## 3 MIMO System Model and the Implementation Steps of Channel Estimation
### Proposed RP-WHEVO
The distance between the excited particles and the considered particle is determined using the formula given in Equation (38). \[Dis=\sqrt{\left(c_{2}-c_{1}\right)^{2}+\left(u_{2}-u_{1}\right)^{2}}, \begin{cases} o=1,2,\dots m\\ l=1,2,3,\dots,m-1\end{cases}  \tag{38}\]  
In Equation (38), the terms \(o^{th}\) and \(l^{th}\) are the two nearest particles with the coordinates \([c_{1},c_{2}]\) and \([u_{1},u_{2}]\) where the total distances between them are represented by \(Dis\). The second best position \(C_{o}^{New}\) is updated using the position vector \(C_{mh}\) of the nearest particle, and the formula is given by Equation (39). \[C_{o}^{New}=C_{i}\Big{(}C_{mh}\Big{(}C_{o}^{k}\Big{)}\Big{)}, \begin{cases}o=1,2, \dots m\\ k=gamma\end{cases}  \tag{39}\]  
If the particles have less stability, then the beta decay process is observed to boost the durability level of the member by updating the position. The position updating process is controlled by using the best level of stability \(C_{best}\) and the center of the particle \(C_{cent}\) in the search space. The new movement of a particle is determined using the formula provided in Equation (40). \[C_{o}^{New}=C_{o}+\frac{\left(t_{1}\times C_{ND}-t_{2}\times C_{VQ}\right)}{DA_ {o}},o=1,2,3\dots m \tag{40}\]  
In Equation (40), the ongoing position of the \(o^{th}\) particle is represented by \(C_{o}\) and \(C_{VQ}\) denotes the center position. Here, the terms \(t_{1}\) and \(t_{2}\) indicate the two random numbers in the range \([0,1]\). The \"exploration and exploitation phase\" of the algorithm is improved by updating the best stability level and the nearest position of the particle. The EVO algorithm is executed in two loops that have three different updated positions while two positions are updated during the exploration phase, which leads to the local optimum problem, and the remaining one position is updated during the exploitation phase. The best global position of the candidate is updated. Algorithm 1 gives the pseudocode for the proposed RP-WHEVO algorithm, and the flowchart of the implemented RP-WHEVO algorithm is given in Figure 3.  
```
1: Set the size of the population as \(G\) and the maximum number of iterations as \(Y\)
2: The initial population of both the EVO algorithm and WHO algorithm are initiated
3: The fitness value is calculated for every solution
4: Create a number of groups and assign their leader based on fitness value
5: For \(r\to 1 to Y\)
6: For \(Q\to 1 to G\)
7: If \(\Big{(}y<2*\frac{\text{max}i\sigma}{4}\&\&\&y\geq\frac{\text{max}i\sigma}{4} \Big{)}\)
8: Evaluate the position by means of the WHO algorithm
9: Else
10: Evaluate the position by means of the EVO algorithm
11: End if
12: End
13: End
14: Obtain the best solution
15: End
```  
**Algorithm 1**Proposed RP-WHEVO  
as Harris Hawks Optimization (HHO) [28], Reptile Search Algorithm (RSA) [29], Wild Horse Optimization (WHO) [26], and Energy Value Optimization (EVO) [27] algorithms and with recent channel estimation techniques such as Deep Neural Network (DNN) [30], Sparse Code Multiple Access (SCMA) [31], Long Short Term Memory (LSTM) [32], and Autoencoder + LSTM [33]. The simulation parameters of the designed channel estimation in the MIMO system are given in Table 2.