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An adaptive subcarrier allocation and an adaptive modulation for multiuser orthogonal frequency-division multiplexing (OFDM) are considered. The optimal subcarrier and bit allocation problems, which are previously formulated as nonlinear optimizations, are reformulated into and solved by integer programming (IP). A suboptimal approach that performs subcarrier allocation and bit loading separately is proposed. It is shown that the subcarrier allocation in this approach can be optimized by the linear-programming (LP) relaxation of IP, while the bit loading can be performed in a manner similar to a single-user OFDM. In addition, a heuristic method for solving the LP problem is presented. The LP-based suboptimal and heuristic algorithms are considerably simpler to implement than the optimal IP, plus their performances are close to those of the optimal approach
Kim et al. (Sat,) studied this question.