  In this paper, we describe a general algorithmic framework for solving linear
signal or feature fusion optimization problems in a distributed setting, for
example in a wireless sensor network (WSN). These problems require linearly
combining the observed signals (or features thereof) collected at the various
sensor nodes to satisfy a pre-defined optimization criterion. The framework
covers several classical spatial filtering problems, including minimum variance
beamformers, multi-channel Wiener filters, principal component analysis,
canonical correlation analysis, (generalized) eigenvalue problems, etc. The
proposed distributed adaptive signal fusion (DASF) algorithm is an iterative
method that solves these types of problems by allowing each node to share a
linearly compressed version of the local sensor signal observations with its
neighbors to reduce the energy and bandwidth requirements of the network. We
first discuss the case of fully-connected networks and then extend the analysis
to more general network topologies. The general DASF algorithm is shown to have
several existing distributed algorithms from the literature as a special case,
while at the same time allowing to solve new distributed problems as well with
guaranteed convergence and optimality. This paper focuses on the algorithm
derivation of the DASF framework along with simulations demonstrating its
performance. A technical analysis along with convergence conditions and proofs
are provided in a companion paper.
