FM click statistics in the presence of phase noise

The probability distribution function of the FM clicks is derived for the case of a carrier impaired by Wiener-Lèvy phase noise and detected by a limiter-discriminator receiver with pre- and post-detection filtering. The analysis is performed accounting for the effects of predetection (RF) filtering on signal and phase noise and holds for \Deltat\nu/B<<1, \Delta\nu being the 3-dB linewidth of the unmodulated carrier and B the bandwidth of the RF filter. How small \Delta\nu/B is to be will depend on the kind of RF filter. For the raised cosine filter with small rolloff \eps considered here the analysis holds for \Delta\nu/B<\eps. For other kinds of filters having transfer functions with smoother rolloffs, such as one- or two-pole filters, the condition \Delta\nu/B<0.1 is sufficient. For these normalized linewidths it is found that the phase noise affects the statistics of the clicks only through the signal envelope changes it causes (FM/AM conversion).