Closed-form error analysis of noncoherent FSK for dual hop relay network in Nakagami-m fading channel

We analyze the end-to-end error performance of M-ary frequency shift keying (MFSK) with noncoherent detection over independent and non-identical flat Nakagami-m fading channels. A dual-hop relay transmission using amplify-and-forward (AF) protocol with average power scaling (APS) mechanism is considered. Generalized closed-form expressions for the average symbol error probability (ASEP) of noncoherent MFSK has been obtained following the cumulative distribution function (CDF) approach. Moreover, we derive a simplified closed-form expression for the ASEP over high signal-to-noise ratio (SNR) over the source-relay link. Computer simulations are performed to validate our proposed mathematical analysis. The obtained error probability expressions will help the design of two-hop relay networks adopting MFSK in determining various system parameters such as the transmission power at the source and the gain factor at the relay.