# Compressive Sampling with Multiple Bit Spread Spectrum-Based Data Hiding
## 4 Experimental Result
### Audio Quality Performance in Relation to \(r\), \(M\), Payload, and Compression Ratio  
From Section 3.6, we selected \(M\) and \(r\) values to obtain CR \(>1\) and payload \(>20\) bps using \(p=r\) as displayed in Figure 3b with the blue circle symbol. Using the selected \(M\) and \(r\) from \(M\in\{34,66,98,\cdots,482\}\) and \(r\in\{0.01M,0.02M,\cdots,0.5M\}\), we applied the simulation onto five clips as the hosts. The simulation consisted of the embedding process, the data detection process, and the audio reconstruction process. It calculated the BER between the detected watermark and the original watermark, and it finally calculated the audio quality from the reconstructed audio in the ODG performance parameter. The simulation results are displayed in Figure 4a,b. From the simulation using all combinations of parameters \(M\) and \(r\) with five clips, we obtained a perfect watermark detected without any errors or BER = 0 on average. Figure 4a shows the trade-off relation between CR and payload with a negative exponential relation. Red star symbols mean the mapping between CR and payload with ODG \(\geq-1\), while blue dot symbols mean the mapping between CR and payload with ODG \(<-1\). We also plot the blue dots and the red stars in Figure 4b, in the relation between ODG and \(M\). We can say that the longer the length of audio processed for embedding and compression, the worse the reconstructed audio quality. For the above case with five selected clips, good reconstructed audio quality or ODG\(\geq-1\) was obtained when \(M<128\) samples with certain values of \(r\). The required \(M\) parameter did not have to be large until 482 samples, but only up to 128 samples to achieve audio quality with ODG \(\geq-1\). Figure 4b shows the results. Furthermore, large \(M\) values had a long impact on the time processing of the insertion, detection, and reconstruction. Therefore, we applied the same simulation as the simulation displayed in Figure 4a,b using more detailed \(M\) and \(r\), i.e., \(M\in\{5,6,...,128\}\), \(r\in\{1,2,...,64\}\), which was similar to \(r\in\{0.0156M,0.0234M,...,0.5M\}\) and 50 clips. We averaged the audio quality results from 50 clips, and all watermarks were perfectly detected. The simulation results are displayed in Figure 4c,d. From Figure 4d, there were many more options of \(M\) from five to 128, obtaining the results with ODG \(\geq-1\). The simulation as displayed in Figure 4c also obtained a high CR (up to 7.03) and a high payload (up to 8296 bps). To explore which \(M\) and \(r\) obtained the above result, we also captured the simulation results in the table. Tables 4-6 respectively display the10 highest ODG, payload, and CR with certain \(M\) and \(r\). This simulation result generally showed that we could control the audio quality, payload, and CR by adjusting the \(M\) and \(r\) parameters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(r\) & \(M\) & ODG & C & CR \\ \hline
2 & 8 & \(-0.02\) & 2756.25 & 1.60 \\
2 & 7 & \(-0.02\) & 2756.25 & 1.60 \\
2 & 5 & \(-0.03\) & 4833.33 & 1.11 \\
2 & 10 & \(-0.03\) & 1764 & 2.08 \\
2 & 9 & \(-0.03\) & 1764 & 2.08 \\
2 & 6 & \(-0.03\) & 4900 & 1.12 \\
3 & 12 & \(-0.04\) & 5512.50 & 1.45 \\
3 & 11 & \(-0.04\) & 5512.50 & 1.45 \\
3 & 10 & \(-0.04\) & 5512.50 & 1.45 \\
2 & 12 & \(-0.05\) & 1225 & 2.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: 10 highest ODG. Figure 4: ODG in relation to \(M\), payload, and CR. We applied the simulation using 50 clips with \(M=32\) and \(r\in\{1,2,...,16\}\), which was similar to \(r\in\{0.03M,0.06M,...,0.5M\}\), to see how the audio truncation affected the performance parameters. Figure 5a displays the simulation result. This case also produced a perfect detected watermark or BER = 0 on average. Three performance parameters, i.e., ODG, CR, and payload as the y-axis, are displayed in one figure after being averaged, and the x-axis is the normalized rank or \(r/M\in\{0.03,0.06,...,0.5\}\). The black line with the right triangle symbol shows the average ODG producing \(-1.16\) to \(-0.16\).