Rate Region and Achievable Rates of Full-Duplex Cognitive Radio NOMA Channels Under Imperfect Spectrum Sensing

This paper studies the rate region and the achievable rates of a non-orthogonal multi-access (NOMA) full-duplex (FD) cognitive radio (CR) channel in which multiple secondary users (SU) communicate to a base station under imperfect self-interference suppression (SIS) and spectrum sensing. Towards that goal, we first analyze the sensing performance, i.e., the probabilities of false alarm and miss-detection, of the considered NOMA FD CR channel under the assumption of non-time-slotted activity from the primary network. We use a Markov chain model to combine the sensing results under different sensing scenarios and derive the probability of collision between the primary and secondary networks under realistic imperfect spectrum sensing. Because of this sensing imperfection, the secondary channel is molded as a Gaussian-mixture (GM) channel. Due to the difficulty in obtaining the explicit expressions of the channel capacity and mutual information in GM, we propose new closed-form approximations of the rate region and the achievable rate for each of the users with arbitrarily small errors. These approximations are therefore helpful to analyze the rate region and to establish the achievable rates of the considered FD CR NOMA channel.