The Stability Property of Cognitive Radio Systems with Imperfect Sensing

In this paper, we study the stability property of a cognitive radio system comprised of a set of source-destination pairs having different priorities. In particular, we focus attention on the effect of imperfect sensing on the stability region of the system, which has been overlooked in most of related previous work. The adopted cognitive access protocol allows the secondary user not only to exploit the idle slots of the primary user but also to transmit along with the primary user with some probability. This is aimed at achieving the full utilization of the shared channel with capture, i.e., a transmission can be correctly decoded at the destination, even in the presence of other transmissions, if the received signal-to-interference-plus-noise ratio (SINR) exceeds a certain threshold for successful decoding. The abolition of strong primacy, however, requires the secondary user to properly regulate its multi-access probability in order not to impede the primary user's stability guarantee. To this end, the maximum stability region of the system is characterized which describes the theoretical limit on rates that can be pushed into the system while maintaining the queues stable. Interestingly, we found that even with non-zero sensing error rates, there exists a condition for which we can achieve the identical stability region that is achieved with perfect sensing. This is when the destinations enjoy fairly strong capture, and if then sensing errors do not affect the stability region for the queueing system. For the case when the specified condition does not hold, we precisely quantify the loss due to the imperfect sensing in terms of the size of the stability region. Finally, we study the problem of controlling the operating point of the sensing device over its receiver operating characteristic (ROC) and summarize some key aspects observed in the control.