ACSTSK Adaptive Space-Time Shift Keying Based Multiple-Input Multiple-Output Systems Professor Sheng Chen Electronics and Computer Science University of Southampton Southampton SO7 BJ, UK E-mail: sqc@ecs.soton.ac.uk 398
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-channel interference (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 399
V-BLAST BLAST-type architecture: exploits spatial dimension for multiplexing gain high rate Inter-antenna interference or inter-channel interference prohibitively high complexity for ML detection Assuming N R N T, N T symbols are mapped to N T transmit antennas for transmission in t n = time slot S/P... 2 N T 2... N R Detection N...2 T P/S 400
N S... V-BLAST (2) S/P 2 Precoding... 2 N T 2... N R Detection N...2 S P/S In general, maximum spatial multiplexing order: N S = min{n T,N R } N S symbols are mapped to N T transmit antennas by precoding for transmission in t n = time slot For L-PSK or L-QAM, normalised throughput per time slot R = N s log 2 (L) [bits/symbol] 40
OSTBCs Space-time block codes exploit space and time dimensions maximum diversity gain, at expense of bandwidth efficiency Block of K symbols are mapped to N T transmit antennas for transmission in t n time slots S/P x x 2... x K time slots transmit antennas t n X N T matrix space time map... 2 N T 2... N R Thus, STBC is defined by t n N T complex-valued matrix S C t n N T Orthogonal STBCs: advantage of low-complexity ML detection 402
OSTBCs (2) For L-PSK or L-QAM, normalised throughput per time slot x x x 2 * x 2 * Time slot Time slot 2 R = K t n log 2 (L) [bits/symbol] h h 2 Generally, K t n < Only one OSTBC, Alamouti code t n N T = 2 2 : G 2 = achieves K t n = [ x x 2 x 2 x STBCs cannot offer multiplexing gain ] n n 2 + Linear Combiner x~ x~ 2 Maximum Likelihood Detector y =h x +h 2x 2+n y = h x * +h x * +n 2 h h 2 2 2 x^ ^x 2 Channel Esimator 2 403
LDCs LDCs: between V-BLAST and STBCs, more flexible tradeoff between diversity and multiplexing gains Q symbols, {s q = α q + jβ q C} Q q=, are mapped to N T transmit antennas for transmission in t n time slots The t n N T LDC matrix, S C t n N T, is defined by S = QX α q A q + jβ q B q q= A q,b q C t n N T are set of dispersion matrices For L-PSK or L-QAM, normalised throughput per time slot R = Q t n log 2 (L) [bits/symbol] Inter-antenna interference or inter-channel interference prohibitively high complexity for ML detection 404
Antenna index conveys bits SM and SSK For L-PSK or L-QAM, log 2 (L) bits: select the symbol to transmit Another log 2 (N T ) bits: select the transmit antenna to send the symbol in t n = time slot antenna index 0 0 00 L PSK or L QAM log ( ) 2 L bits Mainly for multiplexing gain Normalised throughput per time slot log 2 ( N T ) bits R = log 2 ( NT L ) [bits/symbol] No inter-antenna interference or inter-channel interference low complexity single-antenna ML detection 405
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 linear dispersion matrices No need for CSI 406
Coherent MIMO Ability of an MIMO system to approach its capacity heavily relies on accuracy of CSI Training based schemes: capable of accurately estimating MIMO channel at expense of large training overhead considerable reduction in system throughput Blind methods: high complexity and slow convergence, also unavoidable estimation and decision ambiguities Semi-blind methods offer attractive practical means of implementing adaptive MIMO systems Low-complexity ML data detection in STSK efficient semi-blind iterative channel estimation and data detection 407
CSTSK Transmitter Coherent STSK block Source Channel coding S/P A A Q A(i) S (i) Space time mapper L PSK/ QAM s(i) N T CSTSK (N T, N R, T n,q) with L-PSK/QAM: N T : number of transmitter antennas N R : number of receiver antennas T n : number of time slots per STSK block, block index i Q: size of linear dispersion matrices L: size of modulation constellation 408
Transmitted Signal Each block S(i) C N T T n is generated from log 2 (L Q) bits by S(i) = s(i)a(i) log 2 (L) bits decides s(i) from L-PSK/QAM modulation scheme s(i) S = {s l C, l L} log 2 (Q) bits selects A(i) from set of Q dispersion matrices A(i) A = {A q C N T T n, q Q} Each dispersion matrix meets power constraint tr [ ] A H q A q = Tn Normalised throughput per time-slot of this CSTSK scheme is R = log 2(Q L) T n [bits/symbol] 409
Design CSTSK (N T, N R, T n,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 t n =, Q = N T and choose A = 0. 0,A 2 = 0. 0,,A Q = 0 0. SM 40
CSTSK Receiver Model Received signal matrix Y(i) C N R T n takes MIMO model Y(i) = HS(i) + V(i) Channel matrix H C N R N T : each element obeys CN(0, ) Noise matrix V(i) C N R T n : each element obeys CN(0,N o ) Signal to noise ratio (SNR) is defined as SNR = E s /N o E s is average symbol energy of L-PSK/QAM modulation scheme Let vec[ ] be vector stacking operator, I M be M M identity matrix and be Kronecker product 4
Equivalent Signal Model Introduce notations y(i) = vec[y(i)] C N R T n v(i) = vec[v(i)] C N R T n H = I T n H C N R T n N T Tn Θ = ˆvec[A ] vec[a Q ] C N T T n Q k(i) = [0 0 {z } q s(i) 0 {z 0} ] T C Q Q q where q is index of dispersion matrix A q activated Equivalent transmitted signal vector k(i) takes value from set K = {k q,l C Q, q Q, l L} which contains Q L legitimate transmitted signal vectors k q,l = [0 0 {z } q s l 0 {z 0} ] T, q Q, l L Q q where s l is the lth symbol in the L-point constellation S Equivalent received signal model: y(i) = H Θ k(i) + v(i) 42
Maximum Likelihood Detection Free from ICI low-complexity single-antenna ML detector, only searching L Q points! Let (q,l) correspond to specific input bits of ith STSK block, which are mapped to s l and A q Then ML estimates (ˆq,ˆl) are given by (ˆq,ˆl) = arg min q Q l L y(i) HΘk q,l 2 = arg min q Q l L y(i) s l ( HΘ ) q 2 where ( HΘ ) q denotes qth column of the matrix HΘ Assume channel s coherence time lasts the duration of τ STSK blocks. Then complexity of detecting τ log 2 (Q L) bits is C ML 4QT n N R ( 3τL + 2NT ) [Flops] 43
Complexity Comparison For STSK, optimal ML detection of τ log 2 (Q L) bits only requires search for a total of τ (Q L) points For simplicity, assuming N T = N R, full optimal ML detection for conventional MIMO with the same rate R requires search for a total of τ N L Q R points, which may become prohibitive K-best sphere decoding approximates ML performance with K set to K = L Q for conventional MIMO requires search for a total of τ ( L Q + ( N R )( L Q ) 2) points while imposing some additional complexity necessitated by Cholesky factorisation 44
Training Based Adaptive CSTSK Assume number of available training blocks is M and training data are arranged as Y tm = [ Y() Y(2) Y(M) ] S tm = [ S() S(2) S(M) ] Least square channel estimate (LSCE) based on (Y tm,s tm ) is given by Ĥ LSCE = Y tm S H tm( StM S H ) tm In order for S tm S H tm to have full rank of N T, it is necessary that M T n N T and this requires a minimum of M = NT T n training blocks However, to achieve an accurate channel estimate, large training overhead is required 45
(4,4,2,4) QPSK Example Convolution code with code rate 2/3, octally represented generator polynomials of G = [23,35] 8 and G = [5,3] 8 Hard-input hard-output Viterbi algorithm decoding (N T = 4,N R = 4, T n = 2, Q = 4) with L = 4 QPSK modulation BER 0 0 0 0 2 0 3 0 4 2 STSK training blocks 30 STSK training blocks Perfect CSI Frame of 800 information source bits, after channel coding, are mapped to τ = 300 STSK blocks Average over 00 channel realisations 0 5 0 6 0 2 4 6 8 0 2 4 SNR (db) 46
NT Semi-Blind Iterative Algorithm Use minimum M = training blocks to obtain initial Ĥ LSCE, and let observation data for ML detector be Y dτ = [ Y() Y(2) Y(τ) ] T n. Set iteration index t = 0 and channel estimate H (t) = ĤLSCE; 2. Given H (t), perform ML detection on Y dτ and carry out channel decoding on detected bits. Corresponding detected information bits, after passing through channel coder again, are re-modulated to yield Ŝ (t) eτ = [ Ŝ (t) () Ŝ(t) (2) Ŝ (t) (τ) ] ; 3. Update channel estimate with decision-directed LSCE H (t+) = Y dτ (Ŝ(t) eτ ) (Ŝ(t) H (Ŝ(t) ) ) H ; eτ eτ 4. Set t = t + : If t < I max, go to Step 2; otherwise, stop. 47
Simulation Settings Performance was assessed using estimated mean square error J MSE ( H) = τ N R T n τx Y(i) H Ŝ(i) 2 i= mean channel estimation error J MCE ( H) = N R N T H H 2 and BER, where H is channel estimate, Ŝ(i) are ML-detected and re-modulated data, and H is true MIMO channel matrix Performance averaged over 00 channel realisations Convolution code with code rate 2/3, octally represented generator polynomials of G = [23, 35] 8 and G = [5, 3] 8 Hard-input hard-output Viterbi algorithm for channel decoding 48
(4, 4, 2, 4) QPSK (Convergence) (N T = 4, N R = 4, T n = 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 SNR=0 db SNR=5 db SNR=0 db 0 0 0 SNR=0 db SNR=5 db SNR=0 db Mean Square Error 0 0 Mean Channel Error 0 0 2 0 3 0 0 2 4 6 8 0 Iterations 0 4 0 2 4 6 8 0 Iterations 49
(4, 4, 2, 4) QPSK (Bit Error Rate) (a) semi-blind with M = 2 training (b) semi-blind with M = 3 training 0 0 0 2 STSK training blocks 3 STSK training blocks 30 STSK training blocks Semi blind iterative Perfect CSI 0 0 0 2 STSK training blocks 3 STSK training blocks 30 STSK training blocks Perfect CSI Semi blind Iterative 0 2 0 2 BER 0 3 BER 0 3 0 4 0 4 0 5 0 5 0 6 0 2 4 6 8 0 2 4 SNR (db) 0 6 0 2 4 6 8 0 2 4 SNR (db) 420
(4, 2, 2, 4) 6QAM (Convergence) (N T = 4, N R = 2, T n = 2, Q = 4) with L = 6 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 Mean Square Error 0 0 0 SNR=0 db SNR=5 db SNR=20 db Mean Channel Error 0 0 2 0 3 SNR=0 db SNR=5 db SNR=20 db 0 2 0 2 4 6 8 0 Iterations 0 4 0 2 4 6 8 0 Iterations 42
(4, 2, 2, 4) 6QAM (Bit Error Rate) Semi-blind with M = 2 training 0 0 0 Perfect CSI 2 training STSK blocks 0 training STSK blocks Semi blind iterative 0 2 BER 0 3 0 4 0 5 0 6 5 0 5 20 25 SNR (db) 422
Summary Space-time shift keying offers a unified MIMO architecture. V-BLAST, OSTBCs, LDCs, SM and SSK are special cases 2. Flexible diversity versus multiplexing gain trade off 3. No ICI and low-complexity single-antenna ML detection A semi-blind iterative channel estimation and data detection scheme for coherent STSK systems. Use minimum number of training STSK blocks to provide initial LSCE for aiding the iterative procedure 2. Proposed semi-blind iterative channel estimation and ML data detection scheme is inherently low-complexity 3. Typically no more than five iterations to converge to optimal ML detection performance obtained with perfect CSI 423
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