Point-process based localization of primary users in collaborative dynamic spectrum access

In this paper, we propose a statistical estimation framework to estimate Primary User (PU) transmitter locations by using the spatial characterization of spectrum usage in a collaborative spectrum sensing context in Dynamic Spectrum Access (DSA) networks. First, a statistical likelihood model of the received power by collaborating Secondary Users (SUs) is constructed by assuming a propagation model and known PU transmitter locations. The added value of the paper is the improvement of this likelihood model by adding the a priori information on the PU transmitter locations in the form of spatial densities and point interactions taken from the theory of point processes. The resulting models are used in a statistical optimization framework to find the Maximum Likelihood (ML) and Maximum A Posteriori (MAP) estimates of the number of PU transmitters and their locations. Since the ML and the MAP estimations do not accept tractable closed-form analytical formulations, we propose to solve the optimization problems by the numerical Nelder-Mead algorithm. To assess the performance, the resulting random field is considered in the form of an interference map. The effects of the number of collaborating SUs, the shadowing standard deviation and the ratio of the number of SUs to the number of PU transmitters on the estimation quality are also evaluated.