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Future Long Term Evolution (LTE) Radio Access Network (RAN) will benefit from a significant degree of self-organization. Autonomic Load Balancing (ALB) is considered as an important self-organizing function in LTE RAN. In this work, distributed ALB is achieved by Autonomic Network Management (ANM). Load conditions of eNBs (E-UTRAN NodeB) can be detected. Sizes and shapes of cellular coverage can be adjusted automatically according to load conditions, so as to balance load. Simulation results demonstrated that by the use of ALB, the system capacity can be improved significantly.