## 6 Performance Evaluation
### Performance Comparison on Signal Reconstruction  
In this part, to eliminate the effect of packet length on sparse signal transmission, we fix the payload length to one byte and model the data loss as random compressive sampling. Then, the original signal can be reconstructed by using the received broken data. The original packets' number is \(N=1024\). With compressive sensing, it only needs 20% of the data to recover the real signal, such as temperature and light [15]. Furthermore, conducting DOA estimation using 20% data is also sufficient [38]. To verify the effectiveness of our CS-based method, we first conduct simulations over a link in the transitional region, in which the packet reception rates (single data transmission) are 20%. The reconstruction comparison is shown in Figure 14. The interpolation method in this test is spline, which is thought to be more efficient than other methods. As we can see, when the PRR is 20%, data loss is quite severe. Even with a maximum of three transmission schemes, the number of received packets still cannot satisfy the interpolation's need to reconstruct the signal accurately. The traditional interpolation \begin{table}
\begin{tabular}{l l} \hline Tx Power & 0 dB \\ Channel number & 11 \\ Simulation time & 4 s \\ Max frame retries & 0 or 2 \\ Overhead length & 10 bytes \\ Minimum packet length & 11 bytes \\ Maximum packet length & 127 bytes \\ Minimum distance between sender and receiver & 98 m \\ Maximum distance between sender and receiver & 128 m \\ \hline \end{tabular}
\end{table} 
Table 2: Parameter settings in NS-3 simulation. method can only recover a few parts of the signal with received broken data, leading to large recovery error, which means adopting the ARQ interpolation-related technique in harsh environments is not very useful, but has extra energy waste and transmission latency; while due to the sparsity of the original signal and the appropriate selection of the projection matrix, a small number of compressive measurements can capture the signal with high probability and high precision. By using the CS reconstruction algorithms, our CS-based method can recover the original signal with a much smaller reconstruction error. Figure 15 further presents the reconstruction error comparison between CS and interpolation methods under different lossy links (different PRR). Figure 15 shows that all four ARQ interpolation methods perform badly when the PRR is below 0.6, even with three-times the data transmission. Just as described previously, interpolation methods are suitable only for a few data loss condition; while thanks to the sparsity of the original signal and the appropriate selection of projection matrix, a small number of compressive measurements can capture the signal with high probability and high precision. As we can conclude from Figure 15, spline interpolation performs the best when the PRR is below 0.6. In the following simulation, we take spline interpolation as the comparison with our CS-based method. Figure 14: Reconstruction comparison. Figure 15: Reconstruction error comparison. To better show how much energy waste and transmission latency can be reduced by using our CS-based method for information transmission in lossy links, we take the recovery error of the CS-based method as a reference to show how many transmissions are needed by the ARQ interpolation method to achieve the same error.