Patent Description:
<CIT> discloses a virtual radar configuration for a 2D array. AMIN <NPL>, relates to sparse arrays and sparse sampling in antijam global navigation satellite systems. <CIT> discloses systems and methods for interpolated virtual aperture radar tracking.

This document describes techniques and systems of a radar system with modified orthogonal linear antenna subarrays. Even with far fewer antenna elements than a traditional radar system, these modified subarrays enable an example radar system to have comparable angular resolution at a lower cost and lower complexity level. For example, a radar system includes a processor and an antenna that can receive electromagnetic energy reflected by one or more objects. The antenna includes a first one-dimensional (1D) (e.g., linear) subarray, a second 1D subarray, and a two-dimensional (2D) subarray. The second 1D subarray is positioned orthogonal to the first 1D subarray. The 2D subarray includes at least four antenna elements not encompassed by the first 1D subarray or the second 1D subarray. The processor can determine, using electromagnetic energy received by the first 1D subarray and the second 1D subarray, first and second angles associated with the one or more objects. The processor then associates, using electromagnetic energy received by the 2D subarray, the first angles and the second angles with respective objects of the one or more objects.

This document also describes methods performed by the above-summarized system and other configurations of the radar system set forth herein, as well as means for performing these methods.

This Summary introduces simplified concepts related to a radar system with modified orthogonal linear antenna subarrays, which are further described below in the Detailed Description and Drawings. This Summary is not intended to identify essential features of the claimed subject matter, nor is it intended for use in determining the scope of the claimed subject matter.

The details of one or more aspects of a radar system with modified orthogonal linear antenna subarrays are described in this document with reference to the following figures. The same numbers are often used throughout the drawings to reference like features and components:.

Radar systems are an important sensing technology that some automotive systems rely on to acquire information about the surrounding environment. Radar systems generally include at least two antennas to transmit and receive EM radiation. Some radar systems include a receive antenna with a two-dimensional (2D) planar array of antenna elements to measure both the azimuth angle and the elevation angle associated with objects. A large aperture in the azimuth direction and the elevation direction of the receive antenna can increase the number of antenna elements and the cost of the radar system.

Some radar systems include a receive antenna with a two-dimensional (2D) planar array of antenna elements to measure both the azimuth angle and the elevation angle of objects. In radar systems with a 2D planar antenna array, the radar system can estimate the angular position of objects using digital beamforming. In digital beamforming, the radar system characterizes the angular information of the object by analyzing the relative phase across the antenna elements of the 2D planar array using a 2D fast Fourier transform (FFT). The angular resolution of such radar systems generally depends on the aperture size of the 2D planar array. A larger aperture size can improve the angular resolution but requires additional antenna elements and increased costs.

Other radar systems include a receive antenna with two orthogonal linear arrays of antenna elements to occupy the azimuth direction and elevation direction of the antenna array. The radar system can use the azimuth linear array and the elevation linear array to measure the azimuth and elevation angles of objects, respectively. These radar systems use matching algorithms to associate the azimuth angle and elevation angle for each object. Although such systems generally include fewer antenna elements than planar 2D arrays, the angle finding for these systems is too complicated for many applications, including automotive applications. In particular, the radar systems use cross-correlation matrix-based methods that require multiple data snapshots from the linear array to associate a single set of angle measurements. Because automotive radar systems generate a single snapshot while a vehicle moves, such methods are inapplicable to automotive applications.

Some other radar systems with orthogonal linear arrays use frequency-modulated continuous-wave signals. These radar systems use a beam-matching method to associate an azimuth angle and an elevation angle. The beam-matching method converts the beam-matching problem to an image-patch matching problem in a range-Doppler domain. This method, however, can only work for applications where only a single object exists in any given range-Doppler bin. If two objects are in the same range-Doppler bin, these radar systems are generally unable to accurately pair the azimuth angle and elevation angle for the respective objects. This inability to accurately associate the azimuth angles and elevation angles restricts these radar systems from automotive radar applications in which multiple objects can often exist in the same range-Doppler bin.

In contrast, this document describes techniques and systems to provide a receive antenna with orthogonal one-dimensional (1D) subarrays and a 2D subarray, for supporting angle finding features. The radar system includes an antenna array with a first 1D subarray, a second 1D subarray, and a 2D subarray. The second 1D subarray is positioned orthogonal to the first 1D subarray. The 2D subarray includes at least four antenna elements not encompassed by the first or second 1D subarrays. In this way, the described systems and techniques can reduce the number of antenna elements while preserving the angular resolution that can otherwise be achieved using a rectangular 2D array with similar aperture sizing.

The radar system determines, using EM energy received by the first and second 1D subarrays, first and second angles, respectively, associated with one or more nearby objects. The radar system then associates, using EM energy received by the 2D subarray, the first and second angles with respective objects of the one or more objects. In this way, the computational complexity for the described radar system to associate the first angles and second angles to respective objects is similar to the computational complexity for a conventional radar system with conventional 2D planar arrays. The described angle-finding technique can be applied to various configurations of the described orthogonal 1D subarrays with a 2D subarray.

This is just one example of the described techniques and systems of a radar antenna with modified orthogonal linear arrays. This document describes other examples and implementations.

<FIG> illustrates an example environment <NUM> in which a radar system <NUM> with modified orthogonal linear antenna subarrays can be implemented. In the depicted environment <NUM>, the radar system <NUM> is mounted to, or integrated within, a vehicle <NUM>. The radar system <NUM> can detect one or more objects <NUM> that are in the vicinity of the vehicle <NUM>. Although illustrated as a car, the vehicle <NUM> can represent other types of motorized vehicles (e.g., a motorcycle, a bus, a tractor, a semi-trailer truck), non-motorized vehicles (e.g., a bicycle), railed vehicles (e.g., a train), watercraft (e.g., a boat), aircraft (e.g., an airplane), or spacecraft (e.g., satellite). In general, manufacturers can mount the radar system <NUM> to any moving platform, including moving machinery or robotic equipment.

In the depicted implementation, the radar system <NUM> is mounted on the front of the vehicle <NUM> and illuminates the object <NUM>. The radar system <NUM> can detect the object <NUM> from any exterior surface of the vehicle <NUM>. For example, vehicle manufacturers can integrate the radar system <NUM> into a bumper, side mirror, headlights, rear lights, or any other interior or exterior location where the object <NUM> requires detection. In some cases, the vehicle <NUM> includes multiple radar systems <NUM>, such as a first radar system <NUM> and a second radar system <NUM>, that provide a larger field-of-view. In general, vehicle manufacturers can design the locations of the one or more radar systems <NUM> to provide a particular field-of-view that encompasses a region of interest. Example fields-of-view include a <NUM>-degree field-of-view, one or more <NUM>-degree fields-of-view, one or more <NUM>-degree fields-of-view, and so forth, which can overlap or be combined into a field-of-view of a particular size.

The object <NUM> is composed of one or more materials that reflect radar signals. Depending on the application, the object <NUM> can represent a target of interest. In some cases, the object <NUM> can be a moving object (e.g., another vehicle) or a stationary object (e.g., a roadside sign).

The radar system <NUM> emits EM radiation by transmitting EM signals or waveforms via antenna elements. In the environment <NUM>, the radar system <NUM> can detect and track the object <NUM> by transmitting and receiving one or more radar signals. For example, the radar system <NUM> can transmit EM signals between <NUM> and <NUM> gigahertz (GHz), between <NUM> and <NUM>, or between approximately <NUM> and <NUM>.

The radar system <NUM> can include a transmitter <NUM> and at least one antenna <NUM> to transmit EM signals. The radar system <NUM> can also include a receiver <NUM> and the at least one antenna <NUM> to receive reflected versions of the EM signals. The transmitter <NUM> includes one or more components for emitting the EM signals. The receiver <NUM> includes one or more components for detecting the reflected EM signals. The transmitter <NUM> and the receiver <NUM> can be incorporated together on the same integrated circuit (e.g., a transceiver integrated circuit) or separately on different integrated circuits.

The radar system <NUM> also includes one or more processors <NUM> (e.g., an energy processing unit) and computer-readable storage media (CRM) <NUM>. The processor <NUM> can be a microprocessor or a system-on-chip. The processor <NUM> can execute instructions stored in the CRM <NUM>. For example, the processor <NUM> can process EM energy received by the antenna <NUM> and determine, using an angle-finding module <NUM>, a location of the object <NUM> relative to the radar system <NUM>. The processor <NUM> can also generate radar data for at least one automotive system. For example, the processor <NUM> can control, based on processed EM energy from the antenna <NUM>, an autonomous or semi-autonomous driving system of the vehicle <NUM>.

The angle-finding module <NUM> obtains EM energy received by the antenna <NUM> and determines azimuth angles and elevation angles associated with the object <NUM>. The angle-finding module <NUM> can be implemented as instructions in the CRM <NUM>, hardware, software, or a combination thereof that is executed by the processor <NUM>.

The radar system <NUM> can determine a distance to the object <NUM> based on the time it takes for the EM signals to travel from the radar system <NUM> to the object <NUM>, and from the object <NUM> back to the radar system <NUM>. The radar system <NUM> can also determine, using the angle-finding module <NUM>, a location of the object <NUM> in terms of an azimuth angle <NUM> and an elevation angle <NUM> based on the direction of a maximum-amplitude echo signal received by the radar system <NUM>.

As an example, <FIG> illustrates the vehicle <NUM> traveling on a road <NUM>. The radar system <NUM> detects the object <NUM> in front of the vehicle <NUM>. The radar system <NUM> can define a coordinate system with an x-axis <NUM> (e.g., in a forward direction along the road <NUM>), a y-axis <NUM> (e.g., perpendicular to the x-axis <NUM> and along a surface of the road <NUM>), and a z-axis <NUM> (e.g., perpendicular to the surface of the road <NUM>). The radar system <NUM> can locate the object <NUM> in terms of the azimuth angle <NUM> and the elevation angle <NUM>. The azimuth angle <NUM> can represent a horizontal angle from the x-axis <NUM> to the object <NUM>. The elevation angle <NUM> can represent a vertical angle from the surface of the road <NUM> (e.g., a plane defined by the x-axis <NUM> and the y-axis <NUM>) to the object <NUM>.

The vehicle <NUM> can also include at least one automotive system that relies on data from the radar system <NUM>, such as a driver-assistance system, an autonomous-driving system, or a semi-autonomous-driving system. The radar system <NUM> can include an interface to an automotive system that relies on the data. For example, the processor <NUM> outputs, via the interface, a signal based on EM energy received by the antenna <NUM>.

Generally, the automotive systems use radar data provided by the radar system <NUM> to perform a function. For example, the driver-assistance system can provide blind-spot monitoring and generate an alert that indicates a potential collision with the object <NUM> that is detected by the radar system <NUM>. In such an implementation, the radar data from the radar system <NUM> indicates when it is safe or unsafe to change lanes. The autonomous-driving system may move the vehicle <NUM> to a particular location on the road <NUM> while avoiding collisions with the object <NUM> detected by the radar system <NUM>. The radar data provided by the radar system <NUM> can provide information about a distance to and the location of the object <NUM> to enable the autonomous-driving system to perform emergency braking, perform a lane change, or adjust the speed of the vehicle <NUM>.

<FIG> illustrate example antennas <NUM> with modified orthogonal linear antenna subarrays. The antennas <NUM> are examples of the antenna <NUM> of the radar system <NUM> in <FIG>, with similar components. The antennas <NUM> include a first 1D subarray <NUM> (e.g., an azimuth subarray), a second 1D subarray <NUM> (e.g., an elevation subarray), and a 2D subarray <NUM> on a printed circuit board (PCB) <NUM>. In operation, the antennas <NUM> can receive EM energy reflected by one or more objects <NUM>.

In the depicted implementations, the first antenna subarray <NUM> is positioned in an azimuth direction and is hereinafter referred to as the azimuth subarray <NUM>. The second antenna subarray <NUM> is positioned in an elevation direction and is hereinafter referred to as the elevation subarray <NUM>. The elevation subarray <NUM> is positioned orthogonal to the azimuth subarray <NUM>. The azimuth subarray <NUM> and the elevation subarray <NUM> can be linear subarrays.

The azimuth subarray <NUM> and the elevation subarray <NUM> can be arranged in an approximately L shape, as illustrated in <FIG>, <FIG>; an approximately T shape, as illustrated in <FIG> and <FIG>; or an approximately cross shape, as illustrated in <FIG>. Radar designers or radar manufacturers can arrange the antenna elements of the azimuth subarray <NUM> and the elevation subarray <NUM> in other approximate shapes with the elevation subarray <NUM> positioned orthogonal to the azimuth subarray <NUM>.

The antenna elements <NUM> of the 2D subarray <NUM> can be arranged in an approximately rectangular shape, as illustrated in <FIG>. These antenna elements <NUM> can be positioned close to (e.g., as illustrated in <FIG>), overlapping with (e.g., as illustrated in <FIG>), or separated from (e.g., as illustrated in <FIG>) the azimuth subarray <NUM> and/or the elevation subarray <NUM>. The antenna elements <NUM> of the 2D subarray <NUM> can also be arranged in a two-dimensional sparse array, as illustrated in <FIG>. The specific arrangement of the azimuth subarray <NUM>, the elevation subarray <NUM>, and the 2D subarray <NUM> can be chosen based on the position and arrangement of other components in the radar system <NUM>.

The azimuth subarray <NUM>, the elevation subarray <NUM>, and the 2D subarray <NUM> include multiple antenna elements <NUM>. The azimuth subarray <NUM> can include M antenna elements <NUM>. The elevation subarray <NUM> can include N antenna elements <NUM>, where N is equal or not equal to M. The 2D subarray <NUM> can include P antenna elements <NUM> not encompassed by the azimuth subarray <NUM> or the elevation subarray <NUM>. In automotive applications, the number of antenna elements <NUM> in the 2D subarray <NUM> can be greater than an anticipated maximum number of objects <NUM> to be detected by the radar system <NUM>. The number of antenna elements <NUM> in the 2D subarray, P, is generally less than the product of M and N (e.g., P « M × N). In some implementations, P is less than half of the product of M and N (e. The total number of antenna elements <NUM> in the antenna <NUM> generally equals M + N + P - <NUM>, where one antenna element <NUM> is shared by the azimuth subarray <NUM> and the elevation subarray <NUM>. The number of antenna elements <NUM> in the antenna <NUM> (e.g., M + N + P - <NUM>) is generally much less than the number of antenna elements <NUM> in a rectangular array (e.g., M × N) with the same aperture sizing.

In the depicted implementations, the azimuth subarray <NUM> includes nine antenna elements <NUM>, the elevation subarray <NUM> includes eight antenna elements <NUM>, and the 2D subarray <NUM> includes six antenna elements <NUM> not encompassed by the azimuth subarray <NUM> or the elevation subarray <NUM>. The antennas <NUM> include <NUM> antenna elements <NUM>, much less than <NUM> antenna elements included in a rectangular array with the same aperture sizing. In other implementations, the azimuth subarray <NUM>, the elevation subarray <NUM>, or the 2D subarray <NUM> can include fewer or additional antenna elements <NUM>. The 2D subarray <NUM> generally includes at least four antenna elements <NUM> not encompassed by the azimuth subarray <NUM> or the elevation subarray <NUM>.

The antenna elements <NUM> in the azimuth subarray <NUM> and the 2D subarray <NUM> are separated by an azimuth distance <NUM>, dAZ. Similarly, the antenna elements <NUM> in the elevation subarray <NUM> and the 2D subarray <NUM> are separated by an elevation distance <NUM>, dEL. As described with respect to <FIG>, the angle-finding module <NUM> uses the azimuth distance <NUM> and the elevation distance <NUM> to associate an elevation angle to an azimuth angle for the object <NUM>.

The azimuth subarray <NUM>, the elevation subarray <NUM>, and the 2D subarray <NUM> can be planar arrays that provide high gain and low loss. Planar arrays are well-suited for vehicle integration due to their small size. For example, the antenna elements <NUM> can be slots etched or otherwise formed in a plating material of one surface of the PCB <NUM> for a substrate-integrated waveguide (SIW) antenna. The antenna elements <NUM> can also be part of an aperture antenna, a microstrip antenna, or a dipole antenna. For example, the azimuth subarray <NUM>, the elevation subarray <NUM>, and the 2D subarray <NUM> can include subarrays of patch elements (e. , microstrip patch antenna subarrays) or dipole elements.

<FIG> illustrates an example flow diagram <NUM> of the radar system <NUM> with modified orthogonal linear antenna subarrays and the angle-finding module <NUM>. The radar system <NUM> of <FIG> can, for example, be the radar system <NUM> of <FIG>. The radar system <NUM> includes two 1D subarrays positioned orthogonal to one another, along with a 2D subarray. In the depicted implementation, the radar system <NUM> includes the azimuth subarray <NUM>, the elevation subarray <NUM>, and the 2D subarray of antenna <NUM>, which can be arranged in a variety of positions, including the arrangements illustrated in <FIG>.

At <NUM>, the angle-finding module <NUM> obtains EM energy <NUM> received by the azimuth subarray <NUM> and determines azimuth angles <NUM> associated with one or more azimuth objects. The azimuth angles <NUM> include <MAT>, where NAZ represents the number of azimuth objects.

At <NUM>, the angle-finding module <NUM> obtains EM energy <NUM> received by the elevation subarray <NUM> and determines elevation angles <NUM> associated with one or more elevation objects. The elevation angles <NUM> include <MAT>, where NEL represents the number of elevation objects. Because two or more of the objects <NUM> can have the same azimuth angles <NUM> and/or the same elevation angles <NUM>, the number of elevation objects, NEL, can be different than the number of azimuth objects, NAZ. For example, the radar system <NUM> can detect three objects <NUM> (e.g., three vehicles in front of the vehicle <NUM>), each of which can have the same elevation angle <NUM> relative to the radar system <NUM> but different azimuth angles <NUM>. As a result, the angle-finding module <NUM> would identify one elevation object but three azimuth objects.

The angle-finding module <NUM> can use various angle-finding functions to determine the azimuth angles <NUM> and the elevation angles <NUM> from the EM energy <NUM> and the EM energy <NUM>, respectively. As non-limiting examples, the angle-finding module <NUM> can use a pseudo-spectrum function, including a Space-Alternating Generalized Expectation-maximization (SAGE), Delay-and-Sum (DS), Minimum Variance Distortionless Response (MVDR), and/or a Multiple Signal Classification (MUSIC) based-function, to calculate the direction of arrival of the EM signals received by the azimuth subarray <NUM> and the elevation subarray <NUM>. As another example, the angle-finding module can use an Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) technique or FFT beamforming to calculate the azimuth angles <NUM> and the elevation angles <NUM>. The angle-finding module <NUM> can determine the azimuth angles <NUM> and the elevation angles <NUM> with relatively low processing complexity and cost.

At <NUM>, the angle-finding module <NUM> associates, using EM energy <NUM> received by the 2D subarray <NUM>, the azimuth angles <NUM> and the elevation angles <NUM> to the objects <NUM>. In particular, the angle-finding module <NUM> determines the azimuth angle <NUM> and the elevation angle <NUM> associated with each of the one or more objects <NUM>. The association of the azimuth angles <NUM> to the elevation angles <NUM> is described in greater detail with respect to <FIG>.

<FIG> illustrates an example flow diagram <NUM> of the angle-finding module <NUM> to associate the azimuth angles <NUM> and the elevation angles <NUM> to respective objects <NUM>. The angle-finding module <NUM> of <FIG> can, for example, be the angle-finding module <NUM> of <FIG>. As described with respect to <FIG>, the angle-finding module <NUM> determines the azimuth angles <NUM> and the elevation angles <NUM> associated with the azimuth objects and the elevation objects, respectively.

At <NUM>, the angle-finding module <NUM> defines a coordinate system for the antenna elements <NUM> of the 2D subarray <NUM>. For example, the angle-finding module <NUM> can denote the coordinate of the most bottom-left antenna element <NUM> of the 2D subarray <NUM> in antenna <NUM>-<NUM> as (<NUM>, <NUM>). The coordinates of the other antenna elements <NUM> in the 2D subarray <NUM> can be denoted as <MAT>, where K represents the total number of antenna elements <NUM> in the 2D subarray and <MAT> and <MAT> represents the azimuth distance <NUM> and the elevation distance <NUM> from the ith antenna element <NUM> to the most bottom-left antenna element <NUM>, respectively.

At <NUM>, the angle-finding module <NUM> generates, using the coordinate system, a dictionary matrix <NUM> of steering vectors that include each of the azimuth angles <NUM> paired with each of the elevation angles <NUM>. If a pair of an azimuth angle <NUM> and an elevation angle <NUM> of a point scatterer is given as (θ, φ), the angle-finding module <NUM> can generate a K × <NUM> steering vector: <MAT> where λ represents the wavelength of the EM signal transmitted and received by the radar system <NUM>.

The angle-finding module <NUM> can use the azimuth angles <NUM>, θ<NUM>,θ<NUM>,···,θNAZ, and the elevation angles <NUM>, φ<NUM>, φ<NUM>, ···,φNEL to form NAZNEL angle pairs. The angles of the objects <NUM> are included within the NAzNEL angle pairs.

For each angle pair (θu, φv), where u ∈ {<NUM>,<NUM>,. , NAZ} and v ∈ {<NUM>, <NUM>,. , NEL}, the angle-finding module <NUM> can define a steering vector for the 2D subarray <NUM> as: <MAT>.

The angle-finding module <NUM> can assemble the steering vectors for the angle pairs into the K × NAZNEL dictionary matrix <NUM>: <MAT>.

At <NUM>, the angle-finding module <NUM> determines, using an L1-minimization based-function and the EM energy <NUM> received by the 2D subarray <NUM>, non-zero elements in a selection vector. The non-zero elements in the selection vector represent actual angle pairs <NUM> of the dictionary matrix <NUM> that correspond to the azimuth angle <NUM> and the elevation angle <NUM> of the respective objects <NUM>.

Because the actual pairs <NUM> of the objects <NUM> should be within the NAzNEL angle pairs, the angle-finding module <NUM> can use the following equation to identify the actual pairs <NUM>: <MAT> where the K × <NUM> vector y represents the measured beam vector of the EM energy <NUM> received by the 2D subarray <NUM>, the NAzNEL × <NUM> vector x represents a parse vector, and the K × <NUM> vector η represents measurement noise. The angle-finding module <NUM> considers x as the selection vector. The steering vectors in A corresponding to the non-zero elements in x represent the actual pairs <NUM>.

The angle-finding module <NUM> can solve for the x in Equation (<NUM>) by solving the following L1-minimization: <MAT> where ε bounds the amount of noise in the data. The angle-finding module <NUM> can solve Equation (<NUM>) using, for example, an Orthogonal Matching Pursuit (OMP) based-function.

<FIG> illustrates an example method <NUM> of the radar system <NUM> with modified orthogonal linear antenna subarrays and the angle-finding module <NUM>. Method <NUM> is shown as sets of operations (or acts) performed, but not necessarily limited to the order or combinations in which the operations are shown herein. Further, any of one or more of the operations may be repeated, combined, or reorganized to provide other methods. In portions of the following discussion, reference may be made to the environment <NUM> of <FIG>, and entities detailed in <FIG>, reference to which is made for example only. The techniques are not limited to performance by one entity or multiple entities, but only by the subject matter of the appended claims.

At <NUM>, an antenna of a radar system receives EM energy reflected by one or more objects. For example, the antenna <NUM> of the radar system <NUM> can receive EM energy reflected by the one or more objects <NUM>.

At <NUM>, first angles associated with one or more first objects are determined using EM energy received by a first 1D subarray of the antenna. The one or more first objects are a first subset of the one or more objects. For example, the processor <NUM> of the radar system <NUM> can determine, using the angle-finding module <NUM> and the EM energy <NUM> received by the azimuth subarray <NUM>, the azimuth angles <NUM> associated with one or more azimuth objects. The one or more azimuth objects are a first subset of the one or more objects <NUM>.

At <NUM>, second angles associated with one or more second objects are determined using EM energy received by a second 1D subarray of the antenna. The one or more second objects are a second subset of the one or more objects. The second 1D subarray is positioned orthogonal to the first 1D subarray. For example, the processor <NUM> can determine, using the angle-finding module <NUM> and the EM energy <NUM> received by the elevation subarray <NUM>, the elevation angles <NUM> associated with one or more elevation objects. The one or more elevation objects are a second subset of the one or more objects <NUM>. The elevation subarray <NUM> is positioned orthogonal to the azimuth subarray <NUM>.

Claim 1:
A radar system (<NUM>) comprising:
an antenna (<NUM>, <NUM>-<NUM>, <NUM>-<NUM>, <NUM>-<NUM>, <NUM>-<NUM>, <NUM>-<NUM>, <NUM>-<NUM>) configured to receive electromagnetic energy reflected by one or more objects, the antenna (<NUM>, <NUM>-<NUM>, <NUM>-<NUM>, <NUM>-<NUM>, <NUM>-<NUM>, <NUM>-<NUM>, <NUM>-<NUM>) comprising:
a first one-dimensional subarray (<NUM>);
a second one-dimensional subarray (<NUM>) positioned orthogonal to the first one-dimensional subarray (<NUM>); and
a two-dimensional subarray (<NUM>) comprising at least four antenna elements (<NUM>) not encompassed by the first one-dimensional subarray (<NUM>) or the second one-dimensional subarray (<NUM>); and
one or more processors (<NUM>) configured to:
determine, using the electromagnetic energy (<NUM>) received by the first one-dimensional subarray (<NUM>), first angles (<NUM>) associated with one or more first objects, the one or more first objects comprising a first subset of the one or more objects;
determine, using the electromagnetic energy (<NUM>) received by the second one-dimensional subarray (<NUM>), second angles (<NUM>) associated with one or more second objects, the one or more second objects comprising a second subset of the one or more objects; and
associate, using the electromagnetic energy (<NUM>) received by the two-dimensional subarray (<NUM>), the first angles (<NUM>) and the second angles (<NUM>) with respective objects of the one or more objects by:
defining a coordinate system for the antenna elements (<NUM>) of the two-dimensional subarray (<NUM>);
generating, using the coordinate system, a dictionary matrix (<NUM>) of steering vectors that include each of the first angles (<NUM>) paired with each of the second angles (<NUM>); and
determining, using an L1-minimization based-function and the electromagnetic energy received by the two-dimensional subarray (<NUM>), non-zero elements in a selection vector, the non-zero elements in the selection vector representing pairs of the first angle and the second angle in the dictionary matrix (<NUM>) that correspond to the first angles (<NUM>) and the second angles (<NUM>) of the respective objects of the one or more objects.