# An Under-Sampling Array Signal Processing Method Based on Improved Hadamard Matrix
## 4 Simulation and Experiments Analysis
### Validation and Analysis Based on Experimental Signals
#### 4.2.2 Results and Analysis of The Array Signal Processing  
First, we compare the general wideband array signal processing method with the uncompressed spatial sparse reconstruction method proposed in this paper to process experimental data, such as the incoherent signal subspace method (ISSM) in Figure 8, and Figure 9 is the proposed method in this paper. For the uncompressed array spatial sparse reconstruction method, it can be found that the resolution of the ISSM method is not as good as the spatial sparse reconstruction method proposed in this paper, so the method proposed in this paper has obvious advantages in wideband array signal processing.  
Figure 6: View of the underwater experiment scene layout.  
We also compare the target detection and reconstruction effects of several different measurement matrices under different compression ratios, as shown in Figures 10 and 11, the reconstructed target with different measurement matrices in 70% and 44% compression ratios respectively. We normalized the final reconstruction amplitude to make the comparison between each matrix more obvious and compared the reconstruction effect before and after compression.  
Figure 8: Detection effect based on incoherent signal subspace method.  
Figure 7: Top view of the layout of the experimental scene.  
Figure 10: The reconstructed targets with different measurement matrices in 70% compression ratios (**a**) the reconstructed targets under uncompressed observations; (**b**) the reconstructed targets with Toeplitz and circulant Deterministic Measurement Matrix; (**c**) the reconstructed targets with based on m-sequence Deterministic Measurement Matrix; and (**d**) the reconstructed targets with sequential Part Hadamard Deterministic Measurement Matrix.  
Figure 9: Reconstruction effect based on spatial sparse reconstruction method.  
And the approximate position of the actual target can be known through the target azimuth estimated by each matrix at high compression ratios, or by the above reconstruction result when uncompressed, and marked as 1, 2, and 3.  
It can be seen from Figure 10 and Table 3 that when in 70% compression ratio, before and after compression, the improved Hadamard matrix has a better ability to capture the three bright spots of the UUV model. It has higher resolution and smaller reconstruction error compared with the sequential partial Hadamard matrix, and it also has a certain inhibitory effect on interference.  
It can be seen from Figure 11 and Table 4 that when in 44% compression ratio, except for the improved Hadamard matrix, the reconstruction performance of several other deterministic measurement matrices for the target is significantly degraded, and the recon  
Figure 11: The reconstructed targets with different measurement matrices in 44% compression ratio: (**a**) the reconstructed targets under uncompressed observations; (**b**) the reconstructed targets with Toeplitz and circulant Deterministic Measurement Matrix; (**c**) the reconstructed targets with based on m-sequence Deterministic Measurement Matrix; and (**d**) the reconstructed targets with sequential Part Hadamard Deterministic Measurement Matrix.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**In 70\% Compression Ratio**} \\ \hline Mark & 1 & 2 & 3 \\ Uncompressed & 81.5\({}^{\circ}\) & 85\({}^{\circ}\) & 88.5\({}^{\circ}\) \\ Improved Hadamard & 81.5\({}^{\circ}\) & 84.5\({}^{\circ}\) & 89\({}^{\circ}\) \\ Toeplitz and circulant & 80\({}^{\circ}\) & 85.5\({}^{\circ}\) & 89\({}^{\circ}\) \\ Based on m-sequence & 80\({}^{\circ}\) & 84\({}^{\circ}\) & 90.5\({}^{\circ}\) \\ Sequential-Part Hadamard & 84.5\({}^{\circ}\) & 88.5\({}^{\circ}\) & 91.5\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The angle of a mark in 70% Compression Ratio.