Abstract
In this paper, we investigate the optimal inter- frequency small cell discovery (ISCD) periodicity for small cells deployed on carrier frequency other than that of the serving macro cell. We consider that the small cells and user terminals (UTs) positions are modeled according to a homogeneous Poisson Point Process (PPP). We utilize polynomial curve fitting to approximate the percentage of time the typical UT misses small cell offloading opportunity, for a fixed small cell density and fixed UT speed. We then derive analytically, the optimal ISCD periodicity that minimizes the average UT energy consumption (EC). Furthermore, we also derive the optimal ISCD periodicity that maximizes the average energy efficiency (EE), i.e. bit- per-joule capacity. Results show that the EC optimal ISCD periodicity always exceeds the EE optimal ISCD periodicity, with the exception of when the average ergodic rate in both tiers are equal, in which the optimal ISCD periodicity in both cases also becomes equal.