  We consider a distributed detection system with communication constraints,
where several nodes are arranged in an arbitrary tree topology, under the
assumption of conditionally independent observations. We propose a cyclic
design procedure using the minimum expected error probability as a design
criterion while adopting a person-by-person methodology. We design each node
jointly together with the fusion center, while other nodes are kept fixed, and
show that the design of each node using the person-by-person methodology is
analogous to the design of a network with two nodes, a network which we refer
to as the restricted model. We further show how the parameters in the
restricted model for the design of a node in the tree network can be found in a
computationally efficient manner. The proposed numerical methodology can be
applied for the design of nodes arranged in arbitrary tree topologies with
arbitrary channel rates for the links between nodes and for a general M-ary
hypothesis testing problem.
