Difference threshold test for M-ary orthogonal FSK signaling in Rayleigh fading channels

We present the difference threshold test (DTT) for M-ary orthogonal frequency shift keying (FSK) signaling in Rayleigh flat fading channels. The proposed DTT declares an erasure whenever the difference between the largest and the second largest energy detector outputs does not exceed a fixed threshold. We show that the DTT is an approximation of the Bayesian erasure test, but provides almost the same performance as the Bayesian erasure test. For (7, 3) and (31, 15) Reed-Solomon (RS)-coded systems, the DTT provides power gains of 0.8 dB and 0.4 dB over the ratio threshold test (RTT), respectively. We prove that the limiting performance of the DTT approaches that of the RTT for very large M.