An Iterative Noncoherent Relay Receiverfor the

Two-way Relay Channel

Terry Ferrett 1

Matthew Valenti 1

Don Torrieri 2

1West Virginia University

2U.S. Army Research Laboratory

June 12th, 2013

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Outline

1 Introduction

2 System Model

3 Relay Receiver

4 Simulation Study

5 Conclusion

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Introduction

1 Introduction

2 System Model

3 Relay Receiver

4 Simulation Study

5 Conclusion

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Introduction

Physical-Layer Network Coding

Two-way relay channel (TWRC)Two source nodes exchange information through a relay node.

Physical-layer network coding (PLNC)

Sources deliberately interfere by transmitting simultaneously to relay.

N1 N2R

Relay broadcasts network-coded information to sources.

N1 N2R

Each source subtracts its own information to reveal the information ofthe other source.

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Introduction

Coherent PLNC with BPSK

x1   x2  

different:  c1+c2=1  

same:  c1+c2=0  

x1  +  x2  

With BPSK and equal-energy coherent channels, only three possiblesignals can be received.

A regenerative relay receiver (decode-and-forward) needs to justdetermine if the same or different signals were transmitted.

The relay forwards either a 0 or 1, depending on whether it thinks thesame or different signals were received.

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Introduction

Noncoherent PLNC with BPSK

x1   x2   x1  +  x2  

?  

In a noncoherent channel, the phases of each source-relay link areunknown and generally different.

The two signals are recieved with an unknown phase offset.

Creates a distorted constellation.

Impossible to create decision regions if full receive CSI not available.

Deviates from the spirit of PLNC.6 / 26

Introduction

Noncoherent PLNC with FSK

x1   x2  

different:  c1+c2=1  

same:  c1+c2=0  

x1  +  x2  

FSK more amenable to noncoherent communications.

Receiver senses energy at the two possible tones to determine if thesame or different signals were transmitted.

Noncoherent PLNC with binary FSK has been published†.†[2] M. C. Valenti, D. Torrieri, and T. Ferrett, “Noncoherent physical-layer network

coding with FSK modulation: Relay receiver design issues,” IEEE Trans. Commun., vol.59, Sept. 2011.

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Introduction

Nonbinary FSK

Capacity of Noncoherent Orthogonal FSK in AWGN W. E. Stark, “Capacity and cutoff rate of noncoherent FSK with nonselective Rician fading,” IEEE Trans. Commun., Nov. 1985. M.C. Valenti and S. Cheng, “Iterative demodulation and decoding of turbo coded M-ary noncoherent orthogonal modulation,” IEEE JSAC, 2005.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

5

10

15

Rate R (symbol per channel use)

Min

imum

Eb/

No

(in d

B)

M=2

M=4

M=16

M=64

Noncoherent combining penalty

min Eb/No = 6.72 dB at r=0.48

It is well known that the energy-efficiency of coded noncoherent FSKimproves with increasing M (number of frequency tones).Can FSK-based noncoherent PLNC also benefit from increasing M?

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System Model

1 Introduction

2 System Model

3 Relay Receiver

4 Simulation Study

5 Conclusion

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System Model

Source Transmission

Each source generates a binary information sequence.

Turbo code applied to sequence producing a channel codeword.

Codeword interleaved and mapped to M-FSK symbols.

Channel

Encoder

Channel

Encoder

DNC

SOMAP

Channel

Decoder

Modulator

NFSK

Modulator

NFSK

Demodulator

Probability

Symbol

Mapper

Super−1

Π

Π

Node 2

u2 X2

u1 X1

Node 1

NY

u

RelayH1

H2

P (q; I)Π

Πv′ v

zz′

c′1

c1

c2c′2

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System Model

Channel Model

Channel gains are i.i.d., zero-mean, complex Gaussian.

Relay receives noisy sum of signals from sources.

Symbols and frames assumed to be perfectly synchronized.

Channel

Encoder

Channel

Encoder

DNC

SOMAP

Channel

Decoder

Modulator

NFSK

Modulator

NFSK

Demodulator

Probability

Symbol

Mapper

Super−1

Π

Π

Node 2

u2 X2

u1 X1

Node 1

NY

u

RelayH1

H2

P (q; I)Π

Πv′ v

zz′

c′1

c1

c2c′2

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Relay Receiver

1 Introduction

2 System Model

3 Relay Receiver

4 Simulation Study

5 Conclusion

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Relay Receiver

Relay Receiver: Goals

The relay receiver detects the network-coded combination of bits

u = u1 ⊕ u2

The relay demodulator forms soft bit metrics (LLRs) on

c = c1 ⊕ c2

where c is a codeword from the codebook generating c1 and c2, and

c = f(u1 ⊕ u2)

c = f(u1)⊕ f(u2)

and f(·) is the linear channel encoding function,

The soft bit metrics on c are passed to the decoder which refines themetrics and feeds them back to the demodulator (BICM-IDprocessing).

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Relay Receiver

Receiver Diagram

Goal of relay receiver is to detect network-coded combination ofsource bits u = u1 ⊕ u2.

Partial CSI (amplitudes known) and no CSI considered

Channel

Encoder

Channel

Encoder

DNC

SOMAP

Channel

Decoder

Modulator

NFSK

Modulator

NFSK

Demodulator

Probability

Symbol

Mapper

Super−1

Π

Π

Node 2

u2 X2

u1 X1

Node 1

NY

u

RelayH1

H2

P (q; I)Π

Πv′ v

zz′

c′1

c1

c2c′2

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Relay Receiver

Super-Symbol Mapping

The demodulator first computes the probability of all possiblecombinations of received symbol for each channel observation

This probability is denoted as P (q; I), where the super-symbol q isdefined as

q = (q1, q2) q1, q2 ∈ D q ∈ D ×D

where:

q1 and q2 represent symbols transmitted by the two sources.D is the set of all possible symbols available at sources.

The cardinality of D ×D is M2, thus the receiver computes M2

probabilities.

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Relay Receiver

DNC Soft Mapper

The DNC soft mapper (DNC-SOMAP) computes the LLR of thenetwork coded bits mapped to each received super symbol.

zk = log

∑q:ck=1

p(y|q)µ−1∏j=0j 6=k

ecjvj

∑q:ck=0

p(y|q)µ−1∏j=0j 6=k

ecjvj

wherezk - LLR of k-th network-coded bit for the received super symbol.c{k,j} - {k, j}-th network-coded bit mapped to super symbol q.y - channel observation for the received super symbol.µ = log2(M).vj - j-th extrinsic LLR fed back from decoder.

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Relay Receiver

Super Symbol Probability Model

The model for p(y|q) depends on the available CSI

When the fading amplitudes are known at the relay,

Case 1: sources transmit different symbols

p(y|q) = exp

{−α

21 + α2

2

N0

}I0

(2|yq1 |α1

N0

)I0

(2|yq2 |α2

N0

)where |yq1 | and |yq2 | are the channel observations for the FSKdimensions associated to symbols q1 and q2Case 2: sources transmit same symbols

p(y|q) = exp

{− α

2

N0

}I0

(2|yq1 |αN0

)where α = |h1 + h2| and is approximated as α =

√α21 + α2

21

1A discussion of this approximation is found inM. C. Valenti, D. Torrieri, and T. Ferrett, Noncoherent physical-layer network codingwith FSK modulation: Relay receiver design issues, IEEE Trans. Commun., vol. 59,Sept. 2011.

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Relay Receiver

Super Symbol Probability Model

When the fading amplitudes are not known at the relay,

Sources transmit different symbols

p(y|q) =[(

1

E1E2

)(1

E1+

1

No

)(1

E2+

1

N0

)]−1× exp

{|yq1 |2E1

N0(N0 + E1)+

|yq2 |2E2N0(N0 + E2)

}Sources transmit same symbols

p(y|q) =(

1

E1 + E2

)(1

E1 + E2+

1

N0

)−1× exp

{|yq1 |2(E1 + E2)

N20 +N0(E1 + E2)

}

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Simulation Study

1 Introduction

2 System Model

3 Relay Receiver

4 Simulation Study

5 Conclusion

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Simulation Study

Metrics and Parameters

This section presents simulated error-rate and capacity performancefor the relay receiver

Error-rate performance is simulated as a function ofFSK modulation order {2, 4, 8}Channel state information {Partial, None}Decoding iterations {1, 2, 4, 30}Decoder feedback {BICM, BICM-ID}

The channel code is a UMTS Turbo code with rate R = 0.6

There is a 1:1 ratio of inner decoder to outer BICM-ID iterations

The sources transmit with equal energy

Channel capacity is simulated as a function of channel stateinformation and modulation order 20 / 26

Simulation Study

Error Rate vs Modulation order and Decoding Iterations

10 12 14 16 18 20 2210

−4

10−3

10−2

10−1

Eb/No (dB)

BE

R

M=2

M=4

M=8

r = 1229/2048CSI

Partial CSI for all casesSolid lines - BICM, dashed lines - BICM-IDFor each modulation order, right-to-left, iterations are 1, 10, 30

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Simulation Study

Error Rate vs Modulation Order and CSI

11 12 13 14 15 16 17 18 19 2010

−4

10−3

10−2

10−1

Eb/No (dB)

BE

R

M=2, No CSIM=2, CSIM=4, No CSIM=4, CSIM=8, No CSIM=8, CSI

r = 1229/2048Iterations = 30

Solid lines - BICM, dashed lines - BICM-ID

Number of iterations is 30 for all cases22 / 26

Simulation Study

Binary Information Rate

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.98

10

12

14

16

18

20

22

24

26

28

30

Rate (R)

Eb

/No

(d

B)

M=2, No CSI, BICM

M=2, CSI, BICM

M=4, No CSI, BICM

M=4, CSI, BICM

M=4, No CSI, BICM−ID

M=4, CSI, BICM−ID

M=8, No CSI, BICM

M=8, CSI, BICM

M=8, No CSI, BICM−ID

M=8, CSI, BICM−ID

M=8M=2 M=4

Solid lines - CSI, Dashed lines - no CSISymbols denote Eb/N0 required to reach error rate 10−4

All receivers perform 30 decoding iterations23 / 26

Conclusion

1 Introduction

2 System Model

3 Relay Receiver

4 Simulation Study

5 Conclusion

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Conclusion

This works presents a relay receiver capable of performingphysical-layer network coding in the two-way relay channel using

noncoherent FSK modulationiterative soft-decision channel decodingCSI for computation of bit metrics

Simulation results using the UMTS Turbo code, 4, and 8-arymodulation, and different levels of channel state information showerror rate improvements between 0.4-0.9 dB over non-BICM-IDsystems.

Approximately 4 dB gain when going from M = 2 to M = 4.

Approximately 2.5 dB gain when going from M = 4 to M = 8.

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Conclusion

Thank you.

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