  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.
