On the Design of Nonlinear Characteristics That Optimize Maximum Likelihood OFDM Performance

Usually, non-linear (NL) distortion is seen as something undesirable that can substantially degrade the performance of communication systems. Multicarrier schemes such as orthogonal frequency division multiplexing (OFDM) suffer particularly from this impairment due to their high envelope fluctuations. However, studies have shown the potential of taking advantage of nonlinear distortion as additional useful information, provided that optimum maximum likelihood (ML) receivers are employed. In fact, the optimum ML performance can potentially be better than those of linear transmitters. In that sense, one might ask what NL characteristics can maximize those performance gains. In this work, we study optimum Cartesian NL characteristics for Gaussian-like signals such as the ones associated with OFDM modulations. It is shown that for input signals with Gaussian distribution, the NL functions that maximize the potential gains of ML detection are based on Hermite polynomials, which are orthogonal under the Gaussian distribution.