Robust Tomlinson-Harashima Precoding With Gaussian Uncertainties for SWIPT in MIMO Broadcast Channels

Nonlinear transceiver based on Tomlinson-Harashima (TH) precoding outperforms the linear minimum mean-square-error (MSE) architecture in terms of minimum achievable MSE. In this paper, we investigate nonlinear TH precoding design problem for simultaneous wireless information and power transfer in multiple-input-multiple-output broadcast channels, where there are one information-decoding (ID) receiver and multiple energy harvesting (EH) receivers. We consider the scenario that the transmitter knows imperfect channel state information of all links and the channel uncertainties are modeled by Gaussian random variables. Our objective is to jointly optimize TH precoding matrices and linear equalizer to minimize average MSE subject to transmit power constraint and EH constraints on average harvested power. We transform the robust transceiver design problem into a difference of convex programming and propose a constrained concave convex procedure (CCCP) based locally optimal solution. To reduce computational complexity, we propose a noniterative upper bound based suboptimal solution that minimizes the upper bound on average MSE. We also extend the CCCP-based locally optimal solution to the single group multicast scenario where there are multiple ID receivers. Simulation results demonstrate that our proposed TH precoding transceiver design achieves lower average MSE than linear precoding transceiver design.