Decentralized binary detection with non-constant SNR profile at the sensors

In this paper, we consider the problem of decentralised binary detection in sensor networks characterised by non-constant observation Signal-to-Noise Ratios (SNRs) at the sensors. In general, SNRs at the sensors could have a generic non-constant distribution. In order to analyse the performance of these decentralised detection schemes, we introduce the concept of sensor SNR profile, and we consider four possible profiles (linear, quadratic, cubic and hyperbolic) as representative of a large number of realistic scenarios. Furthermore, we show how the impact of communication noise in the links between the sensors and the Access Point (AP) depends on the sensor SNR profile (i.e. the spatial distribution of the observation noise). More precisely, different sensor SNR profiles are compared under two alternative assumptions: (i) common maximum sensor SNR or (ii) common average sensor SNR. Finally, we propose an asymptotic (for a large number of sensors) performance analysis, deriving a simple expression for the limiting probability of decision error. We validate our theoretical analysis with experimental results.