Improving passenger safety in cars using novel radar signal processing

According to the group Kids and Cars, since 1990, nearly 1000 kids lost their lives because they were deliberately or unintentionally left in parked vehicles to potentially overheat or freeze. The development of technology able to prevent and address this serious, worldwide problem is crucial. In this paper, we deploy a radar‐based sensor for in‐vehicle presence‐absence detection of a living body. We present a novel radar signal processing technique to identify the presence or absence of a living body in a vehicle using a mm‐wave frequency‐modulated continuous‐wave (FMCW) radar. Our proposed method is based on reflections from breathing cycles creating correlated and consistent micro‐Doppler effects over time. The performance of the system is evaluated with adults and two phantoms mimicking the breathing of children in various scenarios. The results show that we can clearly detect any tiny living body in vehicles with 100% accuracy without a need for any compute‐intensive complex signal processing, making the system of extreme low‐cost. The results demonstrate the high sensitivity and robustness of the mm‐wave system in extensive studies over the course of multiple months.


INTRODUCTION
In 2019, 52 children died of vehicular heatstroke in the United States. 1 Occupancy detection systems are a promising solution to avoid these situations. Multiple solutions for in-vehicle occupancy detection already exist while suffering from various drawbacks. Embedded sensors in seats are primarily used to monitor the deployment of airbags or control the seat belts. Capacitive sensors alone 2 or capacitive sensors with inductive links with switch sensors 3 are used to detect an occupant. However, sensors based on an electric field, capacitive and inductive methods have high false alarm rates. Some car brands have also equipped their models with rear occupant alert 4 using the opening of the back door and motion sensors to trigger a notification. This solution also has a high false alarm rate that has led many users to simply disable them as features.
Carbon dioxide sensors that trigger an alarm when the CO 2 level rises have also been developed. 5 However, the position of doors and windows, the supply of outdoor air, and the proximity of occupants to the sensors are some parameters that impact the signal and reduce the accuracy of the system. 6 In general, occupancy detection can be conducted with video cameras, 7 passive infrared (PIR), 8 and ultrasound (US) sensors, 9 but these methods present limited functionality in different situations and conditions. Vision-based sensors are sensitive to illumination level, and the performance of PIR and US sensors depends on the direction of the sensor and degrades when sensing through materials. 10 Additionally, camera sensors invade the privacy of users. Thermal cameras can also be used for occupancy detection 11 but only achieve a detection accuracy of 91%. This level of accuracy is not sufficient as any missed detection in the case of children left behind can be fatal. Hence, a system that can detect any tiny alive subject with 100% accuracy, as well as a low false alarm rate, is highly required.
The use of a radar system is appealing due to its robustness and reliable functionality under different conditions, protection of privacy and detection through obstacles. 10,12 Radar sensing of human cardiopulmonary movements, [13][14][15] breathing 16 and human gesture are widely used for in-room occupancy detection. Various studies were conducted using different types of radars including, but not limited to, an off-the-shelf system-on-chip operating frequency of 2.405 GHz, 17 a continuous wave (CW) radar at 2.4 GHz, 18 a 60 GHz frequency-modulated continuous-wave (FMCW) radar, 19 a CW radar at 24 GHz 20 and an Ultra-Wideband (UWB) radar with a frequency range of 5.9-10.3 GHz. 21 These studies proved the feasibility of radar-based sensors in occupancy detection. However, for in-vehicle occupancy detection, radar technologies have been comparatively less utilized. In-vehicle occupancy detection has been conducted with an UWB radar in References 22,23 with a central radar signal frequency of 6.8 GHz. The radar and classification were used for finding the position of people in the vehicle and the best classifier achieved an accuracy of 92.02% 22 and 99%. 23 An UWB radar-based device named CarOSense was presented in Reference 24. The system achieved a 94.6% accuracy for the leave-one-out test; however, this system was used with 8 UWB nodes making the system quite expensive to deploy by automakers. These solutions are based on machine learning techniques that are computationally costly and could not be implemented in embedded devices or in the radar Digital Signal Processing (DSP). Moreover, machine-learning-based occupancy detection requires a lot of training data, and the results may be dependent on the type of vehicle the device is used in. For the presence-absence detection (PAD) of a child or pet inside a parked car, a fast and easy-to-implement algorithm that supports regulatory requirements and can be used in all types of vehicles is greatly needed.
In Reference 25, a 24 GHz FMCW radar was used for in-vehicle occupancy detection to detect a passenger's seat location in the back row of a car. However, the system was only tested on an adult in an anechoic chamber, while the real challenge is to use the system in a car. The wave propagation effects in the vehicle interior were assessed in Reference 26, which offers better knowledge for choosing the position of the radar. In Reference 27, a non-broadside patch antenna at 24 GHz was designed to be used for in-vehicle occupancy detection. The capability of the mm-wave frequency to detect a child or an infant was also shown in a simulation scenario in Reference 28.
Moreover, a radio-frequency-based sensor, VitaSense, has been developed for in-vehicle occupancy detection. 29,30 The principles and performance of VitaSense were described in Reference 31. A CW-radar operating at the 24 GHz industrial, scientific and medical (ISM) band was used to detect the movements or breathing of the occupants; however, the system was not tested in an actual car. It was not clear whether one sensor is required for each seat or a single sensor can sufficiently cover all seats. Additionally, the performance of the system was not assessed with a car filled with various stationary objects such as backpacks or shopping bags, which would cause multipath effects. A system that is not only 100% accurate, but also rigorously tested with various real-life scenarios with few false positives is highly required for the detection of children and pets to prevent any potential deaths.
To overcome the drawbacks mentioned above of the currently available systems, as well as to fulfill the aforementioned requirements, we used a low-power, mm-wave multi-input-multi-output (MIMO) FMCW radar sensor for presence-absence living body detection in vehicles. To find the location of the radar that has the maximum coverage in a car, we performed full-wave Electromagnetic computer simulations using the Ansys High Frequency Structure Simulator (HFSS). 32 We chose to use a MIMO radar to increase Signal-to-Noise-Ratio (SNR). This leads to better detection results compared to methods using only one transmitter and one receiver, as will be shown in this work. Contrary to our previous research 33,34 in which we deployed machine learning algorithms to count the number of passengers and identify occupied seats, in this paper, we base our method on a simple signal processing method. In fact, there is no need to know the number of occupants or their location in a parked car as the key required information is the presence or absence of a living body, especially a child or an infant, to prevent death. Unlike machine learning-based methods, we propose a fast, simple, and easy-to-implement signal processing method that detects the presence-absence of any living organism regardless of the type of car. Our novel PAD algorithm is based on the breathing cycles of alive subjects generating correlated and consistent micro-Doppler patterns over time. Since the purpose of the system is to be activated when the car is parked, it is justifiable to assume that there is no consistent motion created by other objects such as a fan or an air conditioner. The only consistent motion in the parked car would be the consistent chest motion of a living body. One of the main advantages of our proposed PAD algorithm is its independency of any pre-defined thresholds or variables to be tuned, making it appropriate for any type of vehicle. We conducted various measurements to evaluate our proposed method. We applied the PAD algorithm to the radar data collected from adults and phantoms mimicking kids' breathing cycles in different scenarios. The results show that the radar sensor coupled with the PAD algorithm is sensitive enough to detect weak targets, even in the case where the target is placed under the car seats. Additionally, the system was tested in a car filled with many stationary targets (clutters).
The remainder of this paper is organized as follows: In Section 2, we describe the system design and our proposed algorithm for in-vehicle PAD of a living body; in Section 3, we discuss the experimental results; and, finally, in Section 4, we draw some conclusions.

FMCW radar concept
Advances in 77 GHz RF design with integrated digital Complementary Metal-Oxide Semiconductor (CMOS) and packaging led to radar-on-chip and antenna-on-chip systems. 35 In our lab, we work closely with Texas Instruments (TI), 33,34 Infineon, 36 and Vayyar's mm-wave systems. 37 Since they have been widely available in evaluation kits, we will only discuss here TI's 77 GHz FMCW radar chips and the corresponding evaluation boards which are built with the low-power 45-nm RF CMOS process. 38 FMCW radars continuously transmit a frequency-modulated signal called a chirp to measure range as well as velocity. In a Time Division Multiplexed (TDM) MIMO FMCW radar, a sequence of chirps is sent in a frame from different transmit antennas. Each chirp consisting of a sinusoid signal with swept frequency from (carrier frequency) f c to f c + B with the bandwidth of B = f max − f min determines the capability of a radar system to resolve separate targets that are close together in range. The received signal is then correlated with the transmit signal creating a beat signal with a frequency of f b containing information about the illuminated scene. In Figure 1, the transmitted and received signals of an FMCW radar and the corresponding beat frequency are shown.
In an FMCW radar, having "up chirps" (i.e., only positive-slope chirps) for a transmitted signal s(t), the received signal at lst antenna element reflected by the target x l (t) can be modeled as (assuming that the target is a single point target): F I G U R E 1 Transmitted, received, and beat signals in an FMCW radar Here, t f and t s are fast and slow time indexes, b l and l are the channel's mismatched magnitude and phase, and f b is the beat frequency. The beat frequency is the frequency of an (IF) signal produced by an object in front of the radar located at the range of R calculated by where S is the rate of increase in the frequency of the sinusoid, and c is the speed of light in free space. Moreover, v, max , l , Δ l (t f ,t s ), and e 1 (t f ,t s ) in Equation (1) are the target's radial velocity, the wavelength corresponding to the start frequency of the FMCW ramp, the phase shift at lst receiver due to the angle of arrival (AoA), the residual phase noise and the additive noise, respectively.
The range of an object is limited by IF bandwidth supported by the radar device written as: where f bmax is the maximum supported IF bandwidth. Since the f bmax is also dependent on the Analog to Digital Converter (ADC) sampling frequency, an ADC sampling rate of F s limits the maximum range of the radar to Since the range estimation of a detected target in the FMCW radar is primarily dependent on the frequency resolution of the Discrete Fourier Transform performed on the base-band signals, the new range resolution of the radar is given by In an FMCW radar, to resolve objects in range, the Fast Fourier Transform (FFT) is performed on the beat signal (range-FFT) that provides the relative radial distances (i.e., range) of various objects scanned by the radar. This is done such that the frequency of the peaks in the range FFT directly corresponds to the range of the target. Moreover, to obtain the velocity information of an object, a sequence of chirps separated by T c (T c = τ + T) called a frame, is required. The frame structure in an FMCW radar is depicted in Figure 2.
The range-FFTs corresponding to each chirp will have peaks in the same location but different phases. The measured phase difference ( ) corresponds to a motion of the object of v ⋅ T c . Therefore, performing the second series of FFTs (Doppler-FFT) across the chirps, the velocity of objects can be calculated by To calculate the unambiguous range of velocity, the phase of the signal should be less than , which is written as: F I G U R E 2 Frame structure in an FMCW radar system

Start Frequency
The frequency the radar signal will start at Used to determine the bandwidth Thus, to detect higher velocities, we require closely spaced chirps (shorter T c ). The velocity resolution (v res ) is inversely proportional to the frame time (T f ) or the number of chirps (N) per frames given by There are several defining characteristics of a chirp affecting the operating conditions of an FMCW radar in specific ways. A chirp structure in an FMCW radar is illustrated in Figure 3 along with defining parameters. The characteristics used to configure a chirp as well as their effects on the operation of the radar are outlined in Table 1.

Radar antenna pattern and installation option
We used the AWR1443Boost radar sensor 39 for our in-vehicle occupancy detection system operating at 76-81 GHz. The radar has a built-in DSP that can process received signals without a need for an external DSP system. However, in our initial feasibility studies, we used a DCA1000 EVM board 40 to capture ADC data (chirp samples) and transfer over the Universal Asynchronous Receiver Transmitter (UART) interface to a PC. Figure 4(A) shows the AWR1443Boost radar system (red board) and the DCA1000 EVM board (green board). As shown in Figure 4(B), the AWR1443Boost has three transmitters (Txs) and four receivers (Rxs). Since children under the age of 13 are recommended to sit in the back seats of a car, 41 we conducted our measurements in a number of three-row seven-seater vans and sports utility vehicles including a 2019 Dodge Caravan and a 2013 Toyota Sienna. Figure 5 shows the inside of the vehicle with the utilized seat numbering system. As our purpose is to detect occupants in seat #3 to seat #7, the radar should be installed while facing the back rows to ensure maximum coverage. To find the best location of the radar that has maximum coverage of the back rows, we performed full-wave Electromagnetic computer simulations in HFSS using a Finite Element Method to simulate the AWR1443Boost antennas. Figure 6(A),(B) shows the simulated gain pattern of the antenna at the frequency of f = 77 GHz at H-plane and E-plane, respectively. The red curves are the results when Tx 1 is the only active transmitter, while the green and blue curves are the patterns of the Tx 2 (Tx 2 is the only active transmitter) and the Tx 3 (Tx 3 is the only active transmitter) antennas, respectively. As shown, the radar antenna has a very wide beam-width at the H-plane with a gain of more than 10 dB, while the E-plane has a narrower beam-width with the maximum beam directed at around = 10 • .
To find the best location of the radar, the radar was held by a mount that was placed in two possible installation options to cover the back rows. The position of the radar in two possible installation options (option # 1 and option # 2), the distances, as well as the relative angles to each seat from the radar antennas are shown in Figure 7

TA B L E 2 Chirp configuration
Regarding the relative angles of each seat to the radar in both option #1 and option #2, the antenna gain relative to each seat is plotted in Figure 8. As shown in Figure 8(A), the radar illuminates all seats with a gain of more than 9 dB for the case of installation option #1. However, the radar in option #2 covers seat #3 and seat # 4 with a gain of less than −10 dB. Consequently, installation option #1 provides better coverage compared with option #2. Therefore, we carried out all our experiments with the radar installed at option #1.

Radar configuration
To achieve the specific performance of the radar with a visibility range of approximately 2.5 m (the length from the radar antennas to the rear of the vehicle did not exceed this number), the chirp configuration in Table 2 was used. Note that these parameters are selected in a way to be paired with our other applications of the radar for in-vehicle occupancy detection. 33,34

Proposed algorithm
The main goal of this research is to develop a radar-based technology to save lives by triggering an alarm when children or pets are left alone in vehicles. Our proposed method is based on the following assumptions: 1. The car is parked.
2. Doors and windows are closed. 3. No object other than a living body has a consistent motion (there is no working fan/air conditioner while the car is parked).
To prevent death, the only essential and crucial required information is the presence or absence of a living body in the car. Thus, there is a strong need for a simple, fast, and easy-to-implement PAD algorithm. Such an algorithm is desired because it could be implemented in a low-power radar DSP that runs the algorithm while the car is parked. Moreover, as any missed case can lead to death, an algorithm with 100% accuracy is highly required. With regards to these requirements, we aim to find an accurate algorithm that just detects the presence of a living body with 100% accuracy without providing any extra information such as the position of passengers, which seats are occupied or the type of occupants. It should be mentioned that to provide all these pieces of information, a more sophisticated algorithm such as a machine-learning-based algorithm is required. This is not simple enough to be implemented in the radar DSP. The mentioned extra information is not crucial or necessary while the car is parked. 33,34 Furthermore, because child sensors and alarms are becoming mandatory in new vehicles, we need an algorithm that detects any living body left behind in the car independent of the car type. Note that the size and type of materials, the number of seats, the temperature, and other objects such as a box, books, and so forth, result in varying noise floors of reflected signals from one car to another one. Multipath effects of the mm-wave signals in the small reflective area such as a car are the major cause of varying thresholds. For example, for a specific car, the noise floor differs when the car is empty versus when the car filled with a large box or package placed on a seat as the box can change thresholds. Additionally, since the size of infants and pets are extremely small, it may not be accurate or even possible to define a proper SNR to distinguish a weak target from noise.
To avoid pre-defining any thresholds or variables to be tuned and to find an algorithm that works in any car, we base our proposed PAD algorithm on the most obvious difference between living organisms and inanimate objects: breathing cycles. The breathing cycles create consistent motions resulting in a consistent micro-Doppler frequency over time. Since the car is parked and windows/doors are also closed, we expect no sources to create consistent motion inside the car other than a living object if left alone in the car. The core of our proposed algorithm, thus, is based on micro-Doppler effects created by the chest motion of an alive subject over time. To start, the received signals were recorded for T To seconds. This means that after the car is stopped, the sensor identifies the presence-absence of a living body after T To sec. To reduce receiver noise as well as to increase the signal intensity, we illuminated the target scene with as much energy as possible using all transmitters and receivers (the MIMO system). It should be mentioned that, commonly, the MIMO feature of the radar is used to obtain the angle of arrival information. However, we use this feature of the MIMO radar to increase the signal intensity to detect any tiny subjects (infants) with a low reflection coefficient. Figure 9(A) illustrates the details of the signal processing procedure of our proposed PAD algorithm. First, in a TDM-MIMO-FMCW radar, N F number of frames, consisting of N number of chirps in a frame, are sent from different transmit antennas. At the receiver, signals are collected (over T To sec with N F number of frames) and assigned to channels such that each one contains the data transmitted and received from and to a unique pair of transceivers. Then, radar cubes containing fast time and slow time data corresponding to each channel are created. Note that each radar cube is an N × K × L matrix where N is the number of chirps in a frame, K is the number of chirp samples, and L is the number of channels. L = N tx × N rx where N tx is the number of transmitters and N rx is the number of receivers. To obtain the range-Profile of one or more living subject(s), the first FFT (Range-FFT) is applied to the received chirp samples.
Regardless of the architecture being used, an inherent drawback of the MIMO-FMCW radar is that there is a certain amount of coupling from the transmitter antenna to the receiver antenna. This mutual coupling describes energy absorbed by one receiver antenna when another nearby antenna is operating. Since the leakage power of the mutual coupling is typically much higher than the actual radar return signals, it is essential to remove mutual coupling between elements. After creating the channels and applying Range-FFT, the mutual coupling removal algorithm is applied between transmitters and receivers. As shown in Figure 9(A), after removing the leakage between transmitters and receivers, the remaining signals contain reflections from both stationary targets (clutters) and living bodies. This then requires an additional technique to distinguish those two from each other. A stationary clutter removal algorithm is performed on each channel to remove all stationary objects inside the car. To do so, the average value of the signal is computed and subtracted from the aggregated signals; removing the average is equivalent to eliminating the stationary scatters. As shown in Figure 9(A), after applying the clutter removal algorithm, signals reflected from all stationary objects, such as car seats and other static objects inside the car, are removed. Hence, the only remaining signal is the one coming from the living body. It is worth mentioning that the capability of discriminating stationary objects from humans is one of the superiorities of the F I G U R E 9 Signal processing flow of proposed in-vehicle algorithm of presence/absence detection of a living body (A) radar raw data pre-processing (B) details of the PAD algorithm that calculate OSs FMCW radar sensor over mechanical sensors that detect objects based on weight, force, acceleration, or pressure. These mechanical sensors lead to a high false alarm rate.
As the Range-Profile of subjects for each channel is created, the next step is to realize how the chest movements of a living body impact the received signals. To show that, one method is to extract the exact breathing waveform. However, extraction of breathing waveform is a complicated scenario that requires knowledge of the proper range of chest motion of the subject representing the correct breathing motion. Finding the proper range requires an extra algorithm since the whole body moves and creates signals at different ranges. Therefore, the process of monitoring the exact breathing waveform adds more complexity to our signal processing chain whereas we need a simple, accurate and fast algorithm.
With regards to these goals, we base our algorithm on the following observations of breathing effects on the received signals over time: 1. Chest movement is consistent over time and thus the micro-Doppler pattern of the received signals of any alive subjects is correlated over time. 2. Even if the living body moves, the micro-Doppler signals coming from the chest movement are correlated over time. 3. Based on the calculated radar configuration summarized in Table 2, and applying clutter removal algorithms, the micro-Doppler frequency around f = 0 Hz is due to the chest motion.
Firstly, to show the impacts of the chest movements on the received signals of each channel, we apply a Short-Time Fourier Transform (STFT) as written by where, w(n) is the window function and x(t) is the signal to be transformed; we used a Hamming window centered around zero with the length of P which is set to 256.
Then, coherent accumulation is firstly performed on range samples, and next on the channels vector to increase the signal intensity to detect any tiny alive object. As mentioned, as the position of a subject is not essential knowledge, we benefit from the MIMO feature of the MIMO FMCW radar to increase the signal intensity and improve the detection.
Consequently, the Joint Time-Frequency (JTF) representation of reflected signals inside a car is calculated as: The resulting output of the JTF is a three-dimensional plot representing the frequency content over time of the signal. The JTF pattern of reflected signals is then delivered to the proposed PAD algorithm. In the PAD algorithm, the JTF pattern of received signals over T To sec is divided into N To segments to generate N To numbers of Observed signals (OSs). Each part of these N To segments is called NO si that consists of NO numbers of signal S i . As shown in Figure 9(B), S i is T s sec of the JTF pattern written as: Finally, OS j is calculated as: The PAD algorithm then will notify the presence of a living body inside a vehicle only if all consecutive OSs are correlated. In other words, if all correlation coefficients are positive over time, written as.
the PAD algorithm will notify the presence of a living body.

EXPERIMENTAL RESULTS
To simulate infant or child subjects, we designed a servo structure and inserted it into a number of dolls and phantoms. The motion of the servo motor -which was controlled by a Raspberry Pi -was used to mimic the breathing motion of a small child, as shown in Figure 10  shows the small doll sitting on the booster seat and the rear-facing infant car seat, respectively. Figure 10(C),(D) shows the baby doll sitting on the booster seat and the rear-facing infant car seat, respectively. In our proposed algorithm, T To can be arbitrarily set to different time durations. For simplicity, we chose 3 min for our tests, meaning that after 3 min, the PAD algorithm would notify the presence of a living body inside a parked car. The radar transmits and collects reflected signals for 3 min, and then the proposed PAD algorithm is performed on the reflected signals. The values of other parameters of the PAD algorithm are set as T s = 0.02 s, NO = 50.
It should be pointed out that in order to show more detail of the results of the PAD algorithm, Table 3 provides eight consecutive correlation coefficients of two consecutive OSs (Equation (13), confirming that with the presence of a living body inside the car, all values of the correlation coefficient are positive.
For the first set of tests, the empty vehicle was tested with no passenger (no phantom, no person) and no extra stationary objects placed inside the vehicle, as seen in Figure 5. The JTF pattern of the recorded signals of the empty car is illustrated in Figure 11(A) before applying the clutter removal (DC cancelation) algorithm. As shown, all clutter creates strong reflections at around zero Doppler frequency. It is evident that there is a strong need to subtract these reflections to detect humans whose chest movements produce micro-Doppler effects around zero Doppler. Figure 11(B) shows the JTF pattern of the empty car after performing clutter removal. As shown, since the car was empty with no moving objects, signals coming from stationary objects inside the car were clearly removed by applying the clutter removal algorithm. Therefore, there is no micro-Doppler effect on the reflected signals in the JTF pattern. To observe the performance and results of the prosed algorithm, the PAD algorithm was applied to the JTF pattern of the empty car, and four consecutive OSs (OS 1 , OS 2 , OS 3 , and OS 4 ) are provided in Figure 12. As shown, all four OSs are random signals with no correlation. In Table 3, eight consecutive correlation coefficients of OSs are provided as Case 1. As seen, since none of the correlation coefficients were positive, the PAD algorithm clearly indicated no presence of an alive subject left inside the car.
The purpose of the second test was to evaluate the performance of the PAD algorithm when the car is filled with objects. In a real-life application, the car would be parked with the doors closed. However, as shown in Figure 13, the back doors were left open and caused some random motion of the objects inside the car. The clutters were added to mimic unexpected objects that would change how signals behave inside a vehicle. The JTF pattern of this scenario is shown in Figure 14. As shown, the random motion of the items inside the car created some spikes in the JTF pattern (shown with red rectangles). However, as Figure 15 shows, four consecutive OSs are not correlated as provided in Table 3 as Case 2 This test indicates that random motions of the car, such as a high-speed wind shaking the parked car suddenly or any small movement of the items in the car, would not result in a false positive. This is because the algorithm is performed on the reflected signals over 3 min, and only if all the OSs are correlated then it identifies the presence of a live subject in the car.
To validate the performance and the robustness of the proposed PAD algorithm in detecting the presence of children and adults, various tests were conducted. Since the vehicles under test were seven-seat vans, the phantoms mimicking babies were tested in each of the seats behind the first row (seat #3 to #7) with different car seats. Also, for more challenging and complicated scenarios, the phantoms were placed under each of the five seats. In addition to the phantoms, the algorithm was assessed when the car was occupied by an adult sitting still on seat #3 to #7. Our experiments also cover the scenarios where an older adult is sitting on seat #3 to #7 while moving his hand and changing his position. To yield a concrete result and to measure various possible conditions, more than 65 different scenarios were tested for more than 3 min per scenario, resulting in more than 300 min of raw radar data being collected and processed. The PAD algorithm was evaluated over all the data collected. It should be mentioned that our proposed PAD algorithm correctly identified the presence of a live subject in all scenarios without any false negatives. In the following, to show the details of the results, we provide three examples of our more than 65 experimental results.
As the first example, Figure 16 illustrates the JTF pattern of the car occupied by an adult sitting on seat #5 without any motion except for his respiration. As shown, the micro-Doppler effects of breathing cycles are clearly consistent over time in the JTF pattern. Then, the PAD algorithm was applied to calculate OSs and check whether the OSs are correlated.
OSs of four successive sets of this scenario are provided in Figure 17, and all correlation coefficient values in Table 3 of Case 3 are positive, showing that all OSs are correlated because of the consistent chest motion. As shown, our proposed algorithm is independent of noise floor (a threshold of SNR) and a frequency range of breathing.
The core of the algorithm is based on the correlation of signals created by the breathing cycles of a living body. The next example is provided for the case of the small doll sitting on the rear-facing seat placed on seat # 3. To show more details, 3D and 2D JTF patterns of the car occupied by the small doll sitting on the rear-facing car seat placed on seat # 3 are shown in Figures 18 and 19, respectively. As illustrated, the presence of the phantom with the consistent motion is clearly visible in the JTF pattern which is the reason the values of correlation coefficients are positive over time. With regards to these patterns, OSs of four successive sets of this scenario are plotted in Figure 20, and eight consecutive correlation coefficient values are provided in Table 3 as Case 4. Similarly, all the OSs are highly correlated and, thus, the algorithm clearly identified the presence of the phantom inside the car.
For more complicated and challenging tests, the dolls were placed on the floor of the car (under seats), as shown in Figure 21. The same process was applied, and the proposed algorithm clearly identified the presence of the doll inside the car. To show how accurately the PAD algorithm can detect the presence of the doll under seats, the JTF patterns of the baby doll under seat #5 is provided in Figure 22. The Doppler effects of the doll's motion are clearly detectable over time in the JTF pattern. The OSs of four consecutive sets after performing the proposed algorithm are provided in Figure 23, and all consecutive values of correlation coefficients are positive, as shown in Table 3 as Case 5. To show the importance of the MIMO feature of the radar in enhancing the signal intensity, the results of the case of collecting signals from one transmitter and one receiver (Tx 1 and Rx 1 ) are provided in Figures 24 and 25. The JTF pattern of the baby doll placed under seat # 5 is provided in Figure 23, showing a weak stripe around 0 KHz. Since the detected signals were not strong enough to be correlated, the PAD algorithm also was unable to find correlations in all consecutive OSs, as could be seen in Figure 24.
As shown, using the MIMO feature of the radar, the PAD algorithm was applied to all scenarios (more than 65 scenarios mentioned above), and, in all cases, the algorithm yielded 100% accuracy in detecting the presence of the phantoms or adults. The PAD algorithm also identified the absence of an alive subject with no false positives.

F I G U R E 25
Four consecutive OSs created by applying the PAD algorithm to the JTF pattern created by the accumulation of signals collected from one transmitter and one receiver (Tx 1 and Rx 1 ) of the car occupied by the baby doll placed under seat # 5

CONCLUSION
The primary purpose of this paper was to showcase the feasibility of using a low-cost radar sensing technology to detect the presence of a small child or infant left behind in a car. To mimic a small child, a phantom with an oscillating metal plate was placed in various car seats and then tested in each seat of the two back rows of a minivan. A novel radar signal processing technique capturing the consistent movement of a living body's chest, which creates consistent Doppler effects over time, was proposed and validated. Plots of the observed signals (OSs) of the phantom chest motion were extracted and compared with each other over time. The results show that if there was no phantom in the vehicle, these observed signals were uncorrelated with each other over time whereas observed signals extracted from a living body were shown to be correlated over time. The proposed algorithm was proven reliable enough to detect the phantoms in all scenarios, including under seats, and was able to detect humans with no false alarms or missed cases.