Residual cognitive network interference due to primary user miss-detection

In this paper, we study the coexistence between a primary user (PU) communication and a cognitive radio (CR) network in a general framework that includes wireless propagation subject to path loss, log-normal shadowing, and Rayleigh fading. The CR network can be composed of just one cognitive user (CU) or by several CUs spatially distributed according to a Poisson point process. Each CU is equipped with a spectrum sensing block that can sense the PU transmission with miss-detection probability that depends on propagation impairments and noise. Therefore, our goal is to evaluate the residual interference that the CR network cause to PU because of miss-detections. We start by determining the outage probability of the PU link interfered by a single CU. Then, we investigate the statistical distribution of the residual interference from multiple CUs, which are active due to PU miss-detection, and follow a non-homogeneous Poisson point process. Numerical results shows the link between PU outage and CU spectrum sensing performance. Therefore, the framework proposed is of practical importance and constitutes an aid for the network designer.