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Self-organizing networks (SONs) aim to raise the level of automated operation in next-generation networks. One of the use cases defined in this field is the optimization of the handover (HO) process, which involves a tradeoff between the amount of signaling load due to HOs and the quality of the active connections in the network. In this paper, first, a sensitivity analysis of the two main HO parameters, i.e., the HO margin (HOM) and the time-to-trigger (TTT), is carried out for different system load levels and user speeds in a Long-Term Evolution (LTE) network. Second, a fuzzy logic controller (FLC) that adaptively modifies HOMs is designed for HO optimization. In this case, different parameter optimization levels (network-wide, cell-wide, and cell-pair-wide) and the impact of measurement errors have been considered. Results of the sensitivity analysis show that tuning HOMs is an effective solution for HO optimization in LTE networks. In addition, the FLC is shown as an effective technique to adapt HOM to different network conditions so that the signaling load in the network is decreased while an admissible level of call dropping is achieved.