Decentralized Eigenvalue Algorithms for Distributed Signal Detection in Cognitive Networks

TL;DR

This paper introduces two decentralized algorithms, DPM and DLA, for computing eigenvalues in distributed networks, enabling spectrum sensing in cognitive radio networks with practical efficiency and robustness.

Contribution

The paper develops and analyzes two novel decentralized eigenvalue algorithms, extending spectral detection methods to distributed wireless networks with error analysis and practical validation.

Findings

Algorithms are equivalent to centralized methods with exact consensus.

Error due to non-ideal consensus diminishes asymptotically.

Distributed eigenvalue-based spectrum sensing is effective in large-scale 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 non-ideal 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).