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In this paper, a novel constellation extension (CE)-based approach is presented to address the high peak-to-average power ratio (PAPR) problem at the transmitter side, which is an important drawback of orthogonal frequency-division multiplexing (OFDM) systems. This new proposal is formulated as a mixed-integer nonlinear programming optimization problem, which employs generalized Benders decomposition (GBD) and branch-and-bound (BB) methods to determine the most adequate extension factor and the optimum set of input symbols to be extended within a proper quarter plane of the constellation. The optimum technique based on GBD, which is denoted as GBD for constellation extension (GBDCE), provides a bound with relevant improvement in terms of PAPR reduction compared with other CE techniques, although it may exhibit slow convergence. To avoid excessive processing time in practical systems, the suboptimum BB for constellation extension (BBCE) scheme is proposed. Simulation results show that BBCE achieves a significant PAPR reduction, providing a good tradeoff between complexity and performance. We also show that the BBCE scheme performs satisfactorily in terms of power spectral density and bit error rate in the presence of a nonlinear high-power amplifier.
branch-and-bound (bb); constellation extension (ce); generalized benders decomposition (gbd); orthogonal frequency-division multiplexing (ofdm); peak power reduction; average power ratio; amplitude predistortion; convex-optimization; tone-reservation; par reduction; signals