# Ambient LED Light Noise Reduction Using Adaptive Differential Equalization in Li-Fi Wireless Link
## 2 Ambient Light Noise Model and Adaptive Differential Equalization
### Interference and Shot Noise Reduction Using Adaptive Differential Equalization
The algorithm to implement the proposed ADE technique performs iterative computation until the difference between adjacent sampling points of digitally sampled NRZ-OOK signal becomes smaller than a preset threshold. In general, iterative operations increase the complexity of DSP and the execution time of the algorithm. Hence, we reduced the execution time by replacing the iterative computation process with the split Bregman adaptive least-squares method [33]. In addition, under the assumption that the amount of calculation can be increased, the proposed ADE technique recovers the waveform of the received NRZ-OOK signal to the closest match to that of the input signal by reducing the difference between adjacent sampling values. Furthermore, a weighting function reflecting the Poisson distribution function is applied to the proposed technique in order to reduce the shot noise effectively. In summary, the proposed ADE technique is based on a conventional TV technique. The proposed ADE technique is based on a conventional TV technique. However, the conventional TV technique has the disadvantage that it is not sensitive to minute changes in the waveform because it is too dependent on the regularization parameter that controls the shape of the waveform. Furthermore, it is effective only for white Gaussian noise. Therefore, the proposed ADE technique applies a higher-order approximation function to the first term on the right side of Equation (11) derived based on the conventional TV technique, as shown in Equation (12). A Poisson weight function was also added to effectively reduce shot noise. In other words, we derived Equation (11) using a conventional TV technique and then derived Equation (12), a mathematical expression of the proposed ADE technique, in order to clearly show the process in which the proposed technique is implemented mathematically. Even in a wireless transmission system exhibiting a transmission rate of more than several hundred Mb/s, the effect of interference noise may still be valid. In general, baseband signals generated by digital modulation such as NRZ-OOK and pulse amplitude modulation (PAM) have their main information concentrated in the low-frequency band near DC. Therefore, since most of the noise generated by the ambient light source, including shot noise, shows low-frequency noise characteristics, baseband signals are affected by interference noise regardless of the transmission rate. The proposed technique makes it possible to reduce shot noise regardless of the transmission rate. This is due to the following reasons. The proposed scheme is implemented using Equations (12) and (13), and there are no terms related to the transmission rate in these equations. The proposed technique works only on the waveform of a signal based on digital sampling. In other words, it can be seen that the proposed scheme operates regardless of the transmission rate. Furthermore, in Equation (13), we focused on reducing shot noise by adding the Poisson function, which is a probabilistic function of shot noise. Therefore, it is possible to reduce shot noise by using the proposed technique even at a higher transmission rate. Fortunately, in the case of a high transmission rate, the bandwidth of the baseband signal increases due to the increase in the transmission rate, but the bandwidth of the interference noise becomes constant regardless of the bandwidth of the baseband signal. Therefore, the impact of interference noise on the baseband signal can be reduced. However, according to the energy conservation law, its SNR decreases as the bandwidth of the base signal increases. This causes the influence of interference noise to increase. Therefore, in order to meet the SNR required by the system, it is necessary to increase the intensity of the baseband signal when the light from the white LED is directly modulated by this. However, if the modulation depth is increased by 1 or more, distortion may occur, and then the SNR of the baseband signal may be reduced.