Non-Rayleigh signal statistics in clustered statistically homogeneous rain

Abstract

As the sample volume of a remote sensing instrument moves through sufficiently variable conditions, recent work shows that the amplitudes and associated intensities can deviate significantly at times from expectations based on Rayleigh signal statistics because fluctuations in the number of scatterers leads to a doubly stochastic measurement process. While non-Rayleigh deviations yield average biases for both logarithmic and linear detectors, perhaps of greater importance is the enhancement of the variance of the bias distribution for square law detectors. In this work the authors explore the potential existence of non-Rayleigh effects even in the statistically homogeneous rain when fluctuations in the number of scatterers should be much less than for the inhomogeneous conditions used in earlier studies. Moreover, in contrast to previous work, recent advances now permit the simulation of correlated rainfall structures having the statistical characteristics of natural rain such as clustering intensity (Hebrew Aleph) and coherence length (X(f)) consistent with observations. The primary objective of this work, then, is to clarify how Hebrew Aleph, X(f), and the geometric parameters characteristic of remote sensing observations such as the distance over which an estimate is made (L), the beamwidth (B), and the spatial displacement between successive independent samples (Δ) affect non-Rayleigh signals statistics in statistically homogeneous rain. This work shows that non-Rayleigh effects can appear whenever Δ ≤ X(f) ≤ L. Moreover, the magnitudes of the non-Rayleigh deviations increase as Hebrew Aleph and Δ/B increase. Although non-Rayleigh effects can be detected by monitoring of the signals, keeping both Δ/B and L as small as possible while increasing sample independence using chirp or signal whitening techniques, for example, should help to minimize non-Rayleigh effects for radars even in statistically inhomogeneous rain.