3.1. Designed Experimental Setup
For experimental comparison, a carefully designed experimental setup is necessary for data capturing. We designed the experimental setup shown in
Figure 1 where several different angles and distances are considered. The experimental setup comprised five discrete data capturing points at a distance of 0.9, 1.2 and 1.5 m each. These distances were chosen given the fact that in most of the research related to vital sign extraction, human subjects are near the radar [
16,
17]. Long-range vital sign measurements are often used in search and rescue operations. The five points in our experimental setup are separated by an angle of 20 degrees and range between positive and negative. Angles above 40 are beyond the scope of our experimentation. In total, there are 15 data capturing points which are highlighted in yellow in
Figure 1. Note that the human participants were at rest during data capturing. Since the main objective of this research is to compare the performance of vital sign extraction in two cases that are without and with beamforming, we captured vital sign data simultaneously in both cases for the sake of a fair comparison.
3.2. FMCW Radar Signal Processing
FMCW radar transmits a saw-tooth modulated signal whose frequency increases linearly with time known as chirp [
2]. The transmitted signal
can be expressed as [
27,
28]
where
represents the bandwidth of the chirp,
represents the time period, and
represents the starting carrier frequency. In (1), the term
B/T defines the ramp of chirp which is directly proportional to the bandwidth and inversely proportional to the time period of one chirp. In a single radar frame, there are several chirps being transmitted together as shown in
Figure 2. As observed in
Figure 2, there exists a delay between the transmitted chirp shown in red and the received chirp shown in green. The corresponding received signal
y from a moving target will be
where
represents the round trip time-delay and can be calculated based on the radial velocity
, distance
, and speed of light
such that
It should be noted that the round trip delay contains the time taken by the signal to reach the target and then reach the receiving antenna.
At the receiver, the received signal is multiplied with the copy of the transmitted signal, and the high frequency values from the resulting terms are ignored to recover a low-frequency signal [
29]. This circuitry is often termed as the mixer, and the output of the mixer is called the intermediate frequency (IF) signal [
30].
For the case of an MIMO radar, the IF signal at each receiver is extracted independently. The overall signal processing chain for an MIMO radar consisting of
receiving channels is shown in
Figure 3. As shown in
Figure 3, the received signal at each channel expressed as
y according to Equation (1) is mixed with a copy of transmitted signal to form the low frequency signal
. The
signal is digitized separately at each RX channel, and fast Fourier transform (FFT) is taken. Afterwards, a 2D matrix is constructed for each receiver where the peak in the FFT range bin will resolve the target (human chest) location. The signal from each RX channel is combined at the end to form a radar data cube (RDC) matrix
, whose dimensions are
here
, and
presents the number of chirps, range FFT size, and number of (virtual) RX antennas, respectively. This radar RDC matrix is generally used to extract target information in different domains such as the range–time domain, the velocity–time domain, and the range–angle domain. Next, we present the beamforming operation being used in this research.
3.3. Beamforming with OTS Radar
Figure 4a describes the theoretical details of RX beamforming with N receiving channels. With multiple (two) transmitters placed at different locations, a distinct non-coherent signal is transmitted by each TX antenna. In order to perform RX beamforming, these transmitted signals are orthogonal in nature [
26]. The RX chain receives the signal being reflected by the target (human chest). With multiple TX and RX, the number of elements of a virtual uniform linear array (
) will be [
31]
In Equation (6), the
and
represent the number of transmitters and receivers, respectively.
Figure 4b represents the virtual array corresponding to a setup shown in
Figure 4a.
Since the distance between two adjacent antennas is far less that the distance between the human target and the receiver, it can be said that the reflected signals for each channel travel in parallel to each other.
In this study, we used receiver beamforming to increase the signal coming from the target direction while minimizing the other directions. As explained earlier, the MIMO radar setup for capturing vital signs is shown in
Figure 4a. Assume that we have
Nrx receiver channels separated by a distance
d which is often a fraction of the wavelength
λ, and the AoA between the radar and the target is
θ, the receiver near the target will receive the reflection first. The main objective of beamforming is to align all the received signals and sum them up as expressed in
Figure 4a. A constant phase increment is required to steer the beam towards the desired reflection. The delay
for a specific
antenna and an angle
can be found as
where
represents
nth RX antenna in the virtual array for beamforming, and
represents the distance between two RX antennas. Note that the OTS FMCW radar under consideration has two TX and four RX antennas which collectively provide 8 virtual RX antennas. As stated earlier, the distance between the two adjacent RX antennas of the OTS FMCW radar is
/2. The above equation can be simplified as
For a specific angle
, the required delay term
in terms of a complex exponential is multiplied with the RDC matrix X, as expressed in
Figure 2. The weight vector of all the eight RX antennas of the OTS FMCW radar under consideration will be
where
is the weight vector to be multiplied with the matrix X having dimensions equal to number of considered RX antennas. The resulting dot product of X and W can be expressed as
where
represents the Hermitian matrix. In (10), the BF represents the beamformed signal which is the combination of each individual RX channel. The process from Equations (7)–(10) is summarized in
Figure 5. As explained earlier, the weight vector is calculated according to Equation (8) and then multiplied with the RDC expressed in (9). The resulting values are summed up (by taking the dot product) to form a unified signal
which increases the reflection for a specified arrival angle. This signal is then used to extract human vital signs.
The MIMO FMCW radar considered in this study is designed by Texas Instruments (TI), Texas, TX, USA (IWR6843 FMCW radar).
Table 1 lists the remainder of the technical specifications of the OTS radar. As shown in
Table 1, with two TX and four RX we have created a
of eight elements.
The antenna pattern of all the transmitter and receiver pairs is shown in
Figure 6 [
32]. The gain in terms of horizontal angle (azimuth) shown in
Figure 6 suggests that as we move away from the zero-degree AoA, the antenna gain decreases significantly.
3.5. Vital Sign Extraction Algorithm
The stepwise adopted vital sign extraction is as follows:
Step 1: Collect the IF signal corresponding to the chest reflection for each receiving channel.
Step 2: Perform range–FFT at each channel.
Localize the target in the range–angle map and find the angle-of-arrival.
Step 3: Perform beamforming to combine the signals from each channel.
Step 3: Remove clutter from the signal using a loop back iterative filter [
25]. For big movements, simple mean removal tilter works well for removing clutter. However, for vital signs, a filter is often deployed since the chest movement itself is small.
Detect the human location.
Extract and accumulate the phase from each radar frame at the point where the human is located.
Use two separate band-pass filters to extract breathing and heart rates.
Use a moving mean filter to further reduce the noise in the radar recordings.
Please note that in our experiment, since we performed experiments with and without beamforming, step 3 will be excluded while extracting vital sign without using beamforming. Instead, only RX-1 is utilized, and the rest of the data is discarded in that case.