Multi-bit Decentralized Detection through Fusing Smart and Dumb Sensors based on Rao Test

Abstract

We consider Decentralized Detection (DD) of an unknown signal corrupted by zero-mean unimodal noise via Wireless Sensor Networks (WSNs). We assume the presence of both smart and dumb sensors: the former transmit unquantized measurements, while the latter employ multi-level quantizations (before transmission through binary symmetric channels) in order to cope with energy and/or bandwidth constraints. The data are received by a Fusion Center (FC), which relies on a proposed Rao test, as a simpler alternative to the Generalized Likelihood Ratio Test (GLRT). The asymptotic performance analysis of the multi-bit Rao test is provided and exploited to propose a (signalindependent) quantizer design approach by maximizing the noncentrality parameter of the test-statistic distribution. Since the latter is a non-linear and non-convex function of the quantization thresholds, we employ the particle swarm optimization algorithm for its maximization. Numerical results are provided to show the effectiveness of Rao test in comparison to GLRT and the boost in performance obtained by (multiple) threshold optimization. Asymptotic performance is also exploited to define detection gain measures allowing to assess gain arising from (a) use of dumb sensors and (b) increasing their quantization resolution.