EM Based Joint Estimation of Frequency Offsets and Channel Gains for TWR-OFDM Systems

Two-way relay network (TWRN) with orthogonal frequency division multiplexing (OFDM) is an emerging paradigm, for high spectral efficiency, increased capacity in 5G wireless communications. The TWRN allows bidirectional information exchange between two users with the assistance of intermediate relay nodes by efficiently using the available spectral resources. By removing back- propagating self-interference each source node obtains the information of other source node. The accuracy of the self-interference cancellation heavily depends on the precision of the joint estimation of impairments i.e. tracking the individual oscillators and perfect channel state information (CSI). In this paper, we propose two expectation maximization (EM) based algorithms, expectation conditional maximization (ECM) and space alternating generalized expectation maximization (SAGE) which iteratively estimate multiple carrier frequency offsets (MCFOs) and frequency-selective channel coefficients in amplify-and-forward (AF) multi-relay cooperative TWR communication systems over a quasi-static channel. The Cramer-Rao lower bounds (CRLBs) for the joint estimation of multiple impairments are derived. The mean square error (MSE) performances of the proposed estimators achieve corresponding CRLBs. The performance is also evaluated by means of system bit error rate (BER). SAGE based algorithm greatly reduces the complexity compared to the ECM based algorithm.