Introduction

Because of the p-n junction barrier and the saturation effect of the light emitting diode (LED), the transmitter front-end has a limited linear dynamic range. Single-carrier pulse modulated signals such as multi-level pulse position modulation (M-PPM) and multi-level pulse amplitude modulation (M-PAM) have a probability density function (PDF) of their intensity levels with finite support of values. As a result, these signals can be conditioned within the limited linear dynamic range and transmitted with negligible non-linear distortion. Multi-carrier signals based on optical orthogonal frequency division multiplexing (O-OFDM), such as direct-current-biased O-OFDM (DCO-OFDM) and asymmetrically clipped O-OFDM (ACO-OFDM) with multi-level quadrature amplitude modulation (M-QAM), follow Gaussian and half-Gaussian distributions of the intensity levels for a large number of subcarriers. As a consequence, such signals have a high peak-to-average power ratio (PAPR), and they are transferred by the optical front-end in a non-linear fashion. This results in an increased bit-error rate (BER) or an increased electrical signal-to-noise ratio (SNR) requirement due to non-linear signal distortion. In order to alleviate this issue, signal pre-distortion with the inverse of the non-linear transfer function can be employed. The linear dynamic range is maximized by pre-distortion, and a linear signal transfer is obtainable between levels of minimum and maximum radiated optical power. As a result, the single-carrier pulse modulation signals are transferred without non-linear distortion and with increased electrical power efficiency. The non-linear distortion of the high PAPR O-OFDM signals is reduced to double-sided signal clipping [131, 132], and these signals also benefit from increased electrical power efficiency.

In this chapter, a generalized piecewise polynomial model is presented for the non-linear distortion function of the transmitter front-end [133]. It is a flexible and accurate representation of transmitter non-linearity. Furthermore, it enables signal pre-distortion with the inverse of the non-linear transfer function for the objective of maximizing the linear dynamic range of the optical front-end. The non-linear distortion of an information-carrying subcarrier in O-OFDM is modeled as a real-valued attenuation factor and additive non-linear noise component with a zero-mean complex-valued Gaussian distribution.