Internodal Distance Distribution and Power Control for Coexisting Radio Networks

In cognitive radio networks, we assume that primary and secondary nodes form a bivariate spatial Poisson point process. In this paper, we derive the probability distribution and some statistics of the internodal distances between nodes of different types. When the number of primary and secondary nodes are weakly correlated, we devise two power control strategies with (i) constant power levels and (ii) power levels decreasing/ increasing with distance, which assure satisfaction of interference constraint at the primary nodes with some given probability. For the second strategy, it is sufficient for the nth secondary neighbor of a primary node to know n in order to satisfy the interference constraint. Furthermore, n can be found if secondary nodes exchange their relative positional information and can be assumed fixed if the rate of change in relative nodal positions, due to mobility of nodes, is slower than the minimum time required for power control.