![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
8](https://image.slidesharecdn.com/commantel14-150711000950-lva1-app6891/85/Multiple-Symbol-Differential-Detection-for-Distributed-Space-Time-Coding-8-320.jpg)
![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
9](https://image.slidesharecdn.com/commantel14-150711000950-lva1-app6891/85/Multiple-Symbol-Differential-Detection-for-Distributed-Space-Time-Coding-9-320.jpg)
![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
10](https://image.slidesharecdn.com/commantel14-150711000950-lva1-app6891/85/Multiple-Symbol-Differential-Detection-for-Distributed-Space-Time-Coding-10-320.jpg)
![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)
11](https://image.slidesharecdn.com/commantel14-150711000950-lva1-app6891/85/Multiple-Symbol-Differential-Detection-for-Distributed-Space-Time-Coding-11-320.jpg)
![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
12](https://image.slidesharecdn.com/commantel14-150711000950-lva1-app6891/85/Multiple-Symbol-Differential-Detection-for-Distributed-Space-Time-Coding-12-320.jpg)
![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 .
13](https://image.slidesharecdn.com/commantel14-150711000950-lva1-app6891/85/Multiple-Symbol-Differential-Detection-for-Distributed-Space-Time-Coding-13-320.jpg)
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 5
- 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 6
- 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 7
- 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 8
- 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 9
- 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 10
- 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) 11
- 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 12
- 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 . 13
- 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 14
- 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 17
- 18. Introduction Differential DSTC Relaying Summary and Conclusions Thank you for your attention! 18