Optimization of signal-to-noise-plus-distortion ratio for dynamic-range-limited nonlinearities

Many components used in signal processing and communication applications, such as power amplifiers and analog-to-digital converters, are nonlinear and have a finite dynamic-range. The nonlinearity associated with these devices distorts the input, which can degrade the overall system performance. Signal-to-noise-plus-distortion ratio (SNDR) is a common metric to quantify the performance degradation. One way to mitigate nonlinear distortions is by maximizing the SNDR. In this paper, we analyze how to maximize the SNDR of the nonlinearities in optical wireless communication (OWC) systems. Specifically, we answer the question of how to optimally predistort a double-sided memory-less nonlinearity that has both a “turn-on” value and a maximum “saturation” value. We show that the SNDR-maximizing response given the constraints is a double-sided limiter with a certain linear gain and a certain bias value. Both the gain and the bias are functions of the probability density function (PDF) of the input signal and the noise power. We also find a lower bound of the nonlinear system capacity, which is given by the SNDR and an upper bound determined by dynamic signal-to-noise ratio (DSNR). An application of the results herein is to design predistortion linearization of nonlinear devices like light emitting diodes (LEDs).