On channel estimation and detection for amplify-and-forward orthogonal frequency division multiplexing-based two-way relay systems under unknown non-reciprocal doubly selective fading channels

Most existing works on two-way relay systems (TWRSs) are based on the assumption that the channels are reciprocal. However, in high-speed moving scenarios, the channels between the multiple access channel phase and broadcast channel phase become non-reciprocal, which significantly complicates the indispensable channel estimation for TWRSs employing coherent detection. In this study, the challenging problem of channel estimation and data detection (CEaDD) is investigated for amplify-and-forward orthogonal frequency division multiplexing-based TWRSs under unknown non-reciprocal doubly selective fading channels. First, an independent CEaDD algorithm according to the minimum mean-square error (MMSE) criterion is proposed. To further improve system performance, an iterative joint CEaDD algorithm employing the variational Bayesian inference (VBI) framework is developed. It is shown by simulations that initialised by the proposed MMSE-based algorithm, the proposed VBI-based iterative algorithm converges in a few iterations and after convergence, its performance approaches the ideal case which assumes perfect knowledge of channel state information.