System hardware

This work employs the BGT60TR13C radar chipset, a frequency-modulated continuous-wave (FMCW) radar chipset developed by Infineon Technologies [23, Reference Trotta, Weber, Jungmaier, Baheti, Lien, Noppeney, Tabesh, Rumpler, Aichner, Albel and Bal24]. FMCW radars offer the advantage of a compact form factor, facilitating their efficient deployment in various applications. These radar systems provide valuable insights into target characteristics such as range and velocity through the analysis of the signals they produce [Reference Jankiraman25, Reference Gurbuz26].

Figure 1(a) depicts a simplified block diagram of the BGT60TR13C chipset, which retains only a single transmitter and receiver. On the transmitter side, a phase-locked loop (PLL) governs the linear frequency sweeping process. A reference oscillator at 80 MHz clocks the loop, and a finite state machine (FSM) controlled by the same reference clock generates a linear voltage ramp. This voltage ramp is applied to a voltage-controlled oscillator (VCO), which generates continuous signals known as chirps. These chirps exhibit linear frequency-modulated (LFM) characteristics, spanning a frequency range from 58.5 to 62.5 GHz for the proposed application. The transmit output power of the LFM signal at the transmitter antenna port is approximately 5 dBm. Following transmission, radar-receiving antennas capture the backscattered signal from the target. Upon reception, the received signal undergoes a low-noise amplification of about 12 dB. It is then time-domain mixed with the transmitter signal, followed by a high-pass filter to eliminate frequencies below 100 kHz and an anti-aliasing filter (AAF) to eliminate frequencies above 600 kHz. As a result, the intermediate frequency (IF) signal is significantly narrower than the originally transmitted signal [23, Reference Trotta, Weber, Jungmaier, Baheti, Lien, Noppeney, Tabesh, Rumpler, Aichner, Albel and Bal24]. This narrow bandwidth greatly enhances subsequent processing efficiency. As part of the successive stages of processing, the IF signal is directed to an analog-to-digital converter (ADC) with a sampling rate of 2 MHz and a resolution of 12 bits. For more information on the chipset hardware, the reader can refer to [23, Reference Trotta, Weber, Jungmaier, Baheti, Lien, Noppeney, Tabesh, Rumpler, Aichner, Albel and Bal24].

Figure 1. (a) FMCW radar block diagram. (b) Infineon’s FMCW radar chipset with a transmitter antenna and three L-shaped receiving antennas.

Further, as shown in Fig. 1(b), the radar system incorporates three receiving antennas arranged in an L-shaped configuration. As a result, the received IF digital signal from all three receiving antennas encompasses valuable target information, such as range, Doppler, and angles. These values can be estimated through additional utilization of digital signal processing algorithms, as will be elaborated in “Gesture Frame Detection: A Key Step in Data Preprocessing for Training Enhancement” section.

System parameters

In the experimental setup, the radar chip is configured to generate 32 chirps per frame. Each chirp undergoes frequency modulation spanning from 58.5 to 62.5 GHz, effectively covering a bandwidth of 4 GHz. A single gesture recording comprises 100 frames, with each frame lasting 30 ms. Thereby, the cumulative duration of a complete gesture recording amounts to approximately 3 seconds. The output shape of the recording is represented as (frames, chirps, samples), and given the presence of three receiving antennas, the final output shape is denoted as (frames, antennas, chirps, samples), with dimensions of (100, 3, 32, 64), respectively. Table 1 provides an overview of the radar operating parameters adopted throughout the work.

Table 1. Radar operating parameters

Based on the aforementioned operating parameters, several key metrics can be derived. The maximum measurable Doppler velocity, i.e.,

(1)\begin{equation} V_{\text{max}} = \frac{c_{\text{o}}}{4 \cdot f_{\text{center}} \cdot T_{\text{c}}}, \end{equation}

is estimated to be 4.13 $m/s$, with c_o representing the speed of light. In the context of Doppler resolution,

(2)\begin{equation} V_{\text{res}} = \frac{2V_{\text{max}}}{N_{\text{c}}}, \end{equation}

an approximate value of 0.26 $m/s$ is obtained. The range resolution:

(3)\begin{equation} R_{\text{res}} = \frac{c_{\text{o}}}{2B}, \end{equation}

stands at 0.038 m. Finally, the maximum unambiguous range,

(4)\begin{equation} R_{\text{max}} = R_{\text{res}} \times \frac{N_s}{2}, \end{equation}

is identified as 1.2 m [Reference Jankiraman25, Reference Gurbuz26].

Gesture dataset acquisition

This paper presents a significant expansion to the previous dataset in [Reference Shaaban, Furtner, Weigel and Lurz1], with an increase in size and a broader range of specifications. The new dataset contains 19,400 recordings for five macro gestures (Push, SwipeRight, SwipeLeft, SwipeDown, and SwipeUp), representing approximately a tenfold increase over the previous dataset, which had 2000 recordings for eight macro and two micro gestures. We have chosen to focus on these five gestures due to their direct relevance to task execution and system control, as well as their user-friendliness and robustness against variations in user execution. Additionally, the dataset incorporates a Background class to indicate the absence of any specific gesture.

Figure 2 presents a visual representation of the execution of these gestures.To ensure comprehensive scenarios and introduce variability, the executed gestures incorporated deliberate variations in angles, distances, and hand dominance (right and left), while concurrently adjusting the radar holder height. The gestures were performed in a room with only static objects (walls, chairs, and tables) and no other moving objects. A single individual performed the gestures with both hands while standing at discrete distances of 0.6, 0.8, and 1.0 m, maintaining three distinct angles relative to the radar at each recording distance: directly facing (0^∘), slightly turned to the left (-30^∘), and slightly turned to the right (30^∘). Similarly, the radar holder height was adjusted while recording within a range of 0.95–1.35 m to capture data from various vertical positions. Figure 3 illustrates the different recording scenarios to clarify the experimental setup.

Figure 2. A visual representation showcasing the execution of the recorded gesture.

Figure 3. Configuration of the radar recording setup, illustrating the range of recording positions, angles, and height adjustments of the radar holder.

The adopted recording criterion and environment yielded a clean, non-noise-limited gesture dataset with minimal intra-class variability between the different gestures while simultaneously incorporating diverse, realistic variations in gesture execution. Given that the dataset comprises a collection of 19,400 recordings, and based on the information provided in “System Parameters” section, the final shape of the dataset, including all available recordings, is presented as (recordings, frames, antennas, chirps, and samples), with respective values of (19,400, 100, 3, 32, 64).

Range information

Initially, the ADC time-domain raw data within each frame undergoes a preprocessing operation to alleviate the potential impact of transmitter-receiver antenna leakage. This operation entails subtracting the mean along the fast-time (a.k.a. samples) dimension, thereby effectively removing the DC component. The presence of static objects in the surrounding environment of the radar system can impede the accurate detection of gesture reflections. To address this issue, a moving target indication (MTI) removal step is employed. By subtracting the mean across the slow-time (a.k.a. chirps) dimension, signals arising from static objects are effectively eliminated, thus enhancing the clarity of gesture reflections. To extract range information, an FFT is applied to the preprocessed and filtered data along the fast-time dimension [Reference Tsang, Corradi, Sifalakis, Van Leekwijck and Latré13]. This allows for the identification of specific frequency components associated with target reflections. Following these steps, the range information (R) is subjected to extra analysis. In this regard, the absolute values of the mean along both antennas and slow-time dimensions are computed, yielding the range profile (R_Profile). This profile provides valuable insights into the spatial distribution and intensity of target reflections.

Range profile processing

After obtaining the R_Profile for each frame, the next step involves identifying the bin with the highest value in the R_Profile, as the global maximum range bin. Further refinement procedures are then conducted to determine the presence of local maxima within the R_Profile. The filtering process applied to the R_Profile includes the following sequential steps:

1. (1) To eliminate insignificant local maxima and mitigate noisy targets in the near field, especially when background responses are of high-magnitude, the R_Profile is smoothed with a 1D Gaussian filter of standard deviation one and subject to dynamic thresholding. Dynamic thresholding assigns a value of zero to any range value below the maximum of 0.1 times the range profile value at the global maximum range bin in the frame under processing and a fixed threshold of $1\times 10^{-4}$. The fixed threshold is selected based on extensive analysis of numerous recordings, which revealed that the noise level associated with a user’s approach to the radar system is typically around this value.

2. (2) In cases where multiple local maxima are detected, precedence is given to the first local maximum identified. This particular bin (R_Gesture) is recognized as the point of interest within the R_Profile, signifying the presence of hand movement.

3. (3) If no local maxima are detected, the bin containing the global maximum is designated as R_Gesture within the R_Profile.

The distinction between the bin containing the global maximum value and the bin associated with the first local maximum is crucial for effectively discerning the hand from the body, given that the hand typically exhibits closer proximity to the radar than the rest of the body.

Doppler profile processing

In order to obtain the Doppler information, a second FFT is applied exclusively to the range information (R) at only the final R_Gesture derived from the range profile processing step. This procedure ensures that only one Doppler FFT [Reference Tsang, Corradi, Sifalakis, Van Leekwijck and Latré13] is performed per frame. Afterward, the absolute values of the mean along the antenna’s dimensions are computed to generate the Doppler profile (D_Profile). The peak value of the signal amplitude in the D_Profile is returned and designated as the P_Gesture in the current frame under processing.

Enhancing gesture onset detection through frame filtering

After processing all frames, the “Range Profile Processing” section determines the R_Gesture and the “Doppler Profile Processing” section generates the corresponding P_Gesture as output. To identify the precise frame in which the gesture occurs, a threshold value of $5\times 10^{-5}$ is established. This threshold was selected after examining several gesture recordings and determining that a frame with a signal amplitude below this value is most likely devoid of any gesture. Consequently, any frame with a P_Gesture value below this threshold is disregarded. Subsequently, the frame with the lowest range bin index among the remaining frames is identified, indicating its closest proximity to the radar. For ease of reference, this frame is denoted as the “Gesture Frame (F_Gesture).” In the context of the gestures, the F_Gesture corresponds to the midpoint of Swipe gestures or approximately the endpoint of Push gestures. This distinction arises from the fact that in Swipe gestures, the hand is closest to the radar when it is in the middle of the gesture, whereas in Push gestures, the hand is nearly at the end of the gesture. As a result of the gesture frame detection process, the index of the F_Gesture for each gesture is returned and stored for later utilization in the upcoming processing of the gesture data, as discussed in the “Refining Time-Domain Gesture Data” section.

Figure 5 shows the R_Profile and D_Profile of the full frames of a SwipeLeft gesture, emphasizing the accurate detection of the F_Gesture where the hand was executing the gesture at its closest proximity to the radar.

Figure 5. Illustration of gesture frame detection for a SwipeLeft gesture. (a) Conventional range spectrogram of a SwipeLeft gesture. (b) Conventional Doppler spectrogram. (c) and (d) R_Profile and D_Profile for all 100 frames within the SwipeLeft gesture, respectively. Frames in the gray areas are discarded due to thresholding during F_Gesture estimation. These frames are not clearly visible in panels (a) and (b), confirming that they represent frames with gesture-accompanying noise rather than those with actual gesture execution. The green dotted line highlights the estimated F_Gesture, indicating the hand’s closest position to the radar during the gesture. The results from panels (c) and (d) are corroborated by the conventional spectrograms in panels (a) and (b).

Spiking neural network

In this work, the utilization of the SCNN proposed in [Reference Shaaban, Furtner, Weigel and Lurz1] is adopted with certain modifications to streamline the model and enhance its computational efficiency. The architecture of the modified SCNN model is illustrated in Fig. 6. Specifically, the three convolutional layers maintain identical kernel sizes, padding, and stride, preserving their characteristics from the original SCNN model. Equally, the fully connected (FC) layer with an input size of 64 is retained. To maintain consistent model performance during both training and inference, batch normalization layers are omitted after each convolutional layer due to their different behaviors in these two processes. Likewise, in place of the synaptic spiking neurons layer, a layer comprising LIF neurons [Reference Gerstner and Kistler22] is introduced after the convolutional and max pooling layers. The LIF neurons exhibit simplified internal dynamics, thereby reducing the overall computational complexity of the model. Finally, considering the five gestures and Background class present in the current dataset, the output of the fully connected layer is constrained to six neurons, aligning with the class labels. The selection of a SCNN is motivated by its ability to process time-domain radar data directly. As illustrated in Fig. 6, the SCNN receives one frame of the recorded gesture at a time, preserving temporal information. Additionally, the input channels of the first convolutional layer are set to 3, corresponding to the three receiving antennas, ensuring the preservation of angular information. Convolution operations are performed on the (chirps, samples) information for each gesture, preserving (Doppler, range) information.

Figure 6. The architecture of the SCNN model is presented, with each convolutional layer annotated with its respective input channels and kernel size. The initial convolutional layer comprises three input channels, indicating that the network receives a single frame (composed of chirps or samples) from a single gesture at a time, with the input channels corresponding to the three antennas. Max-pooling layers with a stride of 2 are utilized. The first layer of LIF spiking neurons converts the output of the initial max-pooled convolutional layer into spike representations, which are then propagated to the subsequent layers of the network. The membrane potential of the final LIF spiking neurons layer is stacked for each frame, denoted by N, indicating the number of frames in the processed gesture.

The LIF neuron, commonly used in computational neuroscience, resembles a resistor-capacitor (RC) circuit at its core. The membrane potential of the LIF neuron undergoes charging and discharging, similar to a capacitor in an RC circuit, as current flows through a resistor. This behavior is characterized by the potential increasing in response to incoming inputs and gradually decreasing in the absence of input due to a leaking mechanism. The LIF neuron, together with the SCNN, are implemented using the snnTorch spiking simulator [Reference Eshraghian28]. As defined in [Reference Eshraghian28], the inner dynamics of the LIF neuron is governed by:

(5)\begin{equation} U_{t} = \beta U_{t-1} + WI_{\text{in}}[t], \end{equation}

where each neuron possesses an intrinsic membrane potential (U_t) that evolves with incoming synaptic inputs ($I_{\text{in}}[t]$) modulated by the synaptic connection weight (W). The membrane potential integrates over time with a leakage term β, commonly represented by an exponential decay function. Similarly, as defined in [Reference Eshraghian28]:

(6)\begin{equation} U_{t} \gt U_{\text{thr}} \Rightarrow S_t = 1, \end{equation}

when the membrane potential (U_t) surpasses a predetermined threshold (U_thr), the neuron generates an output spike (S_t), followed by a reset of its membrane potential by subtracting a threshold value. The LIF neuron’s dynamic behavior allows for effective exploitation of the sequential nature of time-dependent datasets. Figure 7 provides an illustration depicting the operational principle of the LIF neuron.

Figure 7. The LIF spiking neuron operating principle. (a) Spikes as inputs to the LIF neuron over time. (b) The membrane potential integrates over input spikes over time with a decay rate of beta. (c) An output spike is generated only when the membrane potential exceeds the spiking threshold (V_th).

To address the challenges posed by non-differentiable spikes during model training within the spiking domain and enable end-to-end optimization, the surrogate gradient descent method is employed [Reference Neftci, Mostafa and Zenke29]. This approach involves substituting the gradient of non-differentiable spikes in the backward pass with the gradient of a differentiable function, accordingly facilitating effective optimization of the SCNN model. In this study, we utilize the state-of-the-art surrogate gradient shifted arc-tan (ATan) function [Reference Fang, Yu, Chen, Masquelier, Huang and Tian30], representing an advancement over our previous work [Reference Shaaban, Furtner, Weigel and Lurz1]. During the forward pass of training, spikes are generated in accordance with (5) and (6). Nevertheless, during the backward pass, the gradient of the spikes is substituted with the gradient of the ATan function as defined in [Reference Fang, Yu, Chen, Masquelier, Huang and Tian30]:

(7)\begin{equation} \frac{\delta S}{\delta U} = \frac{1}{\pi} \cdot \frac{1}{(1 + (\pi U \frac{\alpha}{2})^2)}, \end{equation}

where U denotes the membrane potential and α denotes the surrogate slope. It is worth noting, that the surrogate slope (α) plays a pivotal role in determining the steepness of the ATan function. Larger values result in a narrower surrogate gradient and a more pronounced transition from the function’s minimum to the maximum value, while a smaller value means a wider surrogate gradient and a gradual transition from the minimum to the maximum value of the function.

Refining time-domain gesture data

As discussed in the “Gesture Dataset Acquisition” section, the dataset comprises a total of $19,400$ recorded gestures. All these gestures undergo the gesture frame detection process outlined in the “Gesture Frame Detection: A Key Step in Data Preprocessing for Training Enhancement” section. As a result of this process, the F_Gesture in which the gesture is clearly presented and in close proximity to the radar is detected. It is important to note that the F_Gesture alone does not capture the entirety of the gesture but provides an indication that the gesture occurred in the vicinity. Windowing around this F_Gesture is performed as the next step. To determine the optimal windowing size, various sizes are proposed and evaluated through comprehensive training and testing processes, as described in the “Training Process Overview” and “Testing Process Overview” sections. A thorough analysis of the results reveals that a window size of 8 around the F_Gesture produces the most favorable outcomes. For the sake of simplicity, only the windowing size yielding the best performance is mentioned here and is subsequently used to generate the results in the “Experimental Results” section. Although, it is worth mentioning that the interpretation of the F_Gesture differs for the Swipe gestures and the Push gesture. For Swipes, four frames before and after the F_Gesture are labeled to accurately represent the gesture, while for the Push gesture, six frames before the F_Gesture and two frames after are labeled to capture the correct execution of the gesture. Accordingly, the overall sequence of processing steps required to transform the ADC time-domain raw radar data into a suitable final time-domain format for model training and inference can be outlined as follows:

1. (1) Conventional Radar Preprocessing: The ADC time-domain raw radar data undergoes standard radar preprocessing steps, including the removal of the DC component and the (MTI) technique. This involves subtracting the mean along the fast-time and slow-time dimensions, respectively.

2. (2) Min-Max Normalization: Within each gesture, the 100 frames undergo a min-max normalization step. This normalization ensures that the values of the chirps and samples within each frame are scaled between zero and one.

3. (3) Gesture Labeling: The index of the F_Gesture obtained from the gesture frame detection process for the current gesture is retrieved. Subsequently, windowing is applied to label eight frames out of the 100 frames as gesture frames, as described in the earlier discussion. The remaining 92 frames are labeled with the Background class label.

4. (4) Saving Processed Gesture Data: The processed data from step 2 is saved as the gesture data file, preserving the processed time-domain representation of the gestures.

5. (5) Saving Gesture Labels: The labeling of the frames from step 3 is saved as the gesture label file.

At the conclusion of this process, the entire dataset comprising 19,400 gestures is transformed into the processed time-domain format. Moreover, refinement of all gestures is performed to assign appropriate labels to the frames capturing the occurrences of the gestures, while simultaneously designating the remaining frames as Background. As a consequence, the dataset is fully prepared for utilization in the tasks of training, validation, and testing.

Time-domain processing approach

The frame-by-frame time-domain processing approach, introduced in [Reference Shaaban, Furtner, Weigel and Lurz1], has undergone modifications to incorporate the newly introduced labeling structure. Unlike the previous implementation [Reference Shaaban, Furtner, Weigel and Lurz1], which assigned a uniform label to all frames within a gesture, the current approach distinguishes between frames that exhibit active gesture performance and those that do not, as discussed in the “Refining Time-Domain Gesture Data” section. The modified processing approach can be summarized as follows:

1. (1) The processed time-domain data obtained from the “Refining Time-Domain Gesture Data” section consists of a sequence of 100 frames, representing a single gesture. These frames serve as the temporal input steps for the SCNN during its forward pass.

2. (2) The membrane potentials of the six LIF neurons in the final layer following the FC layer in the SCNN model are stacked for each frame, as illustrated in Fig. 6.

3. (3) The stacked membrane potentials of size $(100, 6)$ undergo processing through the LogSoftMax function [Reference Bridle31], resulting in predicted log probabilities for each frame within the gesture. LogSoftMax is a common method for transforming unnormalized outputs into log probabilities, a prerequisite for the negative log-likelihood loss (NLLLoss) function [Reference Yao, Zhu, Jiang, Yu, Arai, Bhatia and Kapoor32].

4. (4) Utilizing the NLLLoss function, each frame’s predicted log probability is compared with its corresponding label, derived from the saved label gesture in the “Refining Time-Domain Gesture Data” section. NLLLoss proves appropriate for this task as it operates on log probabilities produced by LogSoftMax. Moreover, combining LogSoftMax with NLLLoss is a standard practice in multi-class classification tasks, such as gesture recognition. Despite that, it is essential to emphasize that the overall loss for the entire gesture, which is vital for backpropagation and updating the trainable parameters of the network, is computed by summing the losses of each frame within the gesture.

Remarkably, unlike the previous work’s approach [Reference Shaaban, Furtner, Weigel and Lurz1], this procedure provides classification per frame, negating the need to aggregate predictions from all frames within a gesture to determine the performed gesture. For this reason, this approach demonstrates its suitability for real-time gesture detection where prediction is needed per frame received from the radar.

Dataset splitting

The dataset of 19,400 time-domain recordings, as defined in the ‘Refining Time-Domain Gesture Data” section, was divided into training, validation, and testing subsets following standard practices. Specifically, 75% of the recordings (14,550) were allocated for training to ensure effective model training. The validation set, which is typically around 25% of the training set, was adjusted to approximately 22% of the training set, resulting in 3201 recordings to maintain a reasonable validation set size. The remaining 4850 recordings were reserved for independent testing, enabling a robust evaluation of the model’s performance. This division aligns with established machine learning practices, taking into account our dataset’s size and ensuring robust model evaluation.

Training process overview

The training process of the SCNN model involves utilizing the training dataset and utilizing the modified time-domain processing approach detailed in the “Time-Domain Processing Approach” section. During training, the adaptive moment estimation (Adam) optimization algorithm is employed to update the model’s trainable parameters [Reference Kingma and Ba33]. Hyperparameter tuning is performed to optimize the training performance of the model before full training. This is done using the Optuna library [Reference Akiba, Sano, Yanase, Ohta and Koyama34] to fine-tune various hyperparameters associated with the model and the spiking LIF neuron.

An Optuna-based hyperparameter optimization environment is set up, where a random value is selected for the Adam optimizer learning rate, weight decay, spiking LIF neuron decay rate, threshold, and surrogate gradient slope for each optimization trial. Table 2 shows the hyperparameter search range, selected based on best-known common practices. The SCNN is then trained for only 20 epochs using the suggested values, and the validation accuracy is calculated for each trial. Through a rigorous hyperparameter tuning process involving more than 200 optimization trials, the optimal values for the learning rate and weight decay of the Adam optimizer are determined to be $4.9\times 10^{-4}$ and $1.27\times 10^{-5}$, respectively. Similarly, the beta decay rates for the membrane potential, threshold, and surrogate gradient slope of the LIF neuron are designated as 0.5, 0.25, and 4.0, respectively. It is worth noting that these values resulted in the highest validation accuracy, thus ensuring that the selected values maximize model performance.

Table 2. Optuna hyperparameter search range

Table 3 provides a comprehensive overview of the optimized and non-optimized hyperparameter values utilized in the training process.

Table 3. Hyperparameters overview

Following hyperparameter optimization, the SCNN model undergoes a 120-epoch training phase. To address the common challenge of overfitting and enhance the model’s ability to generalize to unseen data, the early-stopping approach [Reference Prechelt, Orr and Müller35] is employed. This method is a widely used regularization technique in machine learning, primarily employed to prevent overfitting. It operates by continuously monitoring the model’s performance on the separate validation dataset during training. If no noticeable improvement in the model’s performance on the validation data is observed over a consecutive span of 10 epochs, the training process is halted. In essence, early stopping prevents the model from becoming overly specialized to the training data. This, in turn, improves the model’s capability to generalize to new, unseen data, ultimately enhancing its overall performance.

Testing process overview

Throughout the training process, attention is given to identifying and preserving the model with the lowest validation loss, referred to as the “best model.” In the following testing phase, this best model is retrieved and subjected to testing using the independent and previously unseen test dataset. The testing phase is critical in detecting potential biases and reliably assessing the model’s generalization capabilities since it leverages the best model, which demonstrates reduced sensitivity to overfitting. The model selection process serves as an additional safeguard against overfitting, ensuring that the model’s performance is carefully evaluated based on its true potential.

Effectiveness of the time-domain frame-based prediction approach

This section compares the proposed frame-based prediction approach with the previously introduced record-based prediction approach in [Reference Shaaban, Furtner, Weigel and Lurz1]. Unlike the frame-based approach, the record-based approach cannot distinguish between frames that contain the gesture and non-gesture frames, resulting in assigning the same label to all gesture frames. Consequently, the network performs a single prediction for the entire 100-frame gesture, aiming to detect the presence of the gesture within this duration, rather than making predictions on individual frames. To obtain experimental results, the modified SCNN architecture introduced in this study is trained on the newly introduced dataset using the record-based prediction approach for five separate training runs with different seeds. The mean test accuracy, derived from the best (lowest validation loss) among the five SCNN models, is observed to be 95.40%.

In the newly proposed frame-based prediction solution, during the training process, the SCNN model leverages the time-domain processing approach described in the “Time-Domain Processing Approach” section, enabling it to generate predictions for each frame individually. Likewise, in the testing phase, the accuracy function assesses the model’s performance by evaluating the accuracy of its frame-level predictions for each gesture. The SCNN model is trained on five different random seeds using the frame-based prediction approach. Thereupon, the mean test accuracy is determined by evaluating the performance of the five best models, resulting in an accuracy of 98.45%.

Table 4 confirms that the frame-based prediction approach outperforms the record-based prediction approach in terms of mean test accuracy. Also noteworthy is that the models employed in both approaches were trained on the same dataset and evaluated using the same criteria, highlighting the usefulness of the frame-based approach for reliably predicting gestures.

Table 4. Comparison of time-domain frame-based and record-based approaches

Further analysis

The precision and recall scores obtained from testing the five SCNN models are examined to gain deeper insights into the frame-based prediction approach. The average precision, calculated as 0.90, highlights the model’s ability to accurately identify positive instances. Likewise, the average recall, calculated as 0.89, indicates the model’s effectiveness in capturing relevant information and minimizing false negatives. These metrics serve as valuable indicators of the model’s overall performance and their ability to strike a balance between precision and recall in classification tasks [Reference Buckland and Gey36].

Table 5 presents the consolidated confusion matrix, providing a comprehensive overview of the model’s classification outcomes across the different gestures. This matrix aids in identifying specific areas of improvement and understanding the patterns of misclassifications exhibited by the models. It is noteworthy that the values observed in Table 5 provide insights into the frame distribution within the test data, considering the current frame-based prediction approach. Furthermore, there is a noticeable difference in the number of frames predicted as Background compared to the other classes. This distinction arises from the labeling scheme, where each gesture comprises eight frames explicitly designated as gesture frames, while the remaining 92 frames are assigned the background label, as already noted in the “Gesture Frame Detection: A Key Step in Data Preprocessing for Training Enhancement” and “Refining Time-Domain Gesture Data” sections.

Table 5. Average confusion matrix

Modified evaluation protocol

Upon closer examination of the model’s outcomes and the evaluation of their respective confusion matrix, it becomes apparent that the models consistently demonstrate proficiency in identifying frames in which gestures are performed correctly. Even so, occasional temporal deviations exist, where the models predict the occurrence of a gesture slightly before or after the labeled frames. Considering that each frame spans 30 ms, such marginal deviations in temporal detection do not have a significant impact on real-world practical applications. Figure 8 provides a clear depiction of this behavior. In the investigation, a sequence of three gestures is provided as input to one of the SCNN networks, revealing the infrequent occurrence of incorrect predictions. Nonetheless, it is possible to observe a subtle temporal shift in the predictions. In light of this observation, a decision is made to refine the accuracy measurement approach to account for this characteristic behavior. The refined accuracy comprises the following steps:

1. (1) Initially, the predicted classification labels for each set of 100 frames within a gesture are examined. It is essential to ensure that among these 100 frames, only one non-zero label is present. This criterion guarantees accurate prediction of the Background frames and ensures that each gesture is uniquely identified without any overlapping predictions with other gestures in the same frame sequence.

2. (2) Subsequently, the correspondence between the ground truth non-zero labels and the non-zero predicted values within these 100 frames is validated. This process confirms that the predicted frames accurately capture the presence of the same gesture as indicated by the ground truth labels.

3. (3) To still refine the accuracy, a windowing technique is employed. A window of size 10, centered around the frames containing the 8 non-zero ground truth labels, is utilized. This window encompasses 5 frames preceding and 5 frames succeeding the non-zero labels.

4. (4) Afterward, analysis is conducted to determine if the non-zero predicted frames, signifying the predicted gesture, fall within the designated window. On top of that, a condition is set that the predicted non-zero frames must exhibit a repetition of at least 5 frames compared to the 8 non-zero ground truth frames. Meeting these requirements indicates that the network correctly predicted the gesture, although with a minor temporal variation. Therefore, these predictions are deemed accurate in their entirety.

By incorporating these refined accuracy measurement procedures, the precision and recall values derived from the five SCNN models reach more reasonable levels, with precision achieving 0.980 and recall attaining 0.975. The SCNN models demonstrate an average testing accuracy of 99.75%. Table 6 presents a concise summary of the average confusion matrix obtained from the five SCNN models, offering a comprehensive evaluation of their collective performance. To further validate the effectiveness of the proposed time-domain frame-based solution, a comparison is made to a recent work [Reference Strobel, Schoenfeldt and Daugalas27] utilizing an augmented version of the gesture dataset employed in this work. The authors applied a slim radar conventional preprocessing pipeline to the time-domain data, extracting five features: radial distance, radial velocity, azimuth angles, elevation angles, and signal amplitude per frame. These five features are then fed into an RNN to generate a prediction per frame. An average F1 score of 98.4% is reported. Given the average precision of 0.980 and an average recall of 0.975 achieved by the proposed SCNN model, the average F1 score is 97.7%. This demonstrates that the proposed solution is comparable to solutions based on conventional radar preprocessing pipelines and conventional ANN-based networks with strong temporal learning capabilities.

Table 6. Average refined confusion matrix

Live testing

Live testing plays a critical role in evaluating trained models in real-time scenarios, ensuring their consistency with the results obtained during the testing phase. Real-time retrieval of frames from the radar is achieved using a dedicated Python script. The acquired ADC time-domain frames undergo the time-domain refinement process described in the “Refining Time-Domain Gesture Data” section. The processed time-domain frame is then fed into the SCNN, where predictions for each gesture class are generated based on the membrane potential values of the last layer of LIF spiking neurons, as explained in the “Time-Domain Processing Approach” section. The gesture class with the highest predicted probability is displayed in real-time through the Python script, providing immediate feedback on the detected gesture. During live testing, the radar’s interactive control capabilities are demonstrated by incorporating corresponding movement actions based on the predicted gestures. If no gesture or a Background class is detected, the system remains responsive without triggering any action. Gestures, including SwipeDown, SwipeUp, SwipeLeft, and SwipeRight, are mapped to keyboard actions that simulate pressing the “Down,” “Up,” “Left,” and “Right” keys, respectively. Likewise, the Push gesture corresponds to pressing the “PageUp” key. These interactive controls exemplify the practicality of the radar system, enabling remote control in various scenarios. For instance, it allows seamless control over presentation slides and facilitates engagement in online gaming solely through radar-predicted gestures.

The effectiveness of the proposed real-time solution is validated by live testing from five individuals (three males and two females, aged 25–30 years) uninvolved in the dataset collection process. These individuals performed a set of 20 gestures in a randomized sequence, using both the right and left hands at the same distances and angles used in the gesture recording, as detailed in the “Gesture Dataset Acquisition” section. The solution accurately predicted 96 of the 100 performed gestures, confirming the accuracy, reliability, and suitability of the trained SCNN models for real-time gesture recognition.

Computational complexity

The SCNN model, with a top-level metric of 1.4 million multiply-accumulate (MMAC) operations per frame inference, assumes that LIF spiking neurons display full spiking activity, with all spikes equal to one. The central processing unit (CPU), by default, does not account for single-bit event spikes, treating their multiplication with the single-bit event as a standard multiplication, similar to the ANN. However, this operation should be less costly as it is a multiplication between the synaptic weight and a single-bit event (spike). Therefore the SNN in the worst-case scenario still demonstrates computational efficiency compared to an equivalent ANN. Additionally, since SNNs generate spikes only when they exceed the internal threshold (as discussed in the “Spiking Neural Network” section), the resulting spikes are primarily zeroes with a few occurrences of 1-bit spikes. This eliminates the need for multiplication between synaptic weights and zero spikes, simplifying the MAC operation to just an addition. And, when the spike is a 1-bit, it results in a simpler multiplication than the conventional case, underscoring the computational efficiency and potential of the SCNN model. In the context of hardware implementation, SNNs offer a distinct advantage over conventional ANNs. By leveraging 1-bit spikes, SNNs streamline the computational process, replacing the conventional multiplier with a simpler logical AND operation. This efficient approach reduces the computational complexity associated with synaptic weight multiplication, making SNNs a promising solution for hardware implementations, particularly on neuromorphic hardware where the inherent sparsity of SNNs can be fully leveraged [Reference Schuman, Potok, Patton, Birdwell, Dean, Rose, Plank and Schuman37].

The sparsity of SCNN models is evaluated via live testing, as detailed in the “Live Testing” section. In this approach, one of the SCNN models is executed in real-time, enabling the monitoring of the number of non-zero spikes and zero spikes produced during each frame prediction. Through the calculation of the ratio between zero spikes and the total number of spikes, the sparsity level for each frame prediction is determined. The investigations continually demonstrate a pattern: the sparsity level is consistently high during non-gesture times, ranging from 90% to 97%. Conversely, when a gesture is detected, the sparsity level slightly decreases to around 75%. The consistent generation of sparse predictions by the SCNN model reaffirms the inherent advantage of SNNs over ANNs.