Sensitivity of stable rates in cognitive radio systems to the sensing errors

We study the sensitivity of stable rates to imperfect sensing in cognitive radio systems comprised of a set of source-destination pairs having different priorities. 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 full utilization of the shared channel with capture. 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 at any stabilizable input demand. To this end, the 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 identical stability region that is achieved with perfect sensing, i.e., the stability is insensitive to the sensing errors. This happens when relatively strong capture effect is present. For the case when the stability is sensitive to the sensing errors, we precisely quantify the loss due to the imperfect sensing in terms of the size of the stability region.