### Abstract:

Cognitive radio is a novel approach for better utilization of the scarce, already packed but
highly underutilized radio spectrum. To this end, environment-aware unlicensed secondary
wireless devices are envisioned to share the spectrum with the primary licensed network,
provided that their operation does not impose unmanageable interference on the primary
nodes.
To achieve this coexistence goal, interference modeling is of great significance. Interference, in general, has a stochastic nature not only due to randomness in the propagation
channel, but also due to the random geographic dispersion of nodes. A statistical representation for interference, in which the power levels of the secondary nodes influence the
parameters of the model, is, thus, of considerable interest in analysis and design of cognitive
wireless network.
Stochastic geometry and spatial point processes are used for modeling the coexisting
primary and secondary networks. In particular, we model these networks using spatial
bivariate Poisson processes. We obtain statistical properties of the distances in these
processes and use them for modeling the interference from secondary network on the primary
nodes. We first consider an approximate Gaussian model for interference assuming that
Central Limit Theorem (C.L.T) can be applied. We, then, show that a more accurate
model for interference is the sum of a Normal and a Log-normal random variables. The
power levels of secondary nodes can be adjusted to obtain desirable values for the parameters
in both of these models.
Having this characterization of interference, we propose power control strategies for the
secondary network which assure the satisfaction of interference constraint at the primary
nodes. We show that these strategies are very easy to implement with little coordination requirement. Nodes either need to know where they are located in the sequence of
nodes ordered according to their Euclidean distance to a primary node or need no location
information, based on which strategy is being used.
Given that secondary nodes have imposed power control strategies to coexist with the
primary nodes, we find the lower bound of achievable throughput for the secondary nodes.
We use the statistical properties of distances between secondary nodes and find an upper
bound for the interference of secondary network on an arbitrary secondary node and thereby
a lower bound for its throughput. We show that the approach is applicable to finding the
throughput in a general power-constrained random network.