The Conversion of Area Distributed, Incidental Radio Noise Envelope Distribution Functions by Radio Propagation Processes

The central limit theorem may be invoked for man-made incidental radio noise to establish the limiting statistical distribution which is approached as either the noise source-to-observer distance or the observation frequency is increased. As these parameters separately increase, the distribution of the received noise-voltage envelope for either surface or airborne noise is shown to approach a Rayleigh distribution. Conversion of the impulsive noise voltage envelope distribution to a Rayleigh distribution occurs through a combination of effects associated with both the radio propagation process and the spectral density of the noise sources. Free-space spreading and the dispersion of irregular terrain for low-height antennas are the propagation processes which contribute to the conversion of the noise statistics measured by constant-gain antennas. The noise emission spectra, derivable from a Poisson process below the VHF band and from a white-noise process in the upper VHF and UHF bands contribute the second factor to the noise-dispersion function. Existing in-flight observations, although qualitative, of impulsive noise distribution transformations with increasing range are predicted. Additional predictions of impulsive noise-voltage envelopedistribution conversion to a Rayleigh distribution are made for both airborne and surface observations as either the observation frequency or the range increases.