In future mobile communications systems, network management procedures must be upgraded to consider user quality of experience (QoE) to deal with service diversity. In this work, a computationally efficient centralized method for determining the best configuration of antenna tilts when planning a LTE network is presented. Unlike previous network-centric methods, the proposed self-planning method is driven by QoE criteria. The core of the method is the grouping of cells into clusters without mutual interference, which speeds up the search for the optimal solution with a classical steepest descent algorithm. Method assessment is carried out in a static system-level simulator adjusted with real connection traces. For this purpose, traffic demand in the scenario is broken down per location and service to estimate the QoE obtained by each antenna tilt plan. During the analysis, the method is compared with legacy tilt planning approaches. Results show that the proposed method achieves a near-optimal solution for the overall system QoE with a computational cost lower than state-of-the art algorithms previously reported in the literature.