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In this paper, the problem of mutual information maximization in a two-hop multiple-input multiple-output (MIMO) relay network with simultaneous wireless information and power transfer (SWIPT) is investigated, where the relay node, without constant power supply, harvests the energy for information forwarding. The goal is to maximize the mutual information by using the joint design of source and relay precoders, which is formulated as an optimization problem under the constraints of transmit power and harvested energy. Two scenarios with practical energy harvesting schemes employed at the relay, i.e., power splitting (PS) and time switching (TS) schemes, are considered. Although the formulated optimization problems in the two scenarios are both nondeterministic polynomial-time (NP)-hard, by exploiting the structure of the optimization problems and analyzing the characteristics of precoders, we develop near optimal joint source and relay precoding algorithms for them. Additionally, we analyze the feasible regions of PS and TS ratios, respectively, and propose a backtracking line search based method to find near optimal PS and TS ratios. The main contributions of this paper are as follows: 1) Unlike existing works based on the assumption of ideal Gaussian signals, this paper supposes the inputs to the network are finite-alphabet signals, which is a more practical scenario. 2) The high complexity of mutual information with finite-alphabet signals leads to an intractable optimization problem; however, an efficient solving framework based on semidefinite relaxation (SDR) and Karush-Kuhn-Tucker (KKT) theorem is proposed. Finally, simulation results verify the efficacy of the proposed joint precoding designs.

Joint Precoder Design for SWIPT-Enabled MIMO Relay Networks With Finite-Alphabet Inputs