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An iterative reconstruction method that was proposed for clipping noise cancellation in orthogonal frequency domain multiplexing (OFDM) systems is applied to multilevel quadrature amplitude modulation-based multi-carrier (MC) code division multiple access signals in downlink. The iterative method uses a known distortion function, maybe a nonlinear one such as a successive clipping and filtering process, in the iterations to give an approximation of inverse of the distortion process and then the iterative method removes distortion under a convergence condition. The authors show that MC signal with properly chosen clipping threshold satisfies convergence conditions of the iterative method. In contrast to some of the other reconstruction-based techniques, this method requires no extra bandwidth and side information and it can be implemented with reasonable complexity. Furthermore, the authors show that the proposed iterative scheme can be enhanced by using an extra frequency bandwidth. Exploiting extra bandwidth improves the performance of the reconstruction-based methods in case of using successive clipping and filtering. Simulation results will be used to demonstrate achievable bit-error-rate improvement by the proposed enhanced iterative scheme.