Semi-Blind Joint Timing-Offset and Channel Estimation for Amplify-and-Forward Two-Way Relaying

In this paper, we consider the problem of joint timing-offset and channel estimation for amplify-and-forward (AF) two-way relay networks (TWRNs). This problem is solved for generic pulse-shaping filters, taking into account the filter truncation in practical communication and considering both pilot-based and semi-blind estimation strategies. Beginning with pilot-based estimation, we propose a novel Maximum-likelihood joint timing-offset and channel estimator, as well as an alternative estimator based on the special properties of Zadoff-Chu sequences. The first algorithm offers high accuracy, almost overlapping with the Cramer-Rao bound (CRB), while the second offers very low computational complexity. We then develop a semi-blind estimator based on the expectation maximization (EM) framework, exploiting the underlying Hidden Markov Model to apply Baum-Welch forward-backward recursion. The semi-blind CRB is also obtained as an indicator of the best achievable performance. Using simulations, we show that the semi-blind algorithm yields superior accuracy to pilot-based estimation, as well as improved symbol-error-rates and performs very close to the semi-blind CRB. Additionally, a low-complexity approximate EM algorithm is proposed for the case of rectangular pulses. Finally, we consider the possibility of errors in integer-offset estimation and propose pilot-based and semi-blind generalized likelihood ratio test (GLRT) schemes for correcting such errors.