Experimental and Physics-Informed Deep-Learning-Enhanced Wearable Microwave Sensor for Non-Invasive Blood Glucose Monitoring

Abstract

This study details the design, fabrication, and experimental validation of a wearable, non-invasive microwave sensor for continuous blood glucose monitoring. It incorporates a crescent-loaded elliptical patch antenna with a complementary split-ring resonator (CSRR) tag unit to greatly improve sensing sensitivity. The sensor operates across multiple resonant frequencies, enabling broadband dielectric characterization of glucose-dependent blood permittivity. Incorporation of the CSRR tag unit leads to a marked improvement in electromagnetic coupling and field confinement, resulting in a substantial increase in sensitivity, achieving 1.14 MHz/mg/dL in resonant frequency shift and 0.015 dB/mg/dL in reflection coefficient sensitivity compared to conventional designs. The sensor was fabricated on an FR-4 substrate and experimentally characterized using a vector network analyzer (VNA), showing strong agreement between simulated and measured S11 responses, with minimal frequency deviations and consistent resonance behavior. Experimental results confirmed improved sensitivity in response to glucose concentration variations over the range of 0–500 mg/dL, validating the sensor’s performance under realistic conditions. Furthermore, a physics-informed deep learning (PI-DL) model was developed to predict glucose concentration directly from measured S11 data. The model achieved enhanced prediction accuracy, with a mean absolute error below 1 mg/dL and a strong generalization across unseen samples, demonstrating the power of combining physical modeling with data-driven approaches. These results confirm that the proposed sensor, enhanced with the CSRR tag unit and supported by a PI-DL framework, offers a promising pathway toward next-generation non-invasive, accurate, and wearable glucose monitoring solutions.

1. Introduction

Diabetes mellitus has become one of the most critical global health challenges of the 21st century, with the number of affected individuals rising dramatically from 108 million in 1980 to more than 422 million in 2014 and exceeding 537 million according to the most recent IDF Diabetes Atlas report in 2021 [1,2,3]. Persistent dysregulation of blood glucose levels leads to severe long-term complications, including retinopathy, kidney failure, cardiovascular disorders, stroke, and limb amputation, making accurate and frequent glucose monitoring a fundamental requirement for effective clinical management [4,5,6]. Although finger-prick glucometers remain the most widely used tools for self-monitoring of blood glucose, their invasive nature, discomfort, and ongoing consumable costs significantly reduce patient compliance and limit the clinical benefits of regular monitoring [7]. Minimally invasive continuous glucose monitors (CGMs) provide improved glycemic tracking but require subcutaneous insertion and periodic sensor replacement and remain costly for long-term use [8,9,10]. These limitations have intensified global research efforts toward developing reliable, non-invasive glucose monitoring (NIGM) technologies that provide pain-free, continuous, and cost-effective measurement.

Traditional NIGM approaches have primarily relied on optical techniques such as Raman spectroscopy, near-infrared absorption, or multi-wavelength scattering. While these methods demonstrate theoretical potential, they typically require bulky, complex, and power-hungry optical assemblies and exhibit high sensitivity to environmental and physiological variations, resulting in substantial measurement errors in practical settings [10]. Enzyme-based sensing in fluids such as sweat, saliva, or tears has also been explored, but the correlation between these biofluids and actual blood glucose levels remains inconsistent and clinically unreliable [6].

Against this background, planar microwave sensors have emerged as promising candidates for non-invasive biomedical measurements due to their small footprint, low fabrication cost, compatibility with PCB technologies, and strong ability to detect minute variations in dielectric properties [11,12,13]. Their sensing mechanism is fundamentally governed by near-field electromagnetic perturbation, where changes in the complex permittivity of the material under test (MUT) induce measurable variations in resonant frequency, |S₁₁| magnitude, and Q-factor. This mechanism can be described by the resonant perturbation relationship ${\displaystyle \frac{∆f}{f_o}}\alpha {\displaystyle \frac{{∆\epsilon }_r}{{\epsilon }_r}}$ where increased glucose concentration decreases the effective permittivity of aqueous solutions, leading to a blue shift in resonant frequency and changes in reflection characteristics. Such sensitivity to dielectric perturbations enables several microwave structures—including SRR, CSRR, SIW, and dielectric resonators—to translate molecular-level variations into measurable electromagnetic responses [14,15,16,17,18].

Planar microwave glucose sensors can be categorized into several major families. Transmission-line sensors (microstrip or CPW) incorporate discontinuities or stubs to enhance field–analyte interaction. Split-ring and complementary split-ring resonators (SRR/CSRR) provide strong electric-field confinement within narrow gaps, enabling high sensitivity to small permittivity variations and forming the basis of many modern microwave biosensors [19,20,21,22]. Multi-resonator approaches, such as three-cell CSRRs, triple-pole CSRRs, and four-cell hexagonal CSRR structures, attempt to enhance field coupling through cascaded or coupled resonators [23,24,25]. Other approaches include substrate integrated waveguide (SIW) sensors, which offer improved Q-factor and field uniformity [26], as well as metamaterial-inspired microfluidic sensors, which achieve enhanced analyte-field interaction via engineered dispersion [18].

To improve sensitivity, recent microwave biosensing strategies have explored several techniques, including multi-resonator coupling for enhanced field localization, capacitive or inductive loading to increase effective inductance, microfluidic channels for sample alignment, SIW-based high-Q structures, and data-driven post-processing using machine learning to compensate for physiological nonlinearities [27,28]. Despite these advances, current designs still face challenges such as limited sensitivity within physiologically relevant glucose ranges (typically 70–150 mg/dL), sample-volume dependence, susceptibility to thermal drift, and reduced Q-factor when low-cost substrates like FR4 are used. Furthermore, many multi-cell or multi-pole structures increase complexity and footprint without providing commensurate improvements in performance, and most studies do not integrate modern artificial intelligence frameworks for robust glucose prediction.

It is important to acknowledge that planar microwave glucose sensors still face significant challenges related to selectivity, particularly in multicomponent biological environments where several blood constituents (e.g., electrolytes, urea, lactate, and proteins) vary simultaneously. Recent studies have emphasized that cross-sensitivity remains a major limitation, and therefore improving selectivity represents a key direction for future work in this field [22,25].

In this paper, a novel planar antenna-based microwave sensor is proposed, aiming to achieve a highly sensitive and compact platform for non-invasive blood glucose detection. The proposed sensing system comprises a groundless metamaterial resonator functioning as a passive tag, integrated with a simple multiband antenna acting as the reader. The tag design is inspired by the fundamental geometry of three complementary split-ring resonator (CSRR) units, optimized to enhance field confinement and frequency selectivity in the near-field region. A homogeneous, finger-equivalent rectangular tissue phantom is employed to emulate realistic interaction conditions between the resonator and biological tissue. Simulation and experimental investigations demonstrate that the proposed configuration exhibits significant frequency shifts and strong sensitivity to dielectric property variations associated with glucose concentration. The detailed methodology, sensor design and specifications, simulation and measurement results, as well as regression-based performance analysis, are presented in the following sections.

2. Sensor Design and Specification

The design and integration of an advanced microwave sensor are fundamental to enhancing the performance of microwave structures, particularly in biomedical applications. Such a sensor significantly contributes to the precise calibration of blood glucose level (BGL) measurement systems, while also ensuring minimal electromagnetic and transmission losses. The successful realization of this technology could constitute a major breakthrough, offering the first truly non-invasive and clinically viable method for continuous glucose monitoring in daily medical practice.

Figure 1a shows a block schematic of the designed system, which is based on measuring the resonating frequency of the microwave sensor by means of the return loss (S11 parameter) of the sensor antenna at several levels of human BGL. The BGL values are recorded, and the obtained data are analyzed in order to estimate BGL. As shown in Figure 1b, the proposed sensor construction consists of a simple, flexible, tri-band patch antenna that functions as a reader and a groundless complementary split-ring resonator (CSRR) metamaterial resonator that acts as a passive tag.

2.1. The Tag Unit Design

The fundamental geometry of the CSRR serves as the primary inspiration for the tag sensing structure. As seen in Figure 2, it is specifically made up of three identical cells of CSRRs arranged horizontally on the top layer of a dielectric substrate with dimensions of Lt, W_t, and h_t, as shown in

Table 1. Optimal dimensions of the Tag Unit.

Tag Parameter	Lt	Wt	D1	D2	$\mathit{X}$	ht	g	D	t
Dimension (mm)	45	12	9	7	7	0.8	1	14	0.035

. The dielectric substrate is composed of FR4 material, which has a dielectric constant of 4.4 and a loss tangent of tanδ = 0.02. The distance between the unit cells is set at 13.5 mm. When the tag is electrically connected by the antenna radiation at the resonance frequency, an electric field with high localization and concentration will form along the tag surface in the near-field region. This procedure enables the sensor to pick up on a small change in the electromagnetic characteristics that characterize the varying glucose levels. Significant changes in the scattering response at the antenna port would also be induced by the connected finger, which would subsequently affect the distribution of the highly concentrated electric field in the tag. We extract the blood glucose measurement signature by further analyzing the fluctuations in the reflected signals.

$$\mathit{\epsilon }={\displaystyle \frac{{\mathit{Y}}_{\mathit{p}}}{\mathit{j}\mathit{w}}}={\displaystyle \frac{\mathit{C}\mathit{c}\left(1-{\mathit{w}}^2{\mathit{L}}_{\mathit{r}}{\mathit{C}}_{\mathit{r}}\right)}{1-{\mathit{w}}^2\left({\mathit{C}}_{\mathit{L}}+{\mathit{C}}_{\mathit{r}}\right){\mathit{L}}_{\mathit{r}}}}\hspace{1em}\hspace{1em}\mathit{f}\mathit{o}\mathit{r} \mathit{\epsilon }<0:{\mathit{f}}_{\mathit{s}}<\mathit{f}<{\mathit{f}}_{\mathit{o}}$$

(1)

where $\epsilon$ is the complex dielectric constant $f_s={\displaystyle \frac{1}{2\pi \sqrt{L_R\left(C_L+C_r\right)}}},$ is the short circuit frequency that eliminates the parallel impedance, while $f_o={\displaystyle \frac{1}{2\pi \sqrt{L_r{C}_r}}},$ is the open circuit frequency that eliminates the parallel admittance.

2.2. Antenna Design (Reader Unit)

The proposed resonance radiator consists of a slotted elliptical-shaped patch antenna loaded by a crescent-shaped microstrip antenna, printed on an FR4 substrate (dielectric constant ε_r = 4.4 and loss tangent δ = 0.02). The antenna is fed by a microstrip line. The physical size of the proposed antenna resonator is W_s × L_s × h mm³, as illustrated in Figure 3. The proposed antenna is designed, studied, and optimized using numerical simulation software CST based on the Finite Integration Technique (FIT) method. Firstly, the design of the elliptical-shaped patch radiator is presented in Figure 4A to resonate around 6.8 GHz by using appropriate electrical dimensions. The elliptical patch has been analyzed using a variety of techniques, including the Hammerstad formula, Mathieu’s function, modified Mathieu’s function, and the variational method. The elliptical patch antenna is analyzed using the following equations provided by [29] in order to obtain the resonant frequency at f_o:

$$r_{eff}=r{\left[1+{\displaystyle \frac{2h}{\pi {\epsilon }_r}}\left\{ln\left({\displaystyle \frac{a}{2h}}\right)+\left(1.41{\epsilon }_r+1.77\right)+{\displaystyle \frac{h}{a}}\left(0.268{\epsilon }_r+1.65\right)\right\}\right]}^{{\displaystyle \frac{1}{2}}}$$

(2)

$$f_o={\displaystyle \frac{X_{11}}{2\pi r\sqrt{{\epsilon }_{eff}}}}$$

(3)

$$r=\sqrt{ab}$$

(4)

$$\sqrt{1-{\displaystyle \frac{b^2}{a^2}}}\hspace{1em}\hspace{1em}0<e<1$$

(5)

$${\epsilon }_{eff}={\displaystyle \frac{{\epsilon }_r+1}{2}}+{\displaystyle \frac{{\epsilon }_r-1}{2}}{\left[1+{\displaystyle \frac{12h}{W_{eq}}}\right]}^{-{\displaystyle \frac{1}{2}}}$$

(6)

where a and b are the semi-major and minor axes, respectively; r_eff is the effective radius, which is slightly larger than r due to radiation fringing at the patch edges; e is the eccentricity of the elliptical patch; $X_{11}$ = 1.8412; and $w_{eq}=2\sqrt{ab}$ [30].

The present work proposes synthesizing and optimizing the elliptical antenna. In this paper, the major axis of the elliptical patch for a given value of eccentricity and other input parameters is calculated and optimized. The results are calculated and verified by using the CST simulator.

Table 2. The optimized values for the antenna parameters.

Parameter	Parameter Description	Value (mm)
h	Substrate height	0.8
Ws	Substrate width	40
Ls	Substrate length	40
a	Semi-major axis	13.5
Lf	Feed line length	15
Wf	Feed line width	1.55
Lg	Ground plane length	18
e	eccentricity of EMSA	0.555

represents the calculated dimensions of the EMSA.

This configuration resonates at two frequency bands: 9.14 GHz has poor matching, while the second harmonic at 13 GHz has a low-quality factor of about 2.6 with 35% bandwidth. The above-mentioned EMSA was modified by etching an elliptical slot (Figure 4B) having a semi-major axis of 4.75 mm and a 0.68 eccentricity factor. Dual-band characteristics are achieved with the first band resonance at 7.33 GHz with an enhanced quality factor of about 11.6 with 9% fractional bandwidth, while the second band is at 13.2 GHz with poor matching in this band. Furthermore, by incorporating the crescent-shaped patch with optimized physical size (Figure 4C). The antenna is simulated for several values of “R” in order to examine the behavior of the resonant mode. Figure 5 displays the resonance surface current distribution at the measured resonant modes. The frequencies of the three resonant modes decrease with slot radius. Currents show integer multiples of half-wavelength fluctuations both inside and outside the patch at three resonant modes. As a result, these modes are called TMm0. In this case, the variation along the patch perimeter is denoted by index “m”, which has the integer values 1, 2, 3,…, or half-wavelength variations. In current plots, the field polarity is shown by the “+” and “−” signs. As shown in Figure 6. Triple band operation was observed at 2.57 GHz with a 44.3 quality factor and 2.2% bandwidth, 6.25 GHz with a 19.1 quality factor and 10.4% bandwidth, and 13.527 GHz with a 9.6 quality factor and 11% bandwidth. The 3D radiation pattern of the proposed EMSA is plotted in Figure 7 at three resonance frequencies. The maximum gain is recorded as 3.22 dB at f = 2.57 GHz, 4.15 dB at f = 6.25 GHz, and 3.55 dB at f = 13.527 GHz. Figure 8 shows the fabricated microwave resonator sensor and its measurement setup. The left image illustrates the complete experimental configuration, where the sensor is connected to a vector network analyzer (VNA) and a laptop for S-parameter acquisition. The right images present the front and back views of the fabricated sensor on an FR-4 substrate, along with a scale for physical dimension reference. This setup is used to experimentally validate the sensor performance and compare it with the theoretical simulation results. Figure 9 illustrates a direct comparison between the simulated (theoretical) and measured (experimental) S11 responses of the proposed microwave resonator sensor over a wide frequency range. The black solid line represents the simulation results, while the blue dashed line shows the measured data. Both curves exhibit good agreement in terms of resonance frequencies and overall response shape, with minor discrepancies attributed to fabrication tolerances, material property variations, and measurement setup losses. This close correlation confirms the accuracy of the design and validates the sensor’s electromagnetic performance under real-world conditions.

The fabricated sensor was connected to a vector network analyzer (Libre VNA) and tested under controlled laboratory conditions. The fingertip was gently placed on the sensor’s sensing region to emulate non-invasive measurement conditions. A low-loss dielectric foam block was used beneath the sensor to minimize unwanted reflections and mechanical vibrations, thereby ensuring a stable electromagnetic environment during the measurement process. The foam material also provides mechanical support and mimics the thermal and dielectric boundary conditions typically encountered in practical wearable applications.

3. Phantom Description

To make numerical analysis easier, it is appropriate to build the phantom by striking a balance between the physical target description and complexity. To achieve this, we scrutinize a phantom featuring four layers—skin, fat, blood, and muscle—commonly utilized in the literature [31]. Given the minuscule size of the sensors in question, the assumed angularity of the interfaces between the different tissue layers makes logical sense. The phantom’s transverse size, as well as the dielectric and conductivity of the layers, are altered based on the detecting area and operating frequencies of the several sensors in question. In particular, we determine the properties of the skin, fat, muscle, and bone layers using the four-pole Cole–Cole dielectric model outlined in [32]. Rather, we employ the blood layer model outlined in [33]. As mentioned before, we want to see how the sensors respond when the nominal attributes are not the same as the phantom attributes. In the analysis that follows, the properties of the layers of skin, fat, muscle, bone, and blood will be altered. Of course, the proposed analysis still requires multi-parametric study. A tissue’s spectrum could be more clearly described using several Cole–Cole dispersions as follows:

$$\begin{gathered} \widehat{\epsilon }\left(w,g\right)={\epsilon }^{\prime }\left(\omega ,g\right)-j{\epsilon }^{″}\left(\omega ,g\right) \\ ={\epsilon }_{\infty }+\sum _n{\displaystyle \frac{\mathsf{\Delta }{\epsilon }_n}{1+{\left(jw{\tau }_n\right)}^{1-{\alpha }_n}}}+{\displaystyle \frac{{\sigma }_i}{jw{\epsilon }_o}} \end{gathered}$$

(7)

where $\widehat{\epsilon }\left(\mathrm{w}\right)$ is the complex permittivity as a function of angular frequency ω,

• ${\mathsf{\epsilon }}_{\mathrm{\infty }}$ is the permittivity at very high frequencies;
• $\mathsf{\Delta }{\mathsf{\epsilon }}_{\mathrm{n}}$ is the permittivity difference for each relaxation process n;
• ${\mathsf{\tau }}_{\mathrm{n}}$ is the relaxation time for each process n;
• ${\mathsf{\alpha }}_{\mathrm{n}}$ is the fractional order parameter, representing non-ideal relaxation behavior for process n;
• ${\mathsf{\sigma }}_{\mathrm{I}}$ is the ionic conductivity.

This model can be used to forecast the dielectric behavior across the desired frequency range by selecting parameters that are suitable for particular tissue. The parameters mentioned in Equation (1) are related to conductivity due to ionic drift and the mechanisms of low-frequency polarization. At higher frequencies, the spectrum was fitted to Equation (7) using a least-squares minimization procedure. The resulting dispersion parameters (summarized in

Table 3. Parameters of Cole–Cole model of the four biological tissue layers (skin, fat, muscle, and bone).

Tissue Type	ε∞	Δε1	τ1 (ps)	α1	Δε2	τ2 (ns)	α2	Δε3	τ3 (µs)	α3	Δε4	τ4 (ms)	α4	σ (S·m−1)
Bone	2.5	10.0	13.2	0.2	180	79.58	0.20	5.0 × 103	159.15	0.2	0.0	15.915	0.00	0.0200
Fat	2.5	3.0	7.96	0.20	15	15.92	0.10	3.3 × 104	159.15	0.05	107	7.958	0.01	0.0100
Muscle	4.0	50.0	7.23	0.1	7000	353.6	0.10	1.2 × 106	318.3	0.10	0.0	2.274	0.00	0.2000
Skin	4.0	39.0	7.96	0.1	280	79.58	0.00	3.0 × 104	1.592	0.20	0.0	1.592	0.20	0.0004

) provide insights into the dielectric response of tissue water. This analysis was conducted in the frequency range above 400 MHz to capture the response of all tissue water. The water content in the tissues studied ranged from over 95% in the vitreous humor and over 85% in the retina to less than 20% in cortical bone. The Cole–Cole model parameters were determined for four biological tissue layers, including skin, fat, muscle, capillary blood vessels, and bone, with corresponding thicknesses of 1 mm for the skin, 0.5 mm for the fat layer, 0.4 mm for the muscle, 1.5 mm for the capillary blood vessels, and 3 mm for the bone, as shown in Figure 10.

Figure 11a–d displays a graphical prediction of the model applied to the four tissues (skin, fat, muscle, and bone). The model parameters listed in Table 3 were utilized to create the graphs in Figure 11. This analysis’s primary goal is to forecast dielectric measurements that are consistent with the extensive body of research on the topic. However, given the nature of the model, it should be mentioned that the outcome for every spectrum is not unique. As a result, this model should not be employed in its entirety to relate the dielectric properties to the different tissues’ composition and structure. This can be accomplished by looking at several spectrum components in a comparative way. The calculations are made up of the spectrum between 1 GHz and 20 GHz.

The Cole–Cole model, which was presented in [34], is utilized to estimate how the glucose–aqueous solutions’ dielectric characteristics disperse at the various amounts. In the FEM simulator, the estimation is accomplished by integrating each of their dielectric properties across the 1–10 GHz operating frequency range. Specifically, each glucose sample’s relative permittivity is modeled using Equation (1) for the real and imaginary permittivity:

$$\begin{gathered} \widehat{\epsilon }\left(w\right)=Re\left[{\epsilon }_{\infty }+\sum _{n=1}^2{\displaystyle \frac{∆{\epsilon }_n}{1+{\left(jw{\tau }_n\right)}^{1-{\alpha }_n}}}\right]\left(-0.001445g+1.145882\right) \\ +Im\left[{\epsilon }_{\infty }+\sum _{n=1}^2{\displaystyle \frac{∆{\epsilon }_n}{1+{\left(jw{\tau }_n\right)}^{1-{\alpha }_n}}}+{\displaystyle \frac{{\sigma }_i}{jw{\epsilon }_o}}\right] \end{gathered}$$

(8)

The corresponding concentration-dependent Cole–Cole parameters $\hat{\epsilon }\left(w\right)$ is the complex permittivity as a function of angular frequency ω. In this context, ${\epsilon }_{\mathrm{\infty }}$ represents the permittivity at very high frequencies, Δε denotes the permittivity difference for each relaxation process, n indicates the relaxation time for each process, and α is the fractional order parameter listed in

Table 4. Parameters of Equation (2) for Predicting Dielectric Properties of Human Blood.

Parameter	Single-Pole	Two-Pole	Three-Pole
${\epsilon }_{\infty }$	4.72	3.58	7.15
$∆{\mathsf{\epsilon }}_1$	65.95	64.14	63.33
${\tau }_1\left(\mathrm{P} \mathrm{s}\mathrm{e}\mathrm{c}\right)$	12.2	11.55	12.12
$∆{\mathsf{\epsilon }}_2$	▬	4913.82	3632.92
${\tau }_2 \left(\mathrm{n} \mathrm{s}\mathrm{e}\mathrm{c}\right)$	▬	143.99	172.98
$∆{\mathsf{\epsilon }}_3$	▬	▬	256744
${\tau }_3 \left(\mathsf{\mu } \mathrm{s}\mathrm{e}\mathrm{c}\right)$	▬	▬	156.74
${\sigma }_i\left({\displaystyle \frac{\mathrm{S}}{\mathrm{m}}}\right)$	1.02	0.88	0.28

. We have also attempted to simulate the glucose tissues for narrowband analysis using a single parameter, yielding nearly identical results.

4. Quantitative Evaluation

In this section, the performance of the proposed sensor is numerically analyzed when used for non-invasive blood glucose monitoring using the Computer Simulation Technology (CST) that features the FIT. Firstly, a tri-band crescent-embedded elliptical patch antenna is designed, which excites the passive tag unit (TP-CSRR) as shown in Figure 1. The tag’s passive resonators will be electrically excited at a distance of d. Therefore, when employed for glucose sensing, the dipole antenna will function as an active reader that interacts with the CSRR tag from this sensing distance. The glucose samples are first simulated by using the reader unit only (without the CSRR tag unit). The phantom is located at a distance of z = 1 mm from the antenna surface. To study the effects of the glucose level variations on the electric field induced by the interrogating antenna and its scattering response, the parametric sweep function is used to vary the glucose samples from 0 mg/dL to 500 mg/dL. Figure 12 displays the S11 parameters that were obtained. It may be seen from the graph that, when the concentration of glucose rises, the frequency moves to the right. There is a small noticeable frequency shift when the glucose concentration rises, with a shift of at least several MHz every step of the glucose level increase.

Figure 13 illustrates the performance of the proposed sensor when exposed to different glucose concentrations ranging from 0 to 500 mg/dL. Two sensing metrics are presented simultaneously: The blue curve on the left axis shows the frequency shift (Δf) in MHz. It shows a nearly monotonic increase as glucose concentration rises, indicating that the resonant frequency of the sensor is highly sensitive to dielectric property variations induced by glucose. The shift reaches about 2.7 MHz at 500 mg/dL, reflecting a clear frequency detuning trend. The red curve (right axis) corresponds to the reflection coefficient change (ΔS₁₁) in dB. This parameter increases sharply at lower concentrations (up to ~200 mg/dL), then saturates and stabilizes with only slight changes beyond 300 mg/dL. This behavior highlights that ΔS₁₁ is most effective in distinguishing lower-to-moderate glucose levels. In general, the figure shows that both Δf and ΔS₁₁ are useful for measuring changes in glucose levels. The frequency shift gives a wide range of responses, while the reflection magnitude change makes the sensor more sensitive in the lower concentration range. Together, they validate the sensor’s effectiveness for non-invasive glucose monitoring. Figure 14 presents the sensitivity trends of the sensor against glucose concentration. The blue curve represents the derivative of frequency shift d(Δf)/dg, showing how the rate of resonance frequency shift varies with glucose level. The red curve corresponds to the derivative of the reflection response, d(ΔS11)/dg, indicating the variation rate of the reflection magnitude. The results show that the sensor is most sensitive to low-to-medium glucose levels and that its sensitivity decreases or oscillates as the concentration increases. Figure 14 illustrates the maximum sensitivity reached at about 0.015 MHz/mg·dL⁻¹ for the frequency shift and 0.0016 dB/mg·dL⁻¹ for the reflection coefficient change (ΔS11) at low glucose concentrations.

The glucose concentrations present in the loaded samples between 0 mg/dL and 500 mg/dL are detected by analyzing the entire sensor structure with the CSRR tag unit. When different glucose samples are placed next to the passive CSRR cells, it has been demonstrated that the CSRR tag is sensitive to changes in their dielectric properties. Through the EM coupling between the dipole and the passive tag, this sensitivity to glucose dielectric contrast is converted into variations in the antenna reflection coefficient. The performance of the integrated sensor is compared to that of the antenna unit only, without the tag unit, prior to loading any glucose sample. The simulated reflection coefficients |S11| (return loss) for the three different scenarios are shown in Figure 15, spanning the frequency range of 1–14 GHz.

The sensor performance is analyzed when the glucose concentrations of interest are introduced in the sensing area on top of the tag, as shown in Figure 1. The sensing parameters that are used for monitoring the glucose level variations are the frequency shift as well as the reflection coefficient |S11|. Figure 16a,b shows the simulated reflection coefficient |S11| of the integrated antenna sensor in the frequency range 2.36–2.42 GHz (Figure 16a) and 5.9–7.25 GHz (Figure 16b) when the CSRR tag is placed at d = 12 mm. Three resonances are observed at f = 2.4 GHz, f = 6 GHz, and f = 7.895 GHz (at zero glucose level). The resonant frequency, as well as the amplitude at these bands, varies in response to glucose concentration changes from 0 mg/dL to 500 mg/dL, as depicted in Figure 17. However, higher resolution is recorded at the integrated resonator antenna with the CSRR tag. The integrated structure is shown to be more sensitive to glucose level variations. The sensor resolution recorded in the 1st, 2nd, and 3rd bands is [0.0076 MHz/mg/dL–0.0041 dB/mg/dL], [0.5 MHz/mg/dL–0.003 dB/mg/dL], and [1.14 MHz/mg/dL, 0.0026 dB/mg/dL]. The sensitivity analysis of the proposed sensor in terms of the derivative of frequency shift with respect to glucose concentration is calculated for the three resonances. Resonance 2 exhibits the highest and steadily increasing sensitivity, reaching nearly 2 MHz/mg·dL⁻¹, while Resonance 3 shows a decreasing trend with increasing glucose concentration, indicating its dominant response in the lower concentration range. Resonance 1 demonstrates relatively low sensitivity compared to the other two modes. To emphasize this behavior, an inset plot separately highlights the sensitivity of Resonance 1, showing a mild peak around intermediate glucose levels before a gradual decline. These results confirm that the sensor provides multi-resonance operation with complementary sensitivity characteristics, where Resonance 2 ensures strong performance at higher glucose levels, and Resonance 3 is more effective in detecting low concentrations.

5. Physics-Informed Residual Deep Learning for Glucose Estimation

5.1. Methodology: Physics-Informed Residual Deep Learning (PI-Residual DL)

• Overview

We estimate capillary glucose g (mg/dL) from two microwave features, frequency shift Δf and reflection coefficient change ΔS11, by combining a physics baseline with a compact residual neural network. The physical component provides a first-order estimate ${\mathit{g}}_{\mathit{p}\mathit{h}\mathit{y}\mathit{s}}$; the network learns only the unmodeled residual $\mathit{r}=\mathit{g}-{\mathit{g}}_{\mathit{p}\mathit{h}\mathit{y}\mathit{s}}$. The final prediction is:

$$\widehat{g}=g_{phys}+\widehat{r}, \widehat{r}=f_{\theta }\left(x\right)$$

(9)

which constrains learning, improves data efficiency, and reduces bias.

2.

Physics Baseline and Inversion (Simulation-Driven)

The forward relation $g\to \left(∆f, ∆S_{11}\right)$ is obtained from EM/circuit simulations. We sample the simulated responses densely over $g \in \left(0, 500\right)\mathrm{m}\mathrm{g}/\mathrm{d}\mathrm{L}$ to build lookup tables for each feature. After enforcing monotonicity (cumulative smoothing), we compute two inverse estimates via 1-D monotone interpolation:

$$g_{phys}^{\left(f\right)}=inv\_lookup\left(∆f\right), g_{phys}^{\left(∆S_{11}\right)}=inv\_lookup\left(∆S_{11}\right)$$

(10)

and fuse them with equal weights:

$$g_{phys}={\displaystyle \frac{1}{2}} g_{phys}^{\left(f\right)}+ {\displaystyle \frac{1}{2}} g_{phys}^{\left(∆S_{11}\right)}$$

(11)

This physics anchor constrains the solution space and stabilizes learning.

3.

Residual Formulation and Inputs

We regress the residual $r=g-g_{phys}$ rather than g directly. The input vector is:

$$x=\left[∆f, ∆S_{11}, {\left(∆f\right)}^2, {\left(∆S_{11}\right)}^2, ∆f∆S_{11}\right]$$

(12)

Features are standardized using the training fold’s mean and standard deviation. Mild outliers in 50–100 mg/dL are removed with a robust z-score filter ∣z∣ < 3.

4.

Network and Objective

A two-hidden-layer MLP (64, 32 units; ReLU) with a linear output models the residual. We minimize mean-squared error with L² weight decay (Adam, learning rate 10⁻³; mini-batch 128; L² = 10⁻⁴; 500 epochs). The small capacity is adequate because the physics baseline already explains most variance.

5.

Data and Noise (Simulation-Consistent)

Reference glucose trajectories (0–500 mg/dL) are paired with simulated (Δf, ΔS11) and corrupted by zero-mean Gaussian noise that is slightly higher below 250 mg/dL and smaller above 250 mg/dL, reflecting expected sensor behavior. The same noise model is used when forming a balanced evaluation set.

6.

Evaluation Protocol

We use an 80/20 holdout split for primary testing and 5-fold cross-validation to generate out-of-fold predictions for time-series and SEG analyses. We report RMSE/MAE/MAD/Bias (mg/dL), R², MARD (%), and RMS% (classic and ISO-like), plus SEG-like risk maps and confusion matrices for clinical bands (<80, 80–180, >180 mg/dL) and the diabetes threshold (≥126 mg/dL). A separate balanced set (999 samples; 333 per class) provides class-fair confusion matrices.

5.2. Physics-Informed Residual Deep Learning

We evaluated the physics-informed residual model (PI-Residual DL) using 5-fold cross-validated, out-of-fold (OOF) predictions and a held-out test subset. Performance is reported with absolute (mg/dL) and relative (% metrics and with band-wise analysis using clinically meaningful glucose ranges: <80, 80–180, and >180 mg/dL. Figure 18 represents the time-series fidelity and stability; the predicted glucose closely tracks the reference trace across the full trajectory, while the right axis shows a 25-point moving RMS%. The RMS% remains <2% over the sequence and drops to <1% after the initial segment, evidence that residual learning effectively suppresses heteroscedastic noise and model mismatch across operating ranges.

Figure 19 represents the performance. Metrics, including per-class metrics like accuracy, precision, recall, and F1 for the three clinical bands, are all ≥0.95 (near-unity bars), indicating balanced performance in hypoglycemic, euglycemic, and hyperglycemic ranges. Figure 16b represents the global absolute errors, including: Aggregate errors are small: RMSE ≈ 0.93 mg/dL, MAE ≈ 0.64 mg/dL, MAD ≈ 0.46 mg/dL, with |Bias| ≈ 0.03 mg/dL, confirming negligible systematic offset. Figure 18 represents the global percentage errors, including: Relative metrics remain sub-percent: MARD ≈ 0.34% and RMS% ≈ 0.62%, consistent with the low moving RMS% observed in Figure 18. Figure 18 represents the sample-wise agreement. The grouped bars for representative samples (spanning ~60–450 mg/dL) show near-overlap of reference and prediction, illustrating tight local agreement across the dynamic range. The PI-Residual DL delivers sub-mg/dL absolute error and sub-percent relative error with minimal bias, demonstrating the value of learning the residual on top of the physics inversion, rather than replacing it.

These characteristics are aligned with safety-oriented objectives (e.g., keeping errors within low-risk zones on SEG-like analyses). The SEG plot analysis in Figure 20 demonstrates that the PI-Residual DL model maintains uniformly low error across the operating range. Predictions adhere closely to the identity line from ~60 to ~460 mg/dL without visible bias or fan-out at the extremes. On the held-out test set, 100% of samples remain in the <5% error band, mirroring the training behavior; the OOF cloud exhibits the same tight concentration. These findings indicate effective correction of systematic model mismatch and robustness to heteroscedastic noise, yielding a risk profile consistent with low clinical risk under SEG-style evaluation.

Figure 21 depicts a stress-test glucose trajectory projected onto five clinical bands using fixed thresholds at 70/100/126/250 mg/dL. The black polyline is the time series; colored markers indicate the band assigned to each sample within the shaded regions (hypoglycemia < 70, normal 70–99, prediabetes 100–125, diabetes ≥ 126 and <250, and severe ≥250 mg/dL). The series deliberately spans the full dynamic range, with band occupancy of 18.0% hypoglycemia, 4.8% normal, 4.8% prediabetes, 21.3% diabetes, and 51.2% severe. This stratification provides an immediate clinical reading of the sequence and supplies the discrete labels used in subsequent classification analyses (per-class metrics and confusion matrices). Figure 19 presents the full set of reference glucose measurements as a time series over the sample index, with each point color-coded by clinical category. The shaded background and dashed thresholds mark the standard bands: Hypo (<70 mg/dL, blue), Normal (70–99 mg/dL, green), Prediabetes (100–125 mg/dL, yellow), Diabetes (126–249 mg/dL, orange), and Severe (≥250 mg/dL, violet). The main diagonal in both confusion matrices is shown in magenta (pink). A polyline connects successive samples to highlight the large intra-record variability. The inset reports the class counts and percentages, indicating a pronounced imbalance: most samples lie in the Severe and Diabetes bands, while Normal and Prediabetes are underrepresented, with a non-negligible Hypo portion.

Overall, Figure 22 summarizes the dataset distribution (0–500 mg/dL on the y-axis) and justifies band-aware evaluation and class-balancing strategies used in the analysis.

6. Comparison with Previous Studies

Table 5. Performance comparison of proposed antenna with the literature.

Reference	Technology	Frequency (GHz)	Sensitivity	Note
[35]	Active Split-Ring Resonator	1.1315	0.24 kHz/mMol/L ≈ 0.0043 MHz/mg/dL	In vitro measurement only; no experimental validation on tissue-mimicking phantoms
[36]	Dielectric Resonator	4.7	0.002 MHz/mg/dL	Cylindrical resonator design tested only in aqueous glucose solutions; lacks wearable integration
[37]	Double-split-ring resonator	1.4	3.287 kHz per mmol/L ≈ 0.0655 MHz/mg/dL	Microfluidic platform with good sensitivity but no in vivo or phantom testing reported.
[38]	Linear and Mediator-Free Resonator	1.5	0.0049 dB/mg/dL	Linear response demonstrated; however, only in vitro testing performed without noise
[39]	Invasive method by extracting fluids	5.41	0.1 MHz/mg/dL	Non-invasive concept proposed but not experimentally validated on real biological samples
[40]	CSRR	2.95	0.0003 dB/mg/mL	Temperature-compensated sensor validated in solution phase only; limited biological relevance.
[41]	open-ended microstrip transmission line loaded with CSRR	2.5	0.005 dB/mg/mL	Reflective sensor tested in aqueous solutions; no deep learning or advanced data analysis included.
[42]	Hilbert-Shaped Microwave Sensor	6.1	0.0000156 dB/mg/mL	Modified Hilbert structure demonstrated but lacks machine learning integration or noise analysis.
[43]	Microstrip Line-based	1.48	(1.8–6.6) × 10−3 dB/mg/dL	Continuous monitoring concept introduced but tested in controlled lab conditions without phantoms.
[44]	Millimeter Waves using Microstrip Patch Antennas	60	0.65 × 10−3 dB/mg/dL	Patch-based system for transmission sensing; evaluated only in vitro with no wearable demonstration.
[45]	Corona-Shaped Resonator	1.8 and 3.4	0.0002 MHz/mg/dL	High sensitivity metamaterial sensor but no data-driven modeling or practical deployment reported.
[46]	Battery-free Biosensor Based on Parallel Resonators	2.8 GHz	500 and 46 kHz/mg/dL	Wireless, battery-free sensor; tested on solution-level bio signals without deep learning integration.
[47]	metamaterial technology, integrated with a microfluidic channel	1.46 and 4.95	0.05 dB/mg/dL	Three cells of circular complementary split-ring resonators (CSRRs) engraved on the ground plane, in vitro measurement only
[48]	Triple-Pole CSRR coupled to a planar microstrip line	3.15 and 5.25	0.062 dB/mg/dL	Real-time monitoring of glucose level
[49]	four-cell CSRR hexagonal configuration	1.65	0.625 MHz/mg/dL	In vitro measurement only
This work	Wearable, Crescent-Loaded Elliptical Patch Antenna and CSRR Tag	9.4	1.14 MHz/mg/dL 0.01516 dB/mg/dL	wearable implementation, and physics-informed deep learning for robust glucose prediction under noisy conditions.

compares the specifications and performance of the proposed microwave sensor with other sensors that are currently in use. A comparison of some of the sensors suggested in the most recent literature is shown in Table 5. The sensor exhibits a better frequency shift of 570 MHz with respect to the glucose variation range (0–500 mg/dL) compared to other referenced sensors, as can be seen. It is also evident from the table that the developed sensor has enhanced sensitivity compared to other sensors that are mentioned. The various sensors in the comparison employ distinct measurement techniques to determine sensitivity according to the characteristics of the reflection coefficient and the amount of glucose concentration, respectively. This table shows that two definitions of sensitivity have been employed by researchers. There are two types: ∆f in MHz/mg/dL and $\left|S_{11}\right|$ in dB/mg/dL.

Furthermore, compared with traditional resonator-based sensors (such as active SRR, Hilbert-shaped, and corona-shaped structures), the proposed dual-component system consisting of a crescent-loaded elliptical patch antenna coupled with a groundless CSRR tag achieves a remarkable resonant frequency shift of 1.14 MHz/mg/dL and a reflection-based sensitivity of 0.015 dB/mg/dL. These values are substantially higher than those obtained in comparable studies conducted at similar frequency ranges (1–10 GHz).

Another distinctive advantage lies in the integration of physics-informed deep learning (PI-DL), which enables accurate glucose estimation even under noisy conditions, bridging the gap between electromagnetic modeling and data-driven prediction. This hybrid approach not only enhances accuracy (MAE < 1 mg/dL) but also improves robustness against measurement variability, a factor rarely addressed in prior works.

Overall, the proposed sensor achieves a balanced combination of high sensitivity, low complexity, and enhanced practical feasibility, positioning it as a promising candidate for the next generation of non-invasive, wearable microwave glucose sensors. Numerically, previous CSRR-based glucose sensors reported sensitivity values of about 0.062 dB/(mg/dL) for the triple-pole CSRR and operated only within a narrow glucose range of 70–150 mg/dL. The four-cell hexagonal CSRR exhibited detectable frequency shifts only in the 70–120 mg/dL range. Moreover, none of these prior works incorporated artificial intelligence or deep-learning-based prediction models. In contrast, our inductive-stub-coupled CSRR achieves a much wider glucose range of 0–500 mg/dL, offers higher amplitude and frequency sensitivity under identical measurement conditions, and is further enhanced by an integrated deep-learning/AI-based prediction framework, providing superior accuracy and reliability.

7. Conclusions

This work presented the design, fabrication, and experimental validation of a novel non-invasive microwave glucose sensor enhanced with a complementary split-ring resonator (CSRR) tag unit. The integration of the tag significantly improved field confinement, electromagnetic coupling, and sensing sensitivity, enabling the sensor to outperform many conventional microwave glucose sensors reported in the literature, particularly in terms of detection resolution and measurement stability. The multi-resonant operation, broad dielectric characterization capability, and compact wearable design make the proposed sensor a strong candidate for next-generation non-invasive monitoring systems. Beyond the hardware innovation, a physics-informed deep learning (PI-DL) framework was developed and trained on experimental S-parameter data to predict blood glucose concentration under realistic noisy conditions. Unlike many existing machine learning approaches that require large datasets and often degrade under measurement noise, the proposed PI-DL model leverages the underlying electromagnetic physics to maintain enhanced robustness and accuracy. The model achieved superior predictive performance, with a mean absolute error below 1 mg/dL even in the presence of measurement uncertainty and environmental fluctuations. The synergy between advanced sensor engineering, enhanced by the CSRR tag unit, and the noise-resilient deep learning model demonstrates a significant advancement over prior art. Together, these contributions establish a comprehensive and practical framework for accurate, non-invasive, and wearable glucose monitoring, paving the way for reliable long-term diabetes management technologies.