The data transmission in optical wireless communication (OWC) with incoherent light sources is realized through intensity modulation and direct detection (IM/DD). For this purpose, the transmitted signal needs to be real-valued and non-negative. In practice, this is achieved by single-carrier modulation techniques, such as multi-level pulse position modulation (M-PPM) and multi-level pulse amplitude modulation (M-PAM), and through multi-carrier modulation such as multi-level quadrature amplitude modulation (M-QAM) optical orthogonal frequency division multiplexing (O-OFDM). Conventionally, the average optical power is defined as the first moment of the transmitted signal, while the average electrical power is defined as the second moment of the transmitted signal. In practice, the dynamic range can be linearized through pre-distortion only between levels of minimum and maximum radiated optical power. In addition, eye safety regulations  and/or design requirements also impose an average optical power constraint. Because of these constraints, there is a fixed relation between average electrical power and the average optical power of the single-carrier and multi-carrier signals which varies with the change in the biasing setup, i.e. a combination of direct current (DC) bias and signal variance. The optical-to-electrical (O/E) conversion of the optical signals is investigated in this chapter. In this study, the electrical energy consumption of the OWC system is considered, and therefore the average electrical power carries the information . Here, the received electrical signal-to-noise ratio (SNR) is presented as a function of the channel equalization penalty, the DC-bias penalty, and the non-linear distortion parameters. The analytical framework is verified by means of a Monte Carlo bit-error ratio (BER) simulation [131, 133, 134].
As opposed to a radio frequency (RF) system, where the data-carrying signal modulates the complex-valued bipolar electric field radiated by an antenna, in an OWC system the signal modulates the intensity of the optical emitter, and therefore it needs to be real-valued and unipolar non-negative. Since light emitting diodes (LEDs) are incoherent light sources, it is difficult to collect signal power in a single electromagnetic mode and to provide a stable carrier in an indoor OWC scenario.