A Novel Algorithm for Cooperative Distributed Sequential Spectrum Sensing in Cognitive Radio

This paper considers cooperative spectrum sensing in Cognitive Radios. In our previous work we have developed DualSPRT, a distributed algorithm for cooperative spectrum sensing using Sequential Probability Ratio Test (SPRT) at the Cognitive Radios as well as at the fusion center. This algorithm works well, but is not optimal. In this paper we propose an improved algorithm- SPRT-CSPRT, which is motivated from Cumulative Sum Procedures (CUSUM). We analyse it theoretically. We also modify this algorithm to handle uncertainties in SNR's and fading.Comment: This paper has been withdrawn by the author due to the submission of detailed journal version of the same paper, to arXi

Detection of False Data Injection Attacks in Smart Grid under Colored Gaussian Noise

In this paper, we consider the problems of state estimation and false data injection detection in smart grid when the measurements are corrupted by colored Gaussian noise. By modeling the noise with the autoregressive process, we estimate the state of the power transmission networks and develop a generalized likelihood ratio test (GLRT) detector for the detection of false data injection attacks. We show that the conventional approach with the assumption of Gaussian noise is a special case of the proposed method, and thus the new approach has more applicability. {The proposed detector is also tested on an independent component analysis (ICA) based unobservable false data attack scheme that utilizes similar assumptions of sample observation.} We evaluate the performance of the proposed state estimator and attack detector on the IEEE 30-bus power system with comparison to conventional Gaussian noise based detector. The superior performance of {both observable and unobservable false data attacks} demonstrates the effectiveness of the proposed approach and indicates a wide application on the power signal processing.Comment: 8 pages, 4 figures in IEEE Conference on Communications and Network Security (CNS) 201

Change Detection in Multivariate Datastreams: Likelihood and Detectability Loss

We address the problem of detecting changes in multivariate datastreams, and we investigate the intrinsic difficulty that change-detection methods have to face when the data dimension scales. In particular, we consider a general approach where changes are detected by comparing the distribution of the log-likelihood of the datastream over different time windows. Despite the fact that this approach constitutes the frame of several change-detection methods, its effectiveness when data dimension scales has never been investigated, which is indeed the goal of our paper. We show that the magnitude of the change can be naturally measured by the symmetric Kullback-Leibler divergence between the pre- and post-change distributions, and that the detectability of a change of a given magnitude worsens when the data dimension increases. This problem, which we refer to as \emph{detectability loss}, is due to the linear relationship between the variance of the log-likelihood and the data dimension. We analytically derive the detectability loss on Gaussian-distributed datastreams, and empirically demonstrate that this problem holds also on real-world datasets and that can be harmful even at low data-dimensions (say, 10)

Selecting the number of principal components: estimation of the true rank of a noisy matrix

Principal component analysis (PCA) is a well-known tool in multivariate statistics. One significant challenge in using PCA is the choice of the number of components. In order to address this challenge, we propose an exact distribution-based method for hypothesis testing and construction of confidence intervals for signals in a noisy matrix. Assuming Gaussian noise, we use the conditional distribution of the singular values of a Wishart matrix and derive exact hypothesis tests and confidence intervals for the true signals. Our paper is based on the approach of Taylor, Loftus and Tibshirani (2013) for testing the global null: we generalize it to test for any number of principal components, and derive an integrated version with greater power. In simulation studies we find that our proposed methods compare well to existing approaches.Comment: 29 pages, 9 figures, 4 table