  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).
