A Bayesian Algorithm for Joint Symbol Timing Synchronization and Channel Estimation in Two-Way Relay Networks

This work investigates joint estimation of symbol timing synchronization and channel response in two-way relay networks (TWRN) that utilize amplify-and-forward (AF) relay strategy. With unknown relay channel gains and unknown timing offset, the optimum maximum likelihood (ML) algorithm for joint timing recovery and channel estimation can be overly complex. We develop a new Bayesian based Markov chain Monte Carlo (MCMC) algorithm in order to facilitate joint symbol timing recovery and effective channel estimation. In particular, we present a basic Metropolis-Hastings algorithm (BMH) and a Metropolis-Hastings-ML (MH-ML) algorithm for this purpose. We also derive the Cramer-Rao lower bound (CRLB) to establish a performance benchmark. Our test results of ML, BMH, and MH-ML estimation illustrate near-optimum performance in terms of mean-square errors (MSE) and estimation bias. We further present bit error rate (BER) performance results.