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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 multiple-input/multiple-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. Optimization of performance with individual and total transmitter power constraints on the sensors is studied, and the corresponding power allocation scheme strikes 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 al.gorithm. Simulations show that the proposed power allocation in certain cases only consumes as little as 25% of the total power used by an equal power allocation scheme while achieving the same performance.