Closed-form approximation of the capacity in multi-sector cells: application to LTE tri-sector antenna

This study deals with the ergodic capacity in multi-sector cells. Due to the presence of the antenna gain pattern in the expression of the capacity, the latter may be difficult to express analytically. To overcome this problem, the authors propose to approximate the antenna gain pattern by means of a piecewise linear function, which leads to a general closed-form formulation of the capacity. The obtained expression is applicable for any used antenna. The simulations results are performed by using the long term evolution (LTE) TR 36.942 antenna specification, showing that the proposed closed-form capacity almost matches the exact one. In addition, the authors provide a practical use case of the method, by considering a scenario where the users are clustered within the area covered by the antenna.