## 5 Experiments
### Performance Comparison  
In this subsection, the performance of the proposed algorithm was verified in various movement noise environments, as shown in Table 3. SDPPG signals were measured at pairs of different locations on the subjects: two index fingers (Cases 1, 2, and 3), and one index finger and one toe (Case 4). The subject moved randomly in order to insert movement noise. The noise ratio of channels 1 and 2 in the table implies the ratio of the time period of inserted movement noise to the total experiment time of 120 s. The amount of movement noise on Channel 1 was set to include less than that of Channel 2. \begin{table}
\begin{tabular}{c c c c} \hline  & **Accuracy** & **Sensitivity** & **Specificity** \\ \hline Mean & 0.982 & 1.000 & 0.977 \\ Standard Deviation & 0.010 & 0.000 & 0.014 \\ \hline \end{tabular}
\end{table} 
Table 2: Noise detection Performance. Figure 13: Noise cancellation results: (**a**) an SDPPG signal measured on channel 1; (**b**) an SDPPG signal measured on channel 2; (**c**) an SDPPG signal on output. For performance comparison, three previous noise reduction algorithms, PMAF [10], constant step-size LMS (CS-LMS) [9] and independent component analysis LMS (ICA-LMS) are considered. Since these three algorithms are proposed to reduce noise in a single PPG signal, the algorithms are applied to the PPG signal of Channel 1, which contains a smaller amount of noise than Channel 2. After removing movement noise with the previous algorithms, the corresponding SDPPG signals are computed to compare with the proposed algorithm. Figure 14 shows the experiment results, which are the average of five person results from each case. The noise at output in Figure 14a is the ratio of time period of SDPPG signals with movement noise after noise cancellation to total experiment time. The noise reduction in Figure 14b is the ratio of reduced time period of a noisy SDPPG signal to the time period in which movement noise was inserted on Channel 1. The experiment results show that the proposed algorithm using wavelet transform and diversity combining can effectively reduce movement noise, and it outperforms the previous algorithms, as shown in Figure 14. While more movement noise in the input signal brings more noise in the results, as shown in Cases 1, 2, and 3 of Figure 14a, the output noise of the proposed algorithm is reduced much more than from the other algorithms, as shown in Figure 14b, even if the second channel signal has more noise than, or the same noise as, Channel 1. For example, in Case 3, the proposed algorithm reduces the amount of noise to 8.73% from 30% (i.e., a 70.89% noise reduction) while PMAF, CS-LMS, and ICA-LMS result in 38.29% (\(-\)29.29%), 25.56% (14.79%), and 25.99% (13.38%), respectively. The previous algorithms could not reduce movement noise efficiently while claiming that they improve only PPI variations of a PPG signal [9], [10] and [12], which corresponds to the heart rate variation. Since the PMAF algorithm averages the shapes of multiple periods, the noise can influence the shape of the next periods, which results in deterioration of the SDPPG signals over a greater time duration. Hence, the noise ratios with PMAF increase, and the noise reduction ratios become negative values. When filtering signals, the CS-LMS algorithm partially lessens low-frequency movement noise so that reduction in movement noise is limited. The ICA-LMS algorithm can reduce slow motion artifacts like vertical movement of fingers in heart rates, but it changes and distorts the shape of PPG signals. If the motion artifacts and PPG signals are not independent, the ICA-LMS algorithm performance is degraded, as discussed in [12].