1. DecentralizedEigenvalue 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

2. conditions of practical interest (large-scale networks, small number of
samples, and limited number of iterations).