## 3 MIMO System Model and the Implementation Steps of Channel Estimation
### Proposed RP-WHEVO
\[C_{hj}^{q}=CO\left(C_{hj}^{w},C_{hj}^{r}\right) \tag{32}\]  
In Equation (33), the terms \(C_{hj}^{w}\) and \(C_{hj}^{r}\) represent the positions of host parameters, and the term \(C_{hj}^{q}\) denotes the hybrid updated position. Leaders of the groups lead the entire group to the searching point. First, the dominant group continues their search, and the remaining group waits in a queue until the dominant group finishes their search. The searching operation is determined using the formula given in Equation (33). \[\overline{L}= \begin{cases}2X\cos(2\pi TX)\times(EG-L_{h})+EJ&ifY_{3}>0.5\\ 2X\cos(2\pi TX)\times(EG-L_{h})-EJ&ifY_{3}\leq 0.5\end{cases}  \tag{33}\]  
In Equation (33), the next position of the leader is represented by \(\overline{L}\) and \(EG\) denotes the searching point position. The performance of the algorithm is maintained by selecting the best leader for the group. The leaders are determined based on their fitness value. If any member in the group has a leading fitness value, then the locality of the leader with their respective position will interchange based on Equation (34). \[L_{\text{int}}= \begin{cases}C_{ho}&if\cos y(C_{ho})<\cos y(L_{\text{int}})\\ L_{\text{int}}&if\cos y(C_{ho})>\cos y(L_{\text{int}})\end{cases}  \tag{34}\]  
Thus, the best output solution is obtained by randomly selecting the position. Yet local optimal problems can easily occur, which leads to a decrease in the convergence rate. Energy Valley Optimizer: This is based on nuclear reaction. Here, two sub-atomic particles strike each other to produce a new particle. Most of the particles in the universe are unstable in nature. These unstable particles emit energy in a loss process known as decay. The rate of decay differs based on the particles. The low-energy particle undergoes a decaying process. In this decaying process, external energy is ejected using the emission process. One of the most challenging processes is determining the stability of the particles by utilizing the number of neutrons \(Na_{1}\) and protons \(Pa_{1}\) which are present in the ratio of \(\frac{Na_{1}}{Pa_{1}}\). A small value is considered as the ratio for lightweight particles, and for heavier particles, the value of the ratio is assumed to be a high value. The position of neutron-rich particles moves towards the stability bond, and neutron-less particles undergo the capturing of the electron process to stabilize the neutron and then move to the stability bond. The emission of energy undergoes three decaying processes with various levels of stability. The positively charged particles are denoted by \(\alpha\) particles, the negatively charged particles with high-speed electrons are denoted by \(\beta\) particles, and the high-energy protons are denoted by \(\gamma\) particles. The enrichment bonds between the neutron-rich and neutron-poor particles are determined using the formula given in Equation (35). \[NM=\frac{\sum\limits_{\alpha=1}^{m}MRK_{y}}{G},0=1,2,\ldots G \tag{35}\]  
In Equation (35), the term G represents the enrichment bond and \(MRK\) denotes the neuron enrichment level of the \(o^{th}\) particles. The strength of the particles is determined based on the best and worst levels of stability, and its formula is given by Equation (36). \[StAL_{1}=\frac{MRK-VA}{ED-VA},0=1,2,\ldots m \tag{36}\]  
In Equation (36), the terms \(ED\) and \(VA\) denote the best and worst positions of the particles. If \(\left[MRB_{y}>NM\right]\) so, then the ratio of stability is high. The newly generated particle in the universe is updated based on the particle position vector, and the formula for a position update is given by Equation (37). \[Cv_{o}^{N}=Cv\Big{(}C_{jh}\Big{(}c_{o}^{k}\Big{)}\Big{)}, \begin{cases}o=1,2,\dots m \\ k=alpha\end{cases}  \tag{37}\]  
The stability of the existing particle is increased by using the gamma break-up process. By updating the position in the EVO algorithm, the new solution of the candidate is updated.