## 1 Introduction
The adaptive step-size LMS (AS-LMS) adaptive filter [9] was proposed to reduce motion artifacts using a LMS adaptive filter without additional hardware, but the scheme considered only limited cases such as horizontal and vertical movement and therefore cannot be applied for random movement. The periodic moving average filter (PMAF) [10] was proposed to remove movement noise by considering the periodicity of the PPG signals. PMAF segments the PPG signal into periods and resamples each period. The algorithm mitigates a noise at an instant period by averaging multiple signals, but the noise can be propagated to the next signals, which distorts the signal shape. An adaptive spectrum noise cancellation (ASNC) approach for motion artifacts removal in PPG signals is presented by [PERSON] et al. [11]. However, the proposed ASNC utilizes the onboard accelerometer and gyroscope sensors to detect and remove the artifacts adaptively. [PERSON] et al. [12] proposed a method to extract the clean PPG signals from the motion artifacts corrupted PPG signals. The method combined temporally constrained independent component analysis (clCA) and adaptive filters. The clCA extracts the clean PPG signal, and the adaptive filters recover the amplitude information of the PPG signal. But when motion artifacts and PPG signals have dependency, the performance of the proposed method is degraded, i.e., the PPG signal shapes are distorted. All of the previous studies mainly considered movement noise reduction for measuring heart rates from only PPG signals [6; 7; 8; 9; 10; 11; 12] even though SDPPG signals are more useful for diagnosing diseases [13]. The information can be extracted from the signal shapes, so if the shape of SDPPG  
Figure 1: An example of photoplethysmography (PPG) sensing. signals is distorted the applications are limited for diagnosis. Hence, movement noise reduction is important for SDPPG signals. To remove movement noise generally, and to maintain signal fidelity, we apply signal processing and diversity combining schemes for multiple SDPPG signals. The heart rate is almost periodic with a subject-dependent shape; therefore, a wavelet transform that has multiple bases and changes the time-frequency resolution [14] can detect movement noise effectively. Moreover, the human heart generates a heartbeat whereby PPG signals can be measured at different locations, such as fingers, ears, and toes, as shown in Figure 2. Hence, diversity combining schemes, as with communications, can improve the received PPG signal quality. The quality of each channel is measured by the noise level using the wavelet transform, and the algorithm chooses the best signal. This work can also be applicable to other types of bio-signals that have periodicity and diversity properties for healthcare and disease diagnosis using wearable devices. Compared to earlier work [15], this paper provides more detail of analysis and combining schemes, improves the proposed algorithm, and verifies the algorithm through more simulations and comparisons. The noise detection using wavelet transform and the noise reduction using a diversity combining scheme are explained in detail. The proposed algorithm is verified by comparing with previous algorithms in various environments. The rest of this paper is organized as follows. Section 2 describes the properties of SDPPG signals and problems in measurement. Section 3 overviews the wavelet transform and diversity combining for application in analyzing SDPPG signals. The noise reduction algorithm with wavelet transform and selection combining is proposed in Section 4. Section 5 presents experiment results. Finally, this paper is concluded in Section 6.