# LED Nonlinearity Estimation and Compensation in VLC Systems Using Probabilistic Bayesian Learning  
[PERSON]  
1 School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China 1,2c2 Department of Electrical Engineering, Eindhoven University of Technology (TU/e), Flux Building, 5600 MB Eindhoven, The Netherlands 2,3 College of Computer Science, Sichuan University, Chengdu 610065, China 3,4 School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singaporemultiplexing (OFDM) with high-order quadrature amplitude modulation (QAM) constellations [7] and non-orthogonal multiple access [8; 9; 10; 11], multiple-input multiple-output (MIMO) transmission [12; 13], bandwidth extension using various frequency-domain equalization schemes [14; 15], and so on. Another limitation is that white LEDs suffer from intrinsic nonlinearity which is mainly caused by the thermal effects. It has been shown that LEDs are the major source of nonlinearity in typical VLC systems [16]. Due to LED nonlinearity, the input signal could be severely distorted, especially for OFDM signals which usually have high peak-to-average power ratios (PAPRs) [17]. Generally, there are two approaches to mitigate LED nonlinearity: one is estimation and compensation at transmitter or receiver side and the other is nonlinear equalization. For the first approach, the nonlinear power-current curve of the LED is first estimated, which is then used to compensate the LED nonlinearity. In [18; 19; 20], transmitter-side LED nonlinearity estimation and compensation, i.e., pre-distortion, has been considered. In [21; 22], receiver-side LED nonlinearity estimation and compensation, i.e., post-distortion, has been applied. For pre-distortion, the estimated nonlinear power-current curve of the LED is treated as a priori information and hence an additional feedback channel is required. In contrast, no feedback is required for post-distortion. For both pre-distortion and post-distortion, time domain averaging (TDA) is usually adopted for accurate estimation of the nonlinear power-current curve of the LED before LED nonlinearity compensation. Nevertheless, conventional TDA usually needs a relatively large number of training symbols (TSs) to achieve the expected performance, which inevitably reduce the spectral efficiency of VLC systems. For the second approach, LED nonlinearity is mitigated by employing various nonlinear equalizers, such as Volterra series-based equalizers [17; 23], clustering-based equalizers [24; 25], deep learning-based equalizers [26; 27], and so on. However, nonlinear equalizers usually require a relatively large training overhead and also suffer from high computational complexity, which might not be suitable for implementation in practical VLC systems due to the limited computing capability of user terminals. As a widely used machine learning technique, support vector machine (SVM) has already been applied for the mitigation of fiber nonlinearity in coherent optical OFDM systems [28]. However, SVM is a non-probabilistic machine which usually requires a large number of kernels to approximate the optimal solution and hence its application in practical systems is limited. Recently, probabilistic program induction was proposed, which can substantially improve the accuracy of machine learning algorithms when only a few examples are available [29]. In [30], a probabilistic Bayesian learning (PBL) framework was introduced which can obtain a similar generalization performance as that of SVM but needs much fewer basis functions. The PBL technique has many potential applications such as channel estimation [31], radar imagery [32] and frequency-hopping spectrum estimation [33]. In this paper, we for the first time propose a PBL-based LED nonlinearity estimation and compensation scheme for OFDM-based nonlinear VLC systems.