On Power Allocation for Distributed Detection With Correlated Observations and Linear Fusion

Abstract

We consider a binary hypothesis testing problem in an inhomogeneous wireless sensor network, where a fusion center (FC) makes a global decision on the underlying hypothesis. We assume sensors' observations are correlated Gaussian and sensors are unaware of this correlation when making decisions. Sensors send their modulated decisions over fading channels, subject to individual and/or total transmit power constraints. For parallel-access channel (PAC) and multiple-access channel (MAC) models, we derive modified deflection coefficient (MDC) of the test statistic at the FC with coherent reception. We propose a transmit power allocation scheme, which maximizes MDC of the test statistic, under three different sets of transmit power constraints: total power constraint, individual and total power constraints, individual power constraints only. When analytical solutions to our constrained optimization problems are elusive, we discuss how these problems can be converted to convex ones. We study how correlation among sensors' observations, reliability of local decisions, communication channel model and channel qualities and transmit power constraints affect the reliability of the global decision and power allocation of inhomogeneous sensors.