Robust set-theoretic distributed detection in diffusion networks

We propose novel set-theoretic distributed adaptive filters for cooperative signal detection in diffusion networks, a problem that has been gaining attention owing to its application to cooperative cognitive radio networks. In the proposed method, nodes in a network detect the presence of a signal of interest by means of an inner product between the current term of a series and a known reference vector. Each term of the series is computed from information fusion among neighboring nodes and projections onto closed convex sets, which are constructed with a priori knowledge of the signal of interest and measurements obtained by nodes. In particular, we show that sets based on a priori knowledge are useful to decrease the communication overhead and to provide good detection performance. Our results are rigorous in the sense that no approximations are used to prove convergence properties. In particular, we show conditions to guarantee that the series converge to a point that can reliably identify the signal of interest. Furthermore, we also show that recent results in distributed optimization for dynamic systems can be used to derive algorithms where nodes exchange not only the current vectors of their sequences (as in previous distributed set-theoretic filters), but also side information that influences the above-mentioned sets.