Receiver Design for Noncoherent Digital Network Coding

Transcription

1 Receiver Design for Noncoherent Digital Network Coding Terry Ferrett 1 Matthew Valenti 1 Don Torrieri 2 1 West Virginia University 2 U.S. Army Research Laboratory November 3rd, / 25

2 Outline 1 Introduction 2 System Model 3 Simulation Results 4 Conclusion 2 / 25

3 Network Coding Introduction Relaying technique which increases throughput over store-and-forward relaying. Proven to achieve multicast (one-to-many) capacity in wireline networks. (Ahlswede, 2000) Applied at either the physical layer or the link layer. Source Relay Sink Relay Relay Figure: Multicast Example Sink 3 / 25

4 Two-way Relay Channel Introduction N 1 R N 2 Figure: Two-way relay channel Source nodes N 1 and N 2 exchange information through the relay, R Relay performs either amplify-and-forward or decode-and-forward. Amplify-and-forward - relay forwards received signals Decode-and-forward - relay forwards decoded information - this work 4 / 25

5 Introduction Link-layer vs Digital Network Coding Time Slot 1 N1 Γ S (u 1) R N2 N1 Γ S (u 1) Γ S (u 2) R N2 Time Slot 2 Γ S (u 2) Γ R (u) Γ R (u) N1 R N2 N1 R N2 Time Slot 3 N1 Γ R (u) R Γ R (u) N2 Link-layer network coding (LNC) requires three time slots for relaying. Digital network coding (DNC) only requires two time slots. 5 / 25

6 Introduction Previous Work and Motivation 1 Soft-output relay demodulator which performs digital network coding in a two-way relay network. Demodulator uses continuous-phase frequency shift keying and noncoherent reception. Channel state information improves error-rate performance by 10 db over the no-channel state information case. Improvement over the no-csi case motivates the study of channel estimation. 1 M. C. Valenti, D. Torrieri, and T. Ferrett, Noncoherent physical-layer network coding using binary CPFSK modulation, Proc. IEEE Military Commun. Conf., Oct / 25

7 Introduction Signal Space - Relay Receiver Multiple-access Example 1 Multiple-access Example 2 Tone 1 I h 1 I h 1 + h 2 h 1 h 2 Q Q Tone 2 I I h 2 Q Q 7 / 25

8 Introduction Channel Estimation - DNC Consider a block-fading channel in which the amplitudes of the fading coefficients are constant for a block. The channel estimator computes the magnitudes of the fading coefficients α 1 = h 1 α 2 = h 2 using the magnitude of the noisy sum of fading coefficients, α = h 1 + h 2. I h 1 + h 2 h 1 h 2 Q 8 / 25

9 Source Nodes System Model N 1 R N 2 Both end nodes generate information bit sequences. Turbo channel encoding at each node yields a pair of channel-coded bit sequence. The coded sequences modulated using Binary continuous-phase frequency shift keying. Modulation index h = 1. Unit energy per symbol. Transmission of codewords synchronized in time. 9 / 25

10 System Model Relay Node - Reception Phase N 1 R N 2 DNC Sum of interfered signals received from source nodes. Demodulation and network decoding occur in a single operation. LNC Signals from source nodes received in orthogonal time slots. Demodulation applied separately to each information stream. Network coding applied to soft outputs using log-likelihood ratio arithmetic. 10 / 25

11 System Model Relay Node - Reception Phase N 1 R N 2 DNC Re-encodes using a higher rate Turbo code than the source nodes. LNC Re-encodes using the same rate Turbo code as the source nodes. 11 / 25

12 System Model Relay Node - Broadcast Phase N 1 R N 2 Broadcast phase is not subject to interference. Signal from relay traverses independent fading channels to end nodes. 12 / 25

13 Channel Model System Model Both source-relay channels modeled as Rayleigh block fading channels. Block sizes {8, 16, 32, 64, 128} symbols per block. Fading amplitudes constant per block. Phase distortions uniformly distributed and independent for each symbol (oscillator instabilities, channel phase distortions). 13 / 25

14 Channel Estimator System Model Denote the fading amplitude for the channel from node 1 to the relay as α 1, and node 2 to the relay as α 2. The relay forms estimates of {α 1, α 2 } as {Â, ˆB}. The mapping from estimate to amplitude is independent of ordering. Careful inspection of the log-likelihood ratio at the relay reveals that α 1 and α 2 are commutative. 14 / 25

15 Channel Estimator System Model Log-likelihood ratio of the network-coded bit at the relay. [ ( ) ( ) 2α1 y 1 2α2 y 2 Λ(b) = max F + F, N 0 N 0 ( ) ( )] 2α2 y 1 2α1 y 2 F + F N 0 N 0 [ ( ) ( )] 2α y1 2α y2 max F, F where N 0 N 0 F (x) = log[i 0 (x)] 15 / 25

16 System Model Channel Estimator Transmission Case Detector Determines quantity v to use for fading amplitude estimation. Matched filter output y 1 corresponds to tone 1, and y 2 to tone 2. For a fading block of lenth N, the transmission case detector computes the mapping For i {1,..., N} Tone 1 transmitted by both sources. v i = y 1 Tone 2 transmitted by both sources. Use v i = y 2 Separate tones transmitted. v i = y 1 + y 2 16 / 25

17 Channel Estimator System Model Estimates are computed as 2 Â = 1 ( X + π2 X 2 (Y X) + + π2 ) (X Y ) ˆB = 1 ( X + π2 X 2 (Y X) + π2 ) (X Y ) where X = 1 N Y = 2 N N v i 2 α1 2 + α2 2 i=1 i: v i 2 >β and where β is the median of {v 1,..., v N } v i 2 α α α 1α 2 π 2 J. Hamkins, An analytic technique to separate cochannel FM signals, IEEE Trans. Commun., vol. 48, pp , April / 25

18 Simulation Parameters Simulation Results Performance metrics Bit error-rate at the relay Throughput of DNC vs LNC Forward error-correction code parameters Error-correcting code = {UMTS Turbo code, uncoded} Channel code rate = {1229/2048, 4500/5056, 4500/6400} Relay parameters Fading amplitude knowledge = {perfect, estimated} Network coding technique = {digital, link-layer} Channel parameters Block length N = {8, 16, 32, 64, 128} 18 / 25

19 Simulation Results Uncoded relay error-rate performance - DNC 10 2 N=128 N=32 N=8 BER E b /N 0 Dashed lines - Estimated fading amplitudes Solid lines - Perfect knowledge of fading amplitudes 19 / 25

20 Simulation Results Coded relay error-rate performance - DNC N=128 N=64 N=32 N=16 N=8 BER E b /N 0 Source node channel code rate /2048 Dashed lines - Estimated fading amplitudes Solid lines - Perfect knowledge of fading amplitudes 20 / 25

21 Simulation Results SNR required to reach BER 10 4 vs block length E b /N Symbols per Fading Block Source node channel code rate /2048 * - estimated fading amplitudes - perfect fading-amplitude knowledge. 21 / 25

22 Simulation Results Coded relay error-rate performance - DNC vs LNC N=128 N=64 N=32 N=16 N=8 BER E b /N 0 Source node channel code rate /2048 Solid lines - DNC, estimated fading amplitudes Dashed lines - LNC, estimated fading amplitudes 22 / 25

23 Simulation Results DNC and LNC, performance-matched 10 1 LNC, rate=4500/5056 DNC, rate=4500/5056 DNC, rate=4500/ BER E b /N 0 Estimated fading amplitudes 32 symbols per block 23 / 25

24 Simulation Results Throughput Comparison - DNC vs LNC Source nodes each generate 4500 information bits Fading block size = 32 symbols per block Channel uses DNC LNC Relay Phase Relay Phase Broadcast Phase Total 11,456 15,168 Throughput (information bits per channel use) T (DNC) = 9000/11, 456 T (LNC) = 9000/15, 168 Throughput increase (%) (T (DNC) /T (LNC) 1) % 24 / 25

25 Conclusion Contributions Performance of a computationally simple estimation algorithm. DNC implementation which does not require Perfect power control. Phase synchronism. Estimates of carrier-phase offset. DNC throughput improvement over LNC - 32% Better performance might be achieved using an EM-estimation approach, at the cost of increased complexity. 25 / 25