Decentralized Eigenvalue Algorithms for Distributed Signal Detection in Wireless Networks

Abstract

In this paper, we derive and analyze two algorithms-referred to as decentralized power method (DPM) and decentralized Lanczos algorithm (DLA)-for distributed computation of one (the largest) or multiple eigenvalues of a sample covariance matrix over a wireless network. The proposed algorithms, based on sequential average consensus steps for computations of matrix-vector products and inner vector products, are first shown to be equivalent to their centralized counterparts in the case of exact distributed consensus. Then, closed-form expressions of the error introduced by nonideal consensus are derived for both algorithms. The error of the DPM is shown to vanish asymptotically under given conditions on the sequence of consensus errors. Finally, we consider applications to spectrum sensing in cognitive radio networks, and we show that virtually all eigenvalue-based tests proposed in the literature can be implemented in a distributed setting using either the DPM or the DLA. Simulation results are presented that validate the effectiveness of the proposed algorithms in conditions of practical interest (large-scale networks, small number of samples, and limited number of iterations).Index Terms-Average consensus, eigenvalue-based signal detection, Lanczos algorithm, power method.

A Parallel Distributed Algorithm for the Power SVD Method

“…In this section, we compare the performance of the proposed parallel DPM method with its sequential counterparts and the distributed LA method proposed in [20]. As distributed LA can only calculate the eigenvalues for a Hermitian matrix, we consider the normalized mean square error (NMSE) for the eigenvalue computation as a performance measurement for the power EVD:…”

“…In addition to the above works, it is also worth mentioning a series of works [20], [21] which utilize the so-called Lanzcos algorithm (LA) to perform a parallel PCA. LA was originally proposed by Lanczos [22], which transforms a symmetric ma-trix into a symmetric tridiagonal matrix through an orthogonal transformation, while keeping the eigenvalues unchanged.…”

Distributed Feedback-Aided Subspace Concurrent Opportunistic Communications

“…Actually, it has been studied in a wide variety of fields, such as sensor networks [7], automatic control [8], and machine learning [9], among others. Focusing on distributed wireless networks, readers are referred to [10], [11] and references therein. This paper is organized as follows.…”

Sequential Likelihood Ratio Test for Cognitive Radios

“…(see e.g. [4], [5], [6], [7], [8], [9]). Emphasis is usually put on the reliability of the detector and several strategies have been proposed to improve it, using for instance collaborative sensing schemes [10], [3] and nonparametric detectors [11], [12], [13].…”