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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
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IntroductionDifferential DSTC RelayingSummary and Conclusions
Outline
1 Introduction
2 Differential DSTC Relaying
3 Summary and Conclusions
2
IntroductionDifferential DSTC RelayingSummary and Conclusions
Cooperative Communications
Motivation
Wireless fading channelSpacial diversity: multiple antennas, better spectral efficiencyLimitation in space, power, complexity in many applicationsCooperative diversity
Phone
Base Station
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IntroductionDifferential DSTC RelayingSummary and Conclusions
Cooperative Communications
Cooperative Communications
Non-directional propagation of electromagnetic waves
Users help each other
Virtual antenna array
Source Destination
Relay
Direct channel
Cascaded channel
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IntroductionDifferential DSTC RelayingSummary and Conclusions
Cooperative Communications
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
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IntroductionDifferential DSTC RelayingSummary and Conclusions
Cooperative Communications
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
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IntroductionDifferential DSTC RelayingSummary and Conclusions
Cooperative Communications
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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IntroductionDifferential DSTC RelayingSummary and Conclusions
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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IntroductionDifferential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
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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IntroductionDifferential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
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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IntroductionDifferential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
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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IntroductionDifferential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
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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IntroductionDifferential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
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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IntroductionDifferential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
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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IntroductionDifferential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
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
IntroductionDifferential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
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
IntroductionDifferential DSTC RelayingSummary and Conclusions
Summary and Conclusions
Cooperative Communications
Distributed Space-Time Coding
Differential Detection and its performance in time-varyingchannels
Multiple-Symbol Differential Detection
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