## 5 Experimental Results and Discussion  
An experimental study is conducted to examine 2D-DOA sparse estimation by 2 DTV-CES. The measurements were conducted in the semi-anechoic chamber (500 m\({}^{3}\), cut-off frequency 20 Hz) at the Qingdao University of Technology, China, with a 16-channel 2D-random array of 1 m diameter. Its dimensions are 4 \(\times\) 4 and the microphone spacing d was 8.5 cm. In this experiment, there were two different types of spatially extended sources. One type was a continuous source consisting of four monopole sources in Figure 6a, the other was a dipole source with two loudspeaker drivers closely driven in antiphase in Figure 6b. The two types of extended sources were driven by 2000 Hz acoustic signals and were oriented so that the sources' plane is parallel to the array plane. The sources' plane was located at \(z=0\) cm and the microphone array at \(z=100\) cm. According to the Nyquist sampling theorem, the sampling frequency of 4096 Hz was taken to obtain 10 s date records. Figure 6c depicts the 2D-DOA measurement metric in experimental procedure.  
In order to verify the focusing and block sparsity features of TV-norm regularization of the 2 DV-CES, the coefficient distributions of sound source sparse solution of the three methods were calculated by using continuous sources, and the results are shown in Figure 7. The central position of the continuous source is \(x=17\) cm, \(y=42\) cm. The azimuth coverage is [\(5\lx@math@degree\):\(1\lx@math@degree\):\(50\lx@math@degree\)], and the pitch angle is [\(15\lx@math@degree\):\(1\lx@math@degree\):\(18\lx@math@degree\)]. According to the order of 2D-DOA's estimation, the DOA's estimation was divided into three groups namely a, b, and c. The length of each group is different. The length of group a is 83, group b is 75, and group c is 46. The corresponding amplitudes of group a are linear values decreasing from 1 to 0.6, group b are constant values 1 mixed with linear values, and group c are constant values 1. The array test data were analyzed by 2 DTV-CES, LASSO and Improved ESPRIT  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multicolumn{3}{c}{**Spatial Average Detection Probability (\%)**} \\ \cline{2-4}  & **2 DTV-CES** & **LASSO** & **Improved ESPRIT** \\ \hline Sparsity \(K\) [2:2:20] & 87 & 63 & 4 \\ SNR [\(-\)5:1:20] & 86 & 52 & 0 \\ Computing Speed (s) & 28–31 & 82–88 & 90–95 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The performance comparison of the three methods.  
methods on the MATLAB numerical platform, and the calculated results were shown in Figure 7a, 7b and 7c, respectively. As shown in Figure 7a, 2 DTV-CES clearly shows the division of three complete groups, the amplitude profile of each group is strictly displayed according to the set value, and each 2D-DOA can be effectively estimated. In Figure 7b, the results of LASSO can also be depicted in three groups named a, b, and c. The length of each group is short comparing with it in Figure 7a, and multiple values within the group are overlapped. The amplitude profile of each group is the constant value 1 and did not show any linear changes. Figure 7c shows the results of the Improved ESPRIT method. There are no group a and only a few single values in group b and group c. Comparing the three methods, it can be concluded that 2 DTV-CES has good block focusing, sparsity, and can estimate every DOA value completely and clearly. LASSO shows good sparsity, but it cannot clearly estimate all DOAs with constant amplitude and cannot identified any DOAs with linear amplitude. Improved ESPRIT cannot achieve DOA's estimation of extended sound sources. This result further verifies the role of TV-norm regularization and is consistent with the simulation results in Figures 2 and 3.  
As stated in the review, through the above two kinds of experiments, the advantages of 2 DTV-CES in data sparsity promotion and SNR robustness are effectively demonstrated, and the experimental basis for sparse representation of non-sparse fields is provided.