Optimization of SNDR for amplitude-limited nonlinearities

Many components used in communication systems are nonlinear and have a peak power or peak amplitude constraint. Nonlinearity generates distortions and thus signal-to-noise-and-distortion ratio (SNDR) is an appropriate performance measure. 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 or for optimal linearization of nonlinear devices.