Post-filter optimization in timing recovery based on square-law detection

New results on the post-filter in timing recovery based on square-law detection are presented. A phase noise model for the phase of the timing wave to be recovered is considered. The consequence of phase noise is that the sequence of recovered timing instants is non-ideal, therefore some intersymbol interference arises. This leaves space for optimization of the transfer function of the post-filter. The case of random phase walk and raised-cosine Nyquist filter is analyzed in detail. For this case, we propose a post-filter that is easily implemented and that achieves a mean-square error performance of the optimal filter within 0.14 dB. Additionally, an elegant closed-form formula that gives the mean-square error due to the intersymbol interference that affects the sampled signal is presented.