## 3 MIMO System Model and the Implementation Steps of Channel Estimation
### Proposed RP-WHEVO  
The initiated RP-WHEVO algorithm is used in this hybrid serial cascaded attention network for optimizing the parameters in the autoencoder and the LSTM to improve the spectral coherences of the MIMO system by decreasing the RMSE, MSE, NMSE, and BER of the system. Variables such as hidden neurons and epoch count are optimized using the developed RP-WHEVO algorithm from both the autoencoder and LSTM network. Thus, the proposed RP-WHEVO algorithm optimizes the variables to increase the spectral productivity of the MIMO system during channel estimation. The WHO algorithm can easily fall into local optimal problems that slow down the searching speed of the algorithm, and parallel computation is also a difficult task in the conventional WHO algorithm. These issues are reduced by developing a hybrid and new optimization technique called the RP-WHEVO algorithm. In this RP-WHEVO algorithm, the variable \(y\) is newly introduced for updating the solutions using WHO and EVO algorithms. If the condition \(\left(y<2*\frac{\mathrm{ma}itter}{4}\&\&\&y\geq\frac{\mathrm{ma}itter}{4}\right)\) or \(\left(y<3*\frac{\mathrm{ma}itter}{4}\&\&y\geq 2*\frac{\mathrm{ma}itter}{4}\right)\) is satisfied, then the solution is updated using the WHO algorithm, or else the position is updated using EVO. Here, the term \(y\) denotes the randomly selected parameter and \(\mathrm{ma}itter\) denotes the maximum number of iterations. Finally, the best position is obtained from the procedure of the hybrid RP-WHEVO algorithm. Wild Horse Optimization: This algorithm is proposed to overcome certain challenges, such as high cost in computation and heavy load during cloud computation tasks, and has the power to reduce the local optimal problem. It consists of five main phases for optimization. The first phase starts with creating an initial population and forming a group. The second phase explains the grazing behavior of the horse. The third phase describes how a leader can lead the entire group. Finally, select the best leader and save the best solution in the problem space. Initially, the random population is created and represented as \(\overline{C}=\left\{c_{1},c_{2},\ldots,c_{n}\right\}\) and this initial population is divided into various numbers of groups with a leader, and it is represented by \(Gq\). The total members in the group are represented by \(Gq=\left[C\times QD\right]\), where \(QD\) represents the total percentage of leaders in the group, and it is considered as the controlling parameter for the proposed algorithm. The grazing manner of this algorithm is executed by considering the leader as a center point, and the remaining members search around the center point; the grazing is executed using the formula given in Equation (29). \[B\overline{V}_{o,h}^{k}=2X\cos(2\pi TX)\times\left(L-BV_{o,h}^{k}\right)+L \tag{29}\]  
In Equation (29), the term \(BV_{o,h}^{k}\) represents the member's current position, \(L\) denotes the leader of the group, and \(B\overline{V}_{o,h}^{k}\) the term represents an adaptive function used in the grazing mechanism. The updated position after grazing is represented by \(B\overline{V}_{o,h}^{k}\). The adaptive mechanism \(TX\) is executed using the formula given in Equation (30). \[TX=Y_{2}\oplus AFC+Y_{3}\oplus\left(\approx AFC\right) \tag{30}\]  
In Equation (30), the terms \(Y_{2}\) and \(Y_{3}\) indicate the random numbers in the range of \(\left[0-1\right]\) and \(AFC\) denotes the control parameter. Initially, the values of these parameters start from 1 and gradually reduce to 0. This parameter is determined using the formula in Equation (31). \[AFC=1-py\times\left(\frac{1}{M_{it}}\right) \tag{31}\]  
In Equation (31), the present iteration is represented by \(py\) and \(M_{it}\) indicates the supreme count of iteration for executing the grazing behavior of the algorithm. A new hybrid updated position is formed by using crossover operation, and it is computed using Equation (32).