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We consider a binary hypothesis testing problem in an inhomogeneous wirelesssensor network, where a fusion center (FC) makes a global decision on theunderlying hypothesis. We assume sensors observations are correlated Gaussianand sensors are unaware of this correlation when making decisions. Sensors sendtheir modulated decisions over fading channels, subject to individual and/ortotal transmit power constraints. For parallel-access channel (PAC) andmultiple-access channel (MAC) models, we derive modified deflection coefficient(MDC) of the test statistic at the FC with coherent reception.We propose atransmit power allocation scheme, which maximizes MDC of the test statistic,under three different sets of transmit power constraints: total powerconstraint, individual and total power constraints, individual powerconstraints only. When analytical solutions to our constrained optimizationproblems are elusive, we discuss how these problems can be converted to convexones. We study how correlation among sensors observations, reliability of localdecisions, communication channel model and channel qualities and transmit powerconstraints affect the reliability of the global decision and power allocationof inhomogeneous sensors.

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