Error Performance Analysis and PS Factor Optimization for SWIPT AF Relaying Systems over Rayleigh Fading Channels: Interpretation SWIPT AF Relay as Non-SWIPT AF Relay

This paper presents an analytical study of the bit error rate (BER) and signal-to-noise ratio (SNR) performance in simultaneous wireless information and power transfer (SWIPT) amplify-and-forward (AF) relaying systems over Rayleigh fading channels. A power-splitting (PS) protocol is employed at the energy-constrained relay to divide the received signal for concurrent energy harvesting and information processing. Closed-form and asymptotic BER expressions are derived based on exact and bounded moment-generating functions (MGFs), offering insights into how the SNR balance between the source–relay (SR) and relay–destination (RD) links influences system performance. An asymptotic BER expression further reveals that a SWIPT AF relay system can be interpreted as a generalized AF relaying model, sharing the same diversity order as conventional AF systems. Based on this interpretation, an optimization method for the PS factor is proposed, effectively reducing the BER by reinforcing the weaker link. Simulation results confirm the tightness of the derived expressions and the effectiveness of the optimization strategy. Moreover, the analytical framework is extended to multiple SWIPT relaying systems, where multiple relays operate with individually optimized PS ratios. For such configurations, approximations for the system BER, outage probability, and channel capacity are derived and validated. Results demonstrate that increasing the number of relays significantly improves system performance, and the proposed analysis accurately captures these performance gains under varying channel conditions.