Distributed Nonparametric Sequential Spectrum Sensing under Electromagnetic Interference

A nonparametric distributed sequential algorithm for quick detection of spectral holes in a Cognitive Radio set up is proposed. Two or more local nodes make decisions and inform the fusion centre (FC) over a reporting Multiple Access Channel (MAC), which then makes the final decision. The local nodes use energy detection and the FC uses mean detection in the presence of fading, heavy-tailed electromagnetic interference (EMI) and outliers. The statistics of the primary signal, channel gain or the EMI is not known. Different nonparametric sequential algorithms are compared to choose appropriate algorithms to be used at the local nodes and the FC. Modification of a recently developed random walk test is selected for the local nodes for energy detection as well as at the fusion centre for mean detection. It is shown via simulations and analysis that the nonparametric distributed algorithm developed performs well in the presence of fading, EMI and is robust to outliers. The algorithm is iterative in nature making the computation and storage requirements minimal.Comment: 8 pages; 6 figures; Version 2 has the proofs for the theorems. Version 3 contains a new section on approximation analysi

Data-Efficient Quickest Change Detection with On-Off Observation Control

In this paper we extend the Shiryaev's quickest change detection formulation by also accounting for the cost of observations used before the change point. The observation cost is captured through the average number of observations used in the detection process before the change occurs. The objective is to select an on-off observation control policy, that decides whether or not to take a given observation, along with the stopping time at which the change is declared, so as to minimize the average detection delay, subject to constraints on both the probability of false alarm and the observation cost. By considering a Lagrangian relaxation of the constraint problem, and using dynamic programming arguments, we obtain an \textit{a posteriori} probability based two-threshold algorithm that is a generalized version of the classical Shiryaev algorithm. We provide an asymptotic analysis of the two-threshold algorithm and show that the algorithm is asymptotically optimal, i.e., the performance of the two-threshold algorithm approaches that of the Shiryaev algorithm, for a fixed observation cost, as the probability of false alarm goes to zero. We also show, using simulations, that the two-threshold algorithm has good observation cost-delay trade-off curves, and provides significant reduction in observation cost as compared to the naive approach of fractional sampling, where samples are skipped randomly. Our analysis reveals that, for practical choices of constraints, the two thresholds can be set independent of each other: one based on the constraint of false alarm and another based on the observation cost constraint alone.Comment: Preliminary version of this paper has been presented at ITA Workshop UCSD 201

Online Detection of Change on Information Streams in Wireless Sensor Network Modeled Using Gaussian Distribution

Wireless sensor network (WSN) is deployed to monitor certain physical quantities in a region. This monitoring problem could be stated as the problem of detecting a change in the parameters of a static or dynamic stochastic system. A moving window procedure is proposed to detect the systematic error, which occurs at an unknown time. It can detect the deviation in the mean of sensor measurements keeping variance as constant. The performance measures, such as the average run length (ARL) to detection delay and false alarms are computed for various window sizes. The performance comparison is done against traditional cumulative sum (CUSUM) method. The detection of change in mean using CUSUM is done with smaller delay compared to the proposed moving window detection procedure. In order to calculate CUSUM statistics, the number of measurements to keep in sensor memory increases with time. However, in the proposed moving window detection procedure, the number of stored measurements is limited by the size of the window. Therefore, it is advantageous to use the moving window procedure for change detection in sensor nodes that have very limited memory. A high probability of detection is achieved at the cost of larger window size and higher detection delay. However, we are able to achieve the maximum probability of detection even at a window size of 11