*2.1. Basics of CW Doppler Radar Operation*

A typical architecture of quadrature continuous-wave Doppler radar is shown in Figure 1a. The radar transmitted sinusoidal electromagnetic waves generated in the local oscillator (LO) and amplified in the power amplifier (PA). The transmitted signal reflects from the target, where the reflected signal is modulated in phase. The transmitted signal can be expressed as

$$T(t) = A\tau \cos(2\pi ft + \theta(t)),\tag{1}$$

where *AT* and *f* are the amplitude and the frequency of the transmitted signal, respectively, and θ(*t*) is the phase noise of the local oscillator. The received signal can be expressed as

$$R(t) = A\_R \cos\left(2\pi ft - \frac{4\pi d\_0}{\lambda} - \frac{4\pi \mathbf{x}(t)}{\lambda} + \mathcal{O}\left(t - \frac{2d\_0}{c}\right)\right) \tag{2}$$

where *AR*, *f* and λ are the amplitude, the frequency and the wavelength of the carrier signal, respectively, *c* is the speed of light, *d*<sup>0</sup> is the nominal radar–target distance and *x*(*t*) is the target's relative displacement [7]. The received signal is demodulated using a quadrature demodulator as shown in Figure 1a. The resulting signals are two baseband signals: the in-phase signal (I), which is in phase with the carrier and the quadrature signal (Q), which is phase-shifted from the carrier by 90◦. These signals are expressed as [10]

$$I(t) = A\_I \cos\left(\theta\_0 + \frac{4\pi\mathbf{x}(t)}{\lambda} + \Delta\theta(t)\right) + D\mathbb{C}\_{I\prime} \tag{3}$$

$$Q(t) = A\_Q \sin\left(\theta\_0 + \frac{4\pi\mathbf{x}(t)}{\lambda} + \Delta\theta(t) + \Delta q\right) + DC\_{Q\_{\prime}}\tag{4}$$

where *AI* and *AQ* are amplitudes (*AI* - *AQ* due to the I/Q amplitude imbalance), *DCI* and *DCQ* are DC offsets, θ<sup>0</sup> is the constant phase shift due to the constant nominal distance *d*<sup>0</sup> from (2), Δϕ is the phase shift due to the I/Q phase imbalance and Δθ(*t*) is the total residual phase noise which can be neglected in vital signs detection applications since the distance between the target and the radar system is small [7]. Baseband signals are further digitized using analog-to-digital converters (ADCs) and processed in a digital signal processing unit.

**Figure 1.** (**a**) Architecture of the quadrature Doppler radar used for the measurements; (**b**) Photographs of the Smartex Wearable Wellness System (WWS) used for the electrocardiogram (ECG) measurement; (**c**) Experiment setup.

#### *2.2. Instrumentation*

In this study, a CW Doppler radar with a carrier frequency of 24 GHz was used for heart rate estimation. The recording of the reference ("ground truth") signal for the ANN training and the validation of the estimation accuracy was done using a wearable cardiorespiratory monitoring system (Smartex Wearable Wellness System (WWS), Pisa, Italy) including a single lead ECG and a piezo band as shown in Figure 1b. The ECG sensor was chosen since its accuracy was higher than other heart rate monitors such as pulse oximeters or photoplethysmographs. The system contained a microcontroller for data acquisition and Bluetooth connection for wireless data transmission to the personal computer (PC). It was a CE (Conformité Européenne) certified system. Additionally, the electrodes were connected to the skin using the wet textile fabric, which eliminated any potential irritation that could come from the sticky adhesive electrodes, particularly if applied on non-glabrous skin [34]. The sample rate for the ECG recording was 250 Hz.

The radar system used in the experiment was a Novelic Radar Module, NRM24 [24]. Figure 1c shows the radar module placed in the experimental setup. It was a DC-coupled Doppler radar sensor. The module was compact (8 × 5 × 1 cm) and portable and consisted of two stacked printed circuit boards (PCBs). The radar sensor PCB included the main part of the analog frontend: antennas, an integrated radar transceiver and a phase-locked loop integrated circuit. Antenna beamwidths (*BW*) were *BW*θ, 3-dB = 25◦, *BW*θ, 6-dB = 33◦, *BW*θ, 10-dB = 43◦ (elevation) and *BW*ϕ, 3-dB = 44◦, *BW*ϕ, 6-dB = 65◦, *BW*ϕ, 10-dB = 90◦ (azimuth), whereas the antenna gain was 12 dBi. The maximum power at the transmit antenna input was 10 dBm. The second PCB was the acquisition board, which included baseband amplifiers and filters, a power supply circuitry, an ARM Cortex-M4 based microcontroller (MCU) that integrated a multichannel 12-bit ADC and serial-to-USB converters for data transfer. The baseband

filter had a cut-off frequency of 100 Hz, which was considered high enough for the vital sign detection application. The sampling rate was set to *fS* = 1 kHz, while the data logging on the PC was performed using a custom-made application that communicated via serial connection with the MCU.

The alignment of the datapoints from the Smartex WWS system and the radar system was done by matching timestamps in the logged data.

#### *2.3. Database Recordings*

The radar recordings, as well as the ECG data used as reference, were obtained from 21 healthy human volunteers who took part in the experiments (14 males and 7 females, aged 26.1 ± 5.1, with a height of 179.5 ± 11.6 cm and a weight of 74.2 ± 16.4 kg). Subjects were free of any diagnosed acute/chronic cardiac or respiratory problems, based on their self-report. Participants were acquainted with the protocol in advance and gave informed consent. The study was approved by the ethical committee of the University of Belgrade—School of Electrical Engineering, Serbia. The subjects had the wearable ECG strapped around their thorax and were instructed to sit comfortably on a cushioned seat in front of the radar sensor. The sensor was mounted on a custom stand, facing the participants at a distance of 75 cm. At this distance, the radar beam focused on the torso area, considering −3 dB beamwidths of the antenna (25◦ and 44◦). The participants were told to breathe as they normally would in a relaxed state, without extremely deep and excessive breaths. Additionally, they were asked to refrain from excessive body and hand movements, since the rapid movements could mask the small chest wall movements that come from heartbeats and hence affect the detection. The radar signals obtained for one participant are shown in Figure 2. Three-hundred seconds of data were acquired for each subject.

**Figure 2.** In-phase and quadrature Doppler radar signals during the measurements. The participant was breathing normally in front of the radar sensor.

Figure 3a shows a fragment of recorded time-aligned ECG and radar signals. There was a distinctive signal shape in the radar signals with a time delay in relation to the R wave of the ECG. The heartbeat-related disturbance in the radar signals originated from the mechanical movement of the chest wall during the heartbeat. This disturbance corresponded to the ballistocardiogram J-wave peak [35]. It can be seen that this characteristic signal shape became distorted and was reduced in the presence of breathing and movement.

Many previous works considered that the heartbeat-related displacements could be modeled as a sine wave [16], half-sine pulses [21], Gaussian pulses [22], or as an array of two consecutive pulses [24]. However, the mechanical response of the chest wall has a complex waveform that is difficult to model [33]. Figure 3b shows the heartbeat-related displacement obtained from the radar data shown in Figure 3a, using the extended differentiate and cross-multiply (DACM) demodulation algorithm described in [16]. Before the demodulation, the I/Q imbalance of the radar was measured and compensated offline like in [24]. It can be observed that the heartbeat-related displacement had a complex waveform, which further induced the complex signal shapes of the radar signals. The detector in this paper was trained with the aim to recognize these small distortions in the radar signals, without previous modeling. In order to get a reliable data set for training the detector, the signals were cropped to the period of 200 s of normal breathing (Figure 2, time interval 50–250 s).

**Figure 3.** (**a**) A fragment of the recorded ECG and radar signals. It could be noted that the heartbeats acquired by the ECG amplifier are followed with slight movement patterns picked up by the radar. During the inhale−exhale (see 2–5 s) this movement pattern is distorted. (**b**) A heartbeat-related chest wall displacement obtained using the extended differentiate and cross-multiply (DACM) demodulation of the first 2 s of the radar signals.

#### *2.4. Data Preprocessing*

The detector was envisioned as a binary classifier detecting the occurrence of each heartbeat, but such implementation required the reshaping of the recorded data into an appropriate format. The continuous nature of the reference ECG signal was not suitable for this approach, so it was instead transformed into a binary on/off signal. R peaks were detected using the Pan-Tompkins algorithm [36]. The surrogate reference binary signal ("binarized target signal") was synthesized in the form of a 400 ms pulse with 200 ms delay after each R wave in order to highlight the temporal relationship between the heart's electrical activity (ECG) and the resulting mechanical displacement (radar signal), as shown in Figure 4. The window of 400 ms width with a latency of 200 ms after the R wave was able to cover most of the mechanical rippling observed within the radar signals. This choice is in line with a study performed on 92 healthy subjects which showed that the duration range of the R−J interval was 203–290 ms [37]. Additionally, the selection of the value of the latency parameter (200 ms) for the binarized target signal was confirmed on a recorded dataset of seven randomly selected subjects from our study. Using the simplest model that was tested in the scope of this paper (a feed-forward artificial neural network with a single hidden layer containing 10 units), a series of training and testing with a range of delays and target widths was performed. The tested delay values ranged between 0 ms to 300 ms, and the target widths were tested in the range between 300 ms and 500 ms. These values were selected based on the visual inspection of the signals, and the values that were chosen as optimal (window of 400 ms width with a latency of 200 ms after the R wave) were those that yielded the best model accuracy in terms of the percentage of detected peaks.

The following stage in the signal preprocessing was the decimation of both the binary reference signal and the radar signal to the same sampling rate, which was a prerequisite related to the ANN employment, as each input state required a corresponding target output. To ensure the fast computation without a loss of information in the physiological range, 100 Hz was selected as the sampling rate during this computation.

**Figure 4.** Reference ECG signal (ECG) and the binarized target signal (derived heartbeat events) where the values of "1" represent the presence of the mechanical heart displacement after the R wave, and the values of "0" represent its absence.

The input to the ANN consisted of a 200-sample long vector, corresponding to 1 s of recording, where in-phase and quadrature branches were concatenated so that the first 100 samples in the input corresponded to the in-phase signal and the second 100 samples corresponded to the quadrature signal. Such an input was matched to the value of the reference binary signal as the target output. The choice of 1 s signal memory was based on a small-scale test conducted on a subset of recorded signals in which the memory depth varied between 200 ms and 1 s. The lower bound was sufficient to partially incorporate the mechanical wave observed due to the heartbeats and the upper bound corresponded to the interval between the subsequent heartbeats at a normal heart rate of 60 bpm. These initial test results showed that the increases of memory depth from 200 ms to 500 ms significantly increased ANN performance, while further increases resulted in only incremental gains. Nevertheless, we decided to use the deepest memory as we were not concerned about computational complexity, while using longer intervals was expected to contain more physiologically relevant data that the ANN could learn from, and not overfit to potentially insignificant signal details.
