Adjustable Nonlinear Companding Transform Based on Scaling of Probability Density Function for PAPR Reduction in OFDM Systems

Orthogonal frequency division multiplexing (OFDM) systems suffer from the inherent problem of high peak-to-average power ratio (PAPR). In this article, a novel adjustable nonlinear companding transform is proposed, which is based on scaling of original probability density function (PDF) of OFDM signal amplitudes. The target PDF consists of two parts. The first part with amplitudes no more than the transition point is same to that of original PDF. The second part with amplitudes larger than the transition point and smaller than the cutoff point is obtained by scaling original PDF in dimensions of ordinate and abscissa concurrently, for guaranteeing the constant average power. Companding and decompanding functions are derived, and constraint equation for solving parameters is formulated. Parameters of the proposed algorithm can be adjusted flexibly to achieve desired tradeoffs among algorithmic complexity, bit error rate (BER), out-of-band (OOB) rejection and PAPR reduction performance. Some key properties of the proposed algorithm are theoretically analyzed and proved, which may be much instructive for practical implementations. To further reduce algorithmic complexity, a piecewise curve fitting scheme employing quadratic polynomials is first proposed to simplify companding and decompanding functions. Simulation results confirm analysis results and verify the superiorities of proposed algorithms to other existing algorithms.