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 nonideal, 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 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.