# Double-Layer Compressive Sensing Based Efficient DOA Estimation in WSAN with Block Data Loss
## 4 Experimental Results
### Simulation Settings  
The signals imitating passive acoustic targets are synthesized using four dominant frequencies at 320 Hz, 480 Hz, 640 Hz and 800 Hz. In this section, we assume that the acoustic signal is spread in the air and that the propagation speed is 340 m/s (the following mentioned guidelines on how to design the array geometry can be easily extended to other scenarios, where the acoustic signal may have a different propagation speed). Therefore, the minimum wavelength of the impinging signals is 0.425 m. The received acoustic signals are contaminated with zero-mean, white Gaussian noise. Additionally, the variance of noise can be altered to obtain different SNR values. The sampling rate is set to 4096 Hz, which is much more than twice the highest frequency of interest, to avoid the frequency aliasing effect. We consider a WSAN consisting of a six-element ULA (note that the results in the paper can be easily extended to non-uniform linear arrays) and one FC, where the inter-element spacing in the ULA is set 0.2 m, which is smaller than half of the minimum wavelength of the impinging signals to avoid angle ambiguity effects. Array sensors are connected to the FC through lossy wireless links. For each array sensor, \(N=512\) data samples will be collected to implement one DOA estimation process. The acquired data samples are assembled into data packets for transmission to the FC over lossy wireless links. For the ease of simulation and analysis, we ignore the overhead produced by the packet header and packet footer, and the data packet size is set to 1, 8, 16, 32 and 64, indicating the number of data samples grouped into one data packet. The incident angles (DOAs) of the acoustic signals are constrained within the range from \(-90^{\circ}\)-\(90^{\circ}\), and this angle range is divided into 360 search grids, with 0.5\({}^{\circ}\) spacing. The number of data samples received from each array sensor at the FC is denoted by \(M\). In the following simulations, three evaluation criteria are used to describe and compare the performance of CS-DOA, DCS-DOA and DCS-DDOA. The reconstruction error is defined as \(\eta=\sqrt{\sum_{h=1}^{H}\left\|\tilde{\mathbf{x}}_{h}-\mathbf{x}_{h}\right\| _{2}^{2}}\Big{/}\sum_{h=1}^{H}\left\|\mathbf{x}_{h}\right\|_{2}^{2}\). Following a similar work [28], which takes into account both the errors in estimating the actual source number and the corresponding DOAs, the root mean square error is defined as: \(\text{RMSE}=1\Big{/}L\sum_{l=1}^{L}\text{RMSE}^{(l)}\), and \(\text{RMSE}^{(l)}\) is defined as: when \(\tilde{K}^{(l)}\leq\tilde{K}\),  
\[\text{RMSE}^{(l)}=\sqrt{\frac{\sum_{k=1}^{\tilde{  
In DCS-DOA, a projection operation (active CS process) is introduced at each array sensor. To compensate for the energy consumption generated by the projection operation, we make the projection matrix dimension-reduced; thus, the energy consumption for transmission is reduced. A proper compression ratio of the active CS process is determined through trial and error to make sure that an accurate DOA estimation result can be obtained even when there is a somewhat high packet loss rate. We present the DOA spatial spectrum to make an intuitional comparison between CS-DOA and DCS-DOA. According to the DOA spatial spectrum, DCS-DOA shows a better DOA estimation behavior than CS-DOA. As shown in Figure 10, when the packet size is set to 32, the FC needs 160 data samples from each array sensor to obtain an unambiguous DOA spectrum in CS-DOA, while the number is just 128 in DCS-DOA. When the packet size is 64, as shown in Figure 11, 128 data samples are still enough for DCS-DOA to provide an acceptable DOA estimation result, while CS-DOA fails until the number reaches 192. Figure 10: The comparison of DOA spatial spectrum between CS-DOA and DCS-DOA with packet size = 32. Figure 9: The signal recovery error, DOA estimation RMSE and detection frequency versus the number of received data samples \(M\) under different packet sizes when projection (active CS) is not introduced at each array sensor.