Radar detection of moving objects with wave-shaped separation residuals

Abstract

A multiple-input multiple-output (MIMO) radar system for detecting moving objects is based on an explicit signal model. The explicit signal model accounts for waveform separation residuals by relating measurements of a virtual array to self-terms including a Kronecker product of an object-receiver signature and a transmitter-object signature and cross-terms including a Kronecker product of an object-receiver signature and a transmitter-object residual signature. The radar system uses a spatial MIMO object detector based on the explicit signal model to detect moving objects.

Description

TECHNICAL FIELD

[0001] The present invention relates generally to a radar system for detecting moving objects, and more particularly, to a radar system for detecting moving objects considering waveform separation residuals. BACKGROUND

[0002] The role of automotive radars has emerged from existing advanced driver assistance systems (ADAS) to emerging autonomous driving. Along with ultrasonic, camera, and light detection and ranging (LIDAR) sensors, it aids in the task of sensing and understanding the environment under all-weather conditions at an affordable cost and scalable production. Specifically, automotive radars provide direct measurement of radial velocity, long operating range, millimeter-level small size or sub-terahertz frequency band, and high spatial resolution.

[0003] Among relatively new signaling schemes with better capability to handle mutual interference (e.g., phase-modulated continuous wave (PMC W) and stepped carrier orthogonal frequency-division multiplexing (OFDM)), frequency-modulated continuous wave (FMCW) is overwhelmingly used in the industry for taking advantage of wide frequency bandwidth due to its simple transceiver architecture and low requirement on sampling rate. Meanwhile, to improve spatial resolution, waveform coded multiple-input multiple-output (MIMO) radars have been integrated into automotive radars to expand the virtual array aperture. The virtual array includes unique pair-wise combinations of transmitters and receivers. Typically, MIMO radars can be implemented in time domain by using time-division multiple access (TDMA) or can be implemented in waveform domain. MIMO radars can be implemented in an automotive vehicle and can be used to detect one or more moving objects relative to the automotive vehicle. In highly dynamic environments such as highways, waveform coded MIMO is preferred. Slow MIMO radars, which only need to multiply orthogonal codes on a pulse-to-pulse basis, seem to be a more cost-effective solution for hardware implementation compared to fast MIMO radars, which need to multiply orthogonal codes on a sample-to-sample basis.

[0004] Currently, in MIMO radars, it is assumed that perfect waveform separation is achieved by each receiver of the MIMO radar by applying a respective orthogonal code used at the transmitter for transmitting a signal. It is assumed that each of the waveform reflections corresponding to the perfect separation of the transmitted signals has no waveform residual due to interference from waveform reflections corresponding to other transmitted signals from other transmitters. It is difficult to obtain such ideal waveform separation over all Doppler frequencies and time delays. Therefore, assuming perfect waveform separation at the receiver to detect one or more moving objects can impact the efficiency of the MIMO radar in detecting objects.

[0005] Therefore, there is a need for a radar system that considers waveform separation residuals to improve the efficiency of a radar system in detecting one or more moving objects. SUMMARY

[0006] Motor vehicle radar systems are used, for example, but not limited to, to detect one or more moving objects in the environment of a motor vehicle, such as a highway, a road, traffic lights, etc., around the motor vehicle. The moving objects can be vehicles, pedestrians, etc., in the vicinity of the motor vehicle. Recently, MIMO radars have been incorporated into motor vehicle radar systems due to the ability to achieve higher spatial resolution with fewer number of antenna elements. Waveform coded MIMO is preferred in highly dynamic environments such as highways.

[0007] The motor vehicle radar system in the proposed disclosure incorporates a MIMO radar. Thus, the MIMO radar system comprises a set of transmitters and a set of receivers. Each transmitter in the set of transmitters transmits a reference signal, such as a chirp signal, towards a target. The radar system can comprise a signal generator that generates the reference signals for the set of transmitters. Further, the target can be one or more moving objects or stationary objects. In order to correctly detect the one or more moving objects, the reference signals from different transmitters in the set of transmitters should not interfere with each other. To this end, in the proposed disclosure, the MIMO radar system encodes each reference signal with an orthogonal code, for example, a Hadamard code. The proposed MIMO radar system can comprise an orthogonal code generator that generates the orthogonal code to encode each reference signal transmitted by each transmitter in the set of transmitters. Thus, when two transmitted signals encoded with the orthogonal code interfere, ideally they produce zero and thus minimization of interference can be achieved. Thus, the MIMO radar system transmits several encoded pulses, where each encoded pulse is orthogonal to each other. The orthogonal code is also used for waveform separation at the receivers.

[0008] Further, in the proposed disclosure, the MIMO radar system uses the set of receivers to receive echoes or reflections of the transmitted signals (i.e., the encoded pulses / reference signals). The transmitted signals can reflect from one or more objects, where the one or more objects can be moving or stationary. Each receiver in the plurality of receivers receives a signal that is a superposition of reflections of the plurality of reference signals transmitted by the plurality of transmitters, i.e., each receiver receives a combined signal, where each signal in the combined signal corresponds to a reflection of all the transmitted signals. In order to detect the one or more moving objects, it is important for the radar system to separate each reflection waveform of the transmitted signals from the combined signal that is a superposition of all the reflected transmitted signals.

[0009] Some implementations are based on the insight that the radar system can exploit the orthogonal codes used at the transmitters to achieve waveform separation at the receiver side. To this end, each receiver is configured to multiply the received combined signal with the respective orthogonal code (i.e., chirp signal) used by the transmitter corresponding to that receiver. Due to the orthogonal property of the codes, the product of two different codes will theoretically result in a zero value, while multiplying with the same code results in a non-zero value.

[0010] With this orthogonal property, each receiver can separate from the combined signal a reflected waveform corresponding to the reference signal transmitted by each of the M transmitters. However, perfect waveform separation cannot be achieved over all Doppler frequencies and time delays, i.e., some waveform separation residuals remain in the separated reflected waveforms. These waveform separation residuals are associated with reflections of other transmitted signals. If the waveform residuals are not taken into account when probing the objects, the accuracy of the MIMO radar system to probe one or more moving objects can be affected.

[0011] To this end, in the proposed disclosure, the MIMO radar system uses an explicit signal model that takes into account the imperfect waveform separation effects. Specifically, the explicit signal model takes into account the waveform separation residuals in order to probe one or more moving objects. Some implementations are based on the insight that taking into account the waveform separation residuals increases the accuracy of the MIMO radar system to probe one or more moving objects. The explicit signal model takes into account the waveform separation residuals by relating the measurements of the virtual array to an auto-term and a cross-term, the auto-term including a Kronecker product of an object-receiver signature and a transmitter-object signature, and the cross-term including a Kronecker product of a combination of an object-receiver signature and a residual transmitter-object signature.

[0012] The proposed MIMO radar system implements the explicit signal model by using a baseband range-Doppler object detector and a spatial MIMO detector. The baseband range-Doppler object detector determines the number of detected diagonals based on the echo signals and further estimates the range and velocity corresponding to the detected one or more objects. In some implementations, to achieve this goal, the baseband range-Doppler object detector performs two one-dimensional (ID) Fourier transforms along the slow time and fast time domains on the digitally sampled baseband beat signals. By performing the two ID FFTs, the range Doppler object detector computes a threshold value for detecting the presence or absence of one or more objects. Furthermore, in some implementations, the baseband range-Doppler object detector includes a continuous false alarm rate circuit that compares the energy of the received signals to the threshold value to detect the presence or absence of a real object.

[0013] Some embodiments are based on the realization that determining the spatial location of a moving object requires compensating the baseband signal with the accurate Doppler shift of the detected object from the range-Doppler object detection module. Doppler shift is the change in frequency of a wave relative to an observer (radar system or target) that is moving relative to the source of the waves. Doppler shift is the change in frequency of a sound wave emitted by an object as the object is moving towards the observer. As the object moves away from the observer or towards the observer, the observer can notice a change in the frequency of the sound wave. For example, as a train or truck approaches, an observer (a person) can hear a sound at a certain frequency. As the high-speed train or truck passes by, the sound immediately drops by several octaves. This is caused by the shift in frequency caused by the Doppler effect. The Doppler effect can also be applied to the motion relative to the radar system and the target object.

[0014] For example, if the radar is mounted on or based on a vehicle, the Doppler shift is due to the relative motion between the vehicle-based radar and the target object. For example, if the target is traveling on a highway at 70 mph and the approaching vehicle-based radar is traveling at 50 mph, the radar will show a Doppler shift corresponding to 120 mph. The radar needs to subtract the speed of the radar (50 mph in this example) to obtain the speed of the target. This can have a great advantage in the radar system. By binning the received echoes on both range and Doppler frequency, the target speed and range can be determined. Furthermore, this allows for easy differentiation between moving objects (such as airplanes) and the usually stationary background clutter.

[0015] For example, consider a radar operating at a frequency (f) of 70 GHz, the wavelength (l) of the radar can be calculated as: l = c / f, where c is the speed of light. Thus, l = 0.0043 m or 4.3 mm. When the vehicle-based radar is traveling at 50 mph, it is tracking a target moving ahead in the same direction at 100 mph. In this case, the speed difference is -50 mph or -22.35 m / s.

[0016] Thus, the proposed MIMO radar system uses a spatial MIMO detector that compensates the range and velocity of the detected one or more objects for Doppler shift. When compensating the baseband signal with these detected Doppler values at a discretized Doppler grid, there is a Doppler mismatch between the true Doppler frequency and the detected Doppler frequency. Depending on the Doppler grid step size in the range-Doppler object detection module, this Doppler mismatch can be large or small. The presence of the Doppler mismatch means that the baseband signal has an additional modulation on a pulse-by-pulse basis. Recall that the orthogonal codes are also implemented on a pulse-by-pulse basis, and the result of the Doppler mismatch is that if multiplied by the orthogonal code from one transmitter element, there will be a waveform residue from the contributions of the other transmitter elements due to the additional modulation from the Doppler mismatch.

[0017] Then, the spatial MIMO detector performs waveform separation associated with each transmitter-receiver pair of the virtual array in the presence of the unknown Doppler mismatch.

[0018] Some embodiments are based on the insight that, in order to determine the angle of an object (i.e., the azimuth / elevation of the object), the radar system should consider the echoes of all reference signals together, which forms a Kronecker subspace. To this end, the proposed radar MIMO system includes a spatial MIMO detector that forms a signal vector of size MN, which includes the M separated waveforms from each of the N receivers. The signal vector is then used to determine the spatial position of the object.

[0019] Under perfect waveform separation (i.e., no Doppler mismatch), the above signal vector contains the possible object eigenvectors and a noise vector. However, due to the Doppler mismatch, some embodiments are based on the insight that, if an object is present, the signal vector also contains a possible residuals eigenvector.

[0020] The spatial MIMO detector stacks the separated waveforms of all unique transmitter-receiver pairs into a received signal vector. Due to the way M separated waveforms from each of the N receivers are stacked, the object eigenvector (self-term) is a Kronecker product between a transmitter-object eigenvector and an object-receiver eigenvector.

[0021] In some embodiments, it is found that the residuals eigenvector (cross-term) is a Kronecker product between a transmitter-object residuals eigenvector and an object-receiver eigenvector. The object eigenvector and the residuals eigenvector share the same object-receiver eigenvector, but different transmitter-object eigenvectors.

[0022] In some embodiments, the transmitter-object signature is a function of the relative angle between each transmitter in the transmitter set and the object, the wavelength of the transmitted signal, and the relative distance between two consecutive transmitter elements in the transmitter set. Similarly, the object-receiver signature is a function of the relative angle between each receiver in the receiver set and the object, the wavelength of the received signal, and the relative distance between two consecutive receiver elements in the receiver set.

[0023] Additionally or alternatively, some embodiments further recognize that the transmitter-object residual signature of one transmitter element is a weighted sum of the transmitter-object signatures from all other transmitter elements, where the weights are given by so-called code residuals. The code residual between two transmitter elements is the sum of the products of the orthogonal codes used at the two transmitter elements, weighted by an exponential function with Doppler mismatch as an argument.

[0024] In the case of perfect waveform separation (i.e., zero Doppler mismatch), the code residual is zero because the sum of the products of the orthogonal codes is zero. If the code residual is zero, the transmitter-object residual signature of one transmitter element is also zero. As a result, the signal vector contains only the object signature and noise. For example, in a slow-time MIMO-FMCW radar scheme, the residual signature is zero.

[0025] However, due to the nature of the Doppler mismatch found when detecting moving objects, at least some of the residual signatures are non-zero and need to be accounted for. For velocity estimation, the received echo signal is sampled "slowly"—once per pulse. Due to the slow sampling and the finite number of pulses, the velocity estimate is quantized. Since this quantization defines the resolution of the velocity estimate, the estimated velocity may differ from the actual velocity. Assume that the resolution of the velocity estimate is 5 km / hr. If the actual relative velocity of the moving object is 39 km / hr, the estimated velocity will be 40 km / hr. This difference is the velocity mismatch, which is equivalent to the Doppler mismatch in the frequency domain.

[0026] Some embodiments further recognize that quantization defines the maximum Doppler mismatch. If the maximum Doppler mismatch is known, the transmitter-object residual signature can be approximated as the sum of weighted transmitter-object signatures from only a few preselected transmitter elements (rather than the original all other transmitter elements). This results in a subspace-based transmitter-object residual signature. Together with the object-receiver signature, the overall residual signature is now a Kronecker subspace signal.

[0027] Additionally or alternatively, some embodiments are based on the recognition that a spatial MIMO detector can be implemented using a generalized likelihood ratio test (GLRT). The GLRT algorithm formulates the object detection as a binary hypothesis testing problem, where the waveform residuals or residual signatures appear in the alternative hypothesis only if a target of interest (i.e., an object) is present. The GLRT algorithm can be used to determine the presence or absence of an object in the spatial domain. To this end, the GLRT algorithm determines a hypothesis-based GLRT statistic and compares the GLRT statistic to a pre-determined threshold. Based on the one or more objects detected at a particular spatial location, the MIMO radar system further determines other parameters associated with the detected one or more objects.

[0028] In some embodiments, the parameters include at least one of a radial velocity, a spatial angle, and a distance from the object. The memory is configured to store an explicit signal model that accounts for waveform separation residuals by relating measurements of the virtual array to auto-terms including a Kronecker product of an object-receiver signature and a transmitter-object signature and cross-terms including a Kronecker product of a combination of an object-receiver signature and a residual transmitter-object signature; the processor is configured to detect a moving object by executing a spatial MIMO detector configured to detect the moving object using the explicit signal model; and the output interface is configured to output parameters associated with the detected object.

[0029] Thus, one embodiment discloses a multiple-input multiple-output (MIMO) radar system for detecting moving objects, the system comprising: a set of transmitters and a set of receivers forming a virtual array of unique pair-wise combinations of transmitters and receivers to measure reflections of transmissions. The MIMO system includes a memory configured to store an explicit signal model that accounts for waveform separation residuals by relating measurements of the virtual array to auto-terms including a Kronecker product of an object-receiver signature and a transmitter-object signature and cross-terms including a Kronecker product of a combination of an object-receiver signature and a residual transmitter-object signature; and a processor configured to detect a moving object by executing a spatial MIMO detector configured to detect the moving object using the explicit signal model. An output interface of the MIMO radar system is configured to output parameters associated with the detected object.

[0030] In some embodiments, the processor is configured to execute a baseband range-Doppler object detector configured to detect one or more moving objects, estimate a range and a velocity of each detected moving object, and for each detected moving object, extract a portion of the measurements of the virtual array corresponding to the range of the moving object, compensate the extracted measurements for the velocity (or, equivalently, Doppler shift) of the moving object, and feed the extracted and compensated measurements to a spatial MIMO detector to determine one or a combination of an angle (e.g., azimuth and elevation) of the moving object.

[0031] In some embodiments, each transmitter is configured to transmit a set of frequency modulated pulses to illuminate the scene and form measurements, wherein the baseband range-Doppler object detector is configured to determine a range of a moving object using a fast-time fast Fourier transform (FFT) that samples each transmitted pulse multiple times for range compression, and wherein the baseband range-Doppler object detector is configured to determine a velocity of the moving object using a slow-time FFT that samples each transmitted pulse once for Doppler compression.

[0032] In some embodiments, the number of pulses or the size of the set of frequency modulated pulses defines a resolution of the velocity estimation that results in a Doppler mismatch between an actual velocity of a moving object and a velocity estimated by the baseband detector using the slow-time FFT, and wherein for each transmitter-receiver pair of the virtual array, the frequency modulated pulses of different transmitters are encoded with an orthogonal code on a pulse-by-pulse basis and decoded with a corresponding orthogonal code, wherein a self-term of the explicit signal model captures the decoded transmissions of the transmitter-receiver pair, and wherein a cross-term of the explicit signal model captures a residue of different transmissions in the decoded transmissions of the transmitter-receiver pair caused by the Doppler mismatch.

[0033] In some embodiments, for each transmitter-receiver pair of the virtual array, a combination of the residue transmitter-object signatures of the cross-terms includes a residue transmitter-object signature of all transmitters except the transmitter in the transmitter-receiver pair, wherein a value of the residue transmitter-object signature of a particular transmitter is a function of the Doppler mismatch between an actual velocity of a moving object and a velocity estimated by the baseband detector, and wherein the value of the residue transmitter-object signature of the particular transmitter is set to zero when a maximum value of the residue transmitter-object signature of the particular transmitter determined for a maximum Doppler mismatch is less than a threshold value.

[0034] In some implementations, the combination of transmitter-object residual signatures is approximated as a weighted combination of predetermined maximum Doppler mismatches. In some example implementations, the parameters include at least one of radial velocity, spatial angle, and distance to the detected object.

[0035] In some implementations, the transmitter-object signature is a function of a relative angle between each transmitter in the set of transmitters and the detected object, a wavelength of the transmitted signal, and a relative distance between two consecutive transmitter elements in the set of transmitters; and the object-receiver signature is a function of a relative angle between each receiver in the set of receivers and the detected object, a wavelength of the received signal, and a relative distance between two consecutive receiver elements in the set of receivers.

[0036] In example implementations, the spatial MIMO detector is implemented using a generalized likelihood ratio test (GLRT) algorithm, where the GLRT algorithm determines a GLRT statistic to detect the moving object. Further, the GLRT algorithm formulates and tests a first hypothesis and a second hypothesis, where the first hypothesis is that the transmitted reflections contain only noise, and the second hypothesis is that the transmitted reflections contain reflections from a moving object, waveform separation residuals, and noise.

[0037] In example implementations, the GLRT determines a first distribution under the first hypothesis and a second distribution under the second hypothesis, where the first distribution is a central F-distribution, and where the second distribution is a non-central F-distribution.

[0038] In example implementations, the processor is further configured to compare the GLRT statistic to a predetermined threshold, where the predetermined threshold is based on a number of transmitters and receivers, where the second hypothesis is true when the GLRT statistic is greater than the predetermined threshold, and where the first hypothesis is true when the GLRT statistic is less than the predetermined threshold. BRIEF DESCRIPTION OF DRAWINGS

[0039] [ FIG. 1A ]

[0040] FIG. 1A A slow-time MIMO FMCW automotive radar system architecture for detecting moving objects is illustrated in accordance with some implementations.

[0041] [ FIG. 1B ]

[0042] FIG. 1B An example architecture of a transmitter in accordance with some implementations is illustrated.

[0043] [ FIG. 1C ]

[0044] FIG. 1C An exemplary architecture of a receiver according to some embodiments is illustrated.

[0045] [ FIG. 1D ]

[0046] FIG. 1D Steps of a method performed by a baseband range-Doppler object detector according to some embodiments are illustrated.

[0047] [ FIG. 1E ]

[0048] FIG. 1E Steps of a method performed by a spatial MIMO detector module 107 according to some embodiments are illustrated.

[0049] [ FIG. 1F ]

[0050] FIG. 1F is an exemplary scenario illustrating the relationship between transmitter-object signatures and relative delays according to some embodiments.

[0051] [ FIG. 1G ]

[0052] FIG. 1G is an exemplary scenario illustrating the relationship between object receiver signatures and relative delays according to some embodiments.

[0053] [ FIG. 1H ]

[0054] FIG. 1H Waveform separation within a spatial MIMO detector according to some embodiments is illustrated.

[0055] [ FIG. 1I ]

[0056] FIG. 1I An exemplary signal vector containing the separated waveforms for each transmitter-receiver pair according to example embodiments is shown.

[0057] [ FIG. 1J ]

[0058] FIG. 1J An exemplary scenario for computing transmitter-object residual signatures for elements of a transmitter array according to example embodiments is illustrated.

[0059] [ FIG. 1K ]

[0060] FIG. 1K Waveform components included in the separated waveforms at each transmitter-receiver pair according to some embodiments are illustrated.

[0061] [ FIG. 1L ]

[0062] FIG. 1L An exemplary schematic diagram illustrating subspace transmitter-object residual signature labeling of a transmitter array is exemplified in accordance with some embodiments.

[0063] [ FIG. 1M ]

[0064] FIG. 1M An exemplary schematic diagram illustrating subspace transmitter-object residual signature labeling of a transmitter array is exemplified in accordance with some embodiments.

[0065] [ FIG. 2A ]

[0066] FIG. 2A Steps to implement a spatial domain MIMO detector in accordance with example embodiments are exemplified.

[0067] [ FIG. 2B ]

[0068] FIG. 2B A method to implement a binary hypothesis test using a GLRT algorithm in accordance with example embodiments is exemplified.

[0069] [ FIG. 2C ]

[0070] FIG. 2C Steps to perform pre-whitening of the separated waveforms and signatures in accordance with example embodiments are exemplified.

[0071] [ FIG. 2D ]

[0072] FIG. 2D Steps to compute a GLRT statistic using pre-whitened waveforms and signatures in accordance with example embodiments are exemplified.

[0073] [ FIG. 2E ]

[0074] FIG. 2E A threshold comparison step by computing a test threshold and comparing it to the GLRT statistic in accordance with example embodiments is exemplified.

[0075] [ FIG. 3A ]

[0076] FIG. 3A Receiver operating characteristic (ROC) curves under two-stage waveform separation residual for SINR = 10 dB are shown.

[0077] [ FIG. 3B ]

[0078] FIG. 3B Performance comparison of two object detectors in perspective (known R) and adaptive (unknown R) detection scenarios is shown.

[0079] [ FIG. 3C ]

[0080] FIG. 3C Performance verification of the theoretical (squares with dashed lines) ROC curves versus Monte-Carlo simulation results (circles) is shown for various RINR when SINR = 10 dB.

[0081] [ FIG. 4 ]

[0082] FIG. 4 A block diagram of a MIMO radar system 100 is illustrated in accordance with some embodiments. DETAILED DESCRIPTION

[0083] In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. It will be apparent, however, to one skilled in the art that the present disclosure can be practiced without these specific details. In other instances, devices and methods are shown in block diagram form in order to avoid obscuring the present disclosure.

[0084] As used in this specification and claims, the terms “for example,” “for instance,” and “such as,” and the verbs “comprising,” “having,” “including,” and their other verb forms, when used to describe the disclosure, are each meant to convey that the list following the term or verb is an example of one or more implementations. The term “based on” means at least partially based on. Furthermore, it is to be understood that the use of certain terms or phrases in various places in the specification is for the purpose of description and should not necessarily be regarded as limiting in nature. Any headings used herein are for convenience only and are not to be construed as limiting in any way.

[0085] Generally, a radio detection and ranging (RADAR) system is used to determine whether a target exists and different parameters associated with the target. The target can be one or more objects that are stationary or moving relative to the RADAR. The different parameters associated with the target can be the distance of the object from the RADAR, the speed of the object relative to the RADAR, the angle of the object (e.g., azimuth / elevation), where the angle of the object can be used by the RADAR to determine the location of the object in the spatial domain or the direction of movement of the object relative to the RADAR, etc. Some embodiments are based on the realization that in order to accurately determine the angle of the object, the RADAR system needs multiple transmitters and multiple receivers. To this end, the present disclosure proposes a multiple-input multiple-output (MIMO) RADAR system that includes an array of transmitters and an array of receivers. Referring to FIG. 1AA waveform encoding MIMO RADAR utilizing orthogonal codes applied to pulse-to-pulse basis is detailed. More specifically, each pulse is a frequency modulated continuous wave (FMCW) and all transmitters use the same pulse and the same pulse is repeated multiple times over time to form a train of pulses.

[0086] FIG. 1A A slow-time MIMO-FMCW automotive radar system architecture for detecting moving objects is illustrated in accordance with some embodiments. From FIG. 1A It can be observed from FIG. 1 that the system 100 includes a set of M transmitters 101(a)-101(m) and a set of N receivers 103(a)-103(n). As mentioned above, each transmitter transmits a train of encoded waveform pulses and the same pulse is repeated K times over time to serve as K pulses. Each pulse is a frequency modulated continuous wave (FMCW).

[0087] The multiple transmitters and multiple receivers extend the dimensionality of the RADAR to create a virtual array that includes unique combinations of transmitter and receiver pairs (e.g., Tx#1 and Rx#1, Tx#2 and Rx#1, etc.) to measure the reflections of the transmissions. In addition, the MIMO automotive radar system 100 includes a memory (not shown in the figures) configured to store an explicit signal model that accounts for waveform separation residuals by relating the measurements of the virtual array to self-terms and cross-terms, the self-terms including a Kronecker product of object-receiver signatures and transmitter-object signatures, and the cross-terms including a Kronecker product of combinations of object-receiver signatures and residual transmitter-object signatures. The radar system 100 also includes a processor configured to detect moving objects by executing a spatial MIMO detector configured to use the explicit signal model to detect moving objects. The radar system 100 also includes an output interface configured to output parameters associated with the detected objects.

[0088] The slow-time MIMO-FMCW automotive radar system uses a frequency modulated continuous wave signaling scheme. To this end, the proposed radar system includes a signal generator (not shown in the figures) that generates a radar signal or frequency modulated pulse that is provided to each of the M transmitters. Each pulse includes a plurality of frequencies that increase over time to create a chirp as FIG. 1AThe signal sweep is exemplified (designated in the attached figures). Furthermore, each transmitter is configured to transmit a set of frequency modulated pulses to illuminate the scene and form a measurement. The pulses are transmitted in all directions. In an example implementation, the pulses generated by the signal generator can be chirp signals to be transmitted as radar signals for object detection. As the transmitted signal varies in frequency, the echo has a slightly different frequency compared to the signal transmitted at that moment. The difference between these frequencies is proportional to the echo delay (i.e. the distance from the transmitter to the object), which enables the height to be accurately measured. Furthermore, the N receivers 103(a)-103(n) are configured to receive the reflected echo signals or transmitted reflections. An advantage of the FMCW signaling scheme is that by multiplying the reflected signal with the source FMCW pulse at a low modulus (ADC) sampling rate, the object information can be efficiently saved in the beat signal.

[0089] Some implementations are based on the recognition that the reflections received at each of the N receivers corresponding to all the reference signals transmitted by the M transmitters are to be considered together to determine the angle of the object, which can be used to determine the spatial position of the object. However, the transmissions corresponding to all M transmitters can interfere with each other. To solve this problem, the proposed radar system is configured to use an encoding scheme (e.g. an orthogonal encoding scheme) to minimize the interference, where the frequency modulated pulses of different transmitters are encoded with orthogonal codes on a pulse-by-pulse basis for each transmitter-receiver pair of the virtual array and decoded with the corresponding orthogonal code. According to this encoding scheme, the pulses transmitted by each transmitter are multiplied by K codes c(1) to c(K). As can be observed from the attached figures, the FMCW pulses transmitted by transmitter #1 when encoded with the K codes can be denoted as c1(1) to c1(K), and similarly for the Mth transmitter, the encoded FMCW pulses are denoted as c M (1) to c M (K).

[0090] Furthermore, these pulses are reflected by the target, where the reflected pulses are also referred to as echo signals. The receivers are configured to receive these echo signals. Upon receiving the echo signals, each receiver can use the encoding scheme to decode the received signals and obtain a corresponding to each unique pair-wise transmitted signal. Upon decoding, the receivers can accurately determine parameters such as the spatial position of stationary objects (e.g. trees, streetlights, etc.), the accurate angle of stationary objects (e.g. trees, streetlights, etc.).

[0091] Current radar systems are configured to compensate for Doppler shifts before decoding the return signals to determine spatial angles associated with the detected targets. This compensation approach is referred to as pre-processing from now on. Thus, in pre-processing, the received signals or return signals are first processed in the Doppler domain (or frequency domain) to compensate the received signals for Doppler shifts. The compensated signals are then decoded to estimate the parameters of the objects. Due to the compensation, moving objects appear stationary with respect to the radar, which allows to process the unique pair-wise transmissions separably at each receiver, and thus allows the radar system to determine the spatial angles of the detected objects. The spatial angles can include the transmit angle, receive angle, and elevation angle of the objects in the spatial domain, etc. In this way, the unique pair-wise transmissions are separated, and each separated signal is processed in the spatial domain.

[0092] Some embodiments are based on the recognition that it is not possible to separate the waveforms associated with each unique pair-wise combination from the entire received signal so ideally, because each separated waveform includes residuals or residual waveforms from other transmitters even after compensation. For example, the separated waveform for Tx#1-Rx#1 pair includes residuals from other transmitters such as from Tx#2, Tx#3, Tx#M, etc. Current radar systems use a signal model based on ideal waveform separation, i.e., the current signal model does not account for the residuals. Thus, such radar systems can impact the object detection in the spatial domain, such as the angles of the objects.

[0093] To address this issue, the present disclosure proposes a MIMO automotive radar system based on an explicit signal model that accounts for the residuals to compute the parameters of one or more detected objects. To this end, the proposed MIMO radar system includes a baseband range-Doppler detector 105 and a spatial MIMO detector 107. The baseband range-Doppler detector 105 is further configured to detect one or more moving objects in the Doppler domain, estimate the range and velocity of each detected moving object.

[0094] For each detected moving object, the spatial MIMO detector 107 first selects 133 one of the detected objects, extracts 135 the measurements corresponding to the selected object from all receivers, compensates 135 the extracted measurements with the range and velocity of the detected selected object, filters out 137 the signals contributed from other objects with an additional option of a low-pass filter, and separates 139 the compensated measurements by multiplying by the code used at the transmitter side. With the separated waveforms from all transmitter-receiver pairs, the spatial MIMO detector 107 employs a spatial domain target detection scheme 140 to output the angles of the detected objects.

[0095] It can be seen that the two-step probing (first in range-Doppler domain and then in spatial domain) avoids excessive computation in the spatial domain when no objects are probed in the range-Doppler domain.

[0096] To this end, the baseband range-Doppler probe 105 is configured to combine waveforms obtained from the set of receivers. The baseband range-Doppler probe 105 is further configured to perform a fast Fourier transform (FFT) on the combined waveforms to determine the range of the one or more moving objects probed. The fast Fourier transform samples each transmitted pulse multiple times to perform range compression. The baseband range-Doppler probe 105 is further configured to perform a slow-time FFT to determine the velocity of the one or more moving objects. The slow-time FFT samples each transmitted pulse once to perform Doppler compression.

[0097] For example, consider a radar operating at a frequency (f) of 70 GHz, then the wavelength (l) of the radar can be calculated as l = c / f, where c is the speed of light. Thus, l = 0.0043 m or 4.3 mm. When a vehicle-based radar is traveling at 50 mph, it is tracking a target moving in the same direction at 100 mph ahead. In this case, the speed difference is -50 mph or -22.35 m / s. Another target is traveling at 40 mph ahead towards the vehicle-based radar. This gives a speed difference of 90 mph or 40.2 m / s. The Doppler shift can be calculated as f Doppler = 2v relative / l, which gives a Doppler shift of 2(-13.4 m / s) / (0.0043 m) = -10.40 kHz for the first object and 2(40.2 m / s) / (0.0043 m) = 18.70 kHz for the second object. As mentioned above, with the help of a fast Fourier transform, the range and Doppler frequencies of the objects are probed in the range-Doppler domain. That is, the range-Doppler domain is divided into small grids, whose step size is determined by the ADC sampling frequency, the number of pulses, and the pulse repetition interval (PRI). For the Doppler frequencies, the Doppler domain is discretized into a grid (also referred to as Doppler filter subbands), whose grid size is given by 1 / (T PRI * K), where T PRI is the PRI and K is the number of pulses used at the transmitter. For example, given T PRI = 5 microseconds and K = 32, the grid size of the Doppler domain is about 6.25 kHz, and the discrete grid will be integer multiples of 6.25 kHz (between -K / 2 and K / 2). In this case, it is likely that the first object is probed at the Doppler grid of -2(6.25 kHz) = -12.50 kHz, and it is likely that the second object is probed at the Doppler grid of 3(6.25 kHz) = -18.75 kHz. By comparing these probed Doppler grids with the true (but unknown) Doppler frequencies of -10.40 kHz and 18.70 kHz, it can be easily noticed that there is a Doppler mismatch. This Doppler mismatch will affect the waveform separation on the receiver side of the slow-time MIMO-FMCW automotive radar.

[0098] Thus, the baseband range-Doppler object detector 105 determines the number of objects probed from the scene and estimates the corresponding range and velocity according to the discrete range and Doppler grids. However, the estimated range and velocity are affected by the Doppler mismatch, which means that the estimated range and velocity are not the true range and velocity of the moving objects. Moreover, the Doppler mismatch is unknown, and it is difficult to calculate the unknown Doppler mismatch. If the Doppler mismatch is not considered, it can affect the accuracy of the radar system 100 in probing the spatial position of the moving objects.

[0099] To solve this problem, the radar system 100 uses a spatial MIMO detector 107, which is configured to exploit the maximum Doppler mismatch to identify important residual terms and to neglect negligible residual terms and further to compute the accurate angle of the moving object, i.e. the spatial position of the moving object. To this end, the spatial MIMO detector 107 extracts from the transmitted reflections the waveforms associated with an object of the one or more objects detected and further determines the Doppler mismatch associated with the velocity of the object. To achieve this goal, the spatial MIMO detector 107 is further configured to use the proposed explicit signal model for the pairwise waveform separation described earlier. The spatial MIMO detector 107 performs the compensation and waveform separation for all detected objects one after the other in all directions, i.e. from 0° to 180°. The proposed explicit signal model is mathematically implemented using equation (1) given below

[0100]

[0101] where x is a signal vector containing the separated waveforms associated with each pairwise unique combination. x comprises the waveforms separated by each receiver of the receiver array using the explicit signal model. Each or at least some of the separated waveforms comprise different components such as FIG. 1K the object signature, the residual component and the noise exemplified in equation (2). The explicit signal model comprises an auto-correlation term (auto-term) which is also referred to as the object signature. The auto-term of the explicit signal model captures the decoded transmission of the transmitter-receiver pair. The object signature comprises the object-receiver signature (referenced in FIG. 1G ) and the transmitter-object signature (referenced in FIG. 1F ). Furthermore, the explicit signal model comprises a cross-correlation term (cross-term) which is also referred to as the residual signature of a virtual array consisting of all MN transmitter-receiver pairs. The cross-term of the explicit signal model captures the residual of the different transmission in the decoded transmission of the transmitter-receiver pair caused by the Doppler mismatch. The residual signature also has a Kronecker structure between the object-receiver signature (the same as in the object signature) and the transmitter-object residual signature (referenced in FIG. 1L ).

[0102] As shown in equation (2), the transmitter-object residual signature FIG. 1J ​Each element in the vector is a weighted sum of the transmitter-object signatures from all other transmitters, where the weights are a function of the unknown Doppler mismatch. Thus, by including the residual signatures due to Doppler mismatch in the extended signal model representing the virtual array measurements, a more accurate estimation of the velocity of the moving object is allowed.

[0103] Additionally or alternatively, some embodiments are based on the understanding that by neglecting small weights identified by using a pre-determined maximum Doppler mismatch, the transmitter-object residual signatures can be further approximated as a weighted sum of transmitter-object signatures from a limited number of transmitters.

[0104] Some embodiments are based on the recognition that all transmissions from M transmitters are to be considered together to determine the angle of the object. To this end, the spatial MIMO detector 107 is configured to combine the M separated waveforms from all N receivers into a signal vector x of size MN. Due to the way the M separated waveforms from each of the N receivers are combined / stacked, the object signatures are a Kronecker product between the transmitter-object signatures and the object-receiver signatures. In addition, the signal vector includes residual signatures corresponding to waveform residuals that arise due to Doppler mismatch. The spatial MIMO detector 107 is configured to use this signal vector x to determine the angle of the moving object or the spatial location of the object. Thus, the spatial MIMO detector 107 takes into account the residual signatures corresponding to the waveform residuals in order to compute the spatial location of the moving object.

[0105] In another embodiment, the spatial MIMO detector can be implemented using a Generalized Likelihood Ratio Test (GLRT) algorithm, where the GLRT algorithm determines a GLRT statistic to detect the moving object. The GLRT algorithm formulates the object detection as a binary hypothesis. The spatial MIMO detector 107 initially generates the signal vector x as described above, and further pre-whiten the signal vector x. The spatial MIMO detector 107 can be based on the Kronecker subspace. The GLRT algorithm compares each hypothesis with a pre-determined threshold, and detects the presence or absence of the object at a particular angle in the angular range from 0° to 180°.

[0106] FIG. 1B An exemplary architecture of a transmitter according to some embodiments is illustrated. FIG. 1B is an exemplary representation of all components that can be present at each transmitting element of all M transmitters. Each transmitting element first obtains a baseband FMCW signal waveform s p (t). The transmitting element can obtain the baseband signal from a signal generator configured to generate the FMCW signal waveform s p (t). The baseband FMCW signal waveform can be defined as:

[0107]

[0108] where β denotes the chirp rate and T denotes the pulse duration. The bandwidth of the FMCW waveform is B = βT. The baseband waveform s p (t) is repeated at each transmitter. The baseband signal is a sequence of pulses, e.g., of a chirp signal. The signal is provided to a first local mixer / oscillator (LO) 109, where the baseband signal is encoded with an orthogonal code, e.g., a Hadamard code. Each pulse in the sequence of pulses of the baseband signal is encoded by the orthogonal code sequence. Further, the encoded baseband signal is provided to a second local mixer 111, where the baseband signal is multiplied with a carrier frequency f c . In an example embodiment, f c = 79 GHz. Further, the encoded FMCW pulse is amplified by an amplifier circuit 113 before the waveform is transmitted towards the target via a transmit antenna 115.

[0109] Thus, the K encoded FMCW pulses can be mathematically represented as

[0110]

[0111] where m and k are the indices of the transmitter and the pulse, respectively. Further, c m (k) is the orthogonal code at the mth transmitter for the kth pulse, T PRI is the pulse repetition interval (PRI), f c is the carrier frequency, e.g., f c = 79 GHz, and s p (t) is the baseband FMCW waveform.

[0112] FIG. 1C An exemplary architecture of a receiver according to some embodiments is illustrated. FIG. 1C is an exemplary representation of all components that can be present at each receiving element of all N receivers. As can be observed in FIG. 1C , each receiver 103 receives a signal x n (t). At each receiver, the receiving antenna 117 provides the signal x n (t) to a linear noise amplification module (LNA) 119. The LNA 119 is an electronic amplifier that amplifies very low power signals without significantly degrading their signal-to-noise ratio. After amplification, the LNA 119 forwards the amplified signal to a first receiver-local mixer 121, where the received signal is demodulated using the carrier frequency f c used during modulation. The demodulated signal is denoted by , where

[0113]

[0114] In an example implementation, for an object with a radial velocity of v t at a distance R0, the round-trip propagation delay from the mth transmit antenna to the nth receive antenna can be calculated using equation (5) as follows:

[0115]

[0116] where d t / r and θ t / r are the element spacing and azimuth angle of the transmit and receive antennas, respectively, assuming co-located radar and far-field approximation, i.e., θ r = θ t = θ.

[0117] Thus, when the object is present at an angle θ, the signal demodulated by the nth receiver gives:

[0118]

[0119] where, λ = c / f c , s m (t) is the chirp sequence (or encoded FMCW pulse) transmitted at the transmitter m, and assuming s(t - τ mn ) ~ s(t - τ0). Furthermore, the demodulated signal is provided to the second receiver-local mixer 123 and further mixed with the source FMCW pulse to generate the beat signal. Thus, the second local mixing compresses the FMCW signal to an analog baseband signal or beat signal (b n (t)), where For the kth pulse, this can be further expanded as:

[0120]

[0121] where the term absorbs the additional phase term, and the term c m (k) is the slow-time code. The analog beat signal is then converted to a digital signal using the ADC 125 for further processing.

[0122] To this end, the analog beat signal from each receiver is provided to the baseband range-object detector 105, where the beat signals from all receivers are combined and sampled at t = kT PRI + lAT, where AT and T PRI are the fast-time and slow-time sampling intervals, respectively, to generate:

[0123]

[0124] Among them, f r =(βτ0+2f r v / c)ΔT is the normalized instantaneous (fast) frequency, f d =2f c T PRI v / c is the normalized Doppler (slow-time) frequency, and is the normalized spatial frequency at the transmitter and receiver ( Usually different from ). Therefore, the beat signal at the nth receiver is calculated using c m (k) The sum of the encoded object responses from all transmitted waveforms.

[0125] Then the digital beat signal b at the receiver n (Rx#n) n (l, k) is provided to the baseband range-Doppler detector 105. The baseband range-Doppler detector 105 can be done individually at each receiver or collectively from all receivers. A simple way is to digitally beat the signal b on l and k for each receiver n. n (l,k) is applied twice with a one-dimensional FFT. Thus, at each receiver, a two-dimensional spectrogram can be calculated by taking the magnitude of the two-dimensional FFT at (l,k). All two-dimensional spectrograms from all N receivers (over n) can then be summed to suppress noise and interference, and the summed spectrogram is compared with an appropriate threshold to declare the number of detected objects. The threshold is typically chosen to satisfy a given false alarm probability.

[0126] FIG. 1D The steps of a method performed by a baseband range-Doppler object detector according to some embodiments are illustrated. The baseband range-Doppler detector 105 obtains digital beat signals b from all N receivers. n (l, k) and processes the combined digital beat signal to detect one or more objects. As previously described, the baseband range-Doppler object detector 105 determines the number of moving objects based on the digital beat signal and further estimates the distance and velocity corresponding to the detected one or more objects. To this end, the baseband object detection module 105 includes a continuous false alarm rate (CFAR) circuit. CFAR enables the baseband range-Doppler object detector 105 to select a threshold to distinguish between moving objects and stationary objects.

[0127] To achieve this, the baseband range-Doppler object detector 105 performs sampling using fast-time FFT and slow-time FFT. At step 127, the combined beat signal is sampled using a one-dimensional (1D) fast-time FFT to estimate the range of one or more moving objects detected in the combined beat signal. In the fast-time FFT, the combined beat signal is sampled frequently, i.e., multiple samples per pulse. Since the frequency of each pulse is modulated, it is relatively easy to determine the range in the frequency domain. For example, if the radar system 100 is implemented to estimate the range of moving objects at ranges / R(0-100 meters). The radar system 100 uses K FMCW pulses to detect the objects. Let L be the number of samples within each pulse. Then, the resolution / step size for performing the fast-time FFT on the combined beat signal is calculated as: resolution = R / L.

[0128] Further, at step 129, the combined beat signal is sampled using a one-dimensional (1D) slow-time FFT to estimate the velocity of one or more moving objects detected in the combined beat signal. In the slow-time FFT, the combined signal is sampled with one sample per pulse. The slow-time FFT samples using a fewer or limited number of pulses, which results in quantization of the velocity estimate, as discussed earlier.

[0129] Thus, by performing two 1D FFTs, the baseband range-Doppler object detector 105 calculates a threshold to be used to detect the presence of moving objects. At step 131, the energy of the received signal is compared to the threshold to detect whether a real object is present and whether the object is moving or stationary. The threshold can be optimized by performing the FFT k {FFT l {b n (l,k)}} to optimize the threshold.

[0130] Once an object is detected at the baseband range-Doppler detector 105, the spatial MIMO detector 107 estimates the azimuth / elevation of the target using waveform separation in the slow-time domain with the identified Doppler frequency of the received waveform in the slow-time domain using:

[0131]

[0132] Thus, a virtual array of unique pairwise combinations of transmitters and receivers can be formed using the set of transmitters i and the set of receivers n. The set of transmitters and the set of receivers are configured to detect moving objects using slow-time MIMO radar transmission. For a given range cell l, the waveform separation gives the Tx-Rx virtual array as:

[0133]

[0134] wherein, The measurement code residuals. Furthermore, equation (8) shows that after slow-time waveform separation, a virtual array of MN elements for each detected object can be formed. Furthermore, equation (9) can be further used to identify the spatial extent of the detected object in the Tx-Rx element (i, n) domain.

[0135] The waveform at each virtual element (i, n) is composed of two components: the target signal, weighted by η ii ; and the residual signal, weighted by η im The weighted sum of M-1 components. If Δf d = 0, then because η im = 0 at the same time η ii = K, perfect waveform separation However, small mismatches in the Doppler domain can lead to significant leakage in the separated waveforms. Furthermore, the steering vector representing the set of phase delays of the received waveforms can be formed by stacking all MN virtual elements, where η ii = η

[0136]

[0137] wherein, is a self-correlation term that includes the Kronecker product of the object-receiver signature and the transmitter-object signature, while is a cross-correlation term that includes the Kronecker product of the combination of the object-receiver signature and the residual transmitter-object signature. The transmitter-object signature is a function of the relative angle between the transmitter and the object, the wavelength of the transmitted waveform, and the relative spacing between two consecutive transmitter elements. Similarly, the object-receiver signature is a function of the relative angle between the receiver and the object, the wavelength of the received waveform, and the relative spacing between two consecutive receiver elements. Furthermore, the combination of the residual transmitter-object signature and the waveform separation residuals include different combinations of the transmitted signal with values below and above a threshold. The explicit signal model presented in this disclosure accounts for elements of the waveform separation residuals with values above the threshold. The threshold can be predefined for the radar system.

[0138] FIG. 1ESteps of a method performed by the spatial MIMO detector 107 according to some embodiments are illustrated. The spatial MIMO detector 107 determines the angle (azimuth / elevation) of the object, i.e. the object’s position in the spatial domain. In step 133, one object, and the corresponding range estimate and velocity estimate, is selected from among the one or more objects detected by the baseband range-Doppler object detector 105. For example, the baseband range-Doppler object detector 105 detects three objects and estimates their corresponding ranges and velocities. The baseband range-Doppler object detector 105 provides this information to the spatial MIMO detector 107. The spatial MIMO detector 107 then extracts the waveform associated with one object at a time and processes it to determine the spatial position of that object. The spatial MIMO detector 107 iteratively continues this operation for the remaining two objects.

[0139] In step 135, the beat signal waveform corresponding to the selected object is compensated with the range estimate, so that where The compensation for range is provided and The compensation for Doppler is provided. In step 137, low-pass filtering is performed in the range and Doppler domain, filtering out the residuals from the other objects. In step 139, waveform separation is performed on the virtual array using the same orthogonal encoding scheme used at the transmitter. However, due to the Doppler mismatch, the separation is not perfect and the separated waveforms include residuals from each transmitter-receiver pair, or at least some transmitter-receiver pairs, of the virtual array. To account for these residuals, the explicit signal model mathematically represented in equation (1) uses cross-terms. The residuals in the cross-terms are a function of the unknown Doppler mismatch. Step 140 performs spatial domain object detection by identifying the presence or absence of waveform separation residuals. The spatial MIMO detector 107 is configured to estimate the Doppler mismatch using the explicit signal model, which can then be used to accurately determine the angle of the object.

[0140] After waveform separation, each transmitter-receiver virtual pair contains object signature, residual components, and noise. Furthermore, the separated waveforms from all N receivers are combined in a signal vector x of size MN. The spatial MIMO detector 107 uses the signal vector x to determine the spatial position of each object.

[0141] FIG. 1Fis an exemplary scenario illustrating the relationship between the transmitter-object signatures and the relative delays according to some embodiments. As can be observed in the figure, each of the total of M transmitters (or transmitting elements) in the transmitter array transmits an encoded FMCW pulse or radar signal towards the object 141 (e.g., a car). Assuming that the object 141 is very far from the transmitter array, for a far-field object (the distance from the transmitter to the object is much larger than the wavelength), the relative propagation delay from one transmitting element to another is based on: 1) the relative angle (azimuth / elevation) of transmission between the transmitter and the object; and 2) the distance between the two transmitter elements. For instance, for a uniform linear transmitter array, the relative propagation delay from the second transmitting element to the first transmitting element is calculated using:

[0142]

[0143] where d t is the distance between the two transmitting elements of the transmitter array, θ t is the angle of transmission between each transmitter and the object, and c is the speed of light. Thus, the relative delay from the Mthtransmitting element to the first transmitting element can be calculated as The radar system can use the relative propagation delays to calculate the relative phase delays. For instance, the relative phase difference from the second transmitting element to the first transmitting element is calculated using:

[0144]

[0145] Thus, the relative phase difference between the Mthtransmitting element and the first transmitting element is where the term can be represented by Then, the proposed radar system converts the relative phase delays into transmitter-object signatures. For instance, from the second transmitting element to the first transmitting element, the transmitter-object signature is given as Similarly, from the Mthtransmitting element to the first element, the transmitter-object signature is given as Moreover, by clustering the transmitter-object signatures from all transmitting elements together in a vector, the transmitter-object signatures of the transmitter array can be mathematically represented as:

[0146]

[0147] FIG. 1Gis an exemplary scenario illustrating the relationship between an object receiver signature and relative delay according to some embodiments. As can be observed in the figure, each receiver (or receiving element) out of a total of N receivers receives an echo pulse from an object 141 (e.g., a car). Assuming the object is far away from the receiver array, the relative propagation delay from one receiving element to another receiving element for a far-field object (where the distance from the receiver to the object is much greater than the wavelength) is based on: 1) the relative angle of arrival (azimuth / elevation) between the receiver and the object; and 2) the distance between the two receiving elements. For example, for a uniform linear receiver array, the relative propagation delay from the second receiving element to the first receiving element is calculated using:

[0148]

[0149] Among them, d tr is the distance between two transmitting elements of the transmitter array, θ t is the angle between each receiver and the object, and c is the speed of light. Therefore, the relative delay from the Mth receiving element to the first receiving element can be calculated as The radar system can use the relative propagation delay to calculate the relative phase delay. For example, the relative phase difference from the second receiving element to the first receiving element can be calculated using:

[0150]

[0151] Therefore, the relative phase difference between the Nth receiving element and the first receiving element is Among them Can be Then, the proposed radar system converts the relative phase delay into a receiver-object signature. For example, from the second receiving element to the first receiving element, the object-receiver signature is given as Similarly, from the Nth receiving element to the first receiving element, the object-receiver signature is given as Furthermore, by grouping the object-receiver signatures from all receiving elements together in a vector, the object-receiver signature of the receiver array can be mathematically represented as follows:

[0152]

[0153] FIG. 1H Waveform separation within a spatial MIMO detector is illustrated according to some embodiments. FIG. 1E To provide FIG. 1E An example analysis of the separated waveforms at the output of step 139 is shown. FIG. 1H It can be observed that the spatial MIMO detector 107 receives the echo signal xn (t) separating the waveforms associated with the unique pair combinations. For each receive element, the received signal x n (t) into M waveforms (with waveform separation in the slow time domain). By clustering the M waveforms of each of the N receive elements, there will be a total of MN waveforms from a virtual array of MN transmit-receive elements. All of these separated waveforms are combined in a signal vector x of dimension MN. FIG. 1I An exemplary signal vector containing the separated waveforms of each transmitter-receiver pair is shown according to an example embodiment. From FIG. 1I It can be observed that the vector x includes the separated waveforms b 11 , b 21 , through b M1 , to the separated waveforms b M1 , b M1 , through b MN from the first receiver. Thus, for a virtual array of MN elements (M transmit elements, N receive elements), the object signature is given as and the overall object signature including unknown object amplitudes is given as

[0154] FIG. 1J An exemplary scenario for computing transmitter-object residual signatures for the elements of a transmitter array is illustrated according to an example embodiment. It can be observed from the figure that each of the M transmitters transmits a set of frequency modulated pulses to the object 141. Each of the N receivers obtains a reflected transmission or echo signal from the object 141. The reflected transmissions are processed by the baseband range-Doppler object detector 105 and the spatial MIMO detector 107 as explained earlier. The spatial MIMO detector 107 performs waveform separation. Considering the waveform separation for the nth receiver, the separated waveforms will be b 1n (l), b 2n (l),..., b Mn (l). The combination of the receive element's transmitter-object residual signature (or residual transmitter-object signature) for a transmitter is a weighted sum of the residual transmitter-object signatures of all the other M transmitters except that transmitter, where the weights are the code residuals η, and the code residuals are a function of the Doppler mismatch Δf d Thus, the transmitter-object residual signature of a transmitter (or one element of a transmitter array) is given as:

[0155]

[0156] where, where, cm (k), c i (k) is given by the orthogonal codes used at transmitter m and transmitter i, respectively.

[0157] Therefore, the transmitter-object residual signatures of the elements of the transmitter array include the transmitter-object signatures of all transmitters except the transmitter in the transmitter-receiver pair, where the value of the residual transmitter-object signature of a particular transmitter is a function of the Doppler mismatch between the actual velocity of the moving object and the velocity estimated by the baseband detector. When the maximum value of the residual transmitter-object signature of the particular transmitter determined for the maximum Doppler mismatch is less than a threshold, the value of the residual transmitter-object signature of the particular transmitter is set to zero. This is because if the Doppler mismatch of a particular transmitter-receiver pair is very small, the corresponding Doppler mismatch, i.e., Δf, can be ignored. d =0, then Equation (19) will be simplified to η im =∑ k c m (k)c i (k). Now due to the code c m (k), c i (k) are orthogonal, so for this transmitter-receiver pair, η im = 0. Therefore, the residual transmitter-object signature of the corresponding transmitter-receiver pair will also be zero. Therefore, the calculation of the transmitter-object residual signature of the transmitter in equation (18) is simplified by setting some of the residual transmitter-object signatures to zero.

[0158] In addition, for FIG. 1J In the exemplary scenario shown, consider a transmitter array with eight transmitters and a receiver array with eight receivers forming a virtual array for measuring the reflected transmission. Each transmitting element transmits K = 64 pulses (code for each transmitting element). In the figure, the rows correspond to the eight transmitters and the columns correspond to the receivers. Assuming that at the second receiver, it is desired to extract the waveform corresponding to the second transmitter, the transmitter-object signature (object signature) from the self term is The transmitter-object residual feature signature (residual feature signature) of the cross term is the weighted sum shown in equation (18).

[0159] Each weight in the following equation is given by the code residual, which is a function of the code used by the transmitter, the Doppler mismatch, and the number of pulses. According to equation (18), (the sum of all other cross terms) is given by:

[0160]

[0161] where each element of the formula (20) is represented by a different shading in the figure. The different shadings are an exemplary representation of the transmitter-object residual signature for a transmitter at a given receiver, which is a weighted sum of all other transmitter-object signatures from all other transmitter-receiver pairs. For the separated waveforms associated with the transmitting element 2, the waveforms from the other transmitters act as interference or residuals. Thus, by setting η 22 = 0, the transmitter-object signature corresponding to the second transmitting element is excluded and the transmitter-object signatures corresponding to the other transmitting elements are considered, which provides the sum of all residuals with respect to a particular transmitter, in this case transmitter 2. To take into account the effect of the residuals, the transmitter object residual signature obtains the sum of all residuals with respect to the transmitting element 2.

[0162] Furthermore, by grouping the transmitter-object signatures from all transmitter elements into a vector, the transmitter-object residual signature of the transmitter array (M elements) is given as:

[0163]

[0164] where the vector each element of which is the transmitter-object residual signature with respect to the corresponding transmitter.

[0165] FIG. 1K Waveform components contained by the separated waveforms at each transmitter-receiver pair are exemplified according to some embodiments. The spatial MIMO detector 107 performs the waveform separation and generates the waveforms b 1n (l), b 2n (l),..., b Mn (l). Each of these separated waveforms comprises an object signature, a residual component due to imperfect waveform separation, and noise. For a virtual array of MN elements, the residual signature is given as: where is the object-receiver signature of the receiver array, and is the transmitter-object signature of the transmitter array, as mathematically represented in formula (20). The overall residual signature, which includes unknown amplitudes, is given as: The residual signature is the Kronecker product between the object-receiver signature and the transmitter-object residual signature. The object signature and the residual signature share the same object-receiver signature but different transmitter-object signatures.

[0166] FIG. 1L and FIG. 1MAn exemplary illustration of the subspace transmitter-object residual signature of a transmitter array is exemplified according to some embodiments. As in FIG. 1J As explained in (18) (or (20)), the transmitter-object residual signature of a transmitter is a weighted sum of the transmitter-object signatures from all other transmitters, where the weights of (19) are functions of the unknown Doppler mismatch, the code used at the transmitter, and the number of pulses K. Some embodiments are based on the recognition that the value of the unknown Doppler mismatch is bounded by a maximum Doppler mismatch that depends on the configuration of the MIMO radar system that is known in advance. Therefore, some embodiments replace the unknown Doppler mismatch with a predetermined maximum Doppler mismatch (e.g., half of the size of the Doppler grid used in the range-Doppler object detection), such as the Hadamard code shown in the checkbox illustration 1101. In addition, some embodiments are based on the recognition that if the contribution provided by a cross-term of the extended signal model is small, then the residual combination term in the cross-term corresponding to the maximum Doppler mismatch that provides a small contribution (i.e., a small weight) can be removed. This principle is exemplified in the approximation 1201 that is identified as a white box compared to the other locations 1401 of the locations 1301 that have a small weight (e.g., below a certain threshold).

[0167] By approximating the small code residual terms (exemplified as dark box checkbox illustration 1101) with zeros (white boxes in the approximation 1201), the (Tx-object) residual signature is approximated as a weighted sum of the (Tx-object) object signatures from a limited number of transmitters (as opposed to all other transmitters initially) that present the subspace model of the transmitter-object residual signature. The locations of the small code residuals (white boxes) are identified by using the predetermined maximum Doppler mismatch, the code used at the transmitter, and the number of pulses.

[0168] As a result, instead of taking all other transmitters into account, the transmitter-object residual signature 1501 of a transmitter is approximated as a weighted sum 1601 of the transmitter-object signatures from only a limited number (d) of transmitters. For the example used in (20), it means that

[0169]

[0170] As shown in FIG. 1M All elements of (21) (i.e., the transmitter-object residual signature 110m of the full transmitter array can be individually approximated 120m by ignoring the corresponding small weights. More specifically, by including only the largest d weights in the weighted sum of each element of (21), the transmitter-object residual signature of the full transmitter array can be approximated by the subspace signal 130m:

[0171]

[0172] where the transmitter-object residual subspace matrix is:

[0173]

[0174] where d denotes the subspace dimension.

[0175] Using the subspace model of the transmitter-object residual eigen signatures of the transmitter array in the full signal model of the virtual array, the residual eigen signatures of the virtual array (MNvirtual pairs for M transmitters and N receivers) can be approximated as the Kronecker subspace signal

[0176]

[0177] Thus, the explicit signal model of equation (1) is approximated as follows:

[0178]

[0179] where is the object eigen signature of the full virtual array, is the residual eigen signature of the full virtual array, and w is the noise of all MNtransmitter-receiver pairs.

[0180] If perfect waveform separation is assumed, the explicit signal model of the full virtual array simplifies to the model used in the literature,

[0181]

[0182] FIG. 2A Steps to implement a spatial domain MIMO object detector according to example embodiments are illustrated. These steps are implemented after waveform separation of step 139 as explained earlier with respect to FIG. 1E After waveform separation of step 139, the separated waveforms can be obtained from the signal vector x at step 201. At step 203, all combinations of transmitter-object angles and object-transmitter angles are determined iteratively until all possible angles in the range of 0° to 180°. Further, at step 205, for each combination, the object eigen signature and the residual eigen signature are computed (as discussed earlier). At step 207, object detection and spatial localization are formulated as a binary hypothesis testing problem in the presence of residual waveforms. The binary hypothesis is expressed in equation (27) as

[0183] H0: x = w(l),

[0184]

[0185] where the disturbance is assumed to be Gaussian with zero mean and covariance matrix R, i.e., w ~ CN(0, R). The first hypothesis H0defines that the separated waveform contains only noise / interference / disturbance, i.e., there is no object at the assumed transmit and receive angles. The second hypothesis H1defines that the separated waveform contains only 1) object signature at the assumed angle; 2) residual signature; and 3) noise / interference / disturbance. Furthermore, in step 209, a binary hypothesis is tested to determine whether there is an object at all combinations of transmitter-object angle and object-transmitter angle in the range of 0° to 180°. 2 R). The first hypothesis H0defines that the separated waveform contains only noise / interference / disturbance, i.e., there is no object at the assumed transmit and receive angles. The second hypothesis H1defines that the separated waveform contains only 1) object signature at the assumed angle; 2) residual signature; and 3) noise / interference / disturbance. Furthermore, in step 209, a binary hypothesis is tested to determine whether there is an object at all combinations of transmitter-object angle and object-transmitter angle in the range of 0° to 180°.

[0186] FIG. 2B A method for implementing the binary hypothesis test exemplified in step 209 according to an example embodiment is illustrated. Referring to FIG. 2, the method is illustrated in the following steps: FIG. 2B A detailed analysis of the binary hypothesis test exemplified in step 209 for implementing FIG. 2A After obtaining the separated waveform from the signal vector, in step 211, the signal vector is pre-whitened using the known / estimated covariance matrix R, which corresponds to the disturbance in the signal vector. In the case where R is unknown, it can be estimated from the training signals at adjacent range cells.

[0187] In step 213, the known R or estimated The separated signal from the superposition of transmitted signals is whitened using y = R -1 / 2 x, and y = R -1 / 2 The detection is mapped to the following binary hypothesis test:

[0188] H0: y ~ CN(0, σ 2 I),

[0189]

[0190] Assuming that R has a Kronecker structure then the steering vectors (i.e., transmitter-object signature and object-receiver signature) of dimension M and N, respectively and the transmitter-object residual subspace matrix H r are known.

[0191] Furthermore, in step 213, the GLRT statistic T is computed using the pre-whitened separated waveform and signatures, which can be derived as the maximum likelihood ratio under the two hypotheses. The GLRT statistic is given as:

[0192]

[0193] where T is the test statistic (or GLRT statistic), and f0(y|σ 2 ) and f1(y|α,η,σ 2 ) are the likelihood functions of the whitened signal

[0194]

[0195]

[0196] By 2 For ln f1(y|α,η,σ 2 ) Take the derivative and set it to zero, under H1 σ 2 The maximum likelihood (ML) estimate of

[0197]

[0198] Then, the remaining parameters β = [α, η] can be determined by minimizing the following cost function T ] T ML estimation of

[0199]

[0200] in, Furthermore, the ML estimate of β is as follows:

[0201]

[0202] By Substituting back the cost function, Equation (34) can be obtained as

[0203]

[0204] In formula (34), the Kronecker product property is and As a result, the maximum likelihood under H1 is given by:

[0205]

[0206] Similarly, under H0, maximizing the likelihood is given by:

[0207]

[0208] Therefore, the GLRT statistic (T) determined by the GLRT algorithm is equivalent to the ratio of the energy of the whitened signal projected onto the subspace to the orthogonal complement of the subspace, where the subspace is steered by the whitened signal vector The column space of and the whitened subspace of the waveform residual In step 215, the GLRT statistic T is compared to a predetermined threshold to determine which of the two hypotheses is true. When it is determined that hypothesis H1 is true, the spatial MIMO detector 107 detects the object in the hypothesis combination of transmitter-object angle and object-transmitter angle from the received separated waveforms. The spatial MIMO detector continues to perform binary hypotheses for all combinations of transmitter-object angle and object-transmitter angle ranging from 0° to 180°.

[0209] FIG. 2C The steps of performing pre-whitening of the separated waveforms and eigen signatures according to example embodiments are illustrated. Referring to FIG. 2C The details of the pre-whitening using the known / estimated covariance matrix implemented in step 211 in FIG. 2B The details of the pre-whitening using the known / estimated covariance matrix implemented in step 211 in

[0210]

[0211] In step 219, the transmitter-object eigen signature is pre-whitened using:

[0212]

[0213] In step 221, the object-receiver eigen signature is pre-whitened,

[0214]

[0215] Finally, in step 223, the transmitter-object residual subspace H r is pre-whitened using:

[0216]

[0217] The pre-whitened separated waveforms and eigen signatures are then used to compute the GLRT statistic as explained earlier with reference to FIG. 2B The details of the computation of the GLRT statistic in step 213 shown in The details of the computation of the GLRT statistic in step 213 shown in

[0218] The steps of computing the GLRT statistic using the pre-whitened waveforms and eigen signatures according to example embodiments are illustrated. Referring to FIG. 2D The details of the computation of the GLRT statistic in step 213 shown in FIG. 2D In step 225, an augmented subspace is formed by including the transmitter-object eigen signature and the transmitter-object residual subspace. The augmented subspace is given as: FIG. 2B

[0219]

[0220] At step 227, the Kronecker subspace between the object-receiver signature and the augmented space is computed:

[0221]

[0222] At step 229, two projection matrices are computed: the orthogonal projection and the orthogonal complement projection given as follows:

[0223]

[0224]

[0225] At step 231, the GLRT statistic is computed, for which we set and

[0226] Moreover, to compare the GLRT statistic with a threshold. To select a suitable threshold that satisfies a given false alarm probability, we have the following lemma.

[0227] Lemma: Under the first hypothesis H0, the numerator and the denominator have the following distributions

[0228]

[0229]

[0230] where is the nth element of white noise . Moreover, the projection matrix P A can be decomposed as P A = Q diag{1,..., 1, 0,..., 0} Q H , where Q contains the corresponding eigenvectors and d non-zero eigenvalues. Then the GLRT statistic is the ratio of two independent central Chi-square distributions with 2d and 2(MN - d) degrees of freedom, respectively. As a result, the first distribution under the first hypothesis is obtained as follows:

[0231] Under H0(46)

[0232] where F v1,v2 is the central F-distribution with degrees of freedom vi and v2.

[0233] Given the above lemma and (46), a suitable threshold can be pre-selected.

[0234] FIG. 2EA threshold comparison step by computing a test threshold and comparing it with the GLRT statistic is exemplified according to an example embodiment. Reference is made to FIG. 2E Details of the threshold comparison of step 215 shown in FIG. 2B are given, the threshold λ is chosen to satisfy the false alarm probability

[0235]

[0236] where F 2d,2(MN-d) (z) is the probability distribution function of F-distribution with degrees of freedom 2d and 2(MN-d), and P fa is the given false alarm probability.

[0237] In step 235, the GLRT statistic is compared with the threshold λ, where the hypothesis H1 is true when the GLRT statistic is not smaller than the threshold, otherwise the hypothesis H0 is true. Therefore, Lemma 1 implies that the GLRT is a constant false alarm rate (CFAR) detector. Thus, when the GLRT algorithm determines that the hypothesis H1 is true, then the spatial MIMO detector 107 has detected a moving object at a certain spatial location. On the other hand, when the GLRT algorithm determines that the hypothesis H0 is true, the spatial MIMO detector 107 has not detected an object.

[0238] Performance verification

[0239] Furthermore, the performance of the object detector based on the Kronecker subspace is evaluated to verify the analysis provided above. To this end, the signal-to-interference-plus-noise ratio (SINR) and the residual-to-interference ratio (RINR) are respectively given by

[0240]

[0241]

[0242] where s denotes the steering vector corresponding to N = 16 receivers, t is the steering vector of M = 8 transmitters, and the perturbation covariance matrix R is given as [R] lk = p |l-k| with p = 0.6. The detection performance is evaluated in terms of the receiver operating characteristic (ROC) by using Monte-Carlo trials. Furthermore, for performance comparison, a conventional MIMO detector that ignores the existence of waveform residuals is also considered.

[0243] Detection performance evaluation:

[0244] Reference is made to FIG. 3A to FIG. 3CAn evaluation of the detection performance of the proposed radar system 100 using the explicit signal model is illustrated. FIG. 3A Receiver operating characteristic (ROC) curves for the two-stage waveform separation residual under SINR = 10 dB are shown. FIG. 3B A performance comparison of the two object detectors in the scenario of perspective (known R) and adaptive (unknown R) detection is shown. Furthermore, FIG. 3C The performance verification of the theoretical (dotted squares) ROC curves versus the Monte-Carlo simulation results (circles) under various RINR at SINR = 10 dB is shown.

[0245] Case 1 : When the disturbance represented by the covariance matrix R is known or R = I, first use R -1 / 2 Pre-whiten the received signal x and steering vectors t and s. When SINR = 10 dB, FIG. 3A ROC performance of the conventional detector and the proposed detector under two levels of waveform residual 1) RINR = 10 dB and 2) RINR = 15 dB) is shown. From FIG. 3A It can be observed from the shown plots that by exploiting the target residual, the detection performance can be improved. Furthermore, the greater the target residual component (i.e., the greater the RINR), the greater the performance improvement can be achieved. This observation is intuitive since the stronger the target residual, the greater the separation between the null and alternative hypotheses, and thus the better the detection performance.

[0246] Case 2: When the disturbance matrix R is unknown. In this case, adaptive object detection is performed using the training signals x(l) from the nearby range bin l. FIG. 3B ROC curves for the adaptive and perspective (known R) schemes of the two detectors when RINR = 10 dB and 2) RINR = 10 dB are shown. It can be observed that the detection performance of both detectors degrades when the disturbance covariance matrix has to be estimated from the training signals. Furthermore, in the case of adaptive detection, the proposed detector is still superior to the conventional detector.

[0247] Furthermore, the theoretical performance of the proposed Kronecker subspace-based object detector is verified using Monte-Carlo simulation results. To this end, the inverse of the cumulative distribution function (CDF) of the F-distribution and the CDF of the non-central F-distribution are evaluated. FIG. 3C The simulated ROC curves and the corresponding theoretical performance under various RINR ranging from 7:5 dB to 15 dB are shown. From FIG. 3C It can be observed that for all considered scenarios, the theoretical performance matches the simulated ROC curves very well even in the case of very small false alarm probabilities (e.g., P f = 0.001).

[0248] Example Implementations:

[0249] FIG. 4 A block diagram of a MIMO radar system 100 is illustrated in accordance with some embodiments. The MIMO radar system 100 can have a plurality of interfaces that connect the system 100 with other systems and devices. A network interface controller 401 is adapted to connect the system 100 to a network 405 through a bus 403, which connects the MIMO radar system 100 with a sensing device. For example, the radar system 100 includes a transmitter interface 407 configured to command the set of transmitters 101 to emit coded FMCW pulses. The transmitter interface 407 is in communication with a signal generator 409 that generates the FMCW pulses. In addition, an orthogonal code generator 411 is used to generate different orthogonal codes that are multiplied with the FMCW pulses associated with each of the set of transmitters 101. Using a receiver interface 413 connected to the set of receivers 103, the system 100 can receive reflections, i.e., echo signals 415, from one or more objects corresponding to the transmitted pulses. The received reflections include a superposition of reflections corresponding to all transmitted pulses reflected from the one or more objects. The echo signals are received from the one or more objects through the network 405.

[0250] In addition, the system 100 includes a processor 417 configured to execute stored instructions 419 and a memory 421 that stores the instructions executable by the processor 417. The processor 417 can be a single core processor, a multi-core processor, a computing cluster, or any number of other configurations. The memory 421 can include random access memory (RAM), read only memory (ROM), flash memory, or any other suitable memory system. The processor 417 can be connected through the bus 403 to one or more input and / or output (I / O) devices.

[0251] The instructions can implement a method that accounts for imperfect waveform separation for detecting one or more moving objects. To this end, the instructions include a baseband range-Doppler object detector 105 that obtains the echo signals 415 and detects the one or more objects in the Doppler domain. In addition, the baseband range-Doppler object detector 105 estimates the range of the one or more objects and the velocity of the one or more objects. The instructions also include a spatial MIMO detector 107 that determines whether there is an object at a given combination of transmitter-object angle and object-transmitter angle.

[0252] The MIMO radar system 100 includes an output interface 423 configured to output parameters associated with the detected objects. The parameters can include at least one of a radial velocity, a spatial angle, and a distance to the detected objects. The output interface 423 can output the parameters on a display device 425, store the parameters in a storage medium, and / or transmit the parameters via the network 405. For example, the system 100 can be linked through the bus 403 to a display interface adapted to connect the system 100 to a display device 425 such as a computer monitor, a camera, a television, a projector, or a mobile device. The system 100 can also be connected to an application interface adapted to connect the system 100 to a device for performing various tasks.

[0253] In an example implementation, a motor vehicle can include the proposed MIMO radar system 100. The motor vehicle can be an autonomous vehicle. While the motor vehicle is driving on a highway, the radar system 100 continuously detects one or more moving objects such as vehicles, pedestrians, etc. To this end, the system 100 transmits pulses in all directions and further obtains the corresponding return signals. The return signals include a superposition of reflections from the one or more moving objects corresponding to all transmitted pulses. The system 100 first detects the one or more objects in the Doppler domain, estimates the distance and velocity corresponding to the one or more objects. In addition, the radar system 100 performs waveform separation based on the proposed explicit signaling model.

[0254] The radar system 100 also determines other parameters associated with the detected one or more objects such as the radial velocity of the one or more objects, the distance of the one or more objects, etc. The radar system 100 continuously updates the motor vehicle driver about the detected one or more moving objects. Based on the obtained information, the driver can, for example, steer the motor vehicle, adjust the speed of the motor vehicle, etc. In an example implementation, the radar system 100 determines whether the one or more moving objects are moving towards or away from the motor vehicle. This enables the driver to better control the motor vehicle.

[0255] In various implementations, a MIMO radar system for detecting moving objects includes a set of transmitters and a set of receivers that form a virtual array of unique pairwise combinations of transmitters and receivers to measure reflections of transmissions. For example, in one implementation, the MIMO radar system is mounted on a moving vehicle and is operatively connected to a control system for controlling movement of the vehicle. In one implementation, the control system is disposed on a controlled vehicle such as an autonomous vehicle or a semi-autonomous vehicle. In another implementation, the control system is disposed on a road-side unit (RSU) and is interchangeably connected to a controlled vehicle. Additionally or alternatively, the MIMO radar system can be mounted on the RSU to measure parameters of objects moving within an area controlled by the RSU.

[0256] To this end, in various embodiments, the set of transmitters and receivers are arranged on the controlled vehicle, the RSU, or a combination thereof. The transmitters and receivers can be collocated to form a set of transceivers, or specifically separated. In some embodiments, the MIMO radar system includes multiple transmitters and multiple receivers. In some implementations, the transmitters and / or receivers are equidistant, i.e., the distance between any pair of transmitters or receivers is constant. In this way, the computation of the signature of the transmitters and / or receivers can be simplified.

[0257] Multiple transmitters and receivers of some embodiments are added to improve the spatial resolution. The MIMO radar system transmits mutually orthogonal signals from multiple transmitters, and these waveforms can be extracted from each receiver through a matched set of filters. For example, if the MIMO radar system has 3 transmitters and 4 receivers, 12 signals can be extracted from the receivers due to the orthogonality of the transmitted signals. That is, through digital signal processing of the received signals, a virtual antenna array of 12 elements is created using only 7 antennas, resulting in a finer spatial resolution compared to the phased array counterpart.

[0258] The MIMO radar system of some embodiments is configured to detect a moving object such as another vehicle or a pedestrian, and determine various parameters of the moving object. Examples of the parameters include one or a combination of the following: a distance of the moving object (e.g., a distance from the radar to the moving object), a velocity of the moving object (e.g., an absolute velocity or a relative velocity between the radar and the moving object), an angle of the moving object that defines a direction from the radar to the moving object, and an elevation angle of the moving object (e.g., an absolute or a relative elevation height that defines an elevation height of the radar to an elevation height of the moving object). To estimate both the absolute or the relative parameters of the moving object, the MIMO radar system is connected to various measurement units associated with the controlling vehicle, the RSU, or any other system on which the MIMO radar system is arranged. For example, the MIMO radar system can be connected to a speedometer and an accelerometer of the controlling vehicle to estimate the speed of the controlling vehicle. The MIMO radar system can also be connected to a position estimator (e.g., a GPS) of the controlled vehicle to receive the position information of the vehicle.

[0259] Due to the multiple transmission design that increases the spatial resolution of the MIMO radar system, various embodiments use coded transmissions encoded with orthogonal codes to avoid interference. However, due to the imperfect motion of the detected objects and the computational requirement for simplicity, the separation of some of the transmitted waveforms used by some embodiments includes residuals from other transmissions that can degrade the quality of the parameter estimation.

[0260] To this end, in some embodiments, the MIMO radar system comprises a memory configured to store an explicit signal model that accounts for waveform separation residuals by relating measurements of the virtual array to auto-terms and cross-terms, the auto-terms comprising a Kronecker product of object-receiver signatures of the receiver array and transmitter-object signatures of the transmitter array, the cross-terms comprising a Kronecker product of object-receiver signatures of the receiver array and transmitter-object residual signatures of the transmitter array; and a processor configured to detect a moving object by executing a spatial MIMO detector, the spatial MIMO detector configured to detect the moving object using the explicit signal model. An output interface of the MIMO radar system is configured to output parameters associated with the detected object.

[0261] There are many different reasons that can cause leakage of waveform separation presented by the residuals. For example, in one embodiment, the MIMO radar system has a slow-time MIMO FMCW automotive radar system architecture. According to this architecture, the transmitted signal comprises a sequence of pulses, and each pulse is frequency modulated to simplify range estimation. For example, due to this modulation, it is possible to determine the distance to a detected object by beating the reflected signal with a reference signal and detecting the peaks of the beat signal. The frequency of the peaks corresponds to the distance to the object. To this end, in some embodiments, the reflected signal is fast sampled at each receiver, i.e. multiple times per pulse, to perform such calculations.

[0262] To determine the velocity of a moving object, some embodiments use the Doppler effect, such that the velocity of an object corresponds to a Doppler shift in the received signal caused by the relative motion of the moving object. To estimate such a Doppler shift, the received signal is slowly sampled on a pulse-by-pulse basis. Thus, the number of samples corresponds to the number of pulses. To increase the resolution of the estimated velocity, it is necessary to increase the number of samples. However, an increase in the number of pulses increases the illumination time required to detect an object, which is undesirable in a dynamic changing vehicle scenario. Thus, there can be a mismatch between the actual velocity and the estimated velocity corresponding to an estimation error. This error, referred to herein as Doppler mismatch, causes a residual of the waveform separation.

[0263] For example, in one implementation, the processor of the MIMO radar system is configured to execute a baseband range-Doppler object detector configured to detect one or more moving objects, estimate a range and a velocity of each detected moving object, and for each detected moving object, extract a portion of the measurements of the virtual array corresponding to the range of the moving object, compensate the extracted measurements for the velocity of the moving object, and submit the extracted and compensated measurements to a spatial MIMO detector to determine one or a combination of an angle and an azimuth of the moving object.

[0264] The separation of the range, velocity, and angle estimation simplifies the computation. For example, the range and velocity can be estimated in the range-Doppler domain without the need for waveform separation. Thus, any reflection received by a receiver can be used to estimate the range and velocity. Additionally or alternatively, a combination of received echoes can be used to improve the SNR of the received signal. In other words, a single reflection can be used to determine the range and velocity. However, all reflections are used and the angle and / or azimuth of the moving object is determined uniformly after waveform separation. This uniform estimation forms the Kronecker structure of the explicit signal model described above.

[0265] Additionally, the separation of the range and velocity estimation from the angle estimation allows to determine the angle of multiple moving objects in the scene individually. This is achieved by first detecting the moving objects by the baseband range-Doppler object detector and iteratively performing by the spatial MIMO detector for a portion of the measurements corresponding to a particular moving object. To achieve a better angle estimation, the velocity and range of the detected objects are compensated to move all detected objects at the origin of the spatial MIMO estimator without considering the actual velocity of the moving object. This simplifies the computation but introduces a residual in the waveform separation due to the Doppler mismatch.

[0266] For example, in one implementation, each transmitter is configured to transmit a set of frequency modulated pulses to illuminate the scene and form measurements, wherein the baseband range-Doppler object detector is configured to determine the range of the moving object using a fast-time fast Fourier transform (FFT) that samples each transmitted pulse multiple times for range compression, and wherein the baseband range-Doppler object detector is configured to determine the velocity of the moving object using a slow-time FFT that samples each transmitted pulse once for Doppler compression.

[0267] Here, the size of the set of frequency-modulated pulses defines the resolution of the velocity estimate, which results in a Doppler mismatch between the actual velocity of the moving object and the velocity estimated by the baseband detector using a slow-time FFT, and wherein for each transmitter-receiver pair of the virtual array, the frequency-modulated pulses of different transmitters are encoded on a pulse-by-pulse basis with an orthogonal code and decoded with a corresponding orthogonal code, wherein the self-term of the explicit signal model captures the decoded transmission of the transmitter-receiver pair, and wherein the cross-term of the explicit signal model captures the residual of the different transmissions in the decoded transmission of the transmitter-receiver pair caused by the Doppler mismatch.

[0268] Some embodiments use the following terminology, which is (functionally) interpreted as follows:

[0269] Transmitter-object signature of a transmitter:

[0270] i.

[0271] Object-receiver signature of a receiver:

[0272] ii.

[0273] Transmitter-object signature of a plurality of transmitters (i.e., transmitter array)

[0274]

[0275] Object-receiver signature of a plurality of receivers (i.e., receiver array):

[0276] b.

[0277] Transmitter-object residual signature of a transmitter:

[0278] For the i-th transmitter,

[0279] In the summation, each term is the regular transmitter-object signature of a transmitter (see 1.) and a weight. The weight can be computed as

[0280]

[0281] As a function of the code, the unknown Doppler mismatch, and the number of pulses.

[0282] Transmitter-object residual signature of a transmitter array

[0283]

[0284] Object signature of a virtual array (transmitter-receiver of MN pair):

[0285]

[0286] The Kronecker product of item 3 and item 4 above.

[0287] The residual signature of a virtual array (transmitter-receiver pair of MNs):

[0288]

[0289] The Kronecker product of item 6 and item 4 above.

[0290] In this way, for each transmitter-receiver pair of the virtual array, the transmitter-object residual signature of the transmitter in the transmitter-receiver pair is a weighted sum of the transmitter-object signatures of all transmitters except the transmitter in the transmitter-receiver pair, where the weights are a function of the Doppler mismatch between the actual velocity of the moving object and the velocity estimated by the baseband probe.

[0291] Some embodiments are based on the understanding that the main reason for the Doppler mismatch is the quantization of the velocity estimate caused by the finite number of pulses. The actual Doppler mismatch is unknown and determined online by evaluating the extended signal model. However, the quantization of the velocity estimate can define a maximum Doppler mismatch for each Doppler frequency, while the code, the number of pulses, the arrangement of the receivers and transmitters can define the weight of each maximum Doppler mismatch in the angle estimate. This weight of each maximum Doppler mismatch can be evaluated in advance. To this end, some embodiments set the weight of the calculation of the transmitter-object residual signature of a particular transmitter to zero when the weights corresponding to the transmitter-object signatures of a number of other transmitters determined using the maximum Doppler mismatch are smaller than a threshold. In FIG. 1J In, the weight for the calculation of the transmitter-object residual signature of a particular transmitter is shown in equation (19), where the transmitter-object residual signature of a particular (i.e., the i-th) transmitter is shown in equation (18).

[0292] In this way, the transmitter-object residual signature of a transmitter is a weighted sum of the transmitter-object (regular, i.e., non-residual) signatures of all other transmitters, where the weights are a function of the code, the (unknown) Doppler mismatch and the number of pulses.

[0293] Additionally or alternatively, the knowledge of the maximum Doppler mismatch can simplify the evaluation of the explicit signal model. For example, in one embodiment, the transmitter-object residual signature of a particular transmitter is approximated as a weighted sum of the transmitter-object signatures of a finite number of transmitters instead of all other transmitters. The selection of these transmitters can be determined by using the pre-determined maximum Doppler mismatch.

[0294] In various embodiments, the transmitter-object signature of a transmitter is a function of the relative angle between each transmitter of the set of transmitters and a detected object, the wavelength of the transmitted signal, and the relative distance between two consecutive transmitter elements of the set of transmitters. Additionally, the object-receiver signature of a receiver is a function of the relative angle between each receiver of the set of receivers and a detected object, the wavelength of the received signal, and the relative distance between two consecutive receiver elements of the set of receivers. Referring to FIG. 1F and FIG. 1G The concept of signatures is illustrated. The signatures of the transmitters / receivers and the transmitter / receiver array allow the multiple reflections to be evaluated as a part of a Kronecker structure.

[0295] In alternative embodiments, the MIMO radar system uses a single detector configured to estimate various parameters of a moving object, such as at least one of radial velocity, spatial angle, and distance from a detected object. This embodiment forms a multi-dimensional Kronecker structure of moving object parameters. However, the cross terms defining the waveform separation residual have non-zero values only for a subset of dimensions corresponding to, for example, the angle of the moving object.

[0296] In some embodiments, the spatial MIMO detector is implemented using a generalized likelihood ratio test (GLRT) algorithm, where the GLRT algorithm determines a GLRT statistic to detect a moving object. This embodiment accounts for the noise of the measurements and the waveform separation residual to improve the accuracy of the estimates.

[0297] For example, the GLRT algorithm formulates and tests a first hypothesis that the transmitted reflections contain only noise and a second hypothesis that the transmitted reflections contain reflection signals from a moving object, a waveform separation residual, and noise.

[0298] For example, in some embodiments, the GLRT determines a first distribution under the first hypothesis and a second distribution under the second hypothesis, where the first distribution is a central F-distribution, and where the second distribution is a non-central F-distribution. In one embodiment, the processor is further configured to compare the GLRT statistic to a predetermined threshold, where the predetermined threshold is based on the number of transmitters and receivers and the subspace dimension, where the second hypothesis is true when the GLRT statistic is greater than the predetermined threshold, where the first hypothesis is true when the GLRT statistic is less than the predetermined threshold.

[0299] Embodiments

[0300] This description provides exemplary embodiments only, and is not intended to limit the scope, applicability or configuration of the disclosure. Rather, the following description of the exemplary embodiments will provide those skilled in the art with an enabling description for implementing one or more exemplary embodiments. It is contemplated that various changes can be made in the function and arrangement of elements without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims.

[0301] In the following description, specific details are set forth to provide a thorough understanding of the embodiments. However, persons having ordinary skill in the art will appreciate that the embodiments can be practiced without the specific details. For example, the systems, processes and other elements in the disclosed subject matter can be shown as components in block diagram form in order not to obscure the embodiments in unnecessary detail. In other instances, well-known processes, structures and techniques can be shown without detailed description in order to avoid obscuring the embodiments. Additionally, like reference numbers and symbols can denote like elements throughout the various drawings and figures.

[0302] In addition, various embodiments can be described as a process depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart can describe operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations can be re-arranged. A process can be terminated when its operations are completed, but could also occur intermittently during the process. In addition, not all operations in any particular implementation can occur. A process can correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, its termination can correspond to a return of the function to the calling function or the main function.

[0303] Furthermore, embodiments of the disclosed subject matter can be implemented, at least in part, manually or automatically. Manual or automatic implementation can occur contemporaneously with the events described or it can be subsequent thereto. It will be appreciated that the disclosed subject matter can be implemented in one or more computer programs or software, which execute on programmable computers including computers in the cloud, each computer including a processor, a data storage system (including volatile and non-volatile memory and / or storage elements), at least one input device, and at least one output device. The software program code can be stored in a computer readable medium, which can include one or more types of memory devices, one or more hardware storage devices, or a combination thereof.

[0304] Furthermore, the embodiments of the present disclosure and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their equivalent structures, or in a combination of one or more of them. Some other embodiments of the present disclosure can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory program carrier, for execution by, or to control the operation of, data processing apparatus. Still further, program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them.

[0305] According to embodiments of the present disclosure, the term "data processing apparatus" can encompass all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). The apparatus can also include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0306] A computer program, which can also be referred to or described as a program, software, a software application, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and are interconnected by a communication network. Computers suitable for the execution of a computer program include, by way of example, can be based on general or special purpose microprocessors or both, or any other kind of central processing unit. Generally, a central processing unit receives instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data (e.g., magnetic, magneto optical disks, or optical disks). However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device (e.g., a universal serial bus (USB) flash drive), to name just a few.

[0307] To provide for interaction with a user, implementations of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user’s client device in response to requests received from the web browser.

[0308] Implementations of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front-end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network ("LAN") and a wide area network ("WAN"), e.g., the Internet.

[0309] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

[0310] While this disclosure has described certain preferred embodiments and techniques, this was done for purposes of example. Numerous other adaptations and modifications of the described embodiments and techniques can be applicable in different applied environments and with different types of users. Therefore, the scope of the disclosure is not intended to be limited to the described embodiments and techniques, and one skilled in the art can devise numerous alternative ways of practicing the present disclosure while staying within the scope of the appended claims.

Claims

1. A multiple-input multiple-output (MIMO) radar system for detecting moving objects, the MIMO radar system comprising: a set of transmitters and a set of receivers, the set of transmitters and the set of receivers forming a virtual array of unique pair-wise combinations of said transmitters and said receivers to measure reflections of the transmissions; a memory configured to store an explicit signal model that accounts for waveform separation residuals by correlating measurements of the virtual array with self-terms and cross-terms, the self-terms comprising Kronecker products of object-receiver signatures and transmitter-object signatures, and the cross-terms comprising Kronecker products of object-receiver signatures and transmitter-object residual signatures, wherein the transmitter-object signature is a function of a relative angle between each transmitter in the set of transmitters and a detected object, a wavelength of a transmitted signal, and a relative distance between two consecutive transmitter elements in the set of transmitters; a processor configured to detect a moving object by executing a spatial MIMO detector configured to detect the moving object using the explicit signal model; and An output interface is configured to output parameters associated with the detected object.

2. The MIMO radar system according to claim 1, wherein: The processor is configured to execute a baseband range-Doppler object detector configured to detect one or more moving objects, estimate a range and a velocity of each detected moving object, and, for each detected moving object, extract a portion of the virtual array measurements corresponding to the range of the moving object, compensate the extracted measurements for the velocity of the moving object, and submit the extracted and compensated measurements to the spatial MIMO detector to determine one or a combination of an angle and an azimuth of the moving object.

3. The MIMO radar system according to claim 2, wherein: Each transmitter is configured to transmit a set of frequency modulated pulses to illuminate a scene and form the measurement results, wherein the baseband range-Doppler object detector is configured to determine the range of the moving object using a fast-time Fast Fourier Transform (FFT) that samples each transmitted pulse multiple times for range compression, and wherein the baseband range-Doppler object detector is configured to determine the speed of the moving object using a slow-time FFT that samples each transmitted pulse once for Doppler compression.

4. The MIMO radar system according to claim 3, wherein: The size of the set of frequency modulated pulses defines a resolution of the velocity estimate that results in a Doppler mismatch between the actual velocity of the moving object and the velocity estimated by the baseband detector using the slow-time FFT, and wherein, for each transmitter-receiver pair of the virtual array, the frequency modulated pulses of different transmitters are encoded on a pulse-by-pulse basis with an orthogonal code and decoded with a corresponding orthogonal code, wherein the self-terms of the explicit signal model capture the decoded transmissions of the transmitter-receiver pair, and wherein the cross-terms of the explicit signal model capture the residuals of the different transmissions in the decoded transmissions of the transmitter-receiver pair that are caused by the Doppler mismatch.

5. The MIMO radar system according to claim 2, wherein: For each transmitter-receiver pair of the virtual array, the transmitter-object residual signature includes transmitter-object signatures of all transmitters except the transmitter in the transmitter-receiver pair, wherein the transmitter-object residual signature of a specific transmitter is a function of a Doppler mismatch between an actual velocity of the moving object and a velocity estimated by a baseband detector, and wherein when a maximum value of the transmitter-object residual signature of the specific transmitter determined for a maximum Doppler mismatch is less than a threshold, the transmitter-object signature of the specific transmitter is set to zero.

6. The MIMO radar system according to claim 1, wherein: The transmitter-object residual signature is approximated as a weighted sub-combination of a predetermined maximum Doppler mismatch.

7. The MIMO radar system according to claim 1, wherein: The parameter includes at least one of a radial velocity, a spatial angle, and a distance to a detected object.

8. The MIMO radar system according to claim 1, wherein: The object-receiver signature is a function of the relative angle between each receiver in the set of receivers and the detected object, the wavelength of the received signal, and the relative distance between two consecutive receiver elements in the set of receivers.

9. The MIMO radar system according to claim 1, wherein: The processor uses a single detector configured to estimate parameters of the moving object, the parameters comprising radial velocity, spatial angle, and distance to the moving object, wherein the explicit signal model comprises a multi-V Kronecker structure of the parameters of the moving object, and wherein a cross-term of the explicit signal model has a zero value for a dimension corresponding to the radial velocity and the distance to the moving object, and wherein the cross-term has a non-zero value for a dimension corresponding to the spatial angle of the moving object.

10. The MIMO radar system according to claim 1, wherein: The spatial MIMO detector is implemented using a generalized likelihood ratio test (GLRT) algorithm, wherein the GLRT algorithm determines GLRT statistics to detect the moving object.

11. The MIMO radar system according to claim 10, wherein: The GLRT algorithm formulates and tests a first hypothesis and a second hypothesis, wherein the first hypothesis is that the transmitted reflection contains only noise, and the second hypothesis is that the transmitted reflection contains a reflection signal from the moving object, the waveform separation residual, and noise.

12. The MIMO radar system according to claim 11, wherein: The GLRT algorithm determines a first distribution under the first assumption and a second distribution under the second assumption, wherein the first distribution is a central F distribution, and wherein the second distribution is a non-central F distribution.

13. The MIMO radar system according to claim 12, wherein: The processor is further configured to: comparing the GLRT statistic to a predetermined threshold, wherein the predetermined threshold is based on the number of the transmitters and the receivers, wherein, when the GLRT statistic is greater than the predetermined threshold, the second hypothesis is true, and When the GLRT statistic is less than the predetermined threshold, the first hypothesis is true.

14. A vehicle comprising a controller for controlling movement of the vehicle, wherein: The controller is operatively connected to the output interface of the MIMO radar system of claim 1 and is configured to control movement of the vehicle based on parameters of detected objects.

15. A multiple-input multiple-output (MIMO) radar method for detecting moving objects, wherein: The MIMO radar method uses a processor coupled to a memory storing an explicit signal model that accounts for waveform separation residuals by correlating measurements of a virtual array with self-terms and cross-terms, the self-terms comprising Kronecker products of object-receiver signatures and transmitter-object signatures, and the cross-terms comprising Kronecker products of object-receiver signatures and transmitter-object residual signatures, wherein the transmitter-object signatures are a function of a relative angle between each transmitter in the set of transmitters and a detected object, a wavelength of the transmitted signal, and a relative distance between two consecutive transmitter elements in the set of transmitters, wherein the processor is coupled to stored instructions implementing the method, wherein the instructions, when executed by the processor, perform the steps of the MIMO radar method, the MIMO radar method comprising the steps of: receiving measurements of a set of transmitters and a set of receivers, the set of transmitters and the set of receivers forming a virtual array of unique pair-wise combinations of the transmitters and the receivers to measure reflections of the transmissions; detecting the moving object by executing a spatial MIMO detector configured to detect the moving object using the explicit signal model; and Outputs parameters associated with the detected objects.

Images