Dependence of minimum propagation distance and related attenuation of radio disturbance on the density of randomly located emitters and receivers in limit setting model

The statistical properties of the minimum propagation distance and the related radio propagation loss are theoretically analyzed assuming randomly distributed disturbance sources and receivers for application to the radio-protection limit setting model. It is shown that the minimum distance follows a Rayleigh distribution whose mean-square distance is inversely proportional to the area density of the disturbance sources or that of victim receivers. By using a magnetic dipole model on a metal ground, propagation losses in the near and far fields are presented with the introduction of a piecewise approximation. On the basis of the above results, the probability density function (PDF) of the minimum propagation loss is derived and numerically calculated for various area densities and radio frequencies by a comparison with a log-normal approximation of the PDF. It is found that each PDF exhibits its maximum at a propagation loss related to the root-mean-square minimum propagation distance. The log-normal PDF demonstrates a good approximation of the exact PDF at around its maximum, and enables a rough estimation of the statistics of the propagation loss. The mean value and standard deviation of the minimum propagation loss are also presented for application to the emission limit setting model.