## 1 Introduction  
Photoplethysmography (PPG) is an optical method of obtaining changes in blood volume in tissue. In the general approach of obtaining PPG signals, the tissue in the region of the digital or radial artery is illuminated with light of multiple wavelengths. The light waves interact with the tissues and blood components and are absorbed or scattered in the medium. As the blood volume changes in a certain location of the human body, due to the pulsatile nature of blood flow, the received light intensity also changes with the change in blood volume. Historically, PPG signals have been utilized to detect time-domain properties and quantitative properties of the human body. The time-domain properties include--but are not limited to--respiratory rate [1] and heart rate [2]. The most widely used quantitative property of the human body that is measured with PPG signals is the blood oxygenation (SpO2) parameter [3, 4, 5]. This parameter indicates the percent amount of oxygenated hemoglobin with respect to total hemoglobin count. Recently, a study was conducted to war for potential infection by COVID-19 by estimating SpO2 using PPG signals [3]. The other quantitative properties include blood pressure [4], hypo- and hypervolemia [5], and blood glucose levels [6, 7]. The time-domain properties require single-wavelength PPG (SW-PPG) to evaluate. On the other hand, to estimate the quantitative properties, multiple wavelengths of PPG (MW-PPG) signals are required. Diabetes mellitus is a disease that affects the production and utilization of insulin, which directly modifies the consumption of blood glucose by body cells. A result of diabetes is the presence of an excessive amount of glucose available in the bloodstream. This not only changes the properties of the blood but also causes other serious diseases, including kidney failure [8], heart disease [9], and sudden mortality [10]. For these reasons, the diagnosis of diabetes is very important for reducing the risk of insulin control failure in its early stages. There are several methods available to diagnose diabetes. The main approaches for diagnosis are random, fasting, or oral glucose tests, and glycated hemoglobin test. Estimating blood glucose levels non-invasively for the diagnosis of diabetes is a fairly new topic within the scope of PPG signals [6]. The current state-of-the-art for non-invasive blood glucose estimation is the utilization of external skin tissues and saliva or tears [11; 12]. There are also other non-invasive procedures, with which glucose levels can be estimated [13; 14; 15; 16]. However, the non-invasive glycated hemoglobin (HbA1c) test is the most recent topic of discussion. Since the invasive test of HbA1c requires blood samples, it can be inconvenient for users to perform tests frequently. HbA1c is the non-enzymatic bond of hemoglobin with sugar molecules. The sugar molecules are usually monosaccharides. The more sugar molecules present in the bloodstream of a person, the more the probability of the glycation of hemoglobin increases. Moreover, the final product of glycation (HbA1c) is very stable and does not usually alter within the life cycle of the glycated hemoglobin molecule. Due to these factors, the HbA1c level in a human body is a very slow varying parameter, and is usually considered equivalent to the three-month weighted average of the blood sugar level [17]. Measurement of hyperglycemia-associated conditions was performed on mice models to classify normal, obese, and diabetic groups in a recent study [18]. In another study, the researchers designed a method to estimate HbA1c by measuring breath acetone components [19]. There are only two papers that conducted studies on the estimation of glycated hemoglobin using PPG signals. One of the studies performed an in vitro analysis from the blood sample [20], and the other study was designed to measure the HbA1c by in vivo measurement [21].