Distributed Inference of Channel Occupation Probabilities in Cognitive Networks via Message Passing

In this paper we propose a novel, versatile graph model to solve efficiently and in a fully distributed fashion problems of collaborative inference in Cognitive Networks. Specifically, we develop an algorithm that estimates the probabilities of channel occupation for secondary network nodes; the algorithm can be used either to compute multiple, location-dependent, soft probability estimates relative to each single node, or to make a global decision about the presence of primary users in the overall area where a cognitive network operates. These goals are achieved by exchanging messages among cognitive nodes without the need of any centralized controller or fusion center. The proposed approach is based on the representation of the network as a factor graph which incorporates in itself three elements: 1) spectrum sensing measurements collected by individual nodes; 2) spatial correlations existing between pairs of neighboring nodes; 3) temporal evolution of the probability of presence of primary users. Bayesian inference on the resulting graph is then performed by iterative Belief Propagation, using the Sum-Product rule. Thanks to the correspondence between graph nodes and physical network nodes, the algorithm is implemented according to a Network Message Passing strategy where messages are actual packets sent by network nodes to neighbors. To determine the spatial interaction coefficients, that are a key component in the model, we derive a learning procedure that allows to set the parameters according to empirical statistics (e.g., a set of past observations or training data). Again, this procedure is completely distributed and can be implemented by each node based on local (neighbors') information only.