Statistical Behavior of a Fading Signal

A general analysis of the statistical behavior of the envelope V(t)e"t'(n of a fading signal is presented in this paper. Our principal interests are the probability, P(V ^ L), that the amplitude V(t) will fade below a specified signal level L* ; the expected number, N(L), of fades per unit time below the specified level L; and the average duration, t(L), of fades below L. These statistics are all functions of the signal level L. The theory presented herein has been developed to complement and extend the empirical results developed by my colleagues at Bell Telephone Laboratories1 ~e from their extensive experimental experience. Published data of other workers have also been considered. The previous theoretical works on the statistics of a fading signal often assume a complex Gaussian model for the fading signal. The theoretical support for this assumption is that, by the central limit theorem, the real and the imaginary parts of the sum of a large number of independent interfering signals will be approximately Gaussian. * More precisely speaking, in a long time period containing a large number of fades, the distribution P(V ^ L) represents the expected fraction of this long time period that the signal amplitude V will fade below L. 3211