On Sensing Performance of Multi-Antenna Mobile Cognitive Radio Conditioned on Primary User Activity Statistics

Abstract

In limited space scenarios, the antennas in a multiantenna cognitive radio (CR) system are closely spaced and often experience correlation among them. In this paper, the sensing performance of arbitrarily correlated antennas over the Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading channel for the mobile CR user is analysed. In particular, the analytical expression for the average detection probability for a mobile CR user employing the selection combining with arbitrarily correlated triple diversity branches is derived as a special case. Moreover, to characterize the performance of an energy detector under mobility, the area under the curve of a receiver operating characteristic is analysed. Furthermore, as the sensing decisions can be utilized to improve the sensing performance, a comprehensive analysis of sensing performance of the mobile secondary user conditioned on the primary user (PU) activity statistics is carried out. We assume the PU traffic to be following the Discrete-Time Markov Chain (DTMC) model, and its <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$idle$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$busy$ </tex-math></inline-formula> periods to be following generalised Pareto distribution. The analytical framework is substantiated by Monte Carlo simulations. Results indicate that antenna correlation deteriorates detection performance. Moreover, the detection performance deteriorates further due to the mobility of CR users, especially in the deep fading channel scenarios. Furthermore, findings also suggest that under mobility, the sensing performance improves if the duty cycle of the PU channel is low. This work provides a realistic sensing framework for CR enabled vehicles.