differential modulation and non-coherent detection in wireless relay networks
TRANSCRIPT
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
Outline
1 Introduction
2 Differential AF Relaying
3 Differential DSTC Relaying
4 Summary and Conclusions
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IntroductionDifferential AF Relaying
Differential 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 AF Relaying
Differential 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 AF Relaying
Differential DSTC RelayingSummary and Conclusions
Cooperative Communications
Cooperative Topologies
hsrhrd
DestinationRelay
Source
Figure : Single-branch dual-hop relaying without direct link for coverageextension.
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
Cooperative Communications
Cooperative Topologies
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.
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
Cooperative Communications
Cooperative Topologies
Source
Relay
Destination
hsd
hsr hrd
Figure : Single-branch dual-hop relaying with direct link.7
IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
Cooperative Communications
Cooperative Topologies
SourceDestination
Relay 1
Relay 2
Relay R
hsr1
hsr2
hsrR
hrd1
hrd2
hrdR
hsd
Figure : Multi-branch dual-hop relaying with direct link.8
IntroductionDifferential AF Relaying
Differential 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 AF Relaying
Differential 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 AF Relaying
Differential 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 AF Relaying
Differential DSTC RelayingSummary and Conclusions
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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)
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith 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 ), σ2w = N0(1 + A2|h2[k]|2)
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith 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
v [k] = arg minv [k]∈V
|ζ2 − v [k]|2.
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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]
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith 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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith 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
s = arg maxs∈CN
{Eh2
{1
πNdet{Ry}exp
(−yHR−1
y y)}}
(2)
Ry, co-variance matrix of y, depends on h2
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith 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
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith 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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith 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,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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith 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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
Illustrative Results
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
IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith 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 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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelWithout Direct LinkWith Direct Link
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
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
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
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IntroductionDifferential AF Relaying
Differential 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 AF Relaying
Differential 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]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
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IntroductionDifferential AF Relaying
Differential 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] + w[k]
w[k] = w[k]− V[k]w[k − 1]
Non-coherent detection
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
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IntroductionDifferential AF Relaying
Differential 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] } , 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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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
Illustrative Results
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.
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
System ModelDifferential DetectionSimulation Results
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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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
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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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
Thank you for your attention!
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IntroductionDifferential AF Relaying
Differential DSTC RelayingSummary and Conclusions
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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