An Iterative Noncoherent Relay Receiver for the Two-way Relay Channel

An Iterative Noncoherent Relay Receiver for the Two-way Relay Channel Terry Ferrett 1 Matthew Valenti 1 Don Torrieri 2 1 West Virginia University 2 U.S. Army Research Laboratory June 12th, 2013 1 / 26

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. N 1 R N 2 Relay broadcasts network-coded information to sources. N 1 R N 2 Each source subtracts its own information to reveal the information of the other source. 4 / 26

Introduction Coherent PLNC with BPSK x 1 x 2 x 1 + x 2 different: c 1 +c 2 =1 same: c 1 +c 2 =0 With BPSK and equal-energy coherent channels, only three possible signals can be received. A regenerative relay receiver (decode-and-forward) needs to just determine if the same or different signals were transmitted. The relay forwards either a 0 or 1, depending on whether it thinks the same or different signals were received. 5 / 26

Introduction Noncoherent PLNC with BPSK x 1 x 2 x 1 + x 2? In a noncoherent channel, the phases of each source-relay link are unknown 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 x 1 x 2 x 1 + x 2 different: c 1 +c 2 =1 same: c 1 +c 2 =0 FSK more amenable to noncoherent communications. Receiver senses energy at the two possible tones to determine if the same 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 15 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. Minimum Eb/No (in db) 10 5 Noncoherent combining penalty M=2 M=4 min E b /N o = 6.72 db at r=0.48 M=16 M=64 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rate R (symbol per channel use) It is well known that the energy-efficiency of coded noncoherent FSK improves 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

Source Transmission System Model Each source generates a binary information sequence. Turbo code applied to sequence producing a channel codeword. Codeword interleaved and mapped to M-FSK symbols. Node 1 u 1 Channel c c NFSK X 1 1 1 Π Encoder Modulator Relay u Node 2 Channel Decoder v z Π Π 1 z v Demodulator DNC SOMAP P (q; I) Super Symbol Probability Mapper u 2 Channel c c NFSK X 2 2 2 Π Encoder Modulator Y H 1 N H 2 10 / 26

Channel Model System 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. Node 1 u 1 Channel c c NFSK X 1 1 1 Π Encoder Modulator Relay u Node 2 Channel Decoder v z Π Π 1 z v Demodulator DNC SOMAP P (q; I) Super Symbol Probability Mapper u 2 Channel c c NFSK X 2 2 2 Π Encoder Modulator Y H 1 N H 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 = u 1 u 2 The relay demodulator forms soft bit metrics (LLRs) on c = c 1 c 2 where c is a codeword from the codebook generating c 1 and c 2, and c = f(u 1 u 2 ) c = f(u 1 ) f(u 2 ) and f( ) is the linear channel encoding function, The soft bit metrics on c are passed to the decoder which refines the metrics and feeds them back to the demodulator (BICM-ID processing). 13 / 26

Receiver Diagram Relay Receiver Goal of relay receiver is to detect network-coded combination of source bits u = u 1 u 2. Partial CSI (amplitudes known) and no CSI considered Node 1 u 1 Channel c c NFSK X 1 1 1 Π Encoder Modulator Relay u Node 2 Channel Decoder v z Π Π 1 z v Demodulator DNC SOMAP P (q; I) Super Symbol Probability Mapper u 2 Channel c c NFSK X 2 2 2 Π Encoder Modulator Y H 1 N H 2 14 / 26

Super-Symbol Mapping Relay Receiver The demodulator first computes the probability of all possible combinations of received symbol for each channel observation This probability is denoted as P (q; I), where the super-symbol q is defined as q = (q 1, q 2 ) q 1, q 2 D q D D where: q 1 and q 2 represent symbols transmitted by the two sources. D is the set of all possible symbols available at sources. The cardinality of D D is M 2, thus the receiver computes M 2 probabilities. 15 / 26

Relay Receiver DNC Soft Mapper The DNC soft mapper (DNC-SOMAP) computes the LLR of the network coded bits mapped to each received super symbol. z k = log q:c k =1 q:c k =0 µ 1 p(y q) j=0 j k µ 1 p(y q) j=0 j k e c jv j e c jv j where z k - 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 = log 2 (M). v j - j-th extrinsic LLR fed back from decoder. 16 / 26

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 α2 1 + α2 2 N 0 } I 0 ( 2 yq1 α 1 N 0 ) ( ) 2 yq2 α 2 I 0 N 0 where y q1 and y q2 are the channel observations for the FSK dimensions associated to symbols q 1 and q 2 Case 2: sources transmit same symbols } ( ) p(y q) = exp { α2 2 yq1 α I 0 N 0 N 0 where α = h 1 + h 2 and is approximated as α = α 2 1 + α2 2 1 1 A discussion of this approximation is found in 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. 17 / 26

Relay Receiver Super Symbol Probability Model When the fading amplitudes are not known at the relay, Sources transmit different symbols [( ) ( 1 1 p(y q) = + 1 ) ( 1 + 1 )] 1 E 1 E 2 E 1 N o E 2 N 0 { yq1 2 E 1 exp N 0 (N 0 + E 1 ) + y q 2 2 } E 2 N 0 (N 0 + E 2 ) Sources transmit same symbols ( ) ( 1 1 p(y q) = + 1 E 1 + E 2 E 1 + E 2 N 0 ) 1 exp { yq1 2 (E 1 + E 2 ) } N0 2 + N 0(E 1 + E 2 ) 18 / 26

Simulation Study 1 Introduction 2 System Model 3 Relay Receiver 4 Simulation Study 5 Conclusion 19 / 26

Metrics and Parameters Simulation Study This section presents simulated error-rate and capacity performance for the relay receiver Error-rate performance is simulated as a function of FSK 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 state information and modulation order 20 / 26

Simulation Study Error Rate vs Modulation order and Decoding Iterations 10 1 M=2 M=4 M=8 r = 1229/2048 CSI 10 2 BER 10 3 10 4 10 12 14 16 18 20 22 Eb/No (db) Partial CSI for all cases Solid lines - BICM, dashed lines - BICM-ID For each modulation order, right-to-left, iterations are 1, 10, 30 21 / 26

Simulation Study Error Rate vs Modulation Order and CSI 10 1 10 2 M=2, No CSI M=2, CSI M=4, No CSI M=4, CSI M=8, No CSI M=8, CSI r = 1229/2048 Iterations = 30 BER 10 3 10 4 11 12 13 14 15 16 17 18 19 20 Eb/No (db) Solid lines - BICM, dashed lines - BICM-ID Number of iterations is 30 for all cases 22 / 26

Simulation Study Binary Information Rate Eb/No (db) 30 28 26 24 22 20 18 16 14 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=2 M=4 M=8 12 10 8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Rate (R) Solid lines - CSI, Dashed lines - no CSI Symbols denote E b /N 0 required to reach error rate 10 4 All receivers perform 30 decoding iterations 23 / 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 performing physical-layer network coding in the two-way relay channel using noncoherent FSK modulation iterative soft-decision channel decoding CSI for computation of bit metrics Simulation results using the UMTS Turbo code, 4, and 8-ary modulation, and different levels of channel state information show error rate improvements between 0.4-0.9 db over non-bicm-id systems. 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. 25 / 26

Conclusion Thank you. 26 / 26