## 4 Genetic-OMP Algorithm  
The sampled signal enters the reconstruction stage after dynamic flexible processing. The reconstruction algorithm is directly related to the performance of the false alarm rate of the recovered support set and the BER of the reconstructed signal. Therefore, for the reconstruction algorithm, we hope that it is easy to realize and has a high accuracy rate. Although the OMP algorithm meets the characteristics of easy implementation, its principle determines that the OMP algorithm is not highly accurate. It needs to be optimized. The genetic algorithm simulates the process of natural selection and reproduction. The fitness in the genetic algorithm quantifies the strengths and weaknesses of individuals in the current environment, which can diminish the influence of the single selection criterion of the OMP algorithm on the accuracy of the results. Random selection in genetic algorithms helps to keep the OMP algorithm from falling into local optimal solutions. The local optimal solution usually cannot represent the global optimal solution. Therefore, we propose a Genetic-OMP algorithm based on the feature factor \(F_{i}\). The degree of match between the observation matrix and the measurement vector is measured by the inner product. We use the inner product as an initial screening strategy to filter out the backup set \(\Theta\). The larger inner product means a higher match, which is probably selected for the final support set \(\Psi\). For further subsequent selection, we utilize the concepts of fitness and random selection in genetic algorithms. Precise selection is performed by constructing the feature factor \(F_{i}\). Before the signal is reconstructed, the dynamic flexibility processing of the signal in the preamble is based on the spatial information entropy. For this precondition, the design of \(F_{i}\) is based on the following two principles. 1. Spatial information gain  
As mentioned above, reconstruction is the process of continually determining the \(\Psi\) by using observation matrices and measurement vectors. Referring to (7), we have \(V=A\Psi U\). It is known that \(\Psi\) has multiple possible values, and \(U\) is determined by \(\Psi\). When \(U\) has unique solutions, that means the spatial information entropy of both should be equal. \[H(V)=H(A\Psi) \tag{26}\]  
If the difference between \(H(V)\) and \(H(A\Psi)\) is large, the selectable range of possible values for \(U\) increases, making it difficult to determine the optimal solution. On the contrary, the smaller selectable range facilitates the determination of the final value. Therefore spatial information gain is used as a factor in designing fitness. The spatial information gain is defined as follows. \[Gain\big{(}A_{j},r_{i}\big{)}=H(r_{i})-H\big{(}A_{j},r_{i}\big{)} \tag{27}\]  
\[H(r_{i})=\sum_{n=1}^{N}\sum_{m=1}^{M}-r_{imm}\ln(r_{imm}) \tag{28}\]  
\[H\big{(}A_{j},r_{i}\big{)}=\sum_{n=1}^{N}-J_{in}\ln(J_{in}) \tag{29}\]  
\[J_{i}=\big{|}\big{<}A_{j},r\big{>}\big{|}=[j_{1i},j_{2i},\ldots j_{IN}],(n=1, \ldots N) \tag{30}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Calculate** & **Meaning** \\ \hline \(K_{1}\) & \(P_{yi}/P_{gi}\) & The power ratio of the signal before and after denoising \\ \(K_{2}\) & \(y_{hi}/\hat{y}_{hi}\) & The peak ratio of the signal before and after denoising \\ \(K_{3}\) & \(y_{Li}/\hat{y}_{Li}\) & The valley ratio of the signal before and after denoising \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The specific values of \(K_{1}\), \(K_{2}\), and \(K_{3}\). where \(H(r_{i})\) is the spatial information entropy of the \(i\)th iteration residual matrix. \(H\big{(}A_{j},r_{i}\big{)}\) is the spatial information entropy of \(J_{i}\). \(J_{i}\) is the inner product of \(A_{j}\) and the residual matrix \(r_{i}\). A larger spatial information gain represents \(A_{j}\) and \(r_{i}\) corresponding to support sets with a larger range of values, which is not conducive to the determination of the reconstructed signal.