Particle Filters for Joint Timing and Carrier Estimation: Improved Resampling Guidelines and Weighted Bayesian Cramer-Rao Bounds

This paper proposes a framework for joint blind timing and carrier offset estimation and data detection using a Sequential Importance Sampling (SIS) particle filter in Additive White Gaussian Noise (AWGN) channels. We assume baud rate sampling and model the intractable posterior probability distribution functions for sampling timing and carrier offset particles using beta distributions. To enable the SIS approach to estimate static synchronization parameters, we propose new resampling guidelines for dealing with the degeneracy problem and fine tuning the estimated values. We derive the Weighted Bayesian Cramer Rao Bound (WBCRB) for joint timing and carrier offset estimation, which takes into account the prior distribution of the estimation parameters and is an accurate lower bound for all considered Signal to Noise Ratio (SNR) values. Simulation results are presented to corroborate that the Mean Square Error (MSE) performance of the proposed algorithm is close to optimal at higher SNR values (above 20 dB). In addition, the bit error rate performance approaches that of the perfectly synchronized case for small unknown carrier offsets and any unknown timing offset. The advantage of our particle filter algorithm, compared to existing techniques, is that it can work for the full range acquisition of carrier offsets.