In asynchronous physical-layer network coding (APNC) systems, the symbolsfrom multiple transmitters to a common receiver may be misaligned. Theknowledge of the amount of symbol misalignment, hence its estimation, isimportant to PNC decoding. This paper addresses the problem ofsymbol-misalignment estimation and the problem of optimal PNC decoding giventhe misalignment estimate, assuming the APNC system uses the root-raised-cosinepulse to carry signals (RRC-APNC). First, we put forth an optimalsymbol-misalignment estimator that makes use of double baud-rate samples. Then,we devise optimal decoders for RRC-APNC in the presence of inaccuratesymbol-misalignment estimates. In particular, we present a new whiteningtransformation to whiten the noise of the double baud-rate samples. Finally, weinvestigate the decoding performance of various estimation-and-decoding schemesfor RRC-APNC. Extensive simulations show that: (i) Our double baud-rateestimator yields substantially more accurate symbol-misalignment estimates thanthe baud-rate estimator does. The mean-square-error (MSE) gains are up to 8 dB.(ii) An overall estimation-and-decoding scheme in which both estimation anddecoding are based on double baud-rate samples yields much better performancethan other schemes. Compared with a scheme in which both estimation anddecoding are based on baud-rate samples), the double baud-rate sampling schemeyields 4.5 dB gains on symbol error rate (SER) performance in an AWGN channel,and 2 dB gains on packet error rate (PER) performance in a Rayleigh fadingchannel.
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