A multi-user cognitive radio full-duplex channel under imperfect spectrum sensing: Achievable rates and energy efficiency

Abstract

In this work, the achievable rates and energy efficiency of a multi-user cognitive radio (CR) uplink channel with full-duplex (FD) are studied. For this multi-user CR channel, secondary users can work in FD mode to simultaneously transmit and listen to the channel. We consider a realistic scenario in which both FD operation and spectrum sensing are imperfect. At first, we examine the sensing performance and the rate region through the evaluation of the probability of miss-detection and the probability of false alarm when the primary user (PU) activity is assumed to be non-time-slotted. Due to an imperfect sensing operation, the cognitive radio channel is modeled as a non-Gaussian channel impacted by a Gaussian-mixture (GM) noise plus PU interference. Under this practical assumption, it is not possible to calculate the achievable rates and the rate region directly. Instead, we derive simple approximations of these metrics which can be easily calculated with arbitrarily small errors. In the second part of the paper, we further evaluate the derivatives of these achievable rates at low-power regimes. This calculation helps us evaluate the energy efficiency and obtain the minimum energy per bit Eb/N0min when Gaussian and discrete input signals are used.