Maximum a-posteriori estimation of sub-sample timing with binary modulation, arbitrary pulse shaping, and AWGN

The maximum a-posteriori estimator for discrete-time sub-sample timing recovery is derived for non-return to zero pulse-shaped base-band waveforms and the additive white Gaussian noise channel. With a training sequence the estimator may be modeled as an M-ary waveform receiver. The performance of the estimator is determined through Monte-Carlo simulation for an example pulse shape for both random pulses and with the simplifying case when a training sequence is used. These results are compared with the union bound for M-ary waveform communications; at high post-integration signal-to-noise ratios the performance of the estimator and the union bound are close for the case of random pulses (data) and approximately equal in the case of a training sequence.