Title

Efficient computational algorithms for the design of distributed detection networks

Date of Award

12-2000

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical Engineering and Computer Science

Advisor(s)

Pramod K. Varshney

Keywords

Distributed detection, Multisensor fusion, Signal detection, Decision trees

Subject Categories

Electrical and Computer Engineering | Signal Processing

Abstract

In a distributed detection network, a cluster of sensors observe a common unknown hypothesis, make preliminary decisions and then transmit them to a fusion center. Based on received sensor decisions, the fusion center makes the final decision with regard to the unknown hypothesis. In this dissertation, we develop some computationally efficient algorithms for the design of distributed detection networks.

First, we consider the problem of distributed binary detection with n i.i.d. sensor observations. Our goal is to obtain the optimum sensor threshold λ and the optimum k -out-of- n fusion rule. For the Bayesian problem, we prove that for a fixed k , the probability of error is a quasiconvex function of λ. We then develop an algorithm to efficiently compute the optimum λ. We further generalize the k -out-of- n fusion rule to allow simultaneous optimization of k and λ. For the Neyman-Pearson detection problem, we show the property of quasiconvexity in a similar manner.

Second, we consider designing multibit quantizers for distributed binary detection. We develop a sensor quantizer that minimizes the mean-squared-error while quantizing the log likelihood ratio. For this quantizer, we develop a Lloyd type of algorithm to compute the quantizer parameters. Our quantizer is then applied to signal detection in additive Generalized Gaussian noise and to diversity signal reception over Rayleigh fading channels.

Third, we consider the problem of distributed M-ary detection. To obtain a low complexity solution, we break the M-ary decision-making process into a sequence of binary decision-making processes. The latter are organized in the form of a binary decision tree (BDT). We develop an information distance based method for the construction of the BDT. We also obtain the optimal decision rules for the internal nodes of the BDT.

Finally, we consider the design of extended Neyman-Pearson tests, in which one hypothesis is tested against a set of hypotheses. The structure of extended Neyman-Pearson tests involves the weighted sum of likelihood ratios and a threshold. We develop an algorithm that intelligently searches through the weight space until it finds the optimum weights. Compared to the exhaustive search method, our algorithm greatly reduces the number of search cycles.

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