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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
2 / 26
Introduction
1 Introduction
2 System Model
3 Relay Receiver
4 Simulation Study
5 Conclusion
3 / 26
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.
4 / 26
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.
5 / 26
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.
7 / 26
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?
8 / 26
System Model
1 Introduction
2 System Model
3 Relay Receiver
4 Simulation Study
5 Conclusion
9 / 26
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
10 / 26
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
11 / 26
Relay Receiver
1 Introduction
2 System Model
3 Relay Receiver
4 Simulation Study
5 Conclusion
12 / 26
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
14 / 26
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.
17 / 26
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
19 / 26
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
21 / 26
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
24 / 26
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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