A Binning Approach to Quickest Change Detection with Unknown Post-Change Distribution

The problem of quickest detection of a change in distribution is considered under the assumption that the pre-change distribution is known, and the post-change distribution is only known to belong to a family of distributions distinguishable from a discretized version of the pre-change distribution. A sequential change detection procedure is proposed that partitions the sample space into a finite number of bins, and monitors the number of samples falling into each of these bins to detect the change. A test statistic that approximates the generalized likelihood ratio test is developed. It is shown that the proposed test statistic can be efficiently computed using a recursive update scheme, and a procedure for choosing the number of bins in the scheme is provided. Various asymptotic properties of the test statistic are derived to offer insights into its performance trade-off between average detection delay and average run length to a false alarm. Testing on synthetic and real data demonstrates that our approach is comparable or better in performance to existing non-parametric change detection methods.Comment: Double-column 13-page version sent to IEEE. Transaction on Signal Processing. Supplementary material include

Performance of Spectrum Sensing Algorithms Under Fading, Electromagnetic Interference and Outliers

In this paper, we study the effects of shadowing-fading, electromagnetic interference and outliers on sequential algorithms in detecting spectral holes in a Cognitive Radio set up. The statistics of the primary signal, channel gain and the EMI are not known. Different nonparametric sequential algorithms are compared to choose appropriate algorithms to be used for energy detection and mean change detection. Modification of a recently developed random walk test is found to work well for energy detection as well as for mean change detection. We show via simulations and analysis that the nonparametric algorithms developed are robust to fading, EMI and outliers