Adaptive Power-Splitting Optimization and MGF-Based SER Analysis for SWIPT AF Relay Systems

This paper investigates adaptive power splitting (PS) for amplify-and-forward (AF) simultaneous wireless information and power transfer (SWIPT) relay systems operating over independent Rayleigh fading channels. Unlike conventional PS schemes optimized according to average channel statistics or a specific long-term performance metric, the proposed method selects the PS ratio using the instantaneous end-to-end signal-to-noise ratio (SNR). By adopting a high-SNR approximation for the source-to-relay link, we uncover a crucial structural insight where the derived optimal PS factor depends exclusively on the instantaneous relay-to-destination (RD) channel state. This offers clear analytical transparency compared to existing complex full-channel state information (CSI) approaches. Leveraging this insightful closed-form expression, we then derive an exact integral representation of the moment-generating function (MGF) of the optimized SNR. Because this representation does not generally reduce to a simple closed form, two tractable upper bounds are developed for symbol error rate (SER) evaluation. Monte Carlo simulations validate the analytical results under independent Rayleigh fading and show that instantaneous SNR-based PS achieves lower SER than the considered fixed and average-statistics-based policies over the simulated operating range.