  In distributed detection systems with wireless sensor networks, the
communication between sensors and a fusion center is not perfect due to
interference and limited transmitter power at the sensors to combat noise at
the fusion center's receiver. The problem of optimizing detection performance
with such imperfect communication brings a new challenge to distributed
detection. In this paper, sensors are assumed to have independent but
nonidentically distributed observations, and a multi-input/multi-output (MIMO)
channel model is included to account for imperfect communication between the
sensors and the fusion center. The J-divergence between the distributions of
the detection statistic under different hypotheses is used as a performance
criterion in order to provide a tractable analysis. Optimizing the performance
(in terms of the J-divergence) with individual and total transmitter power
constraints on the sensors is studied, and the corresponding power allocation
scheme is provided. It is interesting to see that the proposed power allocation
is a tradeoff between two factors, the communication channel quality and the
local decision quality. For the case with orthogonal channels under certain
conditions, the power allocation can be solved by a weighted water-filling
algorithm. Simulations show that, to achieve the same performance, the proposed
power allocation in certain cases only consumes as little as 25 percent of the
total power used by an equal power allocation scheme.
