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In this paper, an efficient Active Constellation Extension (ACE) based on Extension Projection Onto the Convex Sets (EPOCS-ACE) scheme is proposed for reducing Peak-to-Average Power Ratio (PAPR) of Orthogonal Frequency Division Multiplexing (OFDM) signals especially with a large number of sub-carriers and high-order constellation. Utilizing the specially designed iterative procedure, considerable PAPR reduction gains not only can be obtained with just one iteration but also can be adjusted dynamically to adapt the different designed requirements for OFDM systems. Moreover, both the novel peaks-clipping strategy and specific extension rules are designed to ensure BER performance while reducing PAPR. The theoretical analysis in terms of the selection criterion for compensation factors, optimization for correction factor, reachable bound of CCDF and computation complexity is derived. Simulation results show that, compared to existing ACE methods, EPOCS-ACE is able to obtain better overall performance in the aspect of PAPR, BER, and complexity for broadband OFDM systems.