Differential Modulation and Non-Coherent Detection in Wireless Relay Networks

IntroductionDifferential AF Relaying

Differential DSTC RelayingSummary and Conclusions

Differential Modulation and Non-Coherent

Detection in Wireless Relay Networks

PhD Thesisby

M. R. AvendiAdvisor: Prof. Ha H. Nguyen

Department of Electrical & Computer EngineeringUniversity of Saskatchewan

January, 2014

1



Outline

1 Introduction

2 Differential AF Relaying

3 Differential DSTC Relaying

4 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




Cooperative Topologies

hsrhrd

DestinationRelay

Source

Figure : Single-branch dual-hop relaying without direct link for coverageextension.

5





Source

Relay 1

Relay 2

Relay RDestination

hsr1 hrd1hsr2

hrd2hsrR

hrdR

Figure : Multi-branch dual-hop relaying without direct link for coverageextension and diversity improvement.

6





Source

Relay

Destination

hsd

hsr hrd

Figure : Single-branch dual-hop relaying with direct link.7





SourceDestination

Relay 1

Relay 2

Relay R

hsr1

hsr2

hsrR

hrd1

hrd2

hrdR

hsd

Figure : Multi-branch dual-hop relaying with direct link.8




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

9




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




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

11



System ModelWithout Direct LinkWith Direct Link

Differential Amplify-and-Forward Relaying

Rayleigh flat-fading channels, hi [k] ∼ CN (0, σ2i ), i = 0, 1, 2 at

time index k

Auto-correlation between two channel coefficients, n symbolsapart, ϕi (n) = E{hi [k]h∗i [k + n]} = σ2

i J0(2πfin),fi = fDTs normalized Doppler frequency

Transmission process is divided into two phases

h1[k] h2[k]

h0[k]

Source

Relay

Destination

12




Differential Amplify-and-Forward: Phase I

Convert to M-PSK symbols: v [k] ∈ V,V = {e j2πm/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




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 ), σ2w = N0(1 + A2|h2[k]|2)

14




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]


v [k] = arg minv [k]∈V

|ζ2 − v [k]|2.

15




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)16




Channel Time-Series Models

Time-varying models:

Individual channels: hi [k ] = αihi [k − 1] +√1− α2

i ei [k ],i = 0, 1, 2αi = J0(2πfin), auto-correlationei ∼ 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




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




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

s = arg maxs∈CN

{Eh2

{1

πNdet{Ry}exp

(−yHR−1

y y)}}

(2)

Ry, co-variance matrix of y, depends on h2

19




Using Ry = Eh2{Ry}

s = arg mins∈CN

{yHR

−1y y

}= arg min

s∈CN

{‖Us‖2

}(3)

U = (LHdiag{y})∗, C−1 = LLH ,C = A2P0σ

22Rh + (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




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

Simulationf1 changes

f1&f2 change

fade rate

Error

Floor

Analysis

Figure : Error floor vs. fading rate, dual-hop relaying w.o. direct link,DBPSK and two-symbol detection

21




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




Illustrative Results

10 15 20 25 30 35 40 45 50 55 60

10−4

10−3

10−2

10−1

100

Simulation CDDAnalysis CDDSimulation MSD, Case IISimulation MSD, Case IIIAnalysis, MSDCoherent Detection

Coherent

P0/N0 (dB)

BER

Case I

Case II

Case III

Error Floor

Figure : BER in different fading cases and [σ21 , σ

22] = [1, 1] using DBPSK

and CDD (N = 2) and MSDD (N = 10).23




Published Results

M. R. Avendi and Ha H. Nguyen, ”Differential Dual-Hop Re-laying under User Mobility,” submitted to IET CommunicationsJournal

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




Obtaining Diversity: Maximum Ratio Combining (MRC)

ζ0 = y∗0 [k − 1]y0[k], ζ2 = y∗2 [k − 1]y2[k]ζ = b0ζ0 + b2ζ2,v [k] = arg min

v [k]∈V|ζ − v [k]|2.

Proposed combining weights:

b0 = α0/[1 + α20 + (1− α2

0)P0]

b2 = α/[(1 + α2)(1 + A2) + (1− α2)A2P0]

y0[k] y0[k − 1]

ζ0

b0

y2[k] y2[k − 1]

ζ2

ζ

b2

+∗

∗

Delay

Delay

25




Error Performance

Effective SNR: γ0 =α20ρ0

1+α20+(1−α2

0)ρ0, γ2 =

α2ρ21+α2+(1−α2)ρ2

Slow-fading, γ0 ≈ ρ0/2, γ2 ≈ ρ2/2

Fast-fading, γ0 → α20

1−α20, γ2 → α2

1−α2

Pb(E ), function of channel auto-correlations

Fast-fading, Pb(E ) → Error Floor

26




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





0 5 10 15 20 25 30 35 40 45 5010

−6

10−5

10−4

10−3

10−2

10−1

100

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

100

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) relaysusing DBPSK and DQPSK.28




Published Results

M. R. Avendi and Ha H. Nguyen, ”Performance of differentialamplify-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,” IEEEWireless Communications and Networking Conference (WCNC),Shanghai, China, 2013

29




Obtaining Diversity: Selection Combining (SC) method

ζ = argmaxζ0,ζ2

{|ζ0|, |ζ2|}

Non-coherent detection: v [k] = arg minv [k]∈V

|ζ − v [k]|2.

y0[k] y0[k − 1]

ζ0

y2[k] y2[k − 1]

ζ2

ζ∗

∗

Delay

Delay

Selection

30




Selection Combining: Error Performance

Simpler than Maximum-Ratio Combining (MRC)Analysis in slow-fading: diversity of two

0 5 10 15 20 25 3010

−5

10−4

10−3

10−2

10−1

100

SC, simulationSC, analysissemi−MRC, simulation

DQPSKDBPSK

P/N0 (dB)

BER

Figure : Bit-Error-Rate of Differential Amplify-and-Forward relayingusing selection combining

31




Error Performance cont.

Exact performance analysis in time-varying channels

0 5 10 15 20 25 30 35 40 45 50 5510

−6

10−5

10−4

10−3

10−2

10−1

100

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 employingDBPSK

32




Error Performance cont.

Extension to Multi-Relay system

0 5 10 15 20 25 30 35 4010

−6

10−5

10−4

10−3

10−2

10−1

100

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 relaysunder different fading rates and symmetric channels33




Published Results

M. R. Avendi and Ha H. Nguyen, ”Selection combining fordifferential amplify and-forward relaying over Rayleigh-fadingchannels,” IEEE Signal Process. Letters, 2013.

M. R. Avendi and Ha H. Nguyen, ”Performance of SelectionCombining for Differential Amplify-and-Forward Relaying OverTime-Varying Channels,” Revised- submission to IEEE Trans-actions on Wireless Communications

34



System ModelDifferential DetectionSimulation 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




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

36




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]tPhase 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

37




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]


V[k] = arg minV[k]∈V

|y[k] − V[k]y[k − 1]|2

Effective SNR: γ = α2ρ1+α2+(1−α2)ρ

Diversity goes to zero in fast-fading channels

38




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 maxV∈VN−1

{EG

{1

πNdet{Σy}exp

(−yHΣ−1

y y)}}

Simplified metric solvable by sphere decoding

No requirement to instantaneous channel information

Second-order statistics of channels are required

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5 10 15 20 25 30 35 40 45 50

10−4

10−3

10−2

10−1

100

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 IIIError Floor

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

40




Published Results

M. R. Avendi and Ha H. Nguyen, ”Multiple-Symbol DifferentialDetection for Distributed Space-Time Coding,” IEEE Interna-tional Conference on Computing, Management and Telecom-munications (ComManTel), Vietnam, 2014

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Summary and Conclusions

Studied differential encoding and decoding techniques in relaynetworks

Developed a time-series model for cascaded channel

Analysed performance of various topologies: single-branch,multi-branch

Proposed new combining weights for Maximum-RatioCombining method

Developed and analysed selection combining for differentialAF relaying

Developed multiple-symbol differential detection for relaynetworks

Future development: no channel statistics, synchronizationerrors

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Thank you for your attention!

43



Recall: Channel Time-Series Models

Time-varying models:

Individual channels: hi [k ] = αihi [k − 1] +√1− α2

i ei [k ],i = 0, 1, 2αi = J0(2πfin), auto-correlationei ∼ 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]︸︷︷︸

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Differential Modulation and Non-Coherent Detection in Wireless Relay Networks

Engineering

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