Difference threshold test for M-FSK signaling with Reed-Solomon coding and diversity combining in Rayleigh fading channels

The difference threshold test (DTT) is considered as a reliability measure in noncoherent M-ary orthogonal frequency shift keying signaling with Reed-Solomon coding and diversity combining under the multichannel environment. The DTT declares erasures when the difference between the largest and second largest energy detector outputs does not exceed a given threshold. We show that the DTT outperforms the ratio threshold test (RTT) for finite modulation size and diversity order. The asymptotic performance for infinite modulation size and diversity order is then investigated. It is proved that the minimum signal-to-noise ratio (SNR) required to achieve error-free communication for the DTT is the same as that for the RTT.