## 1 Introduction  
Wireless sensor networks (WSNs) have attracted a significant amount of attention from researchers and have been widely employed in vast and varied areas, e.g., object tracking, habitat monitoring, military systems, and industrial areas [1; 2; 3]. However, in WSNs, the relay or sensor nodes are typically powered by batteries with finite capacities [4], which are difficult or impossible to replace or recharge in most cases. Thus, the energy supplies will limit the lifetime of WSNs. Saving on energy or prolonging the operation time of energy-constrained nodes has become an important research issue in WSNs. Traditionally, multi-input multi-output (MIMO) can provide an effective way for energy saving [5; 6]. Recently, simultaneous wireless information and power transfer (SWIPT) is considered a promising energy-harvesting (EH) technique to solve the energy scarcity problem and to achieve perpetual communications in energy-constrained WSNs [7; 8; 9], which is extensively applied in the area. To date, two receiver architectures proposed in Reference [10], namely time switching (TS) and power splitting (PS), have been widely used for a colocated energy harvester and information decoder in SWIPT systems [11; 12]. Compared with the TS structure periodically switching between the EH module and information decoding (ID) module, the PS design allows the receiver to complete EH and information processing in the same phase [13; 14; 15; 16; 17]. In Reference [14], the energy-efficient cooperative transmission problem for SWIPT and the power transfer in clustered WSNs was discussed, where the PS architecture was equipped with the receiver. In Reference [15], the joint transceiver design for full-duplex (FD) MIMO SWIPT systems with a PS mode was considered in order to minimize the mean square error (MSE). In Reference [16], the secrecy outage probability minimization problem for the decode-and-forward (DF) relay SWIPT systems with a PS scheme was analyzed. In Reference [17], the energy efficiency problem for SWIPT in a MIMO bidirectional amplify-and-forward (AF) relay network was formulated, where a receiver applied the PS scheme to harvest energy. In the SWIPT context, conventionally, most networks are assumed to operate in the half-duplex (HD) communication mode [18; 19; 20; 21; 22]. Therein, in Reference [19], the performance of an HD bidirectional wireless sensor network (BWSN) with a TS EH strategy was analyzed. In Reference [20], a joint resource optimization scheme for the DF relay SWIPT cognitive sensor networks was proposed. In Reference [21], the authors investigated the joint source and the relay beamforming design in HD sensor networks with SWIPT. The joint source and relay precoding design for the HD bidirectional relay network (BRN) using a PS scheme was proposed in Reference [22]. However, in HD networks, communication nodes can either transmit or receive on a single frequency but not simultaneously [23]. Due to this characteristic, half of the spectrum resources are theoretically wasted. Recent advances suggest that the FD mode enables the concurrent transmission and reception of user signals over the same frequency band for which it can provide nearly double the improvement in spectral efficiency than HD [24]. Therefore, much interest has been turned to incorporating the networks into the FD [25; 26; 27; 28; 29; 30; 31; 32]. Thereinto, in Reference [25], an FD MIMO one-way relay network (OWRN) aided by SWIPT was considered to solve the source and relay beamforming optimization problem using minimum mean-square-error (MSE) criterion. In Reference [26], a joint source and relay beamforming optimization for the FD one-way wireless sensor network (OWSN) with SWIPT using MSE minimization criterion was considered. In Reference [27], the transmission rate maximization problem for an FD OWRN powered by a wireless energy transfer was discussed.