Error analysis of noncoherent FSK with variable gain relaying in dual-hop Nakagami-m relay fading channel

This paper analyzes the error performance of two-hop relay network adopting M-ary frequency shift keying (MFSK) with noncoherent detection. It is assumed that dual-hop relay link consists of a source, a relay, and a destination without a direct path signal from the source to the destination and the relay cooperates with the source through the amplify-and-forward (AF) protocol with instantaneous power scaling (IPS) mechanism. Both the links are statistically independent and undergo non-identical flat Nakagami-m fading. Now, assuming perfect frequency and phase synchronization, we derive a closed-form symbol error probability (SEP) expression for noncoherent MFSK following the cumulative distribution function (CDF) based approach. Also, we observe improvement in error performance while comparing our results with a dual-hop relay transmission under average power scaling (APS) constraint. Computer simulations are performed to validate our proposed mathematical analysis. The obtained error probability expression will prove to be useful for achieving the cooperative diversity with multiple dual-hop relays.