On the level crossing statistics of phase and random FM noise in Nakagami-Q mobile fading channels

Level crossing statistics of phase and random FM noise are studied for Nakagami-q fading channels. Closed form expression for the probability density function of random FM is first derived. Level crossing rate of the phase process is then obtained for an arbitrary crossing level of the phase. Also, conditional probability density functions of random FM and envelope processes, conditioned on crossings of an arbitrary level of the phase, are investigated. It is shown that the derived analytical results are in excellent agreement with those obtained by computer simulations. The results are useful, for example, for the study of the statistics of click noise and phase locked loop schemes when considering the trans- mission over Nakagami-q mobile fading channels.