Optimal Linear Fusion for Distributed Detection Via Semidefinite Programming

• Published in: IEEE transactions on signal processing Vol. 58; no. 4; pp. 2431 - 2436
• Main Authors: Zhi Quan, Wing-Kin Ma, Shuguang Cui, Sayed, A.H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Capacitive sensors; Cognitive radio; Cooperation; Detection, estimation, filtering, equalization, prediction; Distributed detection; Exact sciences and technology; Flexibility; hypothesis testing; Information theory; Information, signal and communications theory; Light rail systems; Linear programming; Miscellaneous; nonconvex optimization; Optimization; Probability; Programming; semidefinite programming; Sensor fusion; Sensors; Signal and communications theory; Signal detection; Signal processing; Signal, noise; Statistical analysis; Statistical distributions; Statistics; Strategy; Studies; Telecommunications and information theory; Testing; Performance evaluation; Non convex programming; Multisensor; hypothesis testing; Distributed system; nonconvex optimization; Matrix decomposition; Flexibility; Optimization; Decision rule; False alarm rate; Hypothesis test; semidefinite programming; Upper bound; Distributed detection; Information processing; Signal processing; Data fusion; Matrix method; Signal detection; Divide and conquer method; Radio communication; Software radio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2009.2039823

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.