Distributed Detection in Sensor Networks Over Fading Channels With Multiple Antennas at the Fusion Centre

Abstract

We develop new and optimal algorithms for distributed detection in sensor networks over fading channels with multiple receive antennas at the Fusion Centre (FC). Sensors observe a hidden physical phenomenon over fading channels and transmit their observations using the amplify-and-forward scheme over fading channels to the FC which is equipped with multiple antennas. We derive the optimal decision rules and the associated probabilities of detection and false alarm for three scenarios of Channel State Information (CSI) availability. For the most difficult case of unknown CSI, we develop two new algorithms to derive the optimal decision rule. The first is based on a Gaussian approximation method where we quantify the approximation error and its rate of convergence (to a true Normal distribution) via a multivariate version of the Berry-Esseen bound. The second is based on a multivariate Saddle-point (Laplace) approximation which is obtained via a non-convex optimisation problem which is solved efficiently via Bayesian Expectation-Maximisation method. We show under which system configuration which algorithm is suitable and should be used. For cases where the distribution of the optimal decision rule can not be derived exactly, we develop a Laguerre series expansion to approximate the resulting distribution. The performance of the proposed algorithms is evaluated via analytic bounds and numerical simulations. We show that the detection performance of the proposed algorithms is significantly superior to a local vote decision fusion based algorithms.