Optimal linear fusion for distributed detection via semidefinite programming

Authors:
Zhi Quan;Wing-Kin Ma;Shuguang Cui;Ali H. Sayed
Affiliations:
Qualcomm Inc., San Diego, CA;Department of Electronic Engineering, Chinese University of Hong Kong, Shatin, N.T., Hong Kong;Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX;Electrical Engineering Department, University of California, Los Angeles, CA
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

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.