Remote physiological sensing using Frequency Modulated Continuous Wave (FMCW) radar has emerged as a promising alternative to contact-based methods due to its non-intrusive nature and privacy preservation. However, existing signal-processing and CNN-based approaches sufer from phase wrapping ambiguities, noise sensitivity, and limited ability to capture long-range dependencies in heartbeat dynamics. In this work, we propose a novel CNN-Transformer framework for supervised radar-based heartbeat measurement. The CNN component extracts local temporal features, while the transformer encoder models long-range dependencies critical for periodic cardiac motion. To further enhance performance, we design a hybrid loss function that integrates Negative Pearson Loss, Signal-to-Noise Ratio (SNR) Loss, and Sparsity Loss, efectively balancing temporal fidelity, noise robustness, and physiologically meaningful frequency representation. We additionally introduce RadHR, a new FMCW radar dataset with recordings from 50 participants, providing a high-quality benchmark for non-contact heartbeat estimation. Extensive experiments on both the public EquiPleth dataset and RadHR demonstrate that our method consistently outperforms existing baselines, achieving state-of-the-art accuracy and robustness under realistic conditions.
W
CEUR Workshop
ISSN1613-0073
Beyond reviews, numerous radar architectures and signal processing pipelines have been explored
for real-world vital sign detection. Impulse-radio ultra-wideband (IR-UWB) radar, owing to its fine
temporal resolution, has been widely applied to monitor heartbeat and respiration. Early systems
demonstrated non-contact heart rate monitoring using IR-UWB signals under controlled conditions
[
In addition to IR-UWB methods, self-calibrating radar systems have been proposed to improve stability
and adaptability across diferent users and scenarios. These approaches automatically adjust system
parameters to mitigate the efects of channel variation and hardware non-idealities, thereby enhancing
robustness for long-term monitoring [
Another emerging application domain is radar-based vital sign monitoring in automotive
environments. Detecting passenger presence and health conditions inside vehicles is particularly challenging
due to vibrations and motion artifacts. Recent studies have conducted both theoretical investigations
[
Despite these advancements, conventional radar-based heartbeat sensing approaches typically rely on
extracting and unwrapping signal phases to recover heartbeat dynamics [
To overcome these limitations, recent advances in supervised deep learning have demonstrated the
ability to learn complex spatiotemporal representations directly from radar signals [
In this work, we propose a supervised FMCW radar-based heartbeat measurement framework that combines CNNs with Transformers. Our main contributions are summarized as follows: • We design a novel framework for radar heartbeat sensing, which integrates 1D CNN layers for local feature extraction with Transformer encoders for modeling long-range temporal dependencies, addressing the limitations of CNN-only baselines. • We collected a new radar dataset (RadHR) containing 50 individuals for heartbeat sensing benchmark, and the dataset will be made public upon request. • The proposed model demonstrates superior resilience against motion artifacts, multipath interference, and low-SNR conditions, which commonly degrade the performance of traditional signal-processing and CNN-based methods. • We conduct extensive experiments on FMCW radar data, showing that our approach consistently outperforms state-of-the-art CNN-based baselines in heartbeat sensing accuracy and robustness.
A range matrix is obtained from FMCW radar raw data to facilitate subsequent analysis and processing. Specifically, the procedure of constructing a range matrix is as follows. In each chirp loop, the FMCW e m i T
E n c o d e r T r a n s fr o m e r D e c o d e r FFT
Q K V
radar transmits a chirp signal () and simultaneously receives the corresponding reflected chirp signal () . Both () and () are linear frequency modulation signals, commonly referred to as chirp signals. In particular, the received signal () is mixed with the in-phase and quadrature (IQ) components of the transmitted signal, denoted as () and () , to produce the complex intermediate frequency (IF) signal () ∈ ℝ , which can be expressed as: () ∝
LPF[ () ⋅ ()] + ,
LPF[ () ⋅ ()] ∝
exp((2 + )), = 2/, = 4 / where LPF denotes the low-pass filter, is the frequency slope of the FMCW signal, is the distance, is the speed of light, and is the wavelength associated with the FMCW starting frequency. The frequency of the IF signal () corresponds to the frequency diference between the transmitted signal () and the received signal () . Consequently, is directly proportional to the signal round-trip time and the distance between the radar and the target. Likewise, the phase is also proportional to the distance, but it is inherently wrapped within the interval [− , ] .
To capture heartbeat dynamics continuously, the radar sequentially transmits chirps [ 1(), 2(), … , ()] and receives the corresponding reflected signals [ 1(), 2(), … , ()] . Accordingly, IF signals [ 1(), 2(), … , ()] are obtained, where each () ∈ ℝ . Since the frequency of each IF signal () is a function of the target distance, a fast Fourier transform (FFT) is applied to each () to generate the corresponding range profile [ ] . Finally, by concatenating all range profiles, the range matrix is constructed as:
= [ 1[ ], 2[ ], … , [ ]] ∈ ℝ × , where represents the number of chirps and denotes the number of range bins. This range matrix serves as the foundation for subsequent feature extraction and heartbeat estimation in our framework.
As described in Section 2.1, the raw FMCW radar signals are converted into a range matrix ∈ ℝ × ,
where is the number of chirps and is the number of range bins. This range matrix captures both
the distance-related amplitude and phase variations, serving as the input for subsequent heartbeat
estimation. Before feeding into the neural network, we take a window of the range matrix ∈ ℝ ×
around the central range bin to get the windowed heartbeat matrix (⋅, ± Δ) ∈ ℝ ×(2Δ+1) as the
input following the previous work [
The first stage of our model is a 1D CNN-based feature extractor, which operates along the temporal dimension of the range matrix. Specifically, for each range bin ∈ [1, ± Δ] , the corresponding (1) (2) where is the number of feature channels output by the CNN. We adopt ReLU activations, batch normalization, and dropout to improve training stability and prevent overfitting.
While CNNs efectively capture local patterns, heartbeat signals exhibit long-range temporal dependencies that CNNs alone may fail to model. To address this, we incorporate a Transformer encoder after the CNN stage. The Transformer employs self-attention mechanisms to model interactions between distant time steps, allowing the network to capture the periodicity and subtle dynamics of cardiac motion. Given the CNN features CNN ∈ ℝ × , the Transformer computes: = ( ), ∈ ℝ × where Trans encodes both local and global temporal information. We adopt multi-head attention to allow the model to focus on multiple temporal patterns simultaneously, followed by a feed-forward network with residual connections and layer normalization. temporal sequence [∶, ] is processed by stacked convolutional layers with small kernel sizes. These layers aim to capture local temporal patterns corresponding to heartbeat-induced chest movements. Formally, the CNN feature extraction can be expressed as: = ( ), ∈ ℝ × (3) (4) (5) (6)
In this work, we design a composite loss function that combines Negative Pearson Loss, Signal-to-Noise
Ratio (SNR) Loss[
To enhance robustness against noise and motion artifacts, we employ an SNR-based loss that emphasizes spectral energy concentration around the true heartbeat frequency. Specifically, the loss is defined as:
The Negative Pearson Loss evaluates the linear correlation between the predicted signal and the ground truth. The Pearson correlation coeficient ranges from −1 to 1, with higher values indicating stronger correlations. To maximize similarity, we minimize the negative Pearson coeficient:
= − ( , ̂ ) where ̂ and denote the predicted and reference heartbeat signals, respectively. This loss function encourages the model to preserve temporal waveform consistency with the ground truth. (y, ŷ) =
∫ 00−+ |Ŷ( )| 2 ∫−0∞− |Ŷ( )| 2 +
∞ ∫ 0+ |Ŷ( )| 2 , 0 = ( ) where ( )
and (̂ )
are the respective Fourier transforms of and ̂ and w is the chosen window size.
We integrate Sparsity Loss with Negative Pearson Loss and SNR Loss motivated by the fact that in FMCW radar-based heartbeat sensing, the heartbeat frequency typically manifests as the dominant spectral peak within a physiologically plausible range (e.g., 45–250 bpm). The Sparsity Loss penalizes predictions that fail to concentrate energy near the main peak within this frequency band: (7) (8) = 1 ∑ = ∗−Δ
= [ ∑ +
∑ = ∗+Δ ] where ∗ = argmax(Y) and ∆ are the frequencies of the spectral peak and padding around the peak, respectively. For all experiments ∆ = 6 beats per minute[18].
The final loss function is a weighted combination of the three terms: = 1 + + 2 where 1, 2 are hyperparameters balancing the contribution of each term.
4.1.1. Equipleth Dataset
The Equipleth radar dataset [
On the EquipIeth dataset, our approach achieves an MAE of 1.82, RMSE of 5.39, and correlation = 0.89 , surpassing previous methods and demonstrating robust performance. Similarly, on the RadHR dataset, our method achieves an MAE of 2.11, RMSE of 2.73, and correlation = 0.92 , outperforming all baselines by a clear margin. Notably, compared with the FFT-based Radar method, our approach reduces the RMSE by more than 85% on RadHR, highlighting the efectiveness of combining CNN and Transformer architectures with our tailored loss design.
To investigate the contribution of each component in the overall loss function, we conduct an ablation study on the EquiPleth dataset. The results are summarized in Table 2.
When only the Pearson Loss is used, the model achieves a relatively high MAE (8.52) and RMSE (14.12), with a poor correlation coeficient (r = 0.33). This indicates that although Pearson Loss enforces correlation, it alone is insuficient for stable reconstruction.
Introducing the SNR Loss significantly improves performance, reducing the MAE to 1.92 and RMSE to 5.33, while the correlation r increases to 0.89. This suggests that the SNR constraint efectively enhances the signal fidelity by improving the signal-to-noise ratio.
Finally, when all three losses (Pearson Loss, SNR Loss, and Sparsity Loss) are combined, the model achieves the best performance, with the lowest MAE (1.82), competitive RMSE (5.39), and the highest correlation (r = 0.89). The improvement demonstrates that the Sparsity Loss further regularizes the prediction, helping the model suppress redundant information and capture more discriminative features.
In this paper, we presented a CNN-Transformer framework for FMCW radar-based heartbeat estimation, coupled with a novel hybrid loss design. By leveraging CNNs for local feature extraction and Transformers for long-range dependency modeling, our approach efectively captures both fine-grained and global temporal patterns of cardiac dynamics. The integration of Pearson Loss, SNR Loss, and Sparsity Loss further enhances robustness by encouraging waveform fidelity, noise suppression, and physiologically consistent spectral concentration. To support the community, we introduced RadHR, a new radar heartbeat dataset comprising recordings from 50 subjects under stationary conditions. Experimental results on both RadHR and the EquiPleth dataset demonstrated that our method outperforms conventional signal-processing and deep learning baselines in terms of MAE, RMSE, and correlation coeficient.
This work was supported by the National Natural Science Foundation of China (Grant No. 62572249), the Natural Science Foundation of Jiangsu Province (Grant No. BK20250742), the Startup Foundation for Introducing Talent of NUIST (Grant No. 1083142501006), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. SJCX25_0518).
During the preparation of this work, the authors used ChatGPT in order to: Grammar and spelling check, Paraphrase, and reword. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content. Blending camera and 77 ghz radar sensing for equitable, robust plethysmography., ACM Trans.
Graph. 41 (2022) 36–1. [15] Q. Hu, Q. Zhang, H. Lu, S. Wu, Y. Zhou, Q. Huang, H. Chen, Y.-C. Chen, N. Zhao, Contactless arterial blood pressure waveform monitoring with mmwave radar, Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies 8 (2024) 1–29. [16] Z. Wu, Y. Xie, B. Zhao, J. He, F. Luo, N. Deng, Z. Yu, Cardiacmamba: A multimodal rgb-rf fusion framework with state space models for remote physiological measurement, IEEE Transactions on Instrumentation and Measurement (2025). [17] J. Speth, N. Vance, P. Flynn, A. Czajka, Non-contrastive unsupervised learning of physiological signals from video, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023, pp. 14464–14474. [18] E. M. Nowara, D. McDuf, A. Veeraraghavan, Systematic analysis of video-based pulse measurement from compressed videos, Biomedical Optics Express 12 (2020) 494–508. [19] S. Sachdeva, Fitzpatrick skin typing: Applications in dermatology, Indian journal of dermatology, venereology and leprology 75 (2009) 93.