multiple-symbol differential detection for distributed space-time coding

IntroductionDifferential DSTC RelayingSummary and Conclusions

Multiple-Symbol Differential Detection forDistributed Space-Time Coding

M. R. Avendi, Ha H. Nguyen and Nguyen Quoc-Tuan

Department of Electrical & Computer EngineeringUniversity of Saskatchewan

April, 2014

1


Outline

1 Introduction

2 Differential DSTC Relaying

3 Summary and Conclusions

2


Cooperative Communications

Motivation

Wireless fading channelSpacial diversity: multiple antennas, better spectral efficiencyLimitation in space, power, complexity in many applicationsCooperative diversity

Phone

Base Station

3




Non-directional propagation of electromagnetic waves

Users help each other

Virtual antenna array

Source Destination

Relay

Direct channel

Cascaded channel

4



Relay Protocols

Decode-and-ForwardAmplify-and-Forward (AF): simplicity of relaying function

Figure: Taken from: A. Nosratinia, T. E. Hunter, A. Hedayat, ”Cooperative communication in

wireless networks,” Communications Magazine, IEEE , vol.42, no.10, pp.74,80, Oct. 2004

5



Relay Strategies

Repetition-based

Phase I Phase II

Source broadcasts Relay 1 forwards Relay 2 forwards Relay i forwards Relay R forwards

Time

Distributed space-time based: Better bandwidth efficiency,higher complexity

Phase I Phase II

Source broadcasts Relays forward simultaneously

Time

6



Detection

Coherent detection

Channel estimation: training symbolsMore channels to estimateOverhead, bandwidth efficiency, mobility of users

Non-coherent detection

Differential modulation and demodulation: no channelestimationInvestigating performance in time-varying environmentsDeveloping simpler detection techniquesDeveloping robust detection techniques

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System ModelDifferential DetectionSimulation Results

Differential Distributed Space-Time Code (D-DSTC)

Rayleigh flat-fading, qi [k], gi [k], i = 1, · · ·RAuto-correlation: Jakes’ fading modelTransmission process is divided into two phases

q1[k]

q2[k]

qR [k]

g1[k]

g2[k]

gR [k]

Source

Destination

Relay 1

Relay 2

Relay R

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System Model

Information convert to space-time codewords V[k] ∈ VV = {Vl |V

∗l Vl = VlV

∗l = IR}

Encoded differentiallys[k] = V[k]s[k − 1], s[0] = [1, 0, · · · , 0]t

Phase I: Source sends s[k] to relays

Phase II: Relays simultaneously forward them to Destination

Received signal at Destination :

y[k] = c√

P0RS[k]h[k] + w[k]

S[k]: Distributed space-time codeh[k]: equivalent channel vectorw[k]: equivalent noise vector

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Two-Symbol Differential Detection

Slow-fading: h[k] ≈ h[k − 1]

y[k] = V[k]y[k − 1] + w̃[k]

w̃[k] = w[k]− V[k]w[k − 1]

Non-coherent detection

V̂[k] = arg minV[k]∈V

|y[k] − V[k]y[k − 1]|2

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Channel Variation Over Time

Common assumption: slow-fading, hi [k] ≈ hi [k − 1], i = 0, 1, 2Depending on velocity, Doppler frequency fDTs

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

fD

Ts=.001

fD

Ts=.01

fD

Ts=.03

Amplitude

time index, k0 10 20 30 40 50 60 70 80 90 100

0

0.2

0.4

0.6

0.8

1

fD

Ts=.001

fD

Ts=.01

fD

Ts=.03

time index, k

Auto-Correlation

Figure: Amplitude |hi [k ]| and auto-correlation of a Rayleigh flat-fadingchannel, hi [k ] ∼ CN (0, 1)

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Multiple-Symbol Differential Detection (MSDD)

Take N received symbols: y = [ yt [1], yt [2], . . . , yt [N] ]t ,

y = c√

P0R S h+ w = c√

P0R S Gq+ w

S = diag { S[1], · · · ,S[N] } , h = [ ht [1], · · · ,ht [N] ]t ,G = diag { G[1], · · · ,G[N] } , q = [ qt [1], · · · ,qt [N] ]t ,w = [ wt [1], · · · ,wt [N] ]t

Maximum Likelihood detection

V̂ = arg maxV∈VN−1

{EG

{1

πNdet{Σy}exp

(−yHΣ−1

y y)}}

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MSDD continue

New semi-optimal metric

V̂ = arg maxV∈VN−1

{1

πNdet{Σ̂y}exp

(−yHΣ̂−1

y y)}

Simplified metric solvable by sphere decoding

No requirement to instantaneous channel information

Second-order statistics of channels are required V̂ =

arg minV∈VN−1

{N−1∑n=1

‖un,nV[n]y[n] +S[n+ 1]N∑

j=n+1un,jS

H [j]y[j]‖2

}.

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Simulation Setup

Three simulation scenarios:

Scenarios fsr frd

Scenario I .001 .001

Scenario II .006 .004

Scenario III .009 .01

Amplification factor: A =√Pi/(P0 + N0)

Power allocation: P0 = P/2, Pi = P/(2R), i = 1, · · · ,R

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Illustrative Results

5 10 15 20 25 30 35 40

10−4

10−3

10−2

10−1

100

Coherent Detection

CDD, Case I

CDD, Case II

MSDSD, Case II

CDD, Case III

MSDSD, Case III

P0/N0 (dB)

BER

Figure: BER results of D-DSTC relaying with two relays using Alamouticode and BPSK.15



Illustrative Results

5 10 15 20 25 30 35 40

10−4

10−3

10−2

10−1

100

Coherent Detection

CDD, Case I

CDD, Case II

MSDSD, Case II

CDD, Case III

MSDSD, Case III

P0/N0 (dB)

BER

Figure: BER results of D-DSTC relaying with two relays using Alamouticode and QPSK.16


Summary and Conclusions


Distributed Space-Time Coding

Differential Detection and its performance in time-varyingchannels

Multiple-Symbol Differential Detection

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Thank you for your attention!

18

multiple-symbol differential detection for distributed space-time coding

Engineering

simpler detection techniques

robust detection techniques

communications magazine

t phase

source broadcasts relays

distributed spacetime

channel spacial diversity

equivalent channel vector