Differential Modulation and Non-Coherent Detection in Wireless Relay Networks

1. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
Differential Modulation and Non-Coherent
Detection in Wireless Relay Networks
PhD Thesis
by
M. R. Avendi
Advisor: Prof. Ha H. Nguyen
Department of Electrical & Computer Engineering
University of Saskatchewan
January, 2014
1

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

3. Introduction
Differential AF Relaying
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 AF Relaying
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 AF Relaying
Differential DSTC Relaying
Summary and Conclusions
Cooperative Communications
Cooperative Topologies
hsr
hrd
Destination
Relay
Source
Figure : Single-branch dual-hop relaying without direct link for coverage
extension.
5

6. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
Cooperative Communications
Cooperative Topologies
Source
Relay 1
Relay 2
Relay R
Destination
hsr1 hrd1
hsr2
hrd2
hsrR
hrdR
Figure : Multi-branch dual-hop relaying without direct link for coverage
extension and diversity improvement.
6

7. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
Cooperative Communications
Cooperative Topologies
Source
Relay
Destination
hsd
hsr hrd
Figure : Single-branch dual-hop relaying with direct link.7

8. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
Cooperative Communications
Cooperative Topologies
Source
Destination
Relay 1
Relay 2
Relay R
hsr1
hsr2
hsrR
hrd1
hrd2
hrdR
hsd
Figure : Multi-branch dual-hop relaying with direct link.8

9. Introduction
Differential AF Relaying
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
9

10. Introduction
Differential AF Relaying
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
10

11. Introduction
Differential AF Relaying
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
11

12. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Differential Amplify-and-Forward Relaying
Rayleigh flat-fading channels, hi [k] ∼ CN(0, σ2
i ), i = 0, 1, 2 at
time index k
Auto-correlation between two channel coefficients, n symbols
apart, ϕi (n) = E{hi [k]h∗
i [k + n]} = σ2
i J0(2πfi n),
fi = fDTs normalized Doppler frequency
Transmission process is divided into two phases
h1[k] h2[k]
h0[k]
Source
Relay
Destination
12

13. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Differential Amplify-and-Forward: Phase I
Convert to M-PSK symbols: v[k] ∈ V,
V = {ej2πm/M , m = 1, . . . , M − 1}.
Differential encoding: s[k] = v[k]s[k − 1], s[0] = 1
h1[k]
h0[k]
Source
Relay
Destination
Received signal at Relay:
y0[k] =
√
P0h0s[k] + w0[k], w0[k] ∼ CN (0, N0)
Received signal at Destination:
y1[k] =
√
P0h1[k]s[k] + w1[k], w1[k] ∼ CN(0, N0)
13

14. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Differential Amplify-and-Forward: Phase II
Amplifying with A and forwarding
h2[k]
Source
Relay
Destination
Received signal at Destination:
y2[k] = A P0h[k]s[k] + w[k]
– Cascaded channel: h[k] = h1[k]h2[k]
– Equivalent noise: w[k] = Ah2[k]w1[k] + w2[k]
– Given h2[k], w[k] ∼ CN(0, σ2
w ), σ2
w = N0(1 + A2|h2[k]|2)
14

15. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Two-Symbol Differential Detection
Slow-fading assumption: h[k] ≈ h[k − 1]
y2[k] = v[k]y2[k − 1] + ˜w[k]
˜w[k] = w[k] − v[k]w[k − 1]
Decision Variable: ζ2 = y∗
2 [k − 1]y2[k]
Non-coherent detection
ˆv[k] = arg min
v[k]∈V
|ζ2 − v[k]|2
.
15

16. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
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)16

17. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Channel Time-Series Models
Time-varying models:
Individual channels: hi [k] = αi hi [k − 1] + 1 − α2
i ei [k],
i = 0, 1, 2
αi = J0(2πfi n), auto-correlation
ei ∼ CN(0, σ2
i ) independent of hi [k − 1]
Cascaded channel: h[k] ≈ αh[k − 1] +
√
1 − α2h2[k − 1]e1[k]
α = α1α2: auto-correlation of cascaded channel
Cascaded link:
y2[k] = αv[k]y2[k − 1] + ˜w[k]
˜w[k] = w[k]−αv[k]w[k−1]+ 1 − α2A P0h2[k − 1]s[k]e1[k]
17

18. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Performance in time-varying channels
Effective SNR
γ2 =
α2ρ2
1 + α2 + (1 − α2)ρ2
Slow-fading, γ2 ≈ ρ2/2
Fast-fading, γ2 → α2
1−α2
Pb(E), function of channel auto-correlations
Fast-fading, Pb(E) → Error Floor
18

19. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Multiple-Symbol Differential Detection (MSDD)
To overcome error floor
Take N received symbols: y = [ y2[1], y2[2], . . . , y2[N] ]t
y = A P0diag{s}diag{h2}h1 + w (1)
where s = [ s[1], · · · , s[N] ]t
, h2 = [ h2[1], · · · , h2[N] ]t
,
h1 = [ h1[1], · · · , h1[N] ]t
and w = [ w[1], · · · , w[N] ]t
.
ML detection
ˆs = arg max
s∈CN
E
h2
1
πN det{Ry}
exp −yH
R−1
y y (2)
Ry, co-variance matrix of y, depends on h2
19

20. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Using Ry = E
h2
{Ry}
ˆs = arg min
s∈CN
yH
R
−1
y y = arg min
s∈CN
Us 2
(3)
U = (LHdiag{y})∗, C−1 = LLH,
C = A2P0σ2
2Rh + (1 + A2σ2
2)N0IN.
Rh = toeplitz{ϕ1(0)ϕ2(0), . . . , ϕ1(N − 1)ϕ2(N − 1)}.
Solve by sphere decoding with low complexity
No requirement to instantaneous channel information
Second-order statistics of channels are required
20

21. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Error Floor vs. Fade Rate
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
10
−4
10
−3
10
−2
10
−1
Simulation
f1 changes
f1&f2 change
fade rate
ErrorFloor
Analysis
Figure : Error floor vs. fading rate, dual-hop relaying w.o. direct link,
DBPSK and two-symbol detection
21

22. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Simulation Setup
Two-symbol detection, N = 2
Multiple-symbol detection, N = 10
Table : Three fading scenarios.
Cases f1 f2 Channels status
Case I 0.001 0.001 both are slow-fading
Case II 0.01 0.001 SR is fast-fading
Case III 0.02 0.01 both are fast-fading
22

23. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Illustrative Results
10 15 20 25 30 35 40 45 50 55 60
10
−4
10
−3
10
−2
10
−1
10
0
Simulation CDD
Analysis CDD
Simulation MSD, Case II
Simulation MSD, Case III
Analysis, MSD
Coherent Detection
Coherent
P0/N0 (dB)
BER
Case I
Case II
Case III
Error Floor
Figure : BER in different fading cases and [σ2
1, σ2
2] = [1, 1] using DBPSK
and CDD (N = 2) and MSDD (N = 10).
23

24. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Published Results
M. R. Avendi and Ha H. Nguyen, ”Differential Dual-Hop Re-
laying under User Mobility,” submitted to IET Communications
Journal
M. R. Avendi and Ha H. Nguyen, ”Differential Dual-Hop Relay-
ing over Time-Varying Rayleigh-Fading Channels,” IEEE Cana-
dian Workshop on Information Theory (CWIT), Toronto, Canada,
2013
24

25. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Obtaining Diversity: Maximum Ratio Combining (MRC)
ζ0 = y∗
0 [k − 1]y0[k], ζ2 = y∗
2 [k − 1]y2[k]
ζ = b0ζ0 + b2ζ2,
ˆv[k] = arg min
v[k]∈V
|ζ − v[k]|2.
Proposed combining weights:
b0 = α0/[1 + α2
0 + (1 − α2
0)P0]
b2 = α/[(1 + α2
)(1 + A2
) + (1 − α2
)A2
P0]
y0[k] y0[k − 1]
ζ0
b0
y2[k] y2[k − 1]
ζ2
ζ
b2
+
∗
∗
Delay
Delay
25

26. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Error Performance
Effective SNR: γ0 =
α2
0ρ0
1+α2
0+(1−α2
0)ρ0
, γ2 = α2ρ2
1+α2+(1−α2)ρ2
Slow-fading, γ0 ≈ ρ0/2, γ2 ≈ ρ2/2
Fast-fading, γ0 →
α2
0
1−α2
0
, γ2 → α2
1−α2
Pb(E), function of channel auto-correlations
Fast-fading, Pb(E) → Error Floor
26

27. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Simulation Setup
Three simulation scenarios:
Scenarios f0 f1 f2
Scenario I .001 .001 .001
Scenario II .01 .01 .001
Scenario III .05 .05 .01
Amplification factor: A = Pi /(P0 + N0)
Power allocation: P0 = P/2, Pi = P/(2R), i = 1, · · · , R
27

28. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Illustrative Results
0 5 10 15 20 25 30 35 40 45 50
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
CDD, Simulation
TVD, Simulation
Analysis
Error Floor
P/N0 (dB)
BER
Scenario I
Scenario II
Scenario III
0 5 10 15 20 25 30 35 40 45 50
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
CDD, Simulation
TVD, Simulation
Analysis
Error Floor
P/N0 (dB)
BER Scenario I Scenario II
Scenario III
Figure : BER of D-AF relaying with two (left) and three (right) relays
using DBPSK and DQPSK.28

29. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Published Results
M. R. Avendi and Ha H. Nguyen, ”Performance of differential
amplify-and-forward relaying in multi-node wireless communi-
cations,” IEEE Transactions on Vehicular Technology, 2013.
M. R. Avendi and Ha H. Nguyen, ”Differential Amplify-and-
Forward relaying in time-varying Rayleigh fading channels,” IEEE
Wireless Communications and Networking Conference (WCNC),
Shanghai, China, 2013
29

30. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Obtaining Diversity: Selection Combining (SC) method
ζ = arg max
ζ0,ζ2
{|ζ0|, |ζ2|}
Non-coherent detection: ˆv[k] = arg min
v[k]∈V
|ζ − v[k]|2.
y0[k] y0[k − 1]
ζ0
y2[k] y2[k − 1]
ζ2
ζ
∗
∗
Delay
Delay
Selection
30

31. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Selection Combining: Error Performance
Simpler than Maximum-Ratio Combining (MRC)
Analysis in slow-fading: diversity of two
0 5 10 15 20 25 30
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
SC, simulation
SC, analysis
semi−MRC, simulation
DQPSK
DBPSK
P/N0 (dB)
BER
Figure : Bit-Error-Rate of Differential Amplify-and-Forward relaying
using selection combining
31

32. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Error Performance cont.
Exact performance analysis in time-varying channels
0 5 10 15 20 25 30 35 40 45 50 55
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
Simulation SC
Analysis SC
Simulation semi−MRC
Lower Bound semi−MRC
Case III
Case II
Case I
Error Floor
P/N0 (dB)
BER
Figure : BER of D-AF relaying using selection combining employing
DBPSK
32

33. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Error Performance cont.
Extension to Multi-Relay system
0 5 10 15 20 25 30 35 40
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
simulation SC
simulation semi−MRC
L=2, Case III
L=3, Case III
L=3, Case I
L=2, Case II
L=2, Case I
P/N0 (dB)
BER
Figure : Simulation BER of D-AF systems with two and three relays
under different fading rates and symmetric channels33

34. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Without Direct Link
With Direct Link
Published Results
M. R. Avendi and Ha H. Nguyen, ”Selection combining for
differential amplify and-forward relaying over Rayleigh-fading
channels,” IEEE Signal Process. Letters, 2013.
M. R. Avendi and Ha H. Nguyen, ”Performance of Selection
Combining for Differential Amplify-and-Forward Relaying Over
Time-Varying Channels,” Revised- submission to IEEE Trans-
actions on Wireless Communications
34

35. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
Recall 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
35

36. Introduction
Differential AF Relaying
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
36

37. Introduction
Differential AF Relaying
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
37

38. Introduction
Differential AF Relaying
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
Effective SNR: γ = α2ρ
1+α2+(1−α2)ρ
Diversity goes to zero in fast-fading channels
38

39. Introduction
Differential AF Relaying
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] } , 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
Simplified metric solvable by sphere decoding
No requirement to instantaneous channel information
Second-order statistics of channels are required
39

40. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
Illustrative Results
5 10 15 20 25 30 35 40 45 50
10
−4
10
−3
10
−2
10
−1
10
0
Coherent
Multiple−Codeword, Case III
Multiple−Codeword, Case II
Two−Codeword, Upper Bound
Two−Codeword, Simulation
P0/N0 (dB)
BER
Case I
Case II
Case III
Error Floor
Figure : BER results of D-DSTC relaying with two relays using Alamouti
code and BPSK.
40

41. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
System Model
Differential Detection
Simulation Results
Published Results
M. R. Avendi and Ha H. Nguyen, ”Multiple-Symbol Differential
Detection for Distributed Space-Time Coding,” IEEE Interna-
tional Conference on Computing, Management and Telecom-
munications (ComManTel), Vietnam, 2014
41

42. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
Summary and Conclusions
Studied differential encoding and decoding techniques in relay
networks
Developed a time-series model for cascaded channel
Analysed performance of various topologies: single-branch,
multi-branch
Proposed new combining weights for Maximum-Ratio
Combining method
Developed and analysed selection combining for differential
AF relaying
Developed multiple-symbol differential detection for relay
networks
Future development: no channel statistics, synchronization
errors
42

43. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
Thank you for your attention!
43

44. Introduction
Differential AF Relaying
Differential DSTC Relaying
Summary and Conclusions
Recall: Channel Time-Series Models
Time-varying models:
Individual channels: hi [k] = αi hi [k − 1] + 1 − α2
i ei [k],
i = 0, 1, 2
αi = J0(2πfi n), auto-correlation
ei ∼ CN(0, σ2
i ) independent of hi [k − 1]
Cascaded channel: h[k] ≈ αh[k − 1] +
√
1 − α2h2[k − 1]e1[k]
α = α1α2: auto-correlation of cascaded channel
Direct link: y0[k] = α0v[k]y0[k − 1] + ˜z0[k]
˜z0[k] = z0[k] − α0v[k]z0[k − 1] + 1 − α2
0 P0s[k]e0[k]
Cascaded link: y2[k] = αv[k]y2[k − 1] + ˜w[k]
˜w[k] = w[k]−αv[k]w[k−1]+ 1 − α2A P0h2[k − 1]s[k]e1[k]
44