Multiple-Symbol Differential Detection for Distributed Space-Time Coding

1. Introduction
Differential DSTC Relaying
Summary and Conclusions
Multiple-Symbol Differential Detection for
Distributed Space-Time Coding
M. R. Avendi, Ha H. Nguyen and Nguyen Quoc-Tuan
Department of Electrical & Computer Engineering
University of Saskatchewan
April, 2014
1

2. Introduction
Differential DSTC Relaying
Summary and Conclusions
Outline
1 Introduction
2 Differential DSTC Relaying
3 Summary and Conclusions
2

3. Introduction
Differential DSTC Relaying
Summary and Conclusions
Cooperative Communications
Motivation
Wireless fading channel
Spacial diversity: multiple antennas, better spectral efficiency
Limitation in space, power, complexity in many applications
Cooperative diversity
Phone
Base Station
3

4. Introduction
Differential DSTC Relaying
Summary 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
4

5. Introduction
Differential DSTC Relaying
Summary and Conclusions
Cooperative Communications
Relay Protocols
Decode-and-Forward
Amplify-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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6. Introduction
Differential DSTC Relaying
Summary 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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7. Introduction
Differential DSTC Relaying
Summary and Conclusions
Cooperative Communications
Detection
Coherent detection
Channel estimation: training symbols
More channels to estimate
Overhead, bandwidth efficiency, mobility of users
Non-coherent detection
Differential modulation and demodulation: no channel
estimation
Investigating performance in time-varying environments
Developing simpler detection techniques
Developing robust detection techniques
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8. Introduction
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
Differential Distributed Space-Time Code (D-DSTC)
Rayleigh flat-fading, qi [k], gi [k], i = 1, · · · R
Auto-correlation: Jakes’ fading model
Transmission 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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9. Introduction
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
System Model
Information convert to space-time codewords V[k] ∈ V
V = {Vl |V∗
l Vl = VlV∗
l = IR}
Encoded differentially
s[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 code
h[k]: equivalent channel vector
w[k]: equivalent noise vector
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10. Introduction
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
Two-Symbol Differential Detection
Slow-fading: h[k] ≈ h[k − 1]
y[k] = V[k]y[k − 1] + ˜w[k]
˜w[k] = w[k] − V[k]w[k − 1]
Non-coherent detection
ˆV[k] = arg min
V[k]∈V
|y[k] − V[k]y[k − 1]|2
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11. Introduction
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
Channel Variation Over Time
Common assumption: slow-fading, hi [k] ≈ hi [k − 1], i = 0, 1, 2
Depending on velocity, Doppler frequency fDTs
0 10 20 30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
f
D
T
s
=.001
fD
Ts
=.01
f
D
T
s
=.03
Amplitude
time index, k
0 10 20 30 40 50 60 70 80 90 100
0
0.2
0.4
0.6
0.8
1
fD
Ts
=.001
f
D
T
s
=.01
fD
Ts
=.03
time index, k
Auto-Correlation
Figure: Amplitude |hi [k]| and auto-correlation of a Rayleigh flat-fading
channel, hi [k] ∼ CN(0, 1)
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12. Introduction
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation 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
V = arg max
V∈VN−1
E
G
1
πNdet{Σy}
exp −yH
Σ−1
y y
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13. Introduction
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
MSDD continue
New semi-optimal metric
V = arg max
V∈VN−1
1
πNdet{Σy}
exp −yH
Σ−1
y y
Simplified metric solvable by sphere decoding
No requirement to instantaneous channel information
Second-order statistics of channels are required V =
arg min
V∈VN−1
N−1
n=1
un,nV[n]y[n] +S[n + 1]
N
j=n+1
un,j SH[j]y[j] 2 .
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14. Introduction
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation 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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15. Introduction
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
Illustrative Results
5 10 15 20 25 30 35 40
10
−4
10
−3
10
−2
10
−1
10
0
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 Alamouti
code and BPSK.15

16. Introduction
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
Illustrative Results
5 10 15 20 25 30 35 40
10
−4
10
−3
10
−2
10
−1
10
0
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 Alamouti
code and QPSK.16

17. Introduction
Differential DSTC Relaying
Summary and Conclusions
Summary and Conclusions
Cooperative Communications
Distributed Space-Time Coding
Differential Detection and its performance in time-varying
channels
Multiple-Symbol Differential Detection
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18. Introduction
Differential DSTC Relaying
Summary and Conclusions
Thank you for your attention!
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