block codes exploit space and time dimensions ⇒ maximum diversitygain, at expense of bandwidth efficiency
• Block of K symbols are mapped to NT transmit antennas for transmission in tntime slots
...
x1
x2
xK
... time
slot
s
N
1
2
T
S/P
spac
e−tim
e m
ap
transmit antennas
matrix
tnX T
N
...
1
2
NR
• Thus, STBC is defined by tn × NT complex-valued matrix S ∈ Ctn×NT
• Orthogonal STBCs: advantage of low-complexity ML detection
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ELEC6014 RCNSs: Advanced Topic Series S Chen
OSTBCs (2)
• For L-PSK or L-QAM, normalisedthroughput per time slot
R =K
tn· log2(L) [bits/symbol]
• Generally, Ktn
< 1
• Only one OSTBC, Alamouti code
tn × NT = 2 × 2 : G2 =
[
x1 x2
−x∗2 x∗
1
]
achieves Ktn
= 1
• STBCs cannot offer multiplexing gain
hh1
x−x1x x22 1
*
n
n1
2
y =−h x +h x +n1 1
1 1
2
222* *
LinearCombiner
ChannelEsimator
h
h1
2
MaximumLikelihoodDetector
x x1 2
x2
x1
~ ~
Time slot 1
Time slot 2*
2
2
+
y =h x +h x +n11 2
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ELEC6014 RCNSs: Advanced Topic Series S Chen
LDCs
• LDCs: “between V-BLAST and STBCs”, more flexible tradeoff between diversityand multiplexing gains
• Q symbols, {sq = αq + jβq ∈ C}Qq=1, are mapped to NT transmit antennas for
transmission in tn time slots
• The tn × NT LDC matrix, S ∈ Ctn×NT , is defined by
S =
QX
q=1
“
αqAq + jβqBq
”
Aq,Bq ∈ Ctn×NT are set of dispersion matrices
• For L-PSK or L-QAM, normalised throughput per time slot
R =Q
tn
· log2(L) [bits/symbol]
• Inter-antenna interference or inter-channel interference ⇒ prohibitively highcomplexity for ML detection
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ELEC6014 RCNSs: Advanced Topic Series S Chen
SM and SSK• Antenna index conveys bits
• For L-PSK or L-QAM, log2(L)bits: select the symbol totransmit
• Another log2(NT ) bits: selectthe transmit antenna to sendthe symbol in tn = 1 time slot
• Mainly for multiplexing gain
11
10
00
L−PSK or L−QAM
01
ante
nna
index
2 NTlog ( )
log ( )2 L bits
bits
• Normalised throughput per time slot
R = log2
(
NT · L)
[bits/symbol]
• No inter-antenna interference or inter-channel interference ⇒ low complexity“single-antenna” ML detection
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Unified MIMO Architecture
• Space-time shift keying (STSK): unified MIMO including V-BLAST, STBCs,LDCs, SM and SSK as special cases
– Fully exploit both spatial and time dimensions– Flexible diversity versus multiplexing gain tradeoff– No ICI with low-complexity single-antenna ML detection
• Coherent STSK (CSTSK):
– Better performance and flexible design– Requires channel state information (CSI)
• Differential STSK:
– Doubling noise power, limited design in modulation scheme and choice of lineardispersion matrices
– No need for CSI
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Coherent MIMO
• Ability of an MIMO system to approach its capacity heavily relies on accuracy ofCSI
• Training based schemes: capable of accurately estimating MIMO channel atexpense of large training overhead ⇒ considerable reduction in system throughput
• Blind methods: high complexity and slow convergence, also unavoidable estimationand decision ambiguities
• Semi-blind methods offer attractive practical means of implementing adaptiveMIMO systems
– Low-complexity ML data detection in STSK ⇒ efficient semi-blinditerative channel estimation and data detection
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ELEC6014 RCNSs: Advanced Topic Series S Chen
CSTSK Transmitter
Coherent STSK block
A1
A
A
S
s(i)
Space−time
mapperQ
Source
Channel
codingS/P
(i)
(i)
1
TNL− PSK/
QAM
• CSTSK (NT , NR, Tn, Q) with L-PSK/QAM:
– NT : number of transmitter antennas– NR: number of receiver antennas– Tn: number of time slots per STSK block, block index i– Q: size of linear dispersion matrices– L: size of modulation constellation
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Transmitted Signal
• Each block S(i) ∈ CNT×Tn is generated from log2(L · Q) bits by
S(i) = s(i)A(i)
• log2(L) bits decides s(i) from L-PSK/QAM modulation scheme
s(i) ∈ S = {sl ∈ C, 1 ≤ l ≤ L}
• log2(Q) bits selects A(i) from set of Q dispersion matrices
A(i) ∈ A = {Aq ∈ CNT×Tn, 1 ≤ q ≤ Q}
Each dispersion matrix meets power constraint tr[
AHq Aq
]
= Tn
• Normalised throughput per time-slot of this CSTSK scheme is
R =log2(Q · L)
Tn
[bits/symbol]
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Design
• CSTSK (NT , NR, Tn, Q) with L-PSK/QAM: high degree of design freedom
– Similar to LDCs, strike flexible diversity versus multiplexing gain trade off– Unlike LDCs, we will show STSK imposes no ICI– Optimisation: number of transmit and receive antennas as well as the set of
dispersion matrices ⇒ desired diversity and multiplexing gains
• Unlike SM and SSK, STSK fully exploits both spatial and time dimensions
– SM and SSK can be viewed as special case of STSK– Set tn = 1, Q = NT and choose
A1 =
10...0
,A2 =
01...0
, · · · ,AQ =
00...1
⇒ SM
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ELEC6014 RCNSs: Advanced Topic Series S Chen
CSTSK Receiver Model
• Received signal matrix Y(i) ∈ CNR×Tn takes MIMO model
Y(i) = HS(i) + V(i)
• Channel matrix H ∈ CNR×NT : each element obeys CN (0, 1)
• Noise matrix V(i) ∈ CNR×Tn: each element obeys CN (0, No)
• Signal to noise ratio (SNR) is defined as
SNR = Es/No
Es is average symbol energy of L-PSK/QAM modulation scheme
• Let vec[·] be vector stacking operator, IM be M × M identity matrix and ⊗ beKronecker product
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Equivalent Signal Model
• Introduce notations
y(i) = vec[Y(i)] ∈ CNRTn×1 H = ITn ⊗ H ∈ C
NRTn×NT Tn
v(i) = vec[V(i)] ∈ CNRTn×1 Θ =
ˆ
vec[A1] · · · vec[AQ]˜
∈ CNT Tn×Q
k(i) = [0 · · · 0| {z }
q−1
s(i) 0 · · · 0| {z }
Q−q
]T ∈ CQ×1
where q is index of dispersion matrix Aq activated
• Equivalent transmitted signal vector k(i) takes value from set
K = {kq,l ∈ CQ×1
, 1 ≤ q ≤ Q, 1 ≤ l ≤ L}
which contains Q · L legitimate transmitted signal vectors
kq,l = [0 · · · 0| {z }
q−1
sl 0 · · · 0| {z }
Q−q
]T, 1 ≤ q ≤ Q, 1 ≤ l ≤ L
where sl is the lth symbol in the L-point constellation S
• Equivalent received signal model: y(i) = HΘk(i) + v(i)
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Maximum Likelihood Detection
• Free from ICI ⇒ low-complexity single-antenna ML detector, only searching L · Qpoints !
• Let (q, l) correspond to specific input bits of ith STSK block, which are mappedto sl and Aq
• Then ML estimates (q, l) are given by
(q, l) = arg min1≤q≤Q1≤l≤L
‖y(i) − HΘkq,l‖2 = arg min
1≤q≤Q1≤l≤L
‖y(i) − sl
(
HΘ)
q‖2
where(
HΘ)
qdenotes qth column of the matrix HΘ
• Assume channel’s coherence time lasts the duration of τ STSK blocks. Thencomplexity of detecting τ log2(Q · L) bits is
CML ≈ 4QTnNR
(
3τL + 2NT
)
[Flops]
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Complexity Comparison
• For STSK, optimal ML detection of τ × log2(Q · L) bits
– only requires search for a total of τ × (Q · L) points
• For simplicity, assuming NT = NR, full optimal ML detection for conventionalMIMO with the same rate R
– requires search for a total of τ × NL·QR points, which may become prohibitive
• K-best sphere decoding approximates ML performance with K set to K = L · Qfor conventional MIMO
– requires search for a total of τ ×(
L · Q +(
NR − 1)(
L · Q)2)
points– while imposing some additional complexity necessitated by Cholesky factorisation
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Training Based Adaptive CSTSK
• Assume number of available training blocks is M and training data are arranged as
YtM =[
Y(1) Y(2) · · · Y(M)]
StM =[
S(1) S(2) · · · S(M)]
• Least square channel estimate (LSCE) based on (YtM ,StM) is given by
HLSCE = YtMSHtM
(
StMSHtM
)−1
• In order for StMSHtM to have full rank of NT , it is necessary that M ·Tn ≥ NT and
this requires a minimum of
M =⌈NT
Tn
⌉
training blocks
• However, to achieve an accurate channel estimate, large training overhead isrequired
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ELEC6014 RCNSs: Advanced Topic Series S Chen
(4, 4, 2, 4) QPSK Example
• Convolution code with code rate2/3, octally represented generatorpolynomials of G1 = [23, 35]8 andG1 = [5, 13]8
• Hard-input hard-output Viterbialgorithm decoding
• (NT = 4, NR = 4, Tn = 2, Q = 4)with L = 4 QPSK modulation
• Frame of 800 information source bits,after channel coding, are mapped toτ = 300 STSK blocks
• Average over 100 channel realisations0 2 4 6 8 10 12 14
10−6
10−5
10−4
10−3
10−2
10−1
100
BE
R
SNR (dB)
2 STSK training blocks30 STSK training blocksPerfect CSI
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Semi-Blind Iterative Algorithm
Use minimum M =⌈
NTTn
⌉
training blocks to obtain initial HLSCE, and let observation
data for ML detector be Ydτ =[
Y(1) Y(2) · · · Y(τ)]
1. Set iteration index t = 0 and channel estimate H(t) = HLSCE;
2. Given H(t), perform ML detection on Ydτ and carry out channel decoding ondetected bits. Corresponding detected information bits, after passing throughchannel coder again, are re-modulated to yield
S(t)eτ =
[
S(t)(1) S(t)(2) · · · S(t)(τ)]
;
3. Update channel estimate with decision-directed LSCE
H(t+1) = Ydτ
(
S(t)eτ
)H(
S(t)eτ
(
S(t)eτ
)H)−1
;
4. Set t = t + 1: If t < Imax, go to Step 2; otherwise, stop.
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Simulation Settings
• Performance was assessed using estimated mean square error
JMSE(H) =1
τ · NR · Tn
τX
i=1
‖Y(i) − H S(i)‖2
mean channel estimation error
JMCE(H) =1
NR · NT
‖H − H‖2
and BER, where H is channel estimate, S(i) are ML-detected and re-modulateddata, and H is true MIMO channel matrix
• Performance averaged over 100 channel realisations
• Convolution code with code rate 2/3, octally represented generator polynomials ofG1 = [23, 35]8 and G1 = [5, 13]8
• Hard-input hard-output Viterbi algorithm for channel decoding
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ELEC6014 RCNSs: Advanced Topic Series S Chen
(4, 4, 2, 4) QPSK (Convergence)
• (NT = 4, NR = 4, Tn = 2, Q = 4) with L = 4 QPSK modulation
• Frame of 800 information source bits, after channel coding, are mapped to τ = 300 STSK blocks
• Semi-blind with M = 2 training STSK blocks
0 2 4 6 8 1010
−1
100
101
Iterations
Me
an
Sq
ua
re E
rro
r
SNR=0 dBSNR=5 dBSNR=10 dB
0 2 4 6 8 1010
−4
10−3
10−2
10−1
100
101
Iterations
Me
an
Ch
an
ne
l Err
or
SNR=0 dBSNR=5 dBSNR=10 dB
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ELEC6014 RCNSs: Advanced Topic Series S Chen
(4, 4, 2, 4) QPSK (Bit Error Rate)
(a) semi-blind with M = 2 training (b) semi-blind with M = 3 training
0 2 4 6 8 10 12 1410
−6
10−5
10−4
10−3
10−2
10−1
100
BE
R
SNR (dB)
2 STSK training blocks3 STSK training blocks30 STSK training blocksSemi−blind iterativePerfect CSI
0 2 4 6 8 10 12 1410
−6
10−5
10−4
10−3
10−2
10−1
100
BE
R
SNR (dB)
2 STSK training blocks3 STSK training blocks30 STSK training blocksPerfect CSISemi−blind Iterative
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ELEC6014 RCNSs: Advanced Topic Series S Chen
(4, 2, 2, 4) 16QAM (Convergence)
• (NT = 4, NR = 2, Tn = 2, Q = 4) with L = 16 QAM modulation
• Frame of 800 information source bits, after channel coding, are mapped to τ = 200 STSK blocks
• Semi-blind with M = 2 training STSK blocks
0 2 4 6 8 1010
−2
10−1
100
Iterations
Me
an
Sq
ua
re E
rro
r
SNR=10 dBSNR=15 dBSNR=20 dB
0 2 4 6 8 1010
−4
10−3
10−2
10−1
Iterations
Me
an
Ch
an
ne
l Err
or
SNR=10 dBSNR=15 dBSNR=20 dB
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ELEC6014 RCNSs: Advanced Topic Series S Chen
(4, 2, 2, 4) 16QAM (Bit Error Rate)
Semi-blind with M = 2training
5 10 15 20 2510
−6
10−5
10−4
10−3
10−2
10−1
100
SNR (dB)
BE
R
Perfect CSI2 training STSK blocks10 training STSK blocksSemi−blind iterative
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ELEC6014 RCNSs: Advanced Topic Series S Chen
Summary
• Space-time shift keying offers a unified MIMO architecture
1. V-BLAST, OSTBCs, LDCs, SM and SSK are special cases2. Flexible diversity versus multiplexing gain trade off3. No ICI and low-complexity single-antenna ML detection
• A semi-blind iterative channel estimation and data detection scheme for coherentSTSK systems
1. Use minimum number of training STSK blocks to provide initial LSCE for aidingthe iterative procedure
2. Proposed semi-blind iterative channel estimation and ML data detection schemeis inherently low-complexity
3. Typically no more than five iterations to converge to optimal ML detectionperformance obtained with perfect CSI
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ELEC6014 RCNSs: Advanced Topic Series S Chen
References
1. P.W. Wolniansky, G.J. Foschini, G.D. Golden and R.A. Valenzuela, “V-BLAST:an architecture for realizing very high data rates over the rich-scattering wirelesschannel,” in Proc. ISSSE’98 (Pisa, Italy), 1998, pp.295–300.
2. V. Tarokh, N. Seshadri and A.R. Calderbank, “Space-time codes for high datarate wireless communication: performance criterion and code construction,” IEEE
Trans. Information Theory, Vol.44, No.2, pp.744–765, March 1998.
3. B. Hassibi and B.M. Hochwald, “High-rate codes that are linear in space and time,”IEEE Trans. Information Theory, Vol.48, No.7, pp.1804–1824, July 2002
4. J. Jeganathan, A. Ghrayeb and L. Szczecinski, “Spatial modulation: optimaldetection and performance analysis,” IEEE Communications Letters, Vol.12, No.8,pp.545–547, Aug. 2008
5. J. Jeganathan, A. Ghrayeb, L. Szczecinski and A. Ceron, “Space shift keyingmodulation for MIMO channels,” IEEE Trans. Wireless Communications, Vol.8,No.7, pp.3692–3703, July 2009
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ELEC6014 RCNSs: Advanced Topic Series S Chen
References (2)
1. S. Sugiura, S. Chen and L. Hanzo, “A unified MIMO architecture subsumingspace shift keying, OSTBC, BLAST and LDC,” in Proc. VTC 2010-Fall (Ottawa,Canada), Sept. 6-9, 2010, 5 pages
2. S. Sugiura, S. Chen and L. Hanzo, “Space-time shift keying: A unified MIMOarchitecture,” in Proc. Globecom 2010 (Miami, USA), Dec.6-10, 2010, 5 pages
3. S. Sugiura, S. Chen and L. Hanzo, “Coherent and differential space-time shiftkeying: A dispersion matrix approach,” IEEE Trans. Communications, DecemberIssue, 2010, 12 pages
4. S. Chen, S. Sugiura and L. Hanzo, “Semi-blind joint channel estimation and datadetection for space-time shift keying systems,” IEEE Signal Processing Letters,Vol.17, No.12, pp.993–996, Dec. 2010.
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