Symbol Misalignment Estimation in Asynchronous Physical-Layer Network Coding

Abstract

Symbol misalignment is inevitable in asynchronous physical-layer network coding (PNC) systems. It is paramount that such symbol misalignment is taken into account in PNC decoding for good performance. Thus, accurate estimation of symbol misalignment is crucial. This paper argues that, when Nyquist pulses (i.e., intersymbol-interference (ISI)-free pulses) are adopted, signal samples only need to be collected at baud rate for optimal symbol misalignment estimation. Based on this principle, we propose a highly accurate symbol misalignment estimation method with low complexity. Our method makes use of the constant amplitude zero autocorrelation sequence (Zadoff–Chu sequence (ZC sequence)). We derive a maximum-likelihood (ML) estimator for symbol misalignment based on the cross-correlation result of the ZC sequence. Unlike previous methods that employ oversampling, our estimation method requires only baud-rate sampling, thus having much lower complexity. Extensive simulations show that our method can accurately estimate both integral and fractional symbol misalignments using sinc pulse and raised-cosine (RC) pulse. The root-mean-square error (RMSE) of the estimation is below 10−2 (in unit of symbol duration) when the SNR is above 15, 18, and 21 dB for 127-, 63-, and 31-bit-length ZC sequences, respectively. Furthermore, our method, being an ML estimation method, has no error floor in the high-SNR regime, whereas the prior methods exhibit an error floor.