## 5 Simulation and Analysis
### The Analysis of the Genetic-OMP Algorithm  
To reduce the \(F_{p}\) of the support set, the reconstruction algorithm needs to be optimized. To better compare the effect of algorithm optimization, this simulation set up four groups, which are the Genetic-OMP algorithm with the compensated denoising process (CD-Genetic-OMP), CD-OMP, COMP, and DTMP.  
Figures 8 and 9 illustrate that CD-Genetic-OMP has lower RMSE and higher correlation coefficients compared to the other schemes. For CD-OMP and CD-Genetic-OMP, although both have undergone signal dynamic flexibility processing, the difference in the reconstruction algorithms results in their different performances in terms of metrics. The genetic-OMP algorithm defines the criteria multidimensionally based on the characteristics of the signal pre-processing in the support set recovery process. It avoids the reduction of accuracy brought by the single criterion of traditional algorithms. At the same time, the incorporation of random selection makes the reconstruction results have the development towards the global optimum. Therefore, the CD-genetic-OMP scheme has better performance in RMSE and better correlation coefficients.  
Figure 10 shows the comparison of the false alarm rate of the reconstructed signal support set under different algorithms. The \(F_{p}\) of the support set under the same algorithm decreases slightly as the SNR increases and the sampling channels increase. Therefore, the main influencing factor of the \(F_{p}\) of the support set is the reconstruction algorithm. The traditional GOMP algorithm and OMP algorithm are similar in principle, with a single  
Figure 6: Support set false alarm rates for recovered signals at different SNRs.  
Figure 7: BERs for recovered signals at different SNRs.  
criterion for determining specific elements in the support set, and thus the false alarm rate of these two is skewed higher than the other groups. Both the DTMP algorithm and the Genetic-OMP algorithm add other criteria for secondary screening. The scheme proposed in this paper is based on feature factors. According to the current environment, the feature factor is constructed based on the signal characteristics. The feature factor effectively measures the match between the individual and the residual matrix. The feature factor is used as the probability that an individual is identified as an element in the support set. It can prevent the algorithm from falling into the local optimal solution. Therefore, the false alarm rate of the support set of our proposed scheme is well suppressed.  
Figure 11 is the spectrum of the reconstructed signal with an \(SNR=-5\) and with 50 sampling. From the figure, it can be more intuitively seen that the Genetic-OMP is a great help in reducing the support set's \(F_{p}\) and increasing the detection probability.  
Figure 8: Root-mean-square-errors of recovered signals at different SNRs.  
Figure 10: Support set false alarm rates of recovered signals at different SNRs.  
Figure 9: Correlation coefficients of recovered signals at different SNRs.  
Figure 12 shows the BER comparison of the reconstructed signals with different SNRs. The least squares solution of the support set is the reconstructed signal. The accuracy of the reconstructed signal affects the BER after demodulation. Our proposed scheme outperforms the conventional scheme in recovering the support set accuracy and reconstructed signal accuracy. Thus, the BER of our proposed scheme is also lower.