## 3 Neural Network Based DPD Architecture  
Neural Networks (NN) are sophisticated networks, similar to the suggested NN based DPD model and they require extensive training data. This model is then cascaded with the RoF link, but its output is not known. However, in the case of an RoF link, the output is known hence, we form an RoF NN model and train it to mirror the original RoF link. Once we have formulated this RoF NN, we can now backpropagate through it and update the parameters in the suggested NN DPD model.  
Supposing that the considered RoF link has a transfer function \(H(n)\) and an output signal \(y(n)\); and a baseband signal \(x(n)\) must be sent through it, DPD aims to calculate the inverse transfer function of this RoF link denoted by \(\hat{I}^{-1}\), whose output will then be denoted by \(\hat{x}(n)\).  
This can be expressed by:  
\[\hat{x}(n)=\hat{I}^{-1}(x(n)) \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No.** & **Author** & **Type** & **Subcategory** & **Parameter** & **Linearization** & **Pos** & **Disadvantages** \\ \hline \multirow{3}{*}{16} & [PERSON]. [PERSON] & & & & & & & Tough synthesis of arbitrary transfer functions in the time domain; due to coupling between different paths, simultaneous correction of both, second and third order is not possible. \\  & & & & & & & & \\ \hline \multirow{3}{*}{17} & [PERSON] et al. [31] & Electrical & Analog & & & & & \\  & & Predistortion & IMD3 & Laser & & & & To compensate arbitrary bandwidth limitation in the frequency domain. \\ \hline \multirow{3}{*}{18} & [PERSON] et al. [32] & Digital & Direct DPD & EVM, ACPR, & & & Only requires transient chirp coefficient, no exhaustive training. & Limited to laser; works only for kilometers of length; complex behavior. \\  & & & & & & & & \\ \hline \multirow{3}{*}{19} & [PERSON] et al. [33] & Digital & DPD for short link & NMSE, ACPR & Laser & & Feasible closed loop DPD & Training is time consuming and complex \\ \hline \multirow{3}{*}{20} & [PERSON] et al. [34] & Digital & DFB based & NMSE, ACPR, & & & Utilization of DVR, GMP, MP & High complexity. \\  & & & & & & & & I/Q imbalance. \\ \hline \multirow{3}{*}{21} & [PERSON] et al. [35] & Digital & ML-NN based & ACPR, EVM & & & Lears nonlinearities of model in contrast with Volterra based methods, avoids requirement of explicit designing of distortion causes & Limited to LTE framework. \\  & & & & & & & & Degradation to 5G ambiguous. \\ \hline \hline \end{tabular}
\end{table}
Table 1: \(Cont.\)While,  
\[y(n)=Gx(n)=I(\hat{x}(n)) \tag{2}\]  
where \(G\) is the gain. The NN here calculates \(\hat{I}^{-1}\) utilized for predistortion. A direct training cannot be implemented for construction of the NN for DPD as the ideal \(\hat{x}(n)\) is not known.  
The option analyzed for performance assessment is illustrated in Figure 5[1].  
Initially, the RoF link is emulated by the second NN. The generic RoF link has \(\hat{x}(n)\) as input and \(\frac{y(n)}{G}\) as output data, considering which, training is executed with the regression based NN model for them. This results in learning of the NN and now an approximate transfer function \(\hat{I}\) can be identified by it. Upon the formation of the RoF NN model, the model weights are fixed after which we connect it with the NN DPD model. Now, we use the original input, i.e., \(x(n)\) and output as training data to calculate error using a loss function. We then backpropagate it via \(\hat{I}\) to train \(\hat{I}^{-1}\).