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This paper considers the problem of mutual information maximization in a two-hop relay network with simultaneous wireless information and power transfer (SWIPT), where the relay nodes use the power splitting (PS) scheme to harvest the energy for information forwarding. Unlike previous research, this paper focuses on a more practical scenario, where the inputs to the network are assumed to be finite-alphabet signals. Although each node in the network is assumed to have single antenna, we show that the relay network can be regarded as an effective multiple-input multiple-output (MIMO) system. Our goal is to perform the joint optimization on the precoder at source and PS ratio at relays to maximize the mutual information. Although the formulated problem is nondeterministic polynomial-time (NP)-hard, we theoretically analyze the optimal PS ratio; then, by using the structure of optimization problem, a near optimal precoder design based on semidefinite relaxation (SDR) is proposed; further, to reduce the complexity of algorithm, another precoder design based on search technique, which exploiting the structure of precoder, is developed only with a slight performance degradation. Simulation results verify the efficacy of proposed precoder designs.INDEX TERMS Finite-alphabet inputs, precoder design, SWIPT, relay network.

This paper investigates the performance of linear precoders in massive multiple-input multipleoutput (MIMO) systems. Different from the existing research, in this paper, we consider a more realistic scenario, where the input signals are taken from finite-alphabet constellation sets, such as phase shift keying (PSK) or quadrature amplitude modulation (QAM), instead of Gaussian signals. The expressions are derived for the achievable mutual information with two commonly known linear precoders, i.e., zero forcing (ZF) and matched filter (MF), in the scenarios were perfect and imperfect channel state information (CSI) is known at the base station (BS). Also, the performance upper bound of mutual information with precoding techniques is analyzed. Both the theoretical analysis and simulation results show that ZF and MF precoders are near optimal when the number of antennas equipped at the BS is much larger than the number of users, which is similar to the case of Gaussian inputs. However, different from the Gaussian inputs, for the case of finite-alphabet inputs, the increase in the number of antennas does not always mean the improvement of performance; specifically, after the number of antennas at the BS, reaches a certain value, more antennas actually almost have no help for the performance improvement of mutual information, which is true whether the CSI is perfect or imperfect.

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 finitealphabet 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. INDEX TERMS Finite-alphabet inputs, joint precoding design, simultaneous wireless information and power transfer (SWIPT), multiple-input multiple-output (MIMO), relay network.

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