Detection of Transmission State of Multiple Wireless Sources: A Statistical Mechanics Approach

Abstract

Consider a random network of static primary wireless sources and a co-located network of secondary wireless devices. The channel coefficients between the two networks are assumed to be known to the secondary users (SUs), e.g., using radio environment maps (REM). However, the operational state of the sources is unknown due to intermittency. In this paper, we study the performance of primary source detection by SUs using a message-passing algorithm. Additionally, we employ methods from statistical mechanics, in particular, the Replica approach, to obtain analytic results for the performance of such networks in the large system-size limit. We test the results through a large-scale simulation analysis, obtaining good agreement. The proposed method provides a simple way to evaluate the performance of the system and assess how it depends on the macroscopic parameters that characterize it, such as the average density of SUs and sources and the signal-to-noise ratio. The main contribution of this paper is the application of an algorithm that quantitatively predicts the parameter value region for which accurate and reliable detection of the operational state of the primary sources can be achieved in a fast and decentralized manner.