  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.
