Effect of Narrow-Band Filters on the Error Probability of M-ary FSK with a Limiter-Discriminator-Integrator Detector

We derive an equation for the error probability of
M
-ary frequency shift keying with a limiter-discriminator-integrator detector in the presence of narrow-band filters in the transmitter and receiver. We present numerical results for the case of quaternary symbols, wide-band transmitter filter, and Butterworth filter in the receiver with 2, 3, and 4 poles. We optimize the sampling time and threshold setting for various values of filter bandwidth. We show the sensitivity of the error probability to errors in sampling time and threshold setting.