In this paper, we provide a closed-form approximation of the Full-duplex Simultaneous wireless information and power transfer (SWIPT) multi-user MIMO (MU-MIMO) system signal-to-interference-and-noise ratio (SINR) distribution for the received signal at the sensor users with perfect and imperfect channel state information (CSI) and transmit antenna selection scheme at the transmitter. We also studied the SINR distribution of the uplink with Zero-Forcing beamforming (ZFBF) and antenna selection at the aggregator (AGG) receiver with transmit antenna selection. The downlink SINR with perfect and imperfect CSI is modeled by a multivariate Beta type II distribution and the uplink with perfect and imperfect CSI is modeled with multivariate Wishart distributions. We compared the proposed distributions analytical results to the Monte-Carlo simulations and we obtained a perfect match.