Optimized Signal Distortion for PAPR Reduction of OFDM Signals with IFFT/FFT Complexity via ADMM Approaches

In this paper, we propose two low-complexity optimization methods to reduce peak-to-average power ratio (PAPR) values of orthogonal frequency division multiplexing (OFDM) signals via alternating direction method of multipliers (ADMM). First, we formulate a non-convex signal distortion optimization model based on minimizing data carrier distortion such that the constraints are placed on PAPR and the power of free carriers. Second, to obtain the model's approximate optimal solution efficiently, we design two low-complexity ADMM algorithms, named ADMM-Direct and ADMM-Relax respectively. Third, we show that, in ADMM-Direct/-Relax, all the optimization subproblems can be solved semi-analytically and the computational complexity in each iteration is roughly O(lNlog2(lN)), where l and N are over sampling factor and carrier number respectively. Moreover, we show that the resulting solution of ADMM-Direct is guaranteed to be some Karush-Kuhn-Tucker (KKT) point of the non-convex model when the iteration algorithm is convergent. For ADMM-Relax, we prove that it has theoretically guaranteed convergence and can approach arbitrarily close to some KKT point of the model if proper parameters are chosen. Simulation results demonstrate the effectiveness of the proposed approaches.