User mobility prediction based on Lagrange's interpolation in ultra-dense networks

The concept of Ultra-Dense Networks (UDNs) was first introduced by Mobile and wireless communications Enablers for the Twenty-twenty Information Society (METIS) and it is considered as a promising technology in the future 5G. In UDNs, due to the dense deployment of femtocells, building User-Centric Networks (UCNs) is a clear trend and Virtual Cells (VCs) are the core function of UCNs. As user mobility prediction can enhance the mobility of UCNs and improve the handover performance of VCs, it is a critical issue in UDNs. Unfortunately, to the best of our knowledge, no literatures about user mobility prediction in UDNs are available. At present, most existing mobility prediction works are carried out in LTE networks and they only consider the cells which are uniformly distributed. What's more, as femtocells are densely deployed, the existing prediction works cannot be applied to UDNs directly. Therefore, we are trying to find a practical scheme with lower algorithmic complexity which can be applied to UDNs. In this paper, we explore a realistic block scenario with femtocells deployed according to Poisson Point Process (PPP). Exploiting context information, we propose a novel approach which fitting users' moving path based on Lagrange's interpolation. We evaluate users' transition probability to neighboring femtocells according to the slope of the trajectory polynomial and the distance between users and neighboring femtocells. Simulation results show that when choosing synchronous transmission points (TPs) based on the distance between users and neighboring TPs, five TPs with the highest transition probability can achieve the highest prediction accuracy. Besides, the combination of distance and direction can reduce the number of synchronous TPs without decreasing the prediction accuracy and it would perform better at a higher speed.