Bayesian Radio Map Estimation: Fundamentals and Implementation via Diffusion Models

Radio map estimation (RME) is the problem of inferring the value of a certain metric (e.g. signal power) across an area of interest given a collection of measurements. While most works tackle this problem from a purely non-Bayesian perspective, some Bayesian estimators have been proposed. However, the latter focus on estimating the map itself, the Bayesian standpoint is adopted mainly to exploit prior information or to capture uncertainty. This paper pursues a more general formulation, where the goal is to determine the posterior distribution of the map given the measurements. Besides handling uncertainty and allowing standard Bayesian estimates, solving this problem is seen to enable minimum mean square error estimation of arbitrary map functionals (e.g. capacity, bit error rate, or coverage area to name a few) while training only for power estimation. A general Bayesian estimator is proposed based on conditional diffusion models and both the Bayesian and non-Bayesian paradigms are compared analytically and numerically to determine when the Bayesian approach is preferable.