Systems and methods for multipath beam nulling
By determining digital beamforming weights to null multipath interference, the radar system enhances tracking accuracy and resource allocation, reducing false targets and improving combat discrimination.
Patent Information
- Application Number
- JP2022535075
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- Priority Date
- 2019-12-10
- Filing Date
- 2020-10-09
- Publication Date
- 2026-01-16
- Estimated Expiration
- 2040-10-09
AI Technical Summary
Radar systems suffer from multipath interference, leading to erroneous object detection, increased signal-to-noise ratio fluctuations, and inefficient resource allocation due to ghost targets and misidentification of objects, which can compromise combat systems.
A method and system that determine digital beamforming weights to form nulls in the direction of multipath interference, using a radar system's processor to apply these weights during reception, thereby eliminating or reducing multipath interference.
Improves tracking accuracy, continuity, and resource allocation by eliminating or substantially eliminating multipath interference, leading to more stable radar measurements and reduced false targets.
Smart Images

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Abstract
Description
[Technical Field]
[0001]
[0000] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Patent Application No. 16 / 708,478, filed December 10, 2019, which is incorporated herein by reference.
[0002] FIELD OF THE INVENTION The present invention relates generally to radar systems and, more particularly, to reducing multipath interference in radar systems. [Background technology]
[0003]
[0002] Radar systems (such as radars) can be used to detect objects. For example, radar systems may be used on aircraft, ships, and / or ground vehicles to detect objects. For each of the various radar applications (e.g., ground, air, maritime, military, commercial, etc.), radar systems may have different requirements and constraints. Typical radar requirements may include the ability to detect objects within a particular field of view, range, and / or altitude with a particular accuracy and / or sensitivity.
[0004]
[0003] A radar system typically includes an emitter and a receiver. The emitter allows electromagnetic waves (e.g., a beam) to be transmitted from the radar system, sometimes in a particular direction. The electromagnetic waves may strike an object, which may reflect at least a portion of the electromagnetic waves back toward the radar system and be received by the receiver.
[0005] One problem with radar systems involves multipath interference. Multipath interference can occur when an emitted electromagnetic signal reflects off objects while propagating toward and / or away from an object of interest (e.g., a desired detection target). For example, ground, mountains, buildings, and / or bodies of water. The electromagnetic signal can reflect back toward the radar system from the interfering object, causing erroneous object detection with an incorrect angle of arrival (e.g., ghost detection) and can also interfere with the detected angle of arrival of the desired target signal. Multipath returns can also increase the apparent length of the target, resulting in misidentification of the target (e.g., combat). For example, a cruise missile may be misclassified as an aircraft, which could alter the object's predicted lethality. Incorrect lethality of the object can cause a combat system receiving instructions from the radar system to improperly shoot down or fail to shoot down the target.
[0006]
[0005] False targets can divert radar resources from the desired mission and / or increase the number of tracks maintained by the radar system, which can delay radar processing time. Multipath can also increase or decrease the signal-to-noise ratio, which can contribute to the likelihood of a track being dropped. Falsely dropping a track can typically cause the radar to redetect the object, which can result in an artificially high number of track changes, which can further impact radar resources, for example, due to reacquiring / initiation of a new track.
[0007]
[0006] Therefore, it is desirable to reduce multipath interference signals in radar systems. Summary of the Invention
[0008] Advantages of the present invention may include the elimination and / or substantial elimination of multipath interference. Other advantages of the present invention may include improvements to tracking accuracy, tracking continuity, combat discrimination, and / or improved radar resource allocation.
[0009] In one aspect, the present invention includes a method for reducing multipath interference. The method may include a radar system determining a first set of digital beamforming weights based on desired directions of one or more analog beams of the radar system, desired directions of one or more digital beams, and an expected direction of a multipath interference signal. The method may also include the radar system determining a second set of digital beamforming weights based on the first set of digital beamforming weights to form nulls in each of the one or more digital beams in the direction of the multipath interference signal. The method may also include the radar system applying the second set of digital beamforming weights during a receive period of the radar system, such that signals received by the radar system are devoid of the multipath interference signal.
[0010] In some embodiments, determining the first set of digital beamforming weights further includes the radar system determining an elevation angle of the multipath interfering signal. In some embodiments, determining the first set of digital beamforming weights further includes determining a position of the multipath interfering signal.
[0011]
[0010] In some embodiments, the method includes the steps of: a radar system determining a position of a target based on multiple reflected signals; a radar system determining a distance between a position of the multipath interference signal and a position of the target; and, if the distance is less than a minimum distance, setting the position of the multipath interference signal to the minimum distance value.
[0012]
[0011] In some embodiments, the step of determining the second set of digital beamforming weights further includes: the radar system determining a first voltage of each digital beam of the radar system in the direction of the multipath interference signal; and the radar system determining a second voltage of a nulling digital beam of the radar system in the direction in which the null is to be formed.
[0013] In some embodiments, the first voltage, the second voltage, or both are complex numbers. In some embodiments, the radar system is a digital beamforming radar. In some embodiments, the method further includes the radar system outputting signals received by the radar system to a display.
[0014] In another aspect, the present invention includes a radar system that reduces multipath interference. The radar system includes one or more antenna arrays, each including a plurality of antennas capable of transmitting and receiving electromagnetic signals. The radar system can include a processor coupled to the one or more antenna arrays. The processor can be configured to control the one or more antenna arrays to: determine a first set of digital beamforming weights based on desired directions of one or more analog beams of the radar system, desired directions of one or more digital beams, and a predicted direction of a multipath interference signal; determine a second set of digital beamforming weights based on the first set of digital beamforming weights to form nulls in each of the one or more digital beams in the direction of the multipath interference signal; and apply the second set of digital beamforming weights during a receive period of the radar system, such that signals received by the radar system are devoid of the multipath interference signal.
[0015]
[0014] The radar system may include determining a first set of digital beamforming weights, the step further including the radar system determining an elevation angle of the multipath interference signal. The radar system may include determining the first set of digital beamforming weights, the step further including determining a position of the multipath interference signal. The processor may be further configured to cause the radar system to perform the steps of: determining a position of a target based on the plurality of reflected signals; determining a distance between the position of the multipath interference signal and a position of the target; and, if the distance is less than a minimum distance, setting the position of the multipath interference signal to the minimum distance value.
[0016]
[0015] In some embodiments, the processor may be further configured to cause the radar system to perform: determining a first voltage of each digital beam of the radar system in the direction of the multipath interference signal; and determining a second voltage of a nulling digital beam of the radar system in the direction forming the null.
[0017] In some embodiments, the first voltage, the second voltage, or both are complex numbers. In some embodiments, the radar system is a digital beamforming radar. In some embodiments, the radar system further outputs signals received by the radar system to a display.
[0018]
[0017] In another aspect, the invention includes a computer program product including instructions that, when executed, cause a computer to perform the steps of: determining a first set of digital beamforming weights based on a desired direction of one or more analog beams of the radar system, a desired direction of one or more digital beams, and a predicted direction of a multipath interference signal; determining a second set of digital beamforming weights based on the first set of digital beamforming weights so as to form a null in each of the one or more digital beams in the direction of the multipath interference signal; and applying the second set of digital beamforming weights during a reception period of the radar system, so that signals received by the radar system are devoid of the multipath interference signal. [Brief explanation of the drawings]
[0019]
[0018] Non-limiting examples of embodiments of the present disclosure are described below with reference to the accompanying drawings, which are listed following this paragraph. Dimensions of features shown in the drawings have been chosen for convenience and clarity of presentation and are not necessarily drawn to scale.
[0020]
[0019] The subject matter grasped as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification. However, the invention, both as to organization and method of operation, together with its objects, features, and advantages, may be understood by reference to the following detailed description when read in conjunction with the accompanying drawings. Embodiments of the invention are illustrated by way of example and not limitation in the figures of the accompanying drawings, in which like reference numerals indicate corresponding, similar, or similar elements. [Figure 1] FIG. 1 is an example of a radar system and an object according to some embodiments of the present invention. [Figure 2]
[0021] FIG. 2 is a flow chart for a method of reducing multipath interference according to some embodiments of the present invention. [Figure 3]
[0022] Figure 3 is a graph showing the output of a prior art radar system that does not mitigate multipath interference. [Figure 4]
[0023] FIG. 4 is a graph illustrating the output of the radar system of FIG. 4 in accordance with some embodiments of the present invention that reduce multipath interference. [Figure 5]
[0024] FIG. 5 is a high-level block diagram of an exemplary computing device that can be used with some embodiments of the present invention.
[0025] It will be understood that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn accurately or to scale. For example, the dimensions of some of the elements may be exaggerated relative to other elements for clarity, or several physical components may be included in one functional block or element. DETAILED DESCRIPTION OF THE INVENTION
[0021]
[0026] In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be understood by those skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known methods, procedures, and components, modules, units, and / or circuits have not been described in detail so as not to obscure the present invention.
[0022]
[0027] Generally, the present invention involves reducing multipath interference in radar systems and / or improving the detection accuracy of radar systems. Radar systems spend part of their operation emitting electromagnetic energy (e.g., signals) and part of their operation receiving (e.g., listening) electromagnetic energy. The emitted electromagnetic energy may strike one or more objects, and at least some of the emitted electromagnetic energy may reflect back to the radar system. In some scenarios, at least some of the reflected electromagnetic energy may be multipath interference (e.g., reflections arising from objects in the radar system's field of view that are not being tracked, such as buildings and / or the ground).
[0023]
[0028] During reception, the radar system can place a null in the direction (or approximately the direction) of the multipath interference, so that the multipath interference can be eliminated and / or substantially eliminated. By determining the direction from which the multipath interference may arrive at the radar system, the multipath interference can be nulled so that its effect on the radar system can be reduced.
[0024]
[0029] 1 illustrates an example of a radar system 100 and an object 110 according to some embodiments of the present invention. The radar system 100 may emit electromagnetic energy (e.g., a transmitted signal). When the transmitted signal strikes an object 110 or 120, at least a portion of the transmitted signal may reflect off the object 110 or 120 (e.g., a mountain) and be received by the radar system 100, which may result in the radar system 100 detecting an incorrect object in the direction of the object 120.
[0025]
[0030] The radar system 100 may include one or more arrays, as known in the art, to perform analog and / or digital beamforming. In the case of analog beam steering, the radar system 100 may have an emitter / receiver that includes a phase shifter for steering the analog beam, for example. The radar system's arrays may be grouped into subarrays, and each element may be referenced by its position within a particular subarray. The element position may be referred to as the element position, x(m,n) and y(m,n), of element m in subarray n. For example, in subarray 3, element 2 may have a position of (2,3).
[0026]
[0031] The radar system 100 can be directed to a target location using analog beam steering. Analog beam steering can direct the radar system toward the target location (e.g., the direction of the radar system's analog beam) and potentially receive one or more reflected signals. The reflected signals can include a portion reflected from the target along a first path (e.g., the direct receive path) and a portion due to multipath interference along a second path (e.g., the indirect receive path). The target location can be defined in a range, azimuth, and elevation coordinate system, or a uv coordinate system, as known in the art. For example, the target location can also be transformed from a uv coordinate system or range, azimuth, and elevation to a sinusoidal space representation, as known in the art.
[0027]
[0032] In some embodiments, the target location is determined by distance (R), azimuth (Θ az ) and elevation angle (Θ el ) can be defined as a coordinate system. az , Θ el ) targets in sine space (u RX , vrx ) can be converted to
[0028]
[0033] In some embodiments, the multipath interference location is determined by the distance (R mp ), azimuth (Θ az_mp ), and elevation angle (Θ el_mp ) coordinate system. (R, Θ az_mp , Θ el_mp The location of the multipath interference in the sine space (u mp , v mp ) can be converted to
[0029]
[0034] In some embodiments, the multipath interference signal is assumed to have the same range and azimuth angle as the target, and only the elevation angle of the multipath interference signal is determined.
[0030]
[0035] In some embodiments, the elevation angle (θ EL R ) is determined as follows: i) Determine the height (h2) of the target above the spherical ground. The height (h2) above the spherical ground can be determined as follows:
[0031]
number
[0032] ii) Determine the ground distance from the radar system to the ground reflection point (G1). The ground distance (G1) can be determined as follows:
[0033]
number
[0034]
number
[0035]
number
[0036]
number
[0037]
number
[0038] In some embodiments, the multipath interference signal is determined as known in the art.
[0039] FIG. 2 is a flowchart of a method for reducing multipath interference in accordance with an exemplary embodiment of the present invention.
[0040] The method may include a radar system (e.g., radar system 100 as described above in FIG. 1) determining a first set of digital beamforming weights based on desired directions of one or more analog beams and / or desired directions of one or more digital beams of the radar system (step 220). The desired directions of the analog beams may be based on a field of view the radar system is intended to cover, a desired direction of a target, user input, or any combination thereof. The desired directions of the one or more digital beams may be related to the desired directions of one or more analog beams of the radar system.
[0041]
[0040] The first set of digital beamforming weights may be determined as follows:
[0042]
number
[0043] The method may also include determining an expected direction of the multipath interference signal relative to a desired direction of one or more analog beams of the radar system (step 220). The expected direction of the multipath interference signal may be determined as described in EQNs 1 through 7 above.
[0044]
[0042] The method may also include a step of determining a second set of digital beamforming weights based on the first set of digital beamforming weights so as to create a null in each of one or more digital beams in the direction of the multipath reflected signal (step 230).
[0045] Determining the second set of digital beamforming weights may include determining a set of beam weights to create a null in a predicted direction of multipath. For example, the beam weights in the predicted null direction may be determined as follows:
[0046]
number
[0047] The sinusoidal spatial position of the null beam can be determined as follows: u null = u mp -u rx EQN. 10 v null = v mp -v rx EQN. 11 where u mp and v mp is the sinusoidal spatial position of the multipath interference received signal, and u rx and v rx is the sinusoidal spatial location of the received signal based on analog beam steering directed to the target location. In some embodiments, if the distance between the target location and the null location is less than a minimum distance (minimumNullSeperation), the sinusoidal spatial location of the null beam can be modified to be separated from the target location. The minimum distance can be an input value. The minimum distance is the minimum separation between the null location and the target location that ensures that nulling (or nulling) the multipath will at least substantially avoid nulling the receive beam from the target. The distance between the target location and the null location (d null ) can be determined as follows:
[0048]
number
[0049] In some embodiments, determining the second set of digital beamforming weights is performed by determining whether the pointing direction of the analog beam is u rx , v rx , the direction in which the null is generated (e.g., u null , v null In the direction of , each digital beam m(V MLE ) for each digital beam m(V MLE ) can be determined as follows: a) Per-element phase determination for analog beam steering:
[0050]
number
[0051] b) Apply weights to the phases per element for analog beam steering as follows:
[0052]
number
[0053]
number
[0054]
number
[0055]
number
[0056]
[0049] The method may also include the radar system outputting the signals received by the radar system to a display (step 250).
[0057]
[0050] Figure 3 is a graph showing the output of a prior art radar system without multipath interference mitigation. In Figure 3, the radar system is tracking an aircraft at an altitude of 200 meters. Figure 4 is a graph showing the output of the radar system of Figure 3 in accordance with some embodiments of the present invention that reduce multipath interference. As can be seen from Figure 4, reducing multipath interference as described by embodiments of the present invention can result in more stable measurements.
[0058] 5 is a high-level block diagram of an exemplary computing device that can be used with embodiments of the present invention. Computing device 300 can include a controller or processor 105, which can be or include, for example, one or more central processing unit processors (CPUs), one or more graphics processing units (GPUs or GPGPUs), a chip, or any suitable arithmetic or computational device, an operating system 315, memory 320, storage 330, input devices 335, and output devices 340. Each of the modules and devices, such as the processors, modules, boards, integrated circuits, and other devices mentioned herein, can be or include a computing device such as that included in FIG. 2, although various units of these entities can be combined into a single computing device.
[0059] Operating system 315 may be or include any code segments designed and / or configured to perform tasks, including coordinating, scheduling, arbitrating, monitoring, controlling, or otherwise managing the operation of computing device 800, such as, for example, scheduling program execution. Memory 320 may be or include, for example, random access memory (RAM), read-only memory (ROM), dynamic RAM (DRAM), synchronous DRAM (SD-RAM), double data rate (DDR) memory chips, flash memory, volatile memory, nonvolatile memory, cache memory, buffers, short-term memory units, long-term memory units, or other suitable memory or storage units. Memory 320 may be or include multiple, possibly different, memory units. Memory 320 may store, for example, instructions for performing methods (e.g., code 325) and / or data such as user responses, interrupts, etc.
[0060] Executable code 325 may be any executable code, such as, for example, an application, a program, a process, a task, or a script. Executable code 325 may be executed by controller 305, perhaps under the control of operating system 315. For example, executable code 325, when executed, causes an antenna to transmit radiation and / or receive radiation for processing according to embodiments of the present invention. In some embodiments, multiple computing devices 300 or device 300 components may be used for multiple functions described herein. One or more computing devices 300 or computing device 300 components may be used for the various modules and functions described herein. Devices including components similar or different to those included in computing device 300 may be used, and may be connected to a network and used as a system. One or more processors 305 may be configured to perform embodiments of the present invention, for example, by executing software or code. Storage 330 may be or may include, for example, a hard disk drive, a floppy disk drive, a compact disk (CD) drive, a recordable CD (CD-R) drive, a universal serial bus (USB) device, or other suitable removable and / or fixed storage unit. Data such as instructions, code, NN model data, parameters, etc. may be stored in storage 330 and loaded from storage 330 into memory 320, where it may be processed by controller 305. In some embodiments, some of the components shown in FIG. 2 may be omitted.
[0061] Input device(s) 335 may be or may include, for example, a mouse, a keyboard, a touch screen or pad, or any suitable input device. It will be appreciated that any suitable number of input devices may be operably connected to computing device 300, as indicated by block 335. Output device(s) 340 may include one or more displays, speakers, and / or any other suitable output device. It will be appreciated that any suitable number of output devices may be operably connected to computing device 300, as indicated by block 340. Any applicable input / output (I / O) devices may be connected to computing device 300, and for example, a wired or wireless network interface card (NIC), a modem, a printer or facsimile machine, a universal serial bus (USB) device, or an external hard drive may be included in input device(s) 335 and / or output device(s) 340.
[0062]
[0055] Embodiments of the present invention may include one or more articles of manufacture (e.g., memory 320 or storage 330) such as a computer or processor non-transitory readable medium or a computer or processor non-transitory storage medium, e.g., a memory, a disk drive, or a USB flash memory, that encode, contain, or store instructions, or may include a computer or processor non-transitory storage medium such as a memory, a disk drive, or a USB flash memory, that encodes or stores instructions, e.g., computer-executable instructions, that, when executed by a processor or controller, perform the methods disclosed herein.
[0063]
[0056] Those skilled in the art will appreciate that the present invention can be embodied in other specific forms without departing from its spirit or essential characteristics. Accordingly, the foregoing embodiments are to be considered in all respects as illustrative rather than limiting the invention described herein. The scope of the present invention is, therefore, indicated by the appended claims, rather than by the foregoing description, and all changes that come within the meaning and range of equivalence of the claims are therefore intended to be embraced therein.
[0064]
[0057] In the foregoing detailed description, numerous specific details are set forth to provide an understanding of the invention. However, those skilled in the art will understand that the invention can be practiced without these specific details. In other instances, well-known methods, procedures, and components, modules, units, and / or circuits have not been described in detail so as not to obscure the invention. Some features or elements described with respect to one embodiment can be combined with features or elements described with respect to other embodiments.
[0065]
[0058] Although embodiments of the invention are not limited in this respect, for example, discussions using terms such as "processing," "operating," "calculating," "determining," "determining," "analyzing," "checking," etc. may refer to operations and / or processes of a computer, computing platform, computing system, or other electronic computing device that process and / or transform data represented as physical (e.g., electronic) quantities in the computer's registers and / or memory into other data similarly represented as physical quantities in the computer's registers and / or memory or other non-transitory storage medium of information (capable of storing instructions that perform operations and / or processes).
[0066]
[0059] Although embodiments of the present invention are not limited in this respect, the terms "plurality" and "multiple" as used herein can include, for example, "multiple" or "two or more." The terms "plurality" or "multiple" can be used throughout the specification to describe two or more components, devices, elements, units, parameters, etc. The term set, when used herein, can include one or more items. Unless explicitly stated, method embodiments described herein are not constrained to a particular order or sequence. Furthermore, some of the described method embodiments or elements thereof can occur or be performed simultaneously, at the same time, or together.
Claims
1. 1. A method for reducing multipath interference, comprising: determining, by the radar system, a first set of digital beamforming weights based on desired directions of one or more analog beams and desired directions of one or more digital beams of the radar system; determining, by the radar system based on the first set of digital beamforming weights, a second set of digital beamforming weights so as to form nulls in each of the one or more digital beams in a uv sinusoidal space in the direction of a multipath interference signal; and applying the second set of digital beamforming weights by the radar system during a receive period of the radar system, so that the signal received by the radar system is devoid of the multipath interfering signal; and wherein determining the second set of digital beamforming weights comprises: the radar system determining, for each digital beam corresponding to each element of a subarray of the radar system, a first complex voltage expected in the direction of the multipath interference signal; and the radar system determining a second complex voltage predicted for a nulling digital beam, the peak digital beam in each null-forming direction; wherein the second set is determined by modifying the first set based on the first complex voltage, the second complex voltage, and a beam weight in a predicted null direction.
2. 10. The method of claim 1, wherein determining the first set of digital beamforming weights further comprises the radar system determining an elevation angle of the multipath interference signal.
3. 2. The method of claim 1, wherein determining the first set of digital beamforming weights further comprises determining a location of the multipath interference signal in the uv sinusoidal space.
4. 4. The method of claim 3, wherein: the radar system determining a location of the target based on the plurality of reflected signals; the radar system determining the distance between the location of the multipath interference signal and the location of the target; and if the distance is less than a minimum distance value, setting the location of the multipath interference signal to the minimum distance value; The method further comprises:
5. 10. The method of claim 1, further comprising the step of the radar system outputting signals received by the radar system to a display.
6. 1. A radar system for reducing multipath interference, comprising: one or more antenna arrays; and a processor coupled to the one or more antenna arrays, each antenna array including a plurality of antennas configured to transmit and receive electromagnetic signals, the processor controlling the one or more antenna arrays to: determining a first set of digital beamforming weights based on desired directions of one or more analog beams and desired directions of one or more digital beams of the radar system; determining a second set of digital beamforming weights based on the first set of digital beamforming weights to form a null in each of the one or more digital beams in a uv sinusoidal space in a direction of a multipath interference signal; and applying the second set of digital beamforming weights during a receive period of the radar system, so that the signal received by the radar system is devoid of the multipath interfering signal; wherein the processor is configured to: determining, for each digital beam corresponding to each element of a subarray of the radar system, a first complex voltage expected in the direction of the multipath interference signal; and determining a second complex voltage predicted for a nulling digital beam, the peak digital beam in the direction forming each null; wherein the second set is determined by modifying the first set based on the first complex voltage, the second complex voltage, and a beam weight in a predicted null direction.
7. 7. The radar system of claim 6, wherein to determine the first set of digital beamforming weights, the processor is configured to determine an elevation angle of the multipath interference signal.
8. 7. The radar system of claim 6, wherein to determine the first set of digital beamforming weights, the processor is configured to determine a position of the multipath interference signal in the uv sinusoidal space.
9. 10. The radar system of claim 8, wherein the processor provides the radar system with: determining a location of the target based on the plurality of reflected signals; determining the distance between the location of the multipath interference signal and the location of the target; and if the distance is less than a minimum distance value, setting the location of the multipath interference signal to the minimum distance value; The radar system is further configured to:
10. 7. The radar system of claim 6, wherein the processor is further configured to output signals received by the radar system to a display.
11. A computer program comprising instructions that, when executed, cause a computer of a radar system to: determining a first set of digital beamforming weights based on desired directions of one or more analog beams and desired directions of one or more digital beams of the radar system; determining a second set of digital beamforming weights based on the first set of digital beamforming weights to form a null in each of the one or more digital beams in a uv sinusoidal space in a direction of a multipath interference signal; and applying the second set of digital beamforming weights during a receive period of the radar system, so that the signal received by the radar system is devoid of the multipath interfering signal; wherein the instructions, when executed, cause the computer to perform the step of determining the second set of digital beamforming weights, determining, for each digital beam corresponding to each element of a subarray of the radar system, a first complex voltage expected in the direction of the multipath interference signal; and determining a second complex voltage predicted for a nulling digital beam, the peak digital beam in the direction forming each null; wherein the second set is determined by modifying the first set based on the first complex voltage, the second complex voltage, and a beam weight in a predicted null direction.
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