Deep Learning-Based Material Characterization Using FMCW Radar With Open-Set Recognition Technique

This article proposes a low-cost and practical alternative to vector network analyzers (VNAs) for characterizing dielectric materials using a calibrated frequency-modulated continuous wave (FMCW) radar measurement setup and a machine learning (ML) model. The calibrated FMCW radar measurement setup has the ability to accurately measure the $S$ -parameters of dielectric materials. In addition, an ML model is developed to extract material parameters such as thickness, dielectric constant, and loss tangent with high accuracy. $K$ -means clustering was additionally applied to significantly reduce the complexity of the neural network (NN). Additionally, a state-of-the-art open-set recognition (OSR) technique was adopted to simultaneously classify known classes and reject unknown classes. The developed model uses a modified version of the class anchor clustering (CAC) distance-based loss, which outperforms the conventional cross-entropy loss. The proposed model was evaluated on several dielectric materials and compared to reference measurements using a VNA and curve fitting. The results indicate that the proposed model is accurate and robust, and that the calibrated radar sensor provides a practical and cost-effective alternative to VNAs in characterizing dielectric materials, as long as the material parameters are within the defined limits.

and nondestructive testing of automotive dielectric radomes and bumpers.The use of Silicon-Germanium technologies has enabled the development of highly miniaturized, highperformance radar circuits on chips that can be mass-produced at low cost.
Frequency-modulated continuous wave (FMCW) radars have been utilized in a range of applications, including high accuracy distance measurements [1], [2], [3], vital signs monitoring [4], [5], [6], and hand gesture recognition [7], [8].They have also been shown in the literature to be effective tools for material characterization, as they offer a low-cost, compact, and accurate solution for characterizing dielectric materials [9], [10], [11], [12].Thus, they can be considered as a practical and industrially viable alternative to vector network analyzers (VNAs).For example, in [9] and [10] an FMCW radar and a calibration procedure are used to measure the S-parameters of dielectric materials, followed by nonlinear least squares curve fitting optimization to extract material parameters such as thickness, dielectric constant, and loss tangent.However, this approach can be prone to inaccuracies due to oscillations at the edges of the recorded frequency range, the possibility of converging to a local solution, and difficulty in rejecting estimated parameters when errors occur or the material is dispersive or has varying electrical characteristics.Precision in material parameter estimates may be compromised by these limitations, which can be problematic for applications that require high precision.
To overcome the aforementioned problems, this article presents a calibrated FMCW radar and a machine learning (ML) model for accurately measuring the complex-valued reflection coefficient of materials and extracting their material parameters.The proposed approach is fast and robust, increasing the likelihood of obtaining correct material parameter estimates on the first try.Additionally, the ML model uses an open-set recognition (OSR) method to reject estimated parameters during testing if the input belongs to an unknown class, which is particularly important in industrial and medical applications.
The article expands upon the work in [11] by providing a more thorough explanation of the radar measurement setup and calibration procedure, and introducing the concept of OSR to the ML model.The contributions of this work can be summarized as follows.
1) First, the article introduces an FMCW radar and a calibration method based on VNA calibration to measure the complex-valued reflection coefficient of a dielectric material.The radar measurement setup is much simpler and cheaper than a VNA, and it maintains very accurate measurements of the S-parameters.2) A novel method is introduced to significantly decrease the complexity of the ML model by adopting the K -means clustering algorithm to partition the reflection coefficient function and to reduce the number of classes in the model.[13] is proposed to enable classes to form tight clusters around fixed class centers in the embedding space.This enables the model to reject samples from unknown classes without deteriorating the accuracy of the model.4) Finally, the model is tested on a variety of materials and compared to reference measurements in extracting the material parameters.The rest of this article is organized as follows.Section II covers the basics of FMCW radar.Section III addresses the problem of material characterization, including the calibration process in Section III-A and the analytic model of a dielectric slab in Section III-B.Section IV describes the steps for generating a training dataset and introduces K -means clustering.Section V focuses on the OSR problem, including related areas (Section V-A), the modified CAC distance-based loss function (Section V-B), the architecture of the developed neural network (NN) (Section V-C), and performance evaluation (Section V-D).Section VI presents the measurement results.Finally, Section VII offers a conclusion.

II. FMCW RADAR FUNDAMENTALS
Fig. 1(a) shows the radar measurement setup consisting of a D-band FMCW radar sensor [14], the Swissto12 material characterization kit (MCK) [15] that is used in the calibration, and a sample material.The radar sensor is mounted to the Swissto12 MCK using a straight waveguide section.The material under test (MUT) is placed between the corrugated waveguide horn antennas of the MCK, which can also be used to determine the thickness of the MUT.The reference measurement setup is shown in Fig. 1(b), consisting of a VNA ZNA67 from Rohde&Schwarz, two Virginia Diodes WR 6.5 D-Band-Extenders, the MCK, and a MUT.Fig. 2 shows the block diagrams of the FMCW radar sensor and the Swissto12 MCK.A fundamental voltage-controlled oscillator (VCO) stabilized by a fractional-N phase-locked loop (PLL) is used to generate a linear frequency sweep from 63 to 91 GHz.The signal is split up into the transmit and the receive paths using an on-chip lumped-element Wilkinson splitter.The VCO signal to the transmit path is multiplied by 2 in frequency and coupled into a WM-1651 (WR6) waveguide.Another splitter is used to separate the transmitted and received signals at the operating frequency of 126-182 GHz.The VCO signal in the receive path is multiplied by 2 in frequency and fed to a downconversion mixer that multiplies the VCO signal with the received signal.The output of the mixer is low-pass filtered and delivered to an ADC.
The transmitted signal with a positive ramp slope is given by where A is the signal amplitude, ω o is the starting angular frequency, and k = 2π B sw /T sw is the ramp slope, with B sw being the sweep bandwidth and T sw the sweep duration.This transmitted signal gets convolved with the impulse response of the target h(t) and then reflected to the radar.Additionally, the received signal is convolved with the impulse response of the radio frequency (RF) path h RF (t), which accounts for various sources of error in the RF path, including waveguide dispersion [1], [16].The relationship between the target's impulse response and its transfer function is given by [9] where F is the Fourier Transform operation, a n is a complex amplitude component and τ n is the delay time of the target's impulse response.Similarly, the RF impulse response can be written as The received signal is then given by The received signal is multiplied by a copy of the transmitted signal at the mixer, and the output of the mixer is the IF signal.The IF signal is low-pass filtered before the ADC, and the filtered signal is given by The IF signal can be rewritten as where It is important to note that, in the case of an ideal IF signal or with a calibrated radar setup, the following relationships hold: As a result, the IF signal can be simplified to which is equivalent to the real part of the target's transfer function.The imaginary part of the transfer function can be determined from the knowledge of the real part using the Hilbert transform H .The target's transfer function can therefore be determined as

A. Calibration Steps
To accurately estimate material parameters such as the dielectric constant (ϵ r ), loss tangent (tan δ), and thickness (d), it is necessary to use a well-calibrated radar.As previously discussed, S-parameter measurements, which include the reflection coefficient of materials, can be obtained using a calibrated radar.However, the measured reflection coefficient can be distorted by various factors such as diffraction at the edges of the material sample, interference from radar hardware, and waveguide dispersion.
Diffraction effects can be compensated for by using a directive antenna, such as a lens antenna [9], [17] or focusing mirrors setup [9], or a material calibration kit [10] like the one used in this work to transmit a plane wave and achieve a normal incident wave on the front surface of the material.The effects of radar hardware are accounted for in the RF transfer function, which will be compensated for in the SHORT measurement during calibration described later.
Additionally, it is necessary to compensate for waveguide dispersion within the measurement setup by using the inverse transfer function of the waveguide, given by where β is the wavenumber within the setup, defined as , k is the free-space wavenumber, and k c is the cutoff wavenumber of the feeding, which is given by k = ω/c.
Before measuring the MUT, two additional measurements are required for the calibration: MATCH and SHORT, as shown in Fig. 2. The MATCH measurement is obtained by measuring without a target material and is used for static error compensation.The SHORT measurement is obtained by measuring a metallic plate target and is used to compensate for the response of the test setup.
The calibration procedure, shown in Fig. 3, can be described as follows.
1) Subtract the MATCH measurement from the raw measurement of the MUT to compensate for static errors.2) Multiply the IF signal by the inverse transfer function of the waveguide H WG to compensate for waveguide dispersion.3) Zero-pad and multiply the signal by the Hann window before performing a Fast Fourier Transform (FFT) to improve resolution in the echo domain and reduce side lobes.4) Transform the signal to the echo domain using FFT.5) Isolate the reflection due to the MUT from surrounding reflections and residual mismatches in the echo domain using a gating window.6) Transform the range-gated signal back to the frequency domain using an Inverse Fast Fourier Transform (IFFT), which also implies a Hilbert transformation.7) Crop the obtained signal to its original length and normalize it using the SHORT measurement.It is important to note that the SHORT measurement undergoes the same calibration steps before the MUT measurement.Thus, the obtained signal of the MUT is normalized by Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.a calibrated SHORT measurement.The final output is the complex-valued reflection coefficient of the MUT.The calibrated signal should be ideally close to the one from the analytic model.However, due to the gating of the MUT in step (5) in the calibration procedure and other uncompensated sources of error, the reflection coefficient may be distorted by oscillations [9], [10], [18], also known as Gibbs phenomenon.Another source of error is the resonance caused by the upper band limit of the MCK (170 GHz).These factors must be considered to accurately estimate the material parameters.

B. Analytic Model of a Dielectric Slab
In the preceding discussion, we demonstrated how a calibrated radar setup can be used to measure the reflection coefficient of a material.In this section, we will describe the analytical model of a dielectric slab.Assuming that the MUT is nondispersive, meaning that its dielectric constant ϵ r is constant over all operating frequencies, the reflection coefficient of a dielectric slab can be written as follows [19]: where 12 is the intrinsic reflection coefficient of the initial reflection and is given by 12 = ( √ ϵ r,1 − √ ϵ r,2 )/( √ ϵ r,1 + √ ϵ r,2 ), and γ represents the propagation constant defined as γ = 2π f √ ϵ r,2 /c.ϵ r,1 is the dielectric constant of the medium, ϵ r,2 = ϵ r (1 − j tan δ) is the complex dielectric constant of the slab, c is the speed of light and f is the frequency.In this work, we assume that the MUT is nondispersive and has low loss, meaning that its dielectric constant ϵ r is relatively constant over the covered frequency range.As a result, the reflection coefficient, as given in (10), depends on four independent variables: frequency f , sheet thickness d, real permittivity ϵ r , and loss tangent tan δ.

IV. DATASET GENERATION A. Methodology
As previously mentioned, the output of the radar model after calibration is the reflection coefficient of a dielectric slab that is distorted by oscillations.The goal of this research is to develop an ML model that can predict the thickness, dielectric constant, and loss tangent from the calibrated radar signal (from the complex-valued reflection coefficient of the material).Initially, the plan was to develop a regression model that had a final layer consisting of three output neurons, with each neuron corresponding to one of the material parameters.However, the results in this work indicate that this model is unable to generalize to real measurements without significant training data and complex architecture.Furthermore, this model cannot utilize OSR techniques to reject estimates in the case of measurement inaccuracies or calibration errors.Regression models output a continuous variable, making it difficult to set limits on the range of values a material parameter can take.Although it is possible to set a threshold to reject samples outside of this range, it may not be as effective when dealing with errors in measurements that result in false estimates within the defined limits.
In contrast, classification models output categorical variables, making it possible to employ OSR techniques to reject unknown samples by setting a threshold for output scores and rejecting samples that fall outside of these thresholds.The classifier's number of classes is determined by considering the range of possible values for the material parameters d, ϵ r , and tan δ, with N d , N ϵ r , and N tan δ denoting the number of samples for each parameter.Multiplying these values gives the total number of possible classes, which could be a significant amount.In this work, we propose an approach that balances the regression and classification methods.Since tan δ has a negligible effect on the resonance frequency, and only affects the notch depth, while the resonance frequency is mainly determined by d and ϵ r , the number of classes can be determined only by N d × N ϵ r .The effect of tan δ on the notch depth can be estimated using a regression approach.In this work, the values for d range from 0.5 to 5.0 mm with a step size of 0.01 mm, resulting in N d = 451, and the values for ϵ r range from 2 to 5 with a step size of 0.01, resulting in N ϵ r = 301.The total number of classes is then N = 135 751, which is still a large number that can increase the complexity of the model.
One way to reduce the complexity of the classification task is to use a partitioning clustering algorithm to decompose the reflection coefficient function into a set of distinct clusters.In this case, the number of classes would be reduced from N to K , where K is much smaller than N .K -means clustering is one such algorithm that can be used for this purpose.It works by partitioning the data into K clusters based on the distance between the data points and the centroids of the clusters.The algorithm iteratively updates the centroids and re-assigns data points to the nearest cluster until convergence.By using Kmeans clustering, the reflection coefficient function can be divided into a smaller number of clusters, which can make the classification task more manageable.In addition, the results in this work indicate that the proposed approach results in an accurate model and it does not require a huge amount of training examples to generalize to real measurements.

B. K-Means Clustering
The K -means clustering algorithm is used to divide a set of input samples into a specified number of clusters by Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.minimizing the objective function where y i ∈ R n , i = 1, . . ., N is the set of input samples, x j ∈ R n , j = 1, . . ., K is the set of cluster centers, and δ i j ∈ 0, 1 is an assignment of a sample i to a corresponding cluster j.The algorithm works in two steps.1) Given the cluster centers {x j }, find the optimal assignments {δ i j * } 2) Given the assignments {δ i j }, find the optimal cluster centers {x * j } In this work, K -means clustering is used to simplify the NN by reducing the number of output classes from N to K .

C. Reducing Classification Complexity With Clustering
The K -means model takes as input the magnitude of the reflection coefficient of a lossless material for all possible values of d and ϵ r .We will later create a training dataset that includes various values of tan δ for randomly selected elements within a cluster, and we expect the NN to be able to predict tan δ for the material.As an optional step, we can normalize the magnitude of the reflection coefficient to values between 0 and 1 before applying K -means clustering.This helps the model group elements with similar resonance frequencies together in the same cluster.
The number of clusters can be chosen by plotting the inertia of the model, which is defined as the sum of squared distances of the samples to their closest cluster center, over different values of K and selecting a value close to the elbow of the curve, as shown in Fig. 4. In this work, the number of clusters was chosen to be 1000, significantly reducing the complexity of the NN used to predict the material parameters.
Next, Fig. 5 illustrates the magnitude of the reflection coefficient for all elements in an arbitrary cluster, represented by the same color, for various values of tan δ.The classifier part of the ML model will treat all of these curves as a single class, while the regressor will determine the loss tangent.
To create a training dataset, we follow the steps shown in Fig. 6.First, we select a random element (d, ϵ r ) from a cluster and a random value of tan δ between 0.0001 and 0.01.We then use the analytic model of a dielectric slab to generate the ideal reflection coefficient for these parameters.The reflection coefficient is multiplied by the short measurement and noise is added.The resulting signal is zero-padded, multiplied by a window, and transformed into the echo domain using the FFT.A sharp window is applied around the target, and the signal is transformed back to the frequency domain using the IFFT.The resulting signal contains ringing artifacts due to the Gibbs phenomenon and is cropped and normalized by the short measurement.This process is repeated for all clusters, resulting in a dataset with 100 000 samples that range from an ideal reflection coefficient to a highly distorted signal.
We then build an ML model that takes the calibrated radar signal as input and determines the material parameters.The model should also be able to reject unknown inputs.In the following section, we introduce the OSR problem and describe the construction of the ML model.

V. OPEN-SET RECOGNITION A. OSR and Related Areas
OSR is a type of multiclass classification problem that can also reject samples from unknown classes.In traditional classification, the model is trained only on samples from known classes, and the goal is to classify those samples accurately.However, during testing, the model may encounter samples from classes that were not seen during training.This can result in misclassification of unknown classes as known classes [13].Anomaly/outlier detection is a similar problem, where the model is trained on known classes and tested on samples from known and unknown classes, with the goal of identifying rare items [20].OSR, on the other hand, not only aims to accurately classify samples into known categories but also to detect and reject samples that do not belong to any of the known categories.
In deep learning models, a softmax layer is often used as the final layer to produce a probability distribution over the known classes.However, softmax does not guarantee that the samples from known classes will form tight clusters in the embedding Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

space, which can result in misclassification of unknown classes as known classes during testing.
There have been several open-set classifiers proposed in the literature, such as OpenMax [21], G-OpenMax [22], OSRCI [23], and CROSR [24].One simple and effective approach is to use the CAC distance-based loss [13], which forces known classes to cluster around fixed class centers (called anchors) in the embedding space.This can be useful for OSR because it allows the model to distinguish between known and unknown classes.In this work, we present a modified version of the CAC loss that achieves similar performance while significantly reducing the complexity of the model, which is more suitable for the material characterization problem.

B. Modified CAC Loss
The CAC loss is a loss function that uses a set of fixed class centers to represent each class.It consists of two terms: a Tuplet loss term, L T , that maximizes the margin between the distance to the true class center and the distances to all other class centers, and an Anchor loss term, L A , that minimizes the distance to the true class center.However, for a large number of classes, the Tuplet loss is not efficient in terms of memory usage and can be slow during training.The Tuplet loss, as defined in [13], for an input x and label y is given by Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.A range-gating window is applied between 0.12 and 0.32 m.

TABLE I PERFORMANCE EVALUATION OF THE CLOSE-AND OPEN-SET LOSS FUNC-TIONS FOR MODEL-A AND MODEL-B
where is number of classes, d y is the distance to the correct class center, and d j denotes the distance to an incorrect class center (of which there are K − 1 in total).In this work, we introduce a modified Tuplet loss that significantly reduces the complexity of the model, while maintaining high accuracy.We demonstrate that it is sufficient to consider only the smallest L distances among the set of distances to all incorrect class centers.Let L denote the set of labels to the L smallest distances of the set of incorrect distances.
The modified Tuplet loss can be written as The modified Tuplet loss maximizes the margin between the distance to the correct class center and the L smallest distances among all distances to the incorrect class centers.
The Anchor loss term, on the other hand, minimizes the distance to the correct class center.It is given by the Euclidean distance between the vector of class logits g and the true class center c y , and is defined as The modified CAC loss, with a hyperparameter λ that controls the strength of the Anchor loss term, is then given by

C. Network Architecture
The ML model developed in this work uses complex-valued input signals, which include both magnitude and phase information, to determine material parameters.Fig. 7 shows the architecture of the developed model.It consists of an encoder that features the input signal, followed by a dense layer and two output layers.The first output layer calculates the Euclidean distance between the logit vector g and fixed class centers c i , while the second output layer estimates the loss tangent of the material.
The encoder consists of a series of three 8 × 1 complexvalued convolutional layers [25].Downsampling occurs through a stride of 8, 4, and 2 in the convolutional layers, respectively.Complex-valued 1-D batch normalization and complex-valued rectified linear unit (ReLU) are used after each convolutional layer.A complex-valued dense layer with K neurons is used before the first output layer.
The model's overall loss is a combination of a modified CAC distance-based loss and a mean-absolute error (MAE) loss for the predicted loss tangent z.The constant α is a hyperparameter that controls the relative importance of the two loss functions.The total loss can therefore be written as To compare the proposed model with a regression-based model, we implemented another regression model using the same encoder, a flattened layer, and an output layer consisting only of three neurons, each corresponding to one of the material parameters.The regressor was compiled using the MAE loss function, and the same training dataset generated for the proposed model was used for training this model as well.The black plot represents all elements of the arbitrary cluster shown in Fig. 5, or the set of (ϵ r , d) pairs for that cluster.

D. Performance Evaluation
To assess the model's ability to identify unknown classes, we divided the K classes into those within the red boundary (797 classes) and those within the orange boundary (203 classes) as shown in Fig. 8.We trained two models: Model-A was trained on the dataset with 797 classes, while Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Model-B was trained on the dataset with 203 classes.During testing, both models were evaluated on the entire testing dataset.
The training dataset for each model was divided into training, validation, and test datasets in a ratio of 6:2:2.Model-A and Model-B were compiled using the Adam optimizer for the closed-set case and Stochastic Gradient Descent with a momentum of 0.9 for the open-set case.The maximum number of epochs was 30, with a learning rate of 0.01 for the first 20 epochs and a learning rate of 0.001 for the next 10 epochs.The performance of the models in terms of classification accuracy, the area under the receiver operating characteristic (AUROC) curve, and the MAE of the estimated loss tangent is summarized in Table I.In addition, Fig. 9 shows the ROC curve for Model-A and Model-B using both the closed-set case (Cross-Entropy loss) and the open-set case (CAC * (L = 10)).It is evident that the open-set model is significantly better at estimating material parameters while rejecting samples from unknown classes compared to the closed-set model.
The output of the first output layer of the model is the most probable cluster.If the thickness of the material is known in advance, the dielectric constant can be easily determined.Otherwise, the output of the model is the elements of the predicted cluster, which is a set of (d, ϵ r ) solutions that correspond to reflection coefficient curves that are 'nearly' the same.If the thickness is known, one can disable all clusters that do not contain the input thickness to ensure that the predicted cluster includes the input thickness.

VI. MEASUREMENT RESULTS
To evaluate the performance of the developed ML models, we conducted measurements on six types of materials.The names and thicknesses of each material are listed in Table II.The VNA measurement setup shown in Fig. 1(b) was used to measure the S-parameters of the materials as reference measurements.The radar measurement setup shown in Fig. 1(a) was used to obtain the raw IF signal for the MUT, MATCH, and SHORT measurements.The raw IF signal of the MUT was calibrated using the procedure described earlier.
Fig. 10 shows the echo domain signals for the SHORT, MATCH, and MUT measurements.The targets were range-gated using a window of size 0.2 m.After calibration, we obtained the complex-valued reflection coefficient of the material.As a reference for estimating the material parameters, curve fitting was used to extract ϵ r and tan δ for the materials using the VNA measurements and the calibrated radar signals.
The reference values are listed in Table II.
Next, the calibrated radar signal was fed to the ML models (Model-A and Model-B) to estimate the material parameters.Model-A predicted the material parameters for the first four MUTs and rejected the last two MUTs, while Model-B did the opposite.The predicted clusters for the six MUTs are shown in Fig. 11.Since the thickness d of each material is known, ϵ r can be easily determined.tan δ is predicted from the second output of the NN.The estimated material parameters are listed in Table II.The table shows a good agreement between the estimated values using the ML models and the reference values.
It is important to note that when using curve fitting to estimate material parameters, the optimizer does not fit the curve on the first try and does not have the ability to reject unknown materials or predict errors in calibration, which can lead to false estimations of the material parameters.On the other hand, the developed ML models do not have these issues.
Using the predicted values from the ML models, we used the analytic model to plot the S-parameters of the MUTs.Fig. 12 shows the magnitude and phase of S11 and S21 for the first four MUTs using the VNA setup and the radar + Model-A, while Fig. 13 shows the results for the last two MUTs using the VNA setup and the radar + Model-B.It is clear that the estimated S-parameters using the developed models are very close to the reference measurements using the VNA.
Finally, we evaluate the performance of the regression model and compare it to the proposed model.The MAE of the thickness, dielectric constant, and loss tangent on the test dataset is 0.046 mm, 0.044, and 0.00047, respectively.Although the model appears to converge well and provide accurate parameter estimates at first glance, it failed to predict any of the six test materials accurately, with predicted values significantly deviating from true values.
The reason behind this is that in order to predict material parameters within the defined parameter limits and with the desired resolution, the model would require a large number of training samples, estimated to be around N d × N ϵ r × N tan δ .However, this number is based only on the ideal reflection coefficient data without any ring artifacts.To account for signal distortion, we would need to increase the number of training samples by an additional multiplying factor, making training infeasible.This suggests that a regression model is not ideal for this problem and requires a considerable amount of representative training data and a complex model architecture to achieve accurate estimates.
On the other hand, the proposed approach provides a more suitable solution that does not require a vast amount of training data or a complex model architecture.Additionally, the proposed method avoids memory issues, generalizes well to real measurements, and provides high accuracy.It can also utilize OSR techniques to reject samples from unknown classes.

VII. CONCLUSION
This article proposed a low-cost method and a practical alternative to VNAs for characterizing dielectric materials using a calibrated FMCW radar and a ML model.The calibrated radar sensor was able to accurately measure the complex-valued reflection coefficient of dielectric materials.Additionally, the ML model was able to extract material parameters, including thickness, dielectric constant, and loss tangent, with high accuracy.The use of K -means clustering allowed to reduce the complexity of the NN.Moreover, OSR techniques improved the model's ability to classify known classes and reject unknown classes.The modified CAC distance-based loss used in the model outperformed the conventional cross-entropy loss in terms of accuracy and ability to reject unknown classes.Overall, the proposed approach is accurate and robust, and is able to provide a practical and cost-effective alternative to VNAs for characterizing dielectric materials, provided that the material parameters fall within the specified range.

Fig. 1 .
Fig. 1.(a) Radar measurement setup consisting of the FMCW radar sensor, the Swissto12 MCK, an MUT, and a laptop.(b) VNA measurement setup consisting of a VNA, two D-band extenders, the Swissto12 MCK, and an MUT.

Fig. 2 .
Fig. 2. Block diagrams of the FMCW radar sensor (left) and the Swissto12 MCK (right).The SHORT and MATCH measurements are used for calibration.

Fig. 3 .
Fig. 3. Steps for calibrating the raw IF signal to obtain the complex-valued reflection coefficient of materials.

Fig. 4 .
Fig. 4. Inertia of the model over the number of clusters.

Fig. 5 .
Fig. 5. Magnitude of the reflection coefficient for all elements of an arbitrary cluster plotted on top of each other at different values of tan δ.

Fig. 6 .
Fig. 6.Steps for generating a training dataset for the NN.

Fig. 8 .
Fig. 8. Magnitude of the reflection coefficient of a lossless material at frequency = 154 GHz and over all assumed values of the dielectric constant and thickness.All elements of the arbitrary cluster shown in Fig. 5 are plotted in black.Region A is used to train Model-A, while Region B is used to train Model-B.Both regions are used for testing each model.

Fig. 9 .
Fig. 9. ROC curves for the closed-and open-set loss functions using Model-A and Model-B.

Fig. 10 .
Fig.10.Echo domain signals of the SHORT, MATCH, and MUT measurements.A range-gating window is applied between 0.12 and 0.32 m.

Fig. 8
Fig. 8 illustrates the magnitude of the reflection coefficient at a frequency of 154 GHz for different values of d and ϵ r .The black plot represents all elements of the arbitrary cluster shown in Fig.5, or the set of (ϵ r , d) pairs for that cluster.To assess the model's ability to identify unknown classes, we divided the K classes into those within the red boundary (797 classes) and those within the orange boundary (203 classes) as shown in Fig.8.We trained two models: Model-A was trained on the dataset with 797 classes, while

Fig. 12 .
Fig. 12. Magnitude and phase of the S-parameters realized by using the predicted values using Model-A versus the VNA measurements for four materials: (a) PE, (b) Acrylic, (c) Acrylic, and (d) PVC.

Fig. 13 .
Fig. 13.Magnitude and phase of the S-parameters realized by using the predicted values using Model-B versus the VNA measurements for two materials: (a) PVC and (b) FR4.
3) An ML model with OSR capabilities is developed to enable the model to work in what we call an openset scenario.A modified version of the class anchor clustering (CAC) distance-based loss function the magnitude components of the IF signal are A IF,n,m = (1/2)A 2 |a n | |b m |, the IF angular frequency components are ω IF,n,m = kτ n + kτ m and the phase components are φ IF,n,m

TABLE II ESTIMATED
MATERIAL PARAMETERS USING THE DEVELOPED ML MODELS VERSUS THE REFERENCE VALUES, WHICH WERE ESTIMATED USING A VNA + CURVE FITTING AND RADAR + CURVE FITTING