Nonlinear MIMO Transceivers Improve Wireless-Powered and Self-Interference-Aided Relaying

This paper investigates the design of robust nonlinear transceivers conceived for multiple-input multiple-output full-duplex wireless-powered relay networks in the face of realistic imperfect channel state information (CSI). A novel self-energy recycling aided relaying protocol is employed, whereby the relay node benefits from energy harvesting (EH) gleaned from the self-interfering link in addition to its primary energy. The proposed nonlinear transceiver relies on a Tomlinson-Harashima (TH) precoder along with an amplify-and-forward (AF) relaying matrix and a linear receiver, where the TH precoder is composed of a feedback matrix and a source precoding matrix. Two different criteria are considered for the robust design of the nonlinear transceiver in the presence of channel estimation errors modeled by the Gaussian distribution. The first one aims to minimize the mean-squared-error (MSE) at the destination subject to a transmit power constraint at the source and an EH constraint at the relay. The resultant optimization problem is converted to four subproblems and solved via an alternating optimization (AO) algorithm that iteratively updates the transceiver coefficients by sequentially addressing each subproblem, while keeping the other matrix variables fixed. The second design criterion aims to minimize the transmit power at the source under both MSE and EH constraints. Similarly, an AO-based iterative algorithm is proposed for solving this problem. Our simulation results show that the robust design advocated is capable of alleviating the effects of CSI errors, hence improving the robustness of the system over that of the corresponding linear designs.