No 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.

Abstract-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.

No abstract

A recent work derived expressions for the induced p-norm of a special class of circulant matrices A(n, a, b) ∈ ℝ n × n , with the diagonal entries equal to a ∈ ℝ and the off-diagonal entries equal to b ≥ 0. We provide shorter proofs for all the results therein using Fourier analysis. The key observation is that a circulant matrix is diagonalized by a DFT matrix. The results comprise an exact expression for ǁAǁ p , 1 ≤ p ≤ ∞, where A = A(n, a, b), a ≥ 0 and for ǁAǁ2 where A = A(n, −a, b), a ≥ 0; for the other p-norms of A(n, −a, b), 2 < p < ∞, upper and lower bounds are derived.