# Neural Network DPD for Agramizing SM-VCSEL-SSMF-Based Radio over Fiber Link Performance
###### Abstract
Efficiently reducing these nonlinearities through linearization techniques has critical importance. In previous years, different linearization methods have been proposed [3; 5; 6; 7; 13; 14; 15; 16; 17; 18; 13];  
Figure 1: Block diagram of Centralized/Cloud Radio Access Network (C-RAN)-based 5G application system comprising backhaul, fronthaul and application scenarios such as stadiums, railways, transport and factories. however, digital predistortion (DPD) demonstrated itself as a successful technique in mollifying the impairments in RoF systems [15; 16; 17; 18]. Traditional Volterra-based methods such as Memory Polynomial (MP) and Generalized Memory Polynomial (GMP) were used successfully in [15; 17; 18], reducing the laser nonlinearities. Similarly, a comparison was shown in [6] where DPD based on Canonical Piecewise Linearization (CPWL) outperformed the traditional Volterra methods by reducing the nonlinearities. Although the performance can be passable, the computation complexity needed for such methods can be extremely high requiring hundreds of coefficients and exhaustive training [18]. Similarly, these methods require the output to come to the central office during the periodical training phase. If the RoF uplink is set for this purpose, the nonlinearities in this case should be compensated. This feedback mechanism adds extra complexity to the process of DPD [6]. In recent years, machine learning (ML) solutions have advanced significantly. Neural networks (NNs) are expected to learn any nonlinear function; therefore, it becomes trivial that NNs can be used for predistortion. NN-based DPD will be very meaningful if we are able to circumvent the bottle neck that was created regarding the complexity of DPD due to Volterra-based methods. NNs were applied for DPD in Power Amplifiers (PA) [25] that rely on indirect learning architecture (ILA) for training the predistorter. The ILA that was initially designed for NNs [26] was applied to DPD for the first time in [27]. As it is well known that in an ILA, a postdistorter learns an inverse model followed by its usage as a predistorter, the learning of a postdistorter is dependent on the noise in the feedback signal [25; 28]. A detailed study on ML utilization for RoF systems was discussed in [29; 30; 31; 32]. [PERSON] et al. in [29] discussed general optical communications and optical networks in terms of ML solutions. Whilst some works on the application of machine learning techniques in radio over fiber systems and networks have been reviewed, due to the general scope, the reviews in this field are relatively brief and limited. Recently, in [30; 31], machine learning techniques were surveyed that include NNs, k-means technique, the convolutional neural network (CNN) and the reinforcement learning category. It also highlights different application scenarios. Recently, a Support Vector Machine (SVM)-based ML method was used to mitigate nonlinearities in A-RoF systems [31; 32]. However, it is a non-NN-based solution. Inspired by the NNs work on PA and the known problems of Volterra-based predistortion using ILA, we, for the first time, propose to counter the nonlinearities in A-RoF for Single Mode VCSEL (SM-VCSEL) using a Standard Single Mode Fiber (SSMF)-based RoF system with a novel DPD method that exploits NNs by evading the ILA. Our proposed methodology is based on the fact that, firstly, we should look for an ideal RoF input signal as it is unknown. Since this ideal RoF input signal is unknown, an NN-based predistorter cannot be trained immediately in the first step. After this step, an NN-DPD model is cascaded with the NN-RoF model. The ideal output of RoF is now known; therefore, it is a straightforward procedure to evaluate the error of the cascaded network (NN-DPD and RoF model). This error can then be backpropagated through the NNs, consequently updating the DPD-NN. This DPD NN can then be cascaded with the actual RoF link. The NN-based predistorter is advantageous, as it is flexible as compared to Volterra-based methods.