In this letter, we propose a novel power splitting protocol for energy harvesting half-duplex AF relaying communication systems. In our proposed system, the relay harvests energy from the source transmissions, by employing adaptive PS protocol, for powering the retransmissions to the destination. The proposed model system is investigated in cases maximize and non-maximize ergodic capacity. Firstly, we perform the analytical mathematical analysis for deriving the integral closed-form expression of the outage probability and the ergodic capacity. Then, the analytical analysis of the system performance can be convinced by Monte-Carlo simulation with helping Mat Lab software. Finally, the numerical analysis provides practical insights into the effect of various system parameters on the system performance of the proposed system. This paper can be considered as a recommendation for the energy harvesting communication network.