Optimal Adaptive Hyperbolic Companding for OFDM

In this paper, we derive and analyze a companding algorithm based on the hyperbolic tangent and inverse hyperbolic tangent functions for use in orthogonal frequency division multiplexing (OFDM) transceivers. Probability density functions (PDFs) that approximate the transmitted and received OFDM signals in the presence of additive white Gaussian noise (AWGN) are derived and used to analyze the degree of companding relative to the signal-to-noise ratio (SNR) and clipping level. A set of optimal companding linearity coefficients for the multi-band OFDM (MB-OFDM) ultra-wideband (UWB) standard are presented.