Asynchronous Physical-Layer Network Coding: Symbol Misalignment Estimation and Its Effect on Decoding

In asynchronous physical-layer network coding (APNC) systems, the symbols from multiple transmitters to a common receiver may be misaligned. Knowledge of the amount of symbol misalignment, hence its estimation, is important to PNC decoding. This paper addresses the problems of symbol-misalignment estimation and optimal PNC decoding given the misalignment estimate, assuming the APNC system uses the root-raised-cosine pulse to carry signals (RRC-APNC). Our contributions are as follows. First, we put forth an optimal symbol-misalignment estimator that makes use of double baud-rate samples. Second, we devise optimal RRC-APNC decoders in the presence of non-exact symbol-misalignment estimates. In particular, we show how to whiten the colored noise in the double baud-rate samples to simplify the design of optimal decoders. Third, we investigate the decoding performance of various estimation-and-decoding schemes for RRC-APNC. Extensive simulations show that: 1) our double baud-rate estimator yields substantially more accurate symbol-misalignment estimates than the baud-rate estimator does; the mean square error gains are up to 8 dB and 2) an overall estimation-and-decoding scheme in which both estimation and decoding are based on double baud-rate samples yields much better performance than other schemes. Compared with a scheme in which both estimation and decoding are based on baud-rate samples, the double baud-rate sampling scheme yields 4.5 dB gains on symbol error rate performance in an additive white Gaussian noise channel, and 2 dB gains on packet error rate performance in a Rayleigh fading channel.