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In this paper, a multi-hypothesis distributed detection technique with non-identical local detectors is investigated. Here, for a global event, some of the sensors/detectors can observe the whole set of hypotheses, whereas the remaining sensors can either see only some aspects of the global event or infer more than one hypothesis as a single hypothesis. Another possible option is that different sensors provide complementary information. The local decisions are sent over a multiple access radio channel so that the data fusion is formed in the air before reaching the decision fusion center (DFC). An optimal energy fusion rule is formulated by considering the radio channel effects and the reliability of the sensors together, and a closed-form solution is derived. A receive beamforming algorithm, based on a modification of Lozano's algorithm, is proposed to equalize the channel gains from different sensors. Sensors with limited detection capabilities are found to boost the overall system performance when they are used along with fully capable sensors. The additional transmit power used by these sensors is compensated by the designed fusion rule and the antenna array gain. Additionally, the DFC, equipped with a large antenna array, can reduce the overall transmit energy consumption without sacrificing the detection performance.
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