On MMSE and VBI detection for TWRNs over unknown non-reciprocal time-frequency dispersive channels

Most existing studies on two-way relay networks (TWRNs) typically assume that the channels are reciprocal. However, in time-frequency dispersive channels, the channels between the multiple access channel phase and broadcast channel phase become highly non-reciprocal, which significantly complicates the indispensable channel estimation for TWRNs employing coherent detection. In this paper, the challenging problem of channel estimation and data detection (CE-DD) is investigated for amplify-and-forward (AF) orthogonal frequency division multiplexing (OFDM)-based TWRNs over unknown non-reciprocal time-frequency dispersive channels. An independent CE-DD algorithm according to the minimum mean-square error (MMSE) criterion is firstly proposed. To further improve system performance, an iterative joint CE-DD algorithm employing the variational Bayesian inference (VBI) framework is then developed. Simulation results show that initialized 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 supposes perfect knowledge of channel state informations.