An Effective Approach to Nonparametric Quickest Detection and Its Decentralized Realization

This dissertation focuses on the study of nonparametric quickest detection and its decentralized implementation in a distributed environment. Quickest detection schemes are geared toward detecting a change in the state of a data stream or a real-time process. Classical quickest detection schemes invariably assume knowledge of the pre-change and post-change distributions that may not be available in many applications. A distribution free nonparametric quickest detection procedure is presented based on a novel distance measure, referred to as the Q-Q distance calculated from the Quantile-Quantile plot. Theoretical analysis of the distance measure and detection procedure is presented to justify the proposed algorithm and provide performance guarantees. The Q-Q distance based detection procedure presents comparable performance compared to classical parametric detection procedure and better performance than other nonparametric procedures. The proposed procedure is most effective when detecting small changes. As the technology advances, distributed sensing and detection become feasible. Existing decentralized detection approaches are largely parametric. The decentralized realization of Q-Q distance based nonparametric quickest detection scheme is further studied, where data streams are simultaneously collected from multiple channels located distributively to jointly reach a detection decision. Two implementation schemes, binary quickest detection and local decision fusion, are described. Experimental results show that the proposed method has a comparable performance to the benchmark parametric cumulative sum (CUSUM) test in binary detection. Finally the dissertation concludes with a summary of the contributions to the state of the art

Decentralized Constraint Satisfaction

We show that several important resource allocation problems in wireless networks fit within the common framework of Constraint Satisfaction Problems (CSPs). Inspired by the requirements of these applications, where variables are located at distinct network devices that may not be able to communicate but may interfere, we define natural criteria that a CSP solver must possess in order to be practical. We term these algorithms decentralized CSP solvers. The best known CSP solvers were designed for centralized problems and do not meet these criteria. We introduce a stochastic decentralized CSP solver and prove that it will find a solution in almost surely finite time, should one exist, also showing it has many practically desirable properties. We benchmark the algorithm's performance on a well-studied class of CSPs, random k-SAT, illustrating that the time the algorithm takes to find a satisfying assignment is competitive with stochastic centralized solvers on problems with order a thousand variables despite its decentralized nature. We demonstrate the solver's practical utility for the problems that motivated its introduction by using it to find a non-interfering channel allocation for a network formed from data from downtown Manhattan

A Unified Multi-Functional Dynamic Spectrum Access Framework: Tutorial, Theory and Multi-GHz Wideband Testbed

Dynamic spectrum access is a must-have ingredient for future sensors that are ideally cognitive. The goal of this paper is a tutorial treatment of wideband cognitive radio and radar—a convergence of (1) algorithms survey, (2) hardware platforms survey, (3) challenges for multi-function (radar/communications) multi-GHz front end, (4) compressed sensing for multi-GHz waveforms—revolutionary A/D, (5) machine learning for cognitive radio/radar, (6) quickest detection, and (7) overlay/underlay cognitive radio waveforms. One focus of this paper is to address the multi-GHz front end, which is the challenge for the next-generation cognitive sensors. The unifying theme of this paper is to spell out the convergence for cognitive radio, radar, and anti-jamming. Moore’s law drives the system functions into digital parts. From a system viewpoint, this paper gives the first comprehensive treatment for the functions and the challenges of this multi-function (wideband) system. This paper brings together the inter-disciplinary knowledge