Nonparametric distributed sequential detection via universal source coding

Abstract

Abstract-We consider nonparametric or universal sequential hypothesis testing when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are primarily motivated from spectrum sensing in Cognitive Radios and intruder detection in wireless sensor networks. We use easily implementable universal lossless source codes to propose simple algorithms for such a setup. The algorithms are first proposed for discrete alphabet. Their performance and asymptotic properties are studied theoretically. Later these are extended to continuous alphabets. Their performance with two well known universal source codes, Lempel-Ziv code and KT-estimator with Arithmetic Encoder are compared. These algorithms are also compared with the tests using various other nonparametric estimators. Finally a decentralized version utilizing spatial diversity is also proposed and analysed.

Distributed nonparametric sequential spectrum sensing under electromagnetic interference

“…See [2], [3], [15], [16], [17] for more recent contributions. Various studies have suggested parametric ([18], [19]) as well as nonparametric ( [20], [21]) solutions to this problem. None of these works studies the effect of EMI or outliers on the detection algorithm.…”

A new algorithm for distributed nonparametric sequential detection

“…References [14] and [15] have studied the distributed decentralised detection problem in a sequential framework, with a noisy reporting MAC. Algorithms in [14] require the probability distributions involved from a parametric family.…”

“…The approach in [15] is non-parametric in the sense that it assumes very little knowledge of one of the distributions. It was shown in [15] that the algorithm KT-SLRT developed in that paper performs better than Hoeffding test (which is asymptotically optimal for discrete alphabet) and non-parametric detectors formed by approximating the unknown density by kernel density estimators and differential entropy estimators (these were compared via some examples with the estimators provided in [15]). KT-SLRT was also compared with sequential Kolmogorov-Smirnoff test and was found to perform better (not reported in [15]).…”

“…It was shown in [15] that the algorithm KT-SLRT developed in that paper performs better than Hoeffding test (which is asymptotically optimal for discrete alphabet) and non-parametric detectors formed by approximating the unknown density by kernel density estimators and differential entropy estimators (these were compared via some examples with the estimators provided in [15]). KT-SLRT was also compared with sequential Kolmogorov-Smirnoff test and was found to perform better (not reported in [15]). In this paper, we present a simpler algorithm to address the problem studied in [15] (it does not use a universal source encoder and also does not require a continuous distribution to be quantized while KT-SLRT does).…”

“…KT-SLRT was also compared with sequential Kolmogorov-Smirnoff test and was found to perform better (not reported in [15]). In this paper, we present a simpler algorithm to address the problem studied in [15] (it does not use a universal source encoder and also does not require a continuous distribution to be quantized while KT-SLRT does). Our algorithm has the added advantage of better performance in most cases, as borne out by simulations and analysis.…”