## 1 Introduction  
Traditional blood glucose testing often requires blood samples, which can be uncomfortable for a patient and increase the risk of skin and red-blood-cell-life abnormalities. On the other hand, the glycated hemoglobin (_HbA1c_) value reflects the average blood glucose level over the previous three months, and it is unaffected by physical activity or food intake for several hours leading up to measurement. High levels of _HbA1c_ indicate poor blood glucose control. As a result, it is used as the most fundamental indicator of the degree of blood glucose control over a period of time and to predict the onset of long-term issues due to diabetes. Human blood consists of 55% yellow liquid plasma, 44% solid red blood cells, and 1% white blood cells and platelets. Hemoglobin is a type of protein found in the red blood cells that plays an important role in transporting oxygen by binding to the oxygen in the blood and to the glucose contained in blood cells. Hemoglobin bound to glucose is called glycated hemoglobin. Regarding glycated hemoglobin, the more glucose there is in the blood, the more the hemoglobin in the red blood cells that binds to the glucose, resulting in higher blood glucose levels. The glycated hemoglobin level is the ratio of glycated hemoglobin to total hemoglobin in the blood. Because the normal lifespan of red blood cells is approximately 4 months and the lifespan of individual red blood cells can vary widely, this test can only provide the \(HbA1c\) estimate over the preceding 3 months. People with diabetes are at increased risk of developing additional medical complications, such as heart diseases, kidney failure, stroke, cataracts, and/or premature death. Therefore, the early diagnosis of diabetes in the prediabetic stage is crucial for preventing deterioration of the blood sugar regulation system. This can be achieved through various blood-based tests, such as the random, oral, and fasting blood glucose tests or the glycated hemoglobin (\(HbA1c\)) test. These tests are used to detect the levels of glucose in the blood, which is a key indicator of diabetes. In diagnosing diabetes, the \(HbA1c\) test is known to have a better performance than the plasma glucose test [1]. Many enzymatic and nonenzymatic electrochemical glucose sensors [2; 3; 4; 5; 6; 7] have been created over the past few decades; however, these approaches are invasive. Immunoassay, ion-exchange high-performance liquid chromatography (HPLC), boronated affinity chromatography, and capillary electrophoresis (CE) are the four most commonly used methods for estimating \(HbA1c\)[8]. Both HPLC-electrospray mass spectrometry (HPLC-ESI/MS) and HPLC-capillary electrophoresis-ultraviolet (HPLC-CE-UV) are recommended by the International Federation on Clinical Chemistry and Laboratory Medicine (IFCC) for measuring \(HbA1c\) levels in human blood [9]. All of these methods still require blood samples. However, the development and practical use of noninvasive \(HbA1c\) estimation tests have been of increasing interest recently. One study [10] only addressed photoplethysmography (PPG) sensor design and did not consider noninvasive in vivo estimation techniques while discussing the estimation of in vitro \(HbA1c\) levels. Based on the measurement conditions related to hyperglycemia, researchers have divided mouse models into diabetic, obese, and normal control categories [11]. In [12], the authors reported that individuals could be divided into diabetic and non-diabetic categories using PPG signals. In another study [13], the \(HbA1c\) levels were calculated by also taking into account the acetone levels in the breath. In our previous study [14], we estimated \(HbA1c\) noninvasively using the Beer-Lambert law-based model with three wavelengths. However, the three wavelengths used made the model complicated and inconvenient for the user, as well. To address these issues, a noninvasive estimation strategy using PPG signals with only two wavelengths is proposed herein.