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.

中文翻译：

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OFDM系统中基于概率密度函数缩放的可调节非线性压扩变换降低PAPR

正交频分复用 (OFDM) 系统存在高峰均功率比 (PAPR) 的固有问题。在本文中，提出了一种新的可调非线性压扩变换，它基于 OFDM 信号幅度的原始概率密度函数 (PDF) 的缩放。目标 PDF 由两部分组成。幅度不超过过渡点的第一部分与原始PDF相同。幅度大于过渡点小于截止点的第二部分是通过同时在纵坐标和横坐标维度上缩放原始PDF获得的，以保证恒定的平均功率。推导了压扩和解扩函数，并建立了求解参数的约束方程。所提出算法的参数可以灵活调整，以在算法复杂度、误码率 (BER)、带外 (OOB) 抑制和 PAPR 降低性能之间实现所需的权衡。对所提出算法的一些关键性质进行了理论分析和证明，这对实际实现可能有很大的指导意义。为了进一步降低算法复杂度，首先提出了一种采用二次多项式的分段曲线拟合方案来简化压扩和解扩函数。仿真结果证实了分析结果并验证了所提出算法相对于其他现有算法的优越性。对所提出算法的一些关键性质进行了理论分析和证明，这对实际实现可能有很大的指导意义。为了进一步降低算法复杂度，首先提出了一种采用二次多项式的分段曲线拟合方案来简化压扩和解扩函数。仿真结果证实了分析结果并验证了所提出算法相对于其他现有算法的优越性。对所提出算法的一些关键性质进行了理论分析和证明，这对实际实现可能有很大的指导意义。为了进一步降低算法复杂度，首先提出了一种采用二次多项式的分段曲线拟合方案来简化压扩和解扩函数。仿真结果证实了分析结果并验证了所提出算法相对于其他现有算法的优越性。