Optimal Sensor Power Allocation for Decentralized Detection in Power Constrained Wireless Sensor Networks

Abstract

We consider a distributed detection network where several sensors amplify and forward their local observations over parallel access channels (PAC) to a fusion center (FC) in order to detect the presence or absence of a deterministic signal in Gaussian noise. Two observation models are studied: i) conditionally independent observations and ii) conditionally correlated observations obeying first-order autoregressive model. Log Likelihood ratio test (LLRT) based detectors are considered at the FC. Closed-form expressions for probability of detection and probability of false alarm are derived to determine the system performance of the proposed scheme. Optimal sensor transmit gains are determined to maximize detection performance under a total power constraint (TPC). Optimal power allocation scheme shows improvement in probability of error performance over equal power allocation scheme for both cases. Finally, it is shown that equal power allocation is asymptotically optimal for both models, as total power becomes infinitely large, irrespective of differences in the path losses in PAC.