A new algorithm for distributed nonparametric sequential detection

Abstract

We consider non parametric sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution with some loose constraints. We propose a simple algorithm to address the problem. This is also generalized to the case when the distribution under the null hypothesis is not fully known. These problems are primarily motivated from wireless sensor networks and spectrum sensing in Cognitive Radios. A decentralized version utilizing spatial diversity is also proposed. Its performance is analysed and asymptotic properties are proved. The simulated and analysed performance of the algorithm are shown to be better than an earlier algorithm addressing the same problem with similar assumptions. We also modify the algorithm for optimizing performance when information about the prior probabilities of occurrence of the two hypotheses are known.

Distributed nonparametric sequential spectrum sensing under electromagnetic interference

“…[3] less accurate and/or difficult to implement. Now we describe our basic distributed algorithm which has been shown to be asymptotically optimal and performs well at practical parameter values ( [27], [21]). It also makes an efficient use of the reporting MAC.…”

“…Since Γ 0l > 0, this goes down exponentially to 0 with | log c| → ∞ at rate Γ 0l γ l . Now consider P 0 [sup 0≤k≤τ (c)Ŵk > | log c|], the second term on the RHS of ( 21). From Theorem 10 in [45], since {Ŵ k } is a submartingale, we get, for an α > 0 with E[e ≤ (e α0| log c| − 1)…”

“…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.…”

Novel distributed sequential nonparametric tests for spectrum sensing

“…Quickest change detection problem literature is summarized in [6]. Distributed sequential detection has been studied in [7], [8], [9] and [10]. The problem considered in [9] and [10] is of sequential distributed detection of two simple hypothesis when the distribution under both hypothesis is known.…”

“…In [7] and [8] Fusion Center (FC) noise is considered but handled very differently from [11] via physical layer fusion. The approach of [7] and [8] has an additional advantage that it requires a single low bandwidth reporting channel with minimal transmission delays. Our present algorithm differs from [7] and [8] in the local algorithms used by the CR nodes.…”