Capacity bounds of finite secondary cognitive radio networks

Though there are works that show the asymptotic capacity bounds in a wireless network considering interference constraints from all transmitting nodes, there are no such evaluation of capacity bounds for finite secondary cognitive radio networks where the primaries pose additional constraints. In this paper, we find the bounds for the maximum achievable capacity of a randomly deployed secondary cognitive radio network with finite number of nodes in the presence of primary users, i.e., in the underlay mode. Since solving the functional constrained optimization problem of maximizing the secondary network's capacity subject to other radio constraints is computationally complex, we derive analytical bounds for the solution. We also show how a pre-engineered deployment with the best possible pairings of transmitters and receivers can help attain the best possible system capacity. The bounds are based on the maximum signal to interference and noise ratio (SINR) of all transmitter-receiver pairs and their geometrical placement. The derived bounds provide an insight about the network's maximum and minimum achievable capacities since solving the optimization problem shows in-scalability both in time and search space dimensionality.