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IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Asynchronous Differential Distributed Space-Time
Coding
M. R. Avendi
Department of Electrical Engineering & Computer ScienceUniversity of California, Irvine
Feb., 2014
1
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Outline
1 Introduction
2 D-DSTC
3 OFDM Systems
4 D-DSTC OFDM
5 Summary
2
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
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-DSTC
OFDM SystemsD-DSTC OFDM
Summary
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
Phase I Phase II
Source broadcasts Relays forwards simultaneously
Time
Which one simpler to implement?
Which one bandwidth efficient?4
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
System Model
All channels are Rayleigh flat-fadingPhase I: Source transmits [s1, s2], (differential encoded)Relays receive [x11, x12] and [x21, x22]Phase II: Relays re-transmit [x11, x12] and [−x∗22, x
∗
21]
[s1, s2]
[x11, x12]
[−x∗22, x∗
21]
[y1, y2]
q1
q2
g1
g2SourceDestination
Relay 1
Relay 2
5
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Synchronized Relay Networks
Perfect relays synchronization
y1 = g1x11 − g2x∗
22 + n1
y2 = g1x12 + g2x∗
21 + n2
[
y1y2
]
= A√
P0
[
s1 −s∗2s2 s∗1
] [
q1g1q∗2g2
]
+
[
w1
w2
]
(1)
RX signal from Relay 1
RX signal from Relay 2
Block k
x11 x12
−x∗22 x∗21
6
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Asynchronous Relay Networks
What causes synchronization error?– Relays at different distances from Destination– Different processing time at relays
Relay 2 is late, 0 ≤ τ ≤ Ts , α = f (τ), β = f (Ts − τ)
y1 = g1x11 − αg2x∗
22 + βg2x∗
21(k−1) + n1
y2 = g1x12 + αg2x∗
21 − βg2x∗
22 + n2
[
y1y2
]
= A√
P0
[
s1 −s∗2s2 s∗1
] [
q1g1αq∗2g2
]
+ ISI+
[
w1
w2
]
(2)
Block (k)Block (k − 1)
τ
x11 x12
−x∗22 x∗21
x11 x12
−x∗22 x∗217
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Asynchronous Relay Networks
What causes synchronization error?– Relays at different distances from Destination– Different processing time at relays
Relay 2 is late, 0 ≤ τ ≤ Ts , α = f (τ), β = f (Ts − τ)
y1 = g1x11 − αg2x∗
22 + βg2x∗
21(k−1) + n1
y2 = g1x12 + αg2x∗
21 − βg2x∗
22 + n2
[
y1y2
]
= A√
P0
[
s1 −s∗2s2 s∗1
] [
q1g1αq∗2g2
]
+ ISI+
[
w1
w2
]
(2)
Block (k)Block (k − 1)
τ
x11 x12
−x∗22 x∗21
x11 x12
−x∗22 x∗217
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Asynchronous Relay Networks
Effect of synchronization error on conventional decoder (CDD)
0 5 10 15 20 25 3010
−4
10−3
10−2
10−1
100
CDD, τ=0CDD, τ=0.2 T
s
CDD, τ=0.4 Ts
CDD, τ=0.6 Ts
CDD, τ=0.3 Ts
P/N0 (dB)
BER
Figure: BER of D-DSTC using BPSK at various synchronizationerrors τ8
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Frequency Selective Channels
Flat-fading channel, one tap filter h[k] = h0:y [k] = h0x [k] + n[k]
Frequency selective channel, multiple taps filter:
h[k] =L−1∑
l=0
hlδ[k − l ]
y [k] = x ∗ h =
L∑
l=0
hlx [k − l ] + n[k]
Inter Symbol Interference (ISI)
Orthogonal frequency-division multiplexing (OFDM)
9
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Point-to-Point OFDM Structure
x = [x1, · · · , xN ], y = [y1, · · · , yN ]yn = Hnxn + nn, n = 1, · · · ,N
bits x
x̂
Add
RemoveCyclic Prefix
Cyclic PrefixModulation
Detection
X Xcp
ISI Channel
YcpYyDFT
IDFT
Frequency diversity can be achieved by using channel codingWhat are drawbacks of OFDM?
10
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Simulation Results
5 10 15 20 25 3010
−4
10−3
10−2
10−1
SNR per bit,[dB]
bit e
rror p
roba
bility
Ncp=0
Ncp=2
Ncp=4
Ncp=6
Ncp=8
theory
Figure: BER of OFDM system over a frequency-selective channel withfour taps, N = 128, using QPSK for different values of cyclic prefix
11
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Differential OFDM
v = [v1, · · · , vN ], x(k) = [x1, · · · , xN ]
Differential Encoding: x(k)n = vnx
(k−1)n , n = 1, · · · ,N
Decoding: y(k)n = vny
(k−1)n + wn, n = 1, · · · ,N
Requires constant channel over two OFDM blocks, i.e., 2Nsymbols
3 dB performance loss compared with coherent detection
12
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Simulation Results
5 10 15 20 25
10−3
10−2
10−1
SNR
BER
Differential OFDM
Coherent OFDM
Figure: BER of Differential and Coherent OFDM system over afrequency-selective channel with four taps, N = 128, using QPSK
13
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Asynchronous vs. Frequency Selectivity
Relay 2 is late:
y1 = g1x11 − αg2x∗
22 + βg2x∗
21(k−1) + n1
y2 = g1x12 + αg2x∗
21 − βg2x∗
22 + n2
Relay 1-Destination channel: flat-fading, g1Relay 2-Destination channel: can be assumed as frequencyselective, [αg2, βg2]What is the difference between [αg2, βg2] and an actualfrequency-selective channel?
Block (k)Block (k − 1)
τ
x11 x12
−x∗22 x∗21
x11 x12
−x∗22 x∗2114
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Differential Distributed Space-Time Coding OFDM(D-DSTC OFDM)
Data symbols:v1 = [v1(1), · · · , v1(N)], v2 = [v2(1), · · · , v2(N)]
Construct space-time matrices:
V(k) =
[
v1(k) −v∗2 (k)v2(k) v∗1 (k)
]
, k = 1, · · · ,N
Encode differentially: s(k) = V(k)s(k−1) =
[
s(k)1
s(k)2
]
Collect symbols:s1 = [s1(1), · · · , s1(N)], s2 = [s2(1), · · · , s2(N)]
S1 = IDFT (s1), S2 = IDFT (s∗2)
15
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
D-DSTC OFDM continue
Phase I: Source transmits [S1,S2]Relays receive [X11,X12] and [X21,X22]Phase II: Relays re-transmit [X11, ctr(X
∗
12)] and[−X22, ctr(X
∗
21)]
[S1,S2]
[X11, ctr(X∗
12)]
[−X22, ctr(X∗
21)]
[Y1,Y2]
q1
q2
g1
g2SourceDestination
Relay 1
Relay 2
16
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
D-DSTC OFDM continue
Circular Time-Reversal: ctr(X) = [X (1),X (N), · · · ,X (2)]
xIDFT−−−→ X
∗
−→ X∗ctr−→ X̃
DFT−−−→ x∗
At Destination: Remove Cyclic Prefix, apply DFTy1 = [y1(1), · · · , y1(N)], y2 = [y2(1), · · · , y2(N)]
y(k) =
[
y1(k)y2(k)
]
= A√
P0
[
s1(k) −s∗2 (k)s2(k) s∗1 (k)
] [
H1
H2
]
+
[
W1
W2
]
,
k = 1, · · · ,N
Differential decoding: y(k) = V(k)y(k−1) + w̃(k)
17
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
D-DSTC OFDM: Pros and Cons
No channel information required
No delay between relays required
Higher delays: cyclic prefix
Complexity similar to OFDM, symbol-by-symbol decoding
Channels have to be static over three OFDM blocks=6N
Destination have to wait four OFDM blocks=8N before startdecoding
18
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
D-DSTC OFDM: Pros and Cons
No channel information required
No delay between relays required
Higher delays: cyclic prefix
Complexity similar to OFDM, symbol-by-symbol decoding
Channels have to be static over three OFDM blocks=6N
Destination have to wait four OFDM blocks=8N before startdecoding
18
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Simulation Results
P0 = P/2, Pr = P/4, A =√
Pr/(P0 + N0)
0 5 10 15 20 25 30
10−3
10−2
10−1
100
Differential, τ=0
Coherent, τ=0
Differential, τ=0.4
Differential, τ=0.6
Differential, τ=0.8
P/N0 (dB)
BER
Figure: BER of D-DSTC OFDM, N = 64, one cyclic prefix, usingBPSK for different sync errors τ19
IntroductionD-DSTC
OFDM SystemsD-DSTC OFDM
Summary
Summary
Asynchronous problem in distributed space-time coding
OFDM approach
Differential encoding and decoding
No channel or delay requirement
Thank You!
20
