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

In this paper, we consider the problem of decentralized binary detection in sensor networks characterized by nonconstant observation signal-to-noise ratios (SNRs) at the sensors. In general, the SNRs at the sensors could have a generic nonconstant distribution. In order to analyze the performance of these decentralized 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 the noise in the communication links between the sensors and the access point (AP) depends on the sensor SNR profile. More precisely, we compare different sensor SNR profiles under two assumptions: (i) common maximum sensor SNR or (ii) common average sensor SNR. Finally, we perform an asymptotic (for a large number of sensors) analysis of the network performance, deriving a simple expression for the limiting probability of decision error.