Optimal Linear Fusion for Distributed Detection Via Semidefinite Programming
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AbstractConsider 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.
All Author(s) ListQuan Z, Ma WK, Cui SG, Sayed AH
Journal nameIEEE Transactions on Signal Processing
Volume Number58
Issue Number4
Pages2431 - 2436
LanguagesEnglish-United Kingdom
KeywordsDistributed detection; hypothesis testing; nonconvex optimization; semidefinite programming
Web of Science Subject CategoriesEngineering; Engineering, Electrical & Electronic; ENGINEERING, ELECTRICAL & ELECTRONIC

Last updated on 2020-21-11 at 00:27