Axis-Crossing Intervals of Rayleigh Processes
A. J. Rainal · Bell System Technical Journal · 1965
Let R(t,a) denote the envelope of a stationary random process consisting of a sinusoidal signal of amplitude$\sqrt{2a}$and frequen f010 plus Gaussian noise of unit variance having a narrow-band power spectral density which is symmetrical about f0. When a = 0 Rice1presented some theoretical results which are very useful for studying statistical properties of the axis-crossing intervals of R(t,0). The axis-crossing points and the axis-crossing intervals of the Rayleigh process R(t,a) are defined in Fig. 1. Some recent work concerning the axis-crossing in tervals of R(t,a) was reported by Levin and Fomin2, Goryainov,3and Rainal.4,5The purpose of this brief is to present some theoretical results when a ≧ 0, These results stcm from a straightforward extension of Rice's analysis. The Rayleigh process R(t,a) occurs at the output of a typical radio or radar receiver duringing the reception of a sinusoidal signal immersed in Gaussian noise.