Physical layer security is a key issue in the full duplex (FD) communication systems due to the broadcast nature of wireless channels. In this paper, the joint design of information and artificial noise beamforming vectors is proposed for the FD simultaneous wireless information and power transferring (FD-SWIPT) systems. To guarantee high security and energy harvesting performance of the FD-SWIPT system, the proposed design is formulated as a sum information transmission rate (SITR) maximization problem under information-leakage and energy constraints. In addition, we consider the fairness issue between the uplink and downlink information transmission rates by formulating a fairness-aware SITR-maximization problem. Although the formulated SITR-maximization and fairness-aware SITR-maximization problems are non-convex, we solve them via semidefinite relaxation and one-dimensional search. The optimality of our proposed algorithms is theoretically proved, and the computation complexities are established. Moreover, we propose two suboptimal solutions to the formulated optimization problems. In terms of the SITR-maximization problem, numerical results show that the performance achieved by one of the two suboptimal algorithms is close to the performance of the optimal algorithm with increasing maximum transmission power of the FD-BST.The upsurging wireless data volume drives the industrial and academic communities to search for efficient ways to boost the usage of the already scarce radio-frequency (RF) spectrum in the fifth generation (5G) wireless communication systems [1]. Full-duplex (FD) technology is considered as one of the promising solutions to improve the RF spectrum utilization due to its ability to double the spectrum efficiency. Moreover, energy efficiency is enhanced given the unchanged power consumption and improved spectrum efficency [1], [2]. However, FD nodes suffer from a strong loopback self-interference (LSI) due to the short distance between the transmitter and receiver sides on an FD node. Several LSI cancellation techniques are proposed in the FD literature, e.g., natural isolation [3], digital-analog domain cancellation [4], and spatial suppression [5]- [7]. By placing the absorptive shielding in the LSI channel, the natural isolation is attractive due to its implementation simplicity. However, the effectiveness of the natural isolation is limited by the form-factor of the wireless devices (i.e., the smaller the device, the less room to implement the isolator). It is even the case that using a high-end duplexer may not be sufficient for communication [5]. An alternative scheme to cancel the LSI is by using the digital and/or analog domain cancellation techniques. However, the dynamic range of the reception circuits is a bottleneck to cancel the strong LSI [2], [8]. As a result, spatial suppression, which is based on the spatial diversity to suppress the LSI, is required before further processing of the received signals [5]-[7]. Simultaneous wireless information and power transferring (SWIPT) sys...