Joint time synchronization and channel estimation for two-way amplify-and-forward relay systems

In this paper, we consider a two-way relay system where two terminals exchange their information via an amplify-and-forward relay in a bi-directional manner. Due to the two-way relay protocol, signals from both terminals travel through different cascaded channels, and this makes synchronization and channel estimation much more complicated than those in conventional one-way relay systems. To cope with these problems, we propose a joint time synchronization and channel estimation scheme based on a specific training sequence arrangement, where each terminal´s training sequence consists of a perfect sequence (with an ideal auto-correlation function) attached by an appropriate cyclic prefix and postfix. The proposed scheme relies on a first channel tap selection process, whose performance is highly dependent on the choice of a threshold to distinguish the signal outputs from noise. By analyzing some possible probability density functions of the correlator output, we derive optimal thresholds for selection of the first channel tap. With these thresholds, the proposed scheme provides better time synchronization performance than the maximum-likelihood approach for low signal-to-noise ratio (SNR) cases; both have similar performance for high SNR cases. It is also shown that the proposed scheme involves much less computational complexity than the maximum-likelihood approach.