Minimum Timing Jitter in Timing Recovery Based on Pre-filtered Square-Law Timing Detection

New results about the pre-filter and the post-filter in timing recovery based on square-law detection are presented. Specifically, in the paper a matched-filter-type condition that guarantees optimality of the pre-filter against channel noise is derived. This condition can be satisfied together with the known condition for self-noise elimination, thus achieving optimality against self-noise and against channel noise simultaneously. The post-filter is optimized by introducing a phase noise model for the phase of the timing wave used at the transmit side for generating the data signal. The case of random phase walk is analyzed in detail, and, having optimized both the pre-filter and the post-filter, we conclude that the minimum variance of the normalized timing error for a given spectral quality of the source timing wave and for a given channel signal-to-noise ratio goes with (alphaT)^-0.5, where T is the symbol repetition interval and alpha is the roll-off factor.