期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 58, 期 4, 页码 2431-2436出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2009.2039823
关键词
Distributed detection; hypothesis testing; nonconvex optimization; semidefinite programming
资金
- National Science Foundation [ECS-0601266, ECS-0725441, CCF-094936, CNS-0721935, CCF-0726740]
- Department of Defense [HDTRA-07-1-0037]
- Hong Kong Research Grant Council [CUHK415908]
- Direct For Computer & Info Scie & Enginr [0942936] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations [0942936] Funding Source: National Science Foundation
Consider the problem of signal detection via multiple distributed noisy sensors. We study a linear decision fusion rule of [Z. Quan, S. Cui, and A. H. Sayed, Optimal Linear Cooperation for Spectrum Sensing in Cognitive Radio Networks, IEEE J. Sel. Topics Signal Process., vol. 2, no. 1, pp. 28-40, Feb. 2008] 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 propose a more efficient solution that employs a divide-and-conquer strategy to divide the decision optimization problem into two subproblems. Each subproblem 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, optimal linear fusion can achieve comparable performance with considerable design flexibility and reduced complexity.
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