Two single-channel SFCW radars were fabricated to verify the capability of the proposed algorithm. Specifically, four groups of experiments were carried out in two different realistic scenarios. The radar description and experiment results are provided below in this section.
4.2. Experiments with Different Target Positions
The first group of experiments was performed to reveal the effect on the proposed algorithm of different target positions. In these experiments, the wall is a solid brick wall with the measured thickness of 0.2 m and relative permittivity of about 9. As shown in
Figure 4, two SFCW radars were placed against the wall with an interval distance of 1.5 m. For the sake of distinction, the experiments are named Experiment 1.1 and Experiment 1.2.
In Experiment 1.1, two human targets with normal respiration were standing at (0 m, 4 m), and (1.5 m, 5 m), based on the given coordinate system, as shown in
Figure 5, where Radars 1 and 2 were separately located at the origin of (0 m, 0 m) and (1.5 m, 0 m). Target 1 at (0 m, 4 m) weighs about 75 kg and is about 1.75 m tall. Target 2 at (1.5 m, 5 m) weighs about 70 kg and is about 1.7 m tall. By manually operating the displaying and controlling host computer, the two radars collected
periods of SFCW echoes. After IFFT processing with a point number of
and two-pulse cancellation for each period, two fast–slow time range profile planes of the two radars were provided (
Figure 6a,b). For ease of observation, the range display was limited from 0 to 8 m. It was obvious that, in the planes of Radar 1, the respiration signal of Target 2 was much lower than that of Target 1 because of the longer propagation range and oblique detection angle of the view while, for Radar 2, the respiration signals of the two targets with approximate propagation ranges and viewing angles had almost identical intensity. Through cross-correlation calculation between the two range profile planes, the correlation coefficient matrix was calculated, as shown in
Figure 6c, where two targets clearly emerged. According to the feature of Gaussian distribution [
25], it is easy to say that the noise in
Figure 6c is non-Gaussian distribution, which means that CFAR detection was unable to provide constant false probability for all matrix elements. Fortunately, two targets were still successfully extracted, as shown in
Figure 6d, by pseudo-CFAR detection with
elements of the sliding window,
elements of the protection window, and
, which verified the feasibility of identifying targets by using a CFAR detector, in this case of non-Gaussian noise background. Each extracted target was composed of multiple conterminous elements with a value of 1, whose centroid element was selected to generate two desired target ranges for two radars by using corresponding row and column coordinates. By placing the extracted target ranges into Equation (
15), the estimated target locations were obtained, as shown in
Figure 6h with two blue crosses. Because of wall-penetration effect, the estimated target locations were obviously displaced from real target locations. After compensation for wall penetration as in Equation (
16), estimations of the target locations were corrected to the vicinities of real locations, marked with two red dots. The coordinates of estimated position of Target 1 and Target 2 are (
m, 4.11 m) and (1.65 m, 5.06 m), respectively.
Mean localization error (MLE) was used to quantitatively evaluate localization accuracy:
where
is the total number of targets,
x and
y are the coordinates of the actual target positions,
and
are the coordinates of the estimated target positions, and
is the target number. The MLE of Experiment 1.1 was about 0.15 m.
Moreover,
Figure 6e,f provide the range profile planes of the two radars after an average cancellation of 300 periods. Compared with
Figure 6a,b from two-pulse cancellation, the average cancellation had better performance in preserving target signals (with higher SNR), while most associated side lobes were retained as well. Through cross-correlation, the retained side lobes were transformed into widespread ghost interferences, as shown in
Figure 6g, hindering the detection of desired main-lobe correlations. Therefore, although the main lobe of the target signal was partly reduced, two-pulse cancellation was a preferred choice for suppressing stationary clutter in the proposed algorithm due to the residual side lobes disappearing in the noise background.
Furthermore, the FFT-based energy accumulation method in [
21] and the single-radar correlation based method in [
22] were performed to compare the proposed algorithm. Specifically, the FFT accumulation along slow-time was performed on each range profile plane in
Figure 6a,b. The generated RD planes are provided in
Figure 7a,b where the target ranges and respiration rates could be extracted together. In accordance with
Figure 6a,
Figure 7a shows that the accumulated respiration signal of Target 2 was much weaker than that of Target 1. In other words, the energy accumulation of FFT inherited the intensity difference of two targets, which made it difficult to identify the weaker target. On the contrary, the two targets were endowed with similar intensities through the proposed cross-correlation operation. Therefore, the aforementioned comparison proved the effectiveness of reducing the intensity difference of multiple targets by cross-correlation of dual-station radars. Besides, through cross-correlation, two ranges of each target associated with two radars were isolated without the additional pairing operation that was necessary for the extracted four target ranges from RD planes in
Figure 7a,b.
According to the single-radar correlation-based method in [
22], the correlation operation was performed on each range column with regard to each radar plane in
Figure 6e,f. As shown in
Figure 7c,d, the single-radar correlation results were blurred by widespread ghost interferences derived from the retained side lobes in the average cancellation. Therefore, based on
Figure 6g and
Figure 7c,d, it is concluded that the average cancellation was unable to support the proposed dual-radar cross-correlation algorithm and the existent single-radar correlation method because of the side lobes of SFCW pulse compression. For simplification, the following dual-radar cross-correlation results and single-radar correlation results were entirely based on the range profile planes from the two-pulse cancellation. Specially,
Figure 7e,f reveals the single-radar correlation results corresponding to the range profile planes in
Figure 6a,b from two-pulse cancellation, where ghost interferences were significantly reduced in contrast to
Figure 7c,d. However, it was also difficult based on the single-radar correlation method to identify weak Target 2 from the results in
Figure 7e. It is noticed that, in
Figure 7c–f, there exist line-like interferences around the diagonal that adversely affected the target detection. The line-like interference is an inherent defect in the single-radar correlation algorithm [
22] because the correlation coefficient between the data vector in each range unit and itself is always 1.
To evaluate cross-correlation performance under extreme conditions, Experiment 1.2 was implemented as shown in
Figure 8 where two human targets stood in a line along with
y-axis. In this case, with regard to Radar 1, the far Target 2 at (0 m, 4 m) fell into the shadow of the near Target 1 at (0 m, 3 m). The target at (0 m, 3 m) weighs about 70 kg and is about 1.7 m tall. The target at (0 m, 4 m) weighs about 75 kg and is about 1.75 m tall. Therefore, from the range profile plane in
Figure 9a and the RD plane in
Figure 10a of Radar 1, the respiration signal of Target 2 almost disappeared. It was verified that the existing method based on energy accumulation suffered from the problem of missed detection of weak target. Meanwhile, as given in
Figure 9b,d for Radar 2, the respiration signals of two targets were captured from another angle of view without a shadow effect, while Target 2 was weaker than Target 1 due to the longer propagation range. Fortunately, by utilizing the proposed algorithm based on dual-station cross-correlation, the weak Target 2 also appeared clearly (
Figure 9c) and was thus detected successfully (
Figure 9d). Furthermore, two pairs of ranges of two targets were obtained to generate the estimation target locations with wall compensation, as shown in
Figure 9h. The coordinates of estimated positions of Target 1 and Target 2 were (0.06 m, 2.95 m) and (0.05 m, 4.12 m), respectively. The MLE was about 0.1 m. It was demonstrated that the cross-correlation operation was able to support robust detection and localization of multiple different intensities of stationary human targets even in the case of a shadowing effect, by exploring the correlation characteristic of each target between two radars.
Moreover, although two range profile planes of average cancellation had a higher SNR, as shown in
Figure 9e,f, the corresponding cross-correlation result in
Figure 9g was seriously blurred by widespread ghost interferences from the retained side lobes. It was further demonstrated that the average cancellation was unavailable to the proposed cross-correlation algorithm with dual SFCW radars.
Figure 10c,d shows the single-radar correlation results, as in [
22]. Obviously, the shadowed weak Target 2 for Radar 1 was missed, as shown in
Figure 10c. By comparing with
Figure 9c, the superiority of the proposed algorithm in weak target detection was validated, guaranteed by two-view observation of dual-station radars because the shadowed weak target in one radar view can be observed effectively in another radar view.
4.3. Experiments with Different Radar Locations
For a comprehensive verification of the proposed algorithm, the following three groups of experiments were accomplished in the other scenes to study the effects of radar location, human-target orientation, and human-target posture. The wall in these three groups of experiments was a solid brick wall with a measured thickness of 0.24 m and relative permittivity of about 8.5. The height of the radar antennas from the ground was 0.54 m. The body type of one human target was about 75 kg weight and 1.7 m height, and the other human target was about 65 kg weight and 1.7 m height.
In this subsection, three experiment results are provided to observe the effect of different radar locations. Specifically, under the fixed origin location of Radar 1, Radar 2 was moved away from Radar 1 in a straight line to separately form three interval distances of two radars, namely 1 m, 2 m and 3 m, corresponding to three experiments, as shown in
Figure 11. In these three experiments, the two human targets stood at coordinates of (0 m, 3 m) and (0 m, 4 m) as in Experiment 1.2. For simplification, the three experiments with the radar intervals of 1 m, 2 m and 3 m are denoted by Experiments 2.1, 2.2 and 2.3, respectively. The coordinates of estimated target positions and MLE of the experiments above are shown in
Table 3.
The experimental results including range profiles of two radars, cross-correlation images, and localization result, are provided in
Figure 12,
Figure 13 and
Figure 14 for Experiments 2.1–2.3, respectively. By comparison, it can be seen that, with the increase of radar interval, the two targets, especially Target 2, gradually disappeared in the clutter background. That is because, in the case of a larger radar interval, the greater ranges and the bigger observation angles between Radar 2 and the two targets reduced respiration-signal intensities. Especially under the joint action of target occlusion, Target 2 was out of the effective detection and localization range of the proposed cross-correlation algorithm.
4.4. Experiments with Different Target Orientations
In this subsection, the influence of target orientation was considered by carrying out three experiments with different orientations of human Target 2, as shown in
Figure 15. These two radars were located at (0 m, 0 m) and (1.5 m, 0 m) as in Experiments 1.1 and 1.2, and the two human targets stood at (0 m, 4 m) and (1.5 m, 5 m), respectively. In these three experiments, Target 1 maintained a fixed orientation that was always facing Radar 1, while Target 2 was endowed with three different orientations, namely, three orientation angles of
,
, and
between target orientation and the baseline of the two radars. For convenience, these three experiments in
Figure 15a–c are labeled Experiments 3.1, 3.2, and 3.3, respectively. The coordinates of estimated target positions and MLE of the experiments above are shown in
Table 4.
As shown in
Figure 16a,b,
Figure 17a,b, and
Figure 18a,b, the respiration signals of Target 2 in the range profile planes of the two radars fell into a decline along with the decrease of orientation angle from
to
. In the case of an orientation angle of
, it was almost impossible to identify the respiration signals in these two range profile planes. That is because the major fluctuations of the human abdomen, caused by respiration, gradually deviated from the observation view of the two radars, while the affiliated minor fluctuations of the scapula part gradually turned toward the radar view. Fortunately, through the presented cross-correlation process, these two targets were clearly highlighted in the cross-correlation images, as shown in
Figure 16c,
Figure 17c, and
Figure 18c. Therefore, through CFAR detection, the range of two targets could be successfully extracted to calculate estimations of target locations, as shown in
Figure 16d,
Figure 17d, and
Figure 18d. Based on the above discussion, it was demonstrated that the proposed cross-correlation algorithm has the favorable ability to adapt different orientations of human targets.