signal to noise and distortion ratio considerations for nonlinear communication channels

Many communications components are nonlinear and have a peak power or peak amplitude constraint. Nonlinearity generates distortions and thus an appropriate performance measure is the signal-to-noise-and-distortion ratio (SNDR). In this paper, we are interested in finding the nonlinear mapping that maximizes the SNDR subject to the peak amplitude constraint. The answer is a soft limiter with gain calculated based on the noise power and the probability density function of the input amplitude. We also investigate a bounding relationship between the SNDR and capacity of the nonlinear channel. The results of this paper can be applied for efficient transmission of high peak-to-average power ratio signals such as OFDM or for optimal linearization of nonlinear devices.