Performance Study for SWIPT Cooperative Communication Systems in Shadowed Nakagami Fading Channels

In this paper, we investigate the performance of simultaneous wireless information and power transfer (SWIPT) cooperative amplify-and-forward (AF) communication systems in shadowed Nakagami- $m$ fading channels. Both coherent and non-coherent modulations, namely, binary phase-shift keying (BPSK) and binary differential phase-shift keying (BDPSK) are considered. We propose closed-form expressions of the moment generating function (MGF) and the probability density function (PDF) for the received signal-to-noise ratio (SNR) of the cooperative link. Based on this, we further derive the average bit-error-rate (BER) and the outage probability expressions for the systems with both BPSK and BDPSK modulations. All of these expressions are given in closed-form except one in single integral that can be easily evaluated using numerical integration methods. Numerical results are used to confirm the validity of the proposed analytical results. It is shown that the performance of the systems is more susceptible to the fading parameter $m$ than to the shadowing level $\sigma_s$ and does not change much with the power splitting ratio.