Asynchronous Differential Distributed Space-Time Coding

1. Introduction
D-DSTC
OFDM Systems
D-DSTC OFDM
Summary
Asynchronous Differential Distributed Space-Time
Coding
M. R. Avendi
Department of Electrical Engineering & Computer Science
University of California, Irvine
Feb., 2014
1

2. Introduction
D-DSTC
OFDM Systems
D-DSTC OFDM
Summary
Outline
1 Introduction
2 D-DSTC
3 OFDM Systems
4 D-DSTC OFDM
5 Summary
2

3. Introduction
D-DSTC
OFDM Systems
D-DSTC OFDM
Summary
Cooperative Communications
Phase I: Source transmits, Relays listen
Phase II: Relays re-broadcast their received signal to
Destination
Virtual antenna array, improving diversity
q1
q2
qR
g1
g2
gR
Source
Destination
Relay 1
Relay 2
Relay R
3

4. Introduction
D-DSTC
OFDM Systems
D-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

5. Introduction
D-DSTC
OFDM Systems
D-DSTC OFDM
Summary
System Model
All channels are Rayleigh flat-fading
Phase 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
g2Source
Destination
Relay 1
Relay 2
5

6. Introduction
D-DSTC
OFDM Systems
D-DSTC OFDM
Summary
Synchronized Relay Networks
Perfect relays synchronization
y1 = g1x11 − g2x∗
22 + n1
y2 = g1x12 + g2x∗
21 + n2
y1
y2
= A P0
s1 −s∗
2
s2 s∗
1
q1g1
q∗
2g2
+
w1
w2
(1)
RX signal from Relay 1
RX signal from Relay 2
Block k
x11 x12
−x∗
22 x∗
21
6

7. Introduction
D-DSTC
OFDM Systems
D-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
y1
y2
= A P0
s1 −s∗
2
s2 s∗
1
q1g1
αq∗
2g2
+ ISI +
w1
w2
(2)
Block (k)Block (k − 1)
τ
x11 x12
−x∗
22 x∗
21
x11 x12
−x∗
22 x∗
21
7

8. Introduction
D-DSTC
OFDM Systems
D-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
y1
y2
= A P0
s1 −s∗
2
s2 s∗
1
q1g1
αq∗
2g2
+ ISI +
w1
w2
(2)
Block (k)Block (k − 1)
τ
x11 x12
−x∗
22 x∗
21
x11 x12
−x∗
22 x∗
21
7

9. Introduction
D-DSTC
OFDM Systems
D-DSTC OFDM
Summary
Asynchronous Relay Networks
Effect of synchronization error on conventional decoder (CDD)
0 5 10 15 20 25 30
10
−4
10
−3
10
−2
10
−1
10
0
CDD, τ=0
CDD, τ=0.2 Ts
CDD, τ=0.4 T
s
CDD, τ=0.6 T
s
CDD, τ=0.3 T
s
P/N0 (dB)
BER
Figure: BER of D-DSTC using BPSK at various synchronization
errors τ8

10. Introduction
D-DSTC
OFDM Systems
D-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
hl δ[k − l]
y[k] = x ∗ h =
L
l=0
hl x[k − l] + n[k]
Inter Symbol Interference (ISI)
Orthogonal frequency-division multiplexing (OFDM)
9

11. Introduction
D-DSTC
OFDM Systems
D-DSTC OFDM
Summary
Point-to-Point OFDM Structure
x = [x1, · · · , xN ], y = [y1, · · · , yN]
yn = Hnxn + nn, n = 1, · · · , N
bits x
ˆx
Add
Remove
Cyclic Prefix
Cyclic Prefix
Modulation
Detection
X Xcp
ISI Channel
YcpYy
DFT
IDFT
Frequency diversity can be achieved by using channel coding
What are drawbacks of OFDM?
10

12. Introduction
D-DSTC
OFDM Systems
D-DSTC OFDM
Summary
Simulation Results
5 10 15 20 25 30
10
−4
10
−3
10
−2
10
−1
SNR per bit,[dB]
biterrorprobability
Ncp=0
Ncp=2
Ncp=4
Ncp=6
Ncp=8
theory
Figure: BER of OFDM system over a frequency-selective channel with
four taps, N = 128, using QPSK for different values of cyclic prefix
11

13. Introduction
D-DSTC
OFDM Systems
D-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., 2N
symbols
3 dB performance loss compared with coherent detection
12

14. Introduction
D-DSTC
OFDM Systems
D-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 a
frequency-selective channel with four taps, N = 128, using QPSK
13

15. Introduction
D-DSTC
OFDM Systems
D-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, g1
Relay 2-Destination channel: can be assumed as frequency
selective, [αg2, βg2]
What is the difference between [αg2, βg2] and an actual
frequency-selective channel?
Block (k)Block (k − 1)
τ
x11 x12
−x∗
22 x∗
21
x11 x12
−x∗
22 x∗
21
14

16. Introduction
D-DSTC
OFDM Systems
D-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

17. Introduction
D-DSTC
OFDM Systems
D-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
g2Source
Destination
Relay 1
Relay 2
16

18. Introduction
D-DSTC
OFDM Systems
D-DSTC OFDM
Summary
D-DSTC OFDM continue
Circular Time-Reversal: ctr(X) = [X(1), X(N), · · · , X(2)]
x
IDFT
−−−→ X
∗
−→ X∗ ctr
−→ ˜X
DFT
−−−→ x∗
At Destination: Remove Cyclic Prefix, apply DFT
y1 = [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) + ˜w(k)
17

19. Introduction
D-DSTC
OFDM Systems
D-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 start
decoding
18

20. Introduction
D-DSTC
OFDM Systems
D-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 start
decoding
18

21. Introduction
D-DSTC
OFDM Systems
D-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
10
0
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, using
BPSK for different sync errors τ19

22. Introduction
D-DSTC
OFDM Systems
D-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