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IntroductionD-OFDM DSTC
SimulationSummary
Differential Distributed Space-Time Coding with
Imperfect Synchronization in Frequency-SelectiveChannels
M. R. Avendi
Center for Pervasive Communications and ComputingDepartment of Electrical Engineering & Computer Science
University of California, Irvine
April, 2014
1
IntroductionD-OFDM DSTC
SimulationSummary
Outline
1 Introduction
2 D-OFDM DSTC
3 Simulation
4 Summary
2
IntroductionD-OFDM DSTC
SimulationSummary
Cooperative Communications
Phase I: Source transmits, Relays listen
Phase II: Relays re-broadcast their received signal toDestination
Virtual antenna array, improving diversity
q1
q2
qR
g1
g2
gRSource
Destination
Relay 1
Relay 2
Relay R
3
IntroductionD-OFDM DSTC
SimulationSummary
Multipath Fading
Mobile PhoneBase Station
4
IntroductionD-OFDM DSTC
SimulationSummary
Fading Effects
Ts
Ts
Ts + Tm
Ts + Tm
timetime
timetimeFlat-Fading
Frequency-Selective
5
IntroductionD-OFDM DSTC
SimulationSummary
Channel Models
Flat-fading channel, one tap filter h[n] = h0:y [n] = h0x [n] + n[n]Frequency selective channel, multiple taps filter:
h[n] =L−1∑l=0
hlδ[n − l ]
y [n] = x [n] ∗ h[n] =L∑
l=0
hlx [n − l ]
Inter Symbol Interference (ISI)Circular convolution
y [n] = x [n]⊗ h[n] =
L∑
l=0
hlx [n − l ]N
DFT/IDFT: Y [m] = X [m]H[m]6
IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
Differential OFDM (D-OFDM) DSTC
Source, R Relays, DestinationFrequency-Selective Channels: {qi ,l},{gi ,l} for i = 1, · · · ,R ,l = 0, · · · , L− 1
Source
Relay 1
Relay 2
Relay R
Destination
{q1,l}
{q2,l}
{qR,l}
{g1,l}
{g2,l}
{gR,l}
Figure: Cooperative network under consideration, Sourcecommunicates with Destination through R relays.
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-DSTC OFDM: Source
{v1[n]}
{vR [n]}
{V[n]}
USTC
Differential
Encoding
IDFT
IDFT
Add Ncp1
Add Ncp1
{s1[n]}
{sR [n]}
{S1[m]}
{SR [m]}
Figure: Encoding process at Source8
IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
Encoding at Source: R = 2 Relays
Consider 2N symbols: {v1[n]}, {v2[n]} for n = 0, · · · ,N − 1.
Encode to Unitary Space-Time Codes (USTC)
V[n] =1√
|v1[n]|2 + |v2[n]|2
[v1[n] −v∗2 [n]v2[n] v∗1 [n]
], (1)
for n = 0, · · · ,N − 1.
Differential Encoding
s[n](k) = V[n](k)s[n](k−1) = [s1[n], · · · , sR [n]],
s[n](0) = [ 1 0 · · · 0 ]t , n = 0, · · · ,N − 1,(2)
Apply IDFT: Sr [m] = IDFT{sr [n]} , for r = 1, · · · ,R andm = 0, · · · ,N − 1
Add Cyclic Prefix Ncp1≥ (L− 1)
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-DSTC OFDM: Relays
Xi ,1[m]
Xi ,R [m]
Zi ,1[m]
Zi ,R [m]Add Ncp2
Add Ncp2
Remove Ncp1
Remove Ncp1
STC Configure
Figure: Configuration process at Relay i , i = 1, · · · ,R .
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-DSTC OFDM: Relays
Remove Cyclic Prefix
Zi ,r [m] =√
P0R (qi [m]⊗ Sr [m]) + Ψi ,r [m], (3)
Ψi ,r [m] ∼ CN (0,N0).
STC configuration
Xi ,1[m]
...Xi ,R [m]
= A
Bi
Zi ,1[m]
...Zi ,R [m]
+ Ci
◦
Z ∗
i ,1[m]...
◦
Z ∗
i ,R [m]
(4)
where A amplification factor and Bi ,Ci combining matrices
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
Continue · · ·
circular time-reversal
◦
Zi ,r [m] =
{Zi ,r [0], m = 0
Zi ,r [N −m], otherwise,(5)
for i , r = 1, · · · ,R and m = 0, · · · ,N − 1.
Add cyclic prefix: Ncp2≥ (L+ dmax), dmax maximum sync
delay
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
Configuration: R = 2 Relays
Combining Matrices
B1 =
[1 00 1
], C1 = 0, B2 = 0, C2 =
[0 −11 0
]. (6)
STC configuration
X1,1[m] = AZ1,1[m],
X1,2[m] = AZ1,2[m],
X2,1[m] = −A◦
Z ∗
2,2[m],
X2,2[m] = A◦
Z ∗
2,1[m].
(7)
for m = 0, · · · ,N − 1.
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-OFDM DSTC: Destination
X1,r [−1] X1,r [0] X1,r [1] X1,r [2]
Xi ,r [−di − 1] Xi ,r [−di ] Xi ,r [−di + 1] Xi ,r [−di + 2]
XR,r [−dR − 1] XR,r [−dR ] XR,r [−dR + 1] XR,r [−dR + 2]
Ts
τi
τR
Figure: Received signals from the relays in the first path at Destination,when Relay i is diTs + τi seconds late, di ∈ Z and 0 ≤ τi ≤ Ts .
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-OFDM DSTC: Destination
Effective pulse-shape: Raised-Cosine, β roll-off factor
p(t) = sinc(t/Ts)cos(πβt/Ts)
(1 − 4β2t2/T 2s ),
Ts
Basedband Signal Sampled Signal
Matched Filter
Figure: Filtering and Sampling.
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-OFDM DSTC: Destination
−2 −1 0 1 2
Relay 1
Relay 2
τ
X1,r [0]
X1,r [1]
X2,r [−d2 − 1]
X2,r [−d2]
X2,r [−d2 + 1]
t/Ts
Figure: Received signals at Destination after the matched-filter using araised-cosine filter with roll-off factor β = 0.9, whenτ1 = 0, τ = τ2 = 0.3Ts .16
IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-OFDM DSTC: Destination
{v1[n]}
{vR [n]}
Differential
Decoding
DFT
DFT
Remove Ncp2
Remove Ncp2
{Y1[m]}
{YR [m]}
{y1[n]}
{yR [n]}
Figure: Decoding process at Destination17
IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-OFDM DSTC: Destination
Remove Cyclic Prefix
Yr [m] =
R∑
i=1
p(τi) (gi [m]⊗ Xi ,r [m − di ]) + Φr [m]
+
R∑
i=1
p(Ts − τi) (gi [m]⊗ Xi ,r [m − 1− di ]) ,
(8)
for m = 0, · · · ,N − 1 and r = 1, · · · ,R , whereΦr [m] ∼ CN (0,N0).
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-OFDM DSTC: Destination
Take DFT
yr [n] =
R∑
i=1
Gi [n]xi ,r [n] + φr [n] (9)
for r = 1, · · · ,R , n = 0, · · · ,N − 1, where
Gi [n] =L−1∑
l=0
gi ,le−j 2πnl
N ,
Gi [n] =(p(τi) + p(Ts − τi)e
−j 2πnN
)Gi [n]e
−j2πndi
N ,
xi ,r [n] = DFT{Xi ,r [m]}, φr [n] = DFT{Φr [m]}.
(10)
Note that φr [n] ∼ CN (0,N0).
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-OFDM DSTC: Destination
In the matrix form:
y[n] = A√
P0RS[n]H[n] + w[n], (11)
where
S[n] =[B1s1[n], · · · , BR sR [n]
],
H[n] = [ H1[n], · · · ,HR [n] ]t ,
Hi [n] = Qi [n]Gi [n],
w[n] =R∑
i=1
Gi [n]Bi ψi [n] + φ[n],
(12)
for i , r = 1, · · · ,R and 0 ≤ n ≤ N − 1. It is noted thatψi ,r [n] ∼ CN (0,N0).
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
Example: R = 2 relays
R = 2 relays using Alamouti STC
y[n] = A√2P0
[s1[n] −s∗2 [n]s2[n] s∗1 [n]
] [H1[n]H2[n]
]+
[w1[n]w2[n]
], (13)
with
H1[n] = Q1[n]G1[n], H2[n] = Q∗
2 [n]G2[n],
w1[n] = A(G1[n]ψ1,1[n]− G2[n]ψ
∗
2,2[n])+ φ1[n],
w2[n] = A(G1[n]ψ1,2[n] + G2[n]ψ
∗
2,1[n])+ φ2[n].
(14)
for 0 ≤ n ≤ N − 1.
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-OFDM DSTC: Received SNR
Noise, for given {gi ,l}, w[n] ∼ CN (0, σ2[n]IR)
σ2[n] = N0
(1 + A2
R∑
i=1
|Gi [n]|2
). (15)
Received SNR for given {gi ,l}
γ(n, {τi}
Ri=1
)=
A2P0
R∑i=1
|Gi [n]2|
N0
(1 + A2
R∑i=1
|Gi [n]|2) , (16)
for n = 0, · · · ,N − 1.
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IntroductionD-OFDM DSTC
SimulationSummary
SourceRelaysDestination
D-OFDM DSTC: RX SNR
0 7 14 21 28 35 42 49 56 6317
17.5
18
18.5
19
19.5
20
τ=0 & 1
τ=0.2 & 0.8
τ=0.4 & 0.6
τ=0.5
n
γ(n,τ
2),
dB
Figure: Average received SNR vs. n and τ = τ2 for a network with tworelays over flat-fading channels, when N = 64, P/N0 = 25dB,P0 = P/2,Pr = P/4, |g1,0|2 = |g2,0|2 = 1.23
IntroductionD-OFDM DSTC
SimulationSummary
Simulation Setup
Networks with R = 2 and R = 4 relays
Flat-Fading and Frequency-Selective fading with length L = 6
For R = 2 relays: Alamouti STC with BPSK and QPSK
For R = 4 relays: QOSTBC with BPSK and π/2-rotatedBPSK
V[n] =1√
4∑i=1
|vi [n]|2
v1[n] −v∗2 [n] −v∗3 [n] v4[n]v2[n] v∗1 [n] −v∗4 [n] −v3[n]v3[n] −v∗4 [n] v∗1 [n] −v2[n]v4[n] v∗3 [n] v∗2 [n] v1[n]
(17)
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IntroductionD-OFDM DSTC
SimulationSummary
Simulation Results
0 5 10 15 20 25 3010
−4
10−3
10−2
10−1
100
τ = (0.4&0.6)Ts
τ = (0.2&0.8)Ts
τ = 0&Ts
D-DSTC, τ = 0
D-DSTC, τ = 0.2Ts
D-DSTC, τ = 0.4Ts
D-DSTC, τ = 0.6Ts
Coherent DSTC, τ = 0
BER
P/N0dB
Figure: Simulation BER, R = 2 relays, flat-fading channels, D-OFDMDSTC(N = 64,Ncp = 1), D-DSTC, and coherent DSTC, using Alamouticode and BPSK, τ1 = 0, τ2 = τ .25
IntroductionD-OFDM DSTC
SimulationSummary
Simulation Results
0 5 10 15 20 2510
−4
10−3
10−2
10−1
100
τ = (0.4&0.6)Ts
τ = (0.3&0.7)Ts
τ = 0&Ts
D-DSTC, τ = 0
BER
P/N0dB
Figure: Simulation BER, R = 4 relays, flat-fading channels, D-OFDMDSTC (N = 64,Ncp = 1) and D-DSTC, using QOSTBC, τ1 = 0, τi = τfor i = 2, 3, 4.26
IntroductionD-OFDM DSTC
SimulationSummary
Simulation Results
0 5 10 15 20 25 30 3510
−4
10−3
10−2
10−1
100
τ = 0.5Ts
τ = (0.4&0.6)Ts
τ = (0.3&0.7)Ts
τ = 0&Ts
BER
P/N0dB
Figure: Simulation BER, R = 2 relays over frequency-selective channels,D-OFDM DSTC (N = 64,Ncp = 7), using Alamouti code and QPSK,τ1 = 0, τ2 = τ .27
IntroductionD-OFDM DSTC
SimulationSummary
Simulation Results
0 5 10 15 20 2510
−4
10−3
10−2
10−1
100
τ = (0.4&0.6)Ts
τ = (0.3&0.7)Ts
τ = (0.2&0.8)Ts
τ = 0&Ts
BER
P/N0dB
Figure: Simulation BER, R = 4 relays over frequency-selective channels,D-OFDM DSTC (N = 64,Ncp = 7), using QOSTBC, τ1 = 0, τi = τ fori = 2, 3, 4.28
IntroductionD-OFDM DSTC
SimulationSummary
Summary
Relay networks in frequency-selective channels
Synchronization Errors
Differential encoding and decoding with and OFDM approach
No channel or delay requirement
3RN coherence interval required
Thank You!
29