Transmission of MFSK Signals in Several Frequency Uncertain Channels

The performance metric (symbol error rate) of the optimum in-the-limit receivers for the detection of a frequency uncertain
M
-ary frequency shift-keyed (MFSK) transmission in additive Gaussian noise is derived. By in-the-limit, we mean the limiting cases of high and low signal-to-noise ratio (SNR). The performance of the two receivers are compared for some special cases. The MFSK wide-band receiving (optimum low SNR receiver for the channel Just described) symbol error rate in a three component-two-path channel is derived when the delay between the direct path and reflected path compared with the data rate is very small.