Adaptive Space-Time Shift Keying Based Multiple-Input ...sqc/EZ412-612/ACSTSK.pdf · Southampton...

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

1


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

2


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


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]

4


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

5


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

6


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

7


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

8


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

9


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

10


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

11


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]

12


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

13


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

14


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)

15


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]

16


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

17


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

18


(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

19


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.

20


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

21


(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


22


(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

23


(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


0 2 4 6 8 1010

−4

10−3

10−2

10−1

Iterations

Me

an

Ch

an

ne

l Err

or


24


(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

25


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

26


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

27


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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