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Cross-layer adaptation offers the possibility to optimize resource utilization in wireless sensor networks with respect to application-specific performance metrics. In this paper, a transmission power allocation algorithm is presented that is adapted to distributed detection in wireless sensor networks with soft decision fusion. Specifically, the objective is to minimize the global probability of detection error given a fixed level of total transmission power in the network. The cross-layer approach for the allocation of transmission power is based on a measure of individual sensor detection quality as well as location information. It leads to significant performance gains compared to uniform power assignment.