Finite-Order Filter Designs for Source and Multiple FDRs in Wideband Cooperative Systems

In this paper, novel finite-order filter designs for source and multiple full-duplex relays (FDRs) are proposed to improve the spectrum efficiency and link reliability of amplify-and-forward cooperative communication networks. In contrast to the single relay, FDRs suffer not only self-interference (SI), but inter-relay interference (IRI). By taking SI and IRI into consideration, this work aims at the joint design of the source filter, relay filters, and the linear minimum squared error (LMMSE) receiver. The finite-order filters are conducted in two stages. In the first stage, the spectrums of the source and FDRs are computed. Since the optimization problem involves the nonlinear equality constraint, we adopt the generic nonlinear equality alternating direction method of multipliers (neADMM) with a damping procedure to find the stationary solution. In the second stage, the filter coefficients are developed to approach the derived spectrums by using a weighted least square criterion. The numerical results justify the validity of the proposed designs. Interestingly, the results show that preserving a certain amount of SI at the FDRs not only reduces the implementation cost but improves the end-to-end signal-to-interference-plus-noise ratio (SINR).