In this paper, we consider joint antenna selection and optimal beamforming for energy efficient delay minimization. We assume multiple-input multi-output (MIMO) system with full duplex simultaneous wireless information and power transfer (FD-SWIPT) where each sensor is equipped with a power splitting (PS) system and can simultaneously receive both energy and information from the aggregator (AGG). We show that the antenna selection and beamforming power control policies are adaptive to the energy state information (ESI), the queue state information (QSI) and the channel state information (CSI). We develop an analytical framework for energy efficient delay-optimal control problem based on the theory of infinite horizon partially observable Markov decision process (POMDP). The infinite-horizon POMDP problem is transformed into an equivalent value Bellman program and solved by near-optimal point-based Heuristic Search Value Iteration (PB-HSVI) method under specific standard conditions. The proposed solution outcome is a set of sub-optimal antenna selection and beamforming control policies. Simulation results reveal an effective trade-off between the contradictory objectives (i.e. delay and power consumption) and show the enhancement in delay by using FD-SWIPT systems in comparison to Half Duplex (HD)-SWIPT systems.