Blind channel estimation for MPSK-based amplify-and-forward two-way relaying

We consider the problem of channel estimation for amplify-and-forward (AF) two-way relay networks (TWRNs). The majority of works on this problem develop pilot-based algorithms that allocate significant resources for training. We will show in this work that such overhead is not necessary when the terminals employ M-ary phase-shift keying (M-PSK). Using the constant-modulus nature of the transmitted symbols, we develop a relaxed blind maximum-likelihood (ML) channel estimator. We study the performance of the ML estimator in the high SNR and large sample-size scenarios, demonstrating that it performs well in both cases. As a benchmark, we also present and analyze an intuitive low-complexity estimator based on sample-averaging. Simulation studies are used to compare the mean-squared error performance of the two algorithms.