Optimal linear fusion for distributed detection via semidefinite programming

13 years 1 months ago

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Consider the problem of signal detection via multiple distributed noisy sensors. We propose a linear decision fusion rule to combine the local statistics from individual sensors into a global statistic for binary hypothesis testing. The objective is to maximize the probability of detection subject to an upper limit on the probability of false alarm. We employ a divide-and-conquer strategy to divide the decision optimization problem into two subproblems, each of which is a nonconvex program with a quadratic constraint. Through a judicious reformulation and by employing a special matrix decomposition technique, we show that the two nonconvex subproblems can be solved by semidefinite programs in a globally optimal fashion. Hence, we can obtain the optimal linear fusion rule for the distributed detection problem. Compared with the likelihood-ratio test approach, the optimized linear fusion rule can achieve comparable detection performance with considerable design flexibility and reduced c...

Zhi Quan, Wing-Kin Ma, Shuguang Cui, Ali H. Sayed

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