Statistical Behavior of a Fading Signal

Abstract

A general analysis of the statistical behavior of the envelope of a fading signal V (t)e ^iϕ(t) is presented in this paper. The statistics include 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 of V (t) below L per unit time; and the average duration &tbar;(L) of fades below L. The model for the fading signal is a constant vector plus a random interfering vector which represents the resultant of all the received extraneous signals and noise. The theoretical results agree with three empirically observed power relationships obtained in deep fades of nondiversity signals: P(V ≤ L) ∝ L ² , N(L) ∝ L and &tbar;(L) ∝ L. The theoretical results are applicable to a wide class of fading problems. The analysis includes the previous works of Rice, Nakagami, Norton, Vogler, Mansfield, and Short as special cases.