Abstract
This paper develops analytical models to investigate the impact of various operation terms and parameters on the downlink performance of spectrum-shared overlaid networks under closed-access small cells deployment. It is considered that closed-access small cells (i.e., femtocells) can not reuse available channels, and can serve only active authorized user equipments (UEs). On the other hand, the macrocell base station can unconditionally reuse available channels to serve active macrocell UEs. The analysis characterizes UEs identities, their likelihoods of being active, and their likelihoods of initiating interference. Moreover, it quantifies interference sources observed from effective femtocells considering their over-loaded and underloaded cell scenarios. The developed results to characterize an active UE performance and the impact of the number of available channels are thoroughly examined. The obtained results are generally applicable for any performance measure and any network channel models. Numerical and simulation examples are presented to clarify the main outcomes of this paper.