Bayesian estimation of mean transmission loss along multiple paths with randomly scattered signals

A general problem is considered in which a source of unknown power transmits to multiple receiver locations. The signal is randomly scattered along each transmission path, for example, by turbulence, a forest, or buildings. At each receiver location, one or more observations of the signal power are collected. It is assumed that the functional form of the probability density function (pdf) of the received signals (an exponential pdf for strong scattering, or a gamma pdf for weak scattering) is known based on an understanding of the scattering process, although the mean transmission losses (TLs) from the source to receivers are uncertain. From the signal observations, we wish to estimate the mean power of the source and the mean TLs for each path. A Bayesian formulation for this problem is presented. An inverse gamma prior is used for the TL, which is the conjugate prior for the exponential or gamma scattered signal pdf (likelihood function). Analytical solutions are then derived for a number of limiting scenarios: (1) unscattered signals along multiple paths with dependent TLs, (2) strongly scattered signals along multiple paths with the same TL, and (3) weakly or strongly scattered signals along multiple paths with independent TLs.A general problem is considered in which a source of unknown power transmits to multiple receiver locations. The signal is randomly scattered along each transmission path, for example, by turbulence, a forest, or buildings. At each receiver location, one or more observations of the signal power are collected. It is assumed that the functional form of the probability density function (pdf) of the received signals (an exponential pdf for strong scattering, or a gamma pdf for weak scattering) is known based on an understanding of the scattering process, although the mean transmission losses (TLs) from the source to receivers are uncertain. From the signal observations, we wish to estimate the mean power of the source and the mean TLs for each path. A Bayesian formulation for this problem is presented. An inverse gamma prior is used for the TL, which is the conjugate prior for the exponential or gamma scattered signal pdf (likelihood function). Analytical solutions are then derived for a number of limiting sc...