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Optimal symbol misalignment estimation in asynchronous physical-layer network coding

In practical asynchronous physical-layer network coding (PNC) systems, the symbols from multiple transmitters to a common receiver may be misaligned. The good performance of an asynchronous PNC decoder hinges on accurate estimation of the symbol misalignment. This paper puts forth an optimal symbol misalignment estimator that considerably improves the estimation accuracy over prior schemes. Our scheme makes use of double baud-rate sampling of the received preambles consisting of Zadoff-Chu (ZC) sequences used by different transmitters. The sampling process is information-lossless because the double baud-rate samples capture all the information embedded in the continuous-time signal shaped by the assumed root-raised-cosine (RRC) pulse. The estimation consists of three steps: (i) cross-correlation of the double baud-rate samples with “interpolated double baud-rate ZC sequences” (ii) noise whitening; (iii) maximum likelihood (ML) estimation of the symbol misalignment. Extensive simulations show that the mean-square-error (MSE) performance of our estimator is superior to that of the baudrate estimator — e.g., for the RRC pulse with roll-off factor 1, our double baud-rate estimator yields improvement 8 dB over the baud-rate estimator. Furthermore, our double baudrate estimator yields square errors of less than 0.001 with 90% probability when the SNR is 10 dB in both AWGN and Rayleigh fading channels.