BER analysis for noncoherent FSK in two-hop relay networks

We analyze the bit-error rate (BER) performance of two-hop relay networks with the amplify-and-forward protocol over Rayleigh fading channels. A relay network adopting noncoherent frequency shift keying (FSK) is considered. We begin by deriving the exact closed-form BER expression for M-ary FSK (MFSK) with perfect frequency synchronization and then obtain the exact BER with a triple integral for MFSK with imperfect frequency synchronization. For a special and practically important case, binary FSK (BFSK) with imperfect frequency synchronization, we obtain the exact BER expression with one integral and then a series expansion of the exact BER expression, which does not require any numerical calculation.