A new connectivity metric for cognitive radio networks

A new connectivity metric is proposed for cognitive radio networks. The analysis is developed based on a generalized model for cognitive radio networks where multiple primary users with independent activity factors are considered. The adjacent matrix elements, representing the weights associated to the network graph edges, are set proportional to the activity factors of primary users. It is shown that the proposed connectivity metric is a monotonically decreasing measure with the primary users activity factors. Furthermore, the metric efficiently determines the network connectivity under different primary users activities. The proposed connectivity metric is compared to the probability of finding a route metric which is commonly used as a measure for network connectivity. It is shown that the proposed metric captures the behavior of the probability of finding a route method with significant complexity reduction. Compared to the algebraic connectivity metric, the proposed metric is more robust in the presence of isolated nodes. Finally, the proposed metric can be utilized to analytically study and design cognitive radio networks.