Mathematical evaluation of spectrum sharing in cognitive radio networks for 5G systems using Markov processes

Nowadays, efficient spectrum usage is one of the most important design principles to take into account in wireless communications due to the exponential growth of mobile devices. In that sense, solutions such as non-orthogonal multiple access (NOMA) and cognitive radio (CR), investigated separately, have been proposed to overcome the spectrum scarcity issue. However, it is important to quantify the benefits of the link of both technologies to improve spectrum utilization. In this work, a novel mathematical model of teletraffic for resource allocation using power-domain NOMA (PD-NOMA) in a cognitive radio (CR) environment, specifically in the interweave spectrum sharing scheme, calculating the birth-death process by teletraffic analysis, is developed. This new methodology involves a mathematical model where users can be born or die as primary or secondary users and are represented by a two-dimensional Markovian process. Mathematical results are validated through simulations considering three different scenarios. In these scenarios, a comparison between PD-NOMA and orthogonal multiple access (OMA) schemes is presented considering the blocking probability and the average number of users. The proposed mathematical model shows convergence to the performed simulations. The outcomes indicate that PD-NOMA increases the blocking probability, however, if this parameter is less than 0.03, the average number of active users is at least 90% higher compared to the OMA case.