differential distributed space-time coding with imperfect synchronization in frequency-selective...

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


SimulationSummary

Outline

1 Introduction

2 D-OFDM DSTC

3 Simulation

4 Summary

2


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


SimulationSummary

Multipath Fading

Mobile PhoneBase Station

4


SimulationSummary

Fading Effects

Ts

Ts

Ts + Tm

Ts + Tm

timetime

timetimeFlat-Fading

Frequency-Selective

5


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


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.

7


SimulationSummary


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


SimulationSummary


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)

9


SimulationSummary


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 .

10


SimulationSummary


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

11


SimulationSummary


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

12


SimulationSummary


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.

13


SimulationSummary


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 .

14


SimulationSummary



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.

15


SimulationSummary



−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


SimulationSummary



{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


SimulationSummary



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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SimulationSummary



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).

19


SimulationSummary



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).

20


SimulationSummary


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.

21


SimulationSummary


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.

22


SimulationSummary


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


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)

24


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


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


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


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


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!

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