Simultaneous wireless information and power transfer (SWIPT) relay networks represent a paradigm shift in the development of wireless networks, enabling simultaneous radio frequency (RF) energy harvesting (EH) and information processing. Different from conventional SWIPT relaying schemes, which typically assume the availability of perfect channel state information (CSI), here we consider the application of noncoherent modulation in order to avoid the need of instantaneous CSI estimation/tracking and minimise the energy consumption. We propose a unified and comprehensive analytical framework for the analysis of time switching (TS) and power splitting (PS) receiver architectures with the amplify-and-forward (AF) protocol. In particular, we adopt a moments-based approach to derive novel expressions for the outage probability, achievable throughput, and average symbol error rate (ASER) of the considered SWIPT system. We quantify the impact of several system parameters, involving relay location, energy conversion efficiency, and TS and PS ratio assumptions, imposed on the EH relay terminal. Our results reveal that the throughput performance of the TS protocol is superior to that of the PS protocol at lower receive signal-to-noise (SNR) values, which is in contrast to the point-to-point SWIPT systems. An extensive Monte Carlo simulation study is presented to corroborate the proposed analysis.