Joint time-frequency synchronization and channel estimation in two-way relay networks

This work investigates joint time-frequency synchronization and channel estimation in two-way relay networks (TWRN) that utilize amplify-and-forward (AF) relay strategy. A two-way transmission model for joint time-frequency synchronization and channel estimation in TWRN is provided. Due to the high dimension and complexity of the model, the maximum likelihood (ML) algorithm is over complex and a standard Markov chain Monte Carlo (MCMC) algorithm is ineffective. We instead develop a hybrid Metropolis-Hastings-Gibbs algorithm in order to facilitate joint time-frequency recovery and effective channel estimation. In particular, we present a reparameterized model to facilitate Gibbs sampling with respect to the self-interference channel. Then the second order truncated Taylor series approximation is adopted for carrier frequency offsets (CFOs) estimation. Furthermore, a heuristic way of determining update order of parameters is proposed and initial value of the Markov chain is discussed as well. To test the robustness and objectivity of our proposed algorithm, two MCMC estimators, each with its own prior distribution, are compared against each other. Numerical results are provided to verify the effectiveness and robustness of proposed algorithm in terms of both mean-square errors (MSE) and estimation bias. The bit error rate (BER) performance results are further offered for comparison.