Performance analysis of code-aided symbol timing recovery on AWGN channels

We analyze the performance of a code-aided (CA) decision-directed (DD) timing synchronizer, which can exploit the dependence structure across coded symbols to improve the timing recovery accuracy. Due to the inherent coupling between timing recovery and decoding, most existing studies rely on extensive simulation rather than on analytical methods to evaluate performance of timing recovery for coded systems. We propose analytical methods in this paper towards this end. A first key step is to approximate timing-offset-induced inter-symbol interference (ISI) as an additive Gaussian noise, since in the low signal-to-noise ratio (SNR) regime the background noise is large enough to mask the ISI. Then, we derive semi-analytical expressions for the mean and variance of extrinsic information as functions of timing offset, building on which we characterize both open-loop and closed-loop performance of decision-directed timing synchronizers. Monte Carlo simulation results corroborate that the proposed method accurately characterizes the performance of CA DD timing recovery, for systems with a wide range of channel bandwidth and different channel codes.