Optimization method for sparse arrays used in MIMO radar

Abstract

A method for designing a sparse MIMO virtual antenna array is disclosed. The method includes: determining the size of an equivalent uniform linear array (ULA) based on a target number of sparse elements of the sparse MIMO virtual antenna array; setting a first optimization target as the maximum signal level of one or more side lobes of the ULA when the beam is directed towards a boresight; setting a second optimization target as the maximum signal level of one or more side lobes of the ULA when the beam is directed towards the edge of the field of view; determining a set of separation distances between antenna array elements of the sparse MIMO virtual antenna array, and simultaneously minimizing the first and second optimization targets simultaneously, or minimizing the sum of the first and second optimization targets; and constructing a sparse MIMO virtual antenna array based on the determined set of separation distances.

Description

[Technical Field]

[0001] The present invention relates to a method for optimizing an antenna array with reduced element count and optimized performance for use in MIMO radar systems. [Background technology]

[0002] With autonomous vehicle research progressing in many countries and over 1.2 billion cars in the world, it's clear to stakeholders, including governments and private companies, that autonomous transportation represents a huge emerging market. However, for autonomous transportation to become a reality, high-performance, reliable, and affordable sensor systems are needed. Technologies such as radar, lidar, ultrasound, and camera arrays are all being used, each with its own advantages, but none are currently suitable for widespread implementation in complex fully autonomous driving scenarios (such as driving in congested city streets) due to insufficient resolution, sensitivity, all-weather capability, or affordability. Radar technology, however, offers an inexpensive solution to most of these problems, with the exception of angular resolution and sensitivity. Both angular resolution and sensitivity can be improved, but at a higher cost.

[0003] The angular resolution or beamwidth of the antenna array aperture is given by the following formula.

number

[0004] Therefore, in conventional radar systems, improving spatial resolution requires a larger antenna array as the number of antenna elements and associated hardware increases. However, increasing the antenna array aperture size to achieve improved spatial resolution makes it very expensive, especially in applications like automotive radar, because it requires a large number of receivers. When low angular resolution is required, a wide beam is sufficient, and this can be achieved using a small antenna array aperture with fewer antenna elements. When high angular resolution is required, a narrower beam is needed, necessitating the use of a larger antenna array aperture with additional elements. This requires additional receivers, increasing the overall radar cost and size. In other words, in applications where low cost is required (such as automotive radar), conventional architectures are limited to a minimum number of elements, i.e., a wide beamwidth. However, the general rule generally applies: the higher the angular resolution, the more antenna elements are required. Conversely, Multiple-Input Multiple-Output (MIMO) radar can mitigate this cost increase to some extent.

[0005] MIMO radar is a type of phased array radar that uses distributed transmitters and receivers to improve spatial resolution and range compared to conventional monostatic radar with an equivalent total number of transmit and receive channels. There are mainly two types of MIMO radar. One is statistical MIMO, which places antennas far apart from each other to provide different "views" of the "scene," and the other is beamforming MIMO, which places antennas close together to work together to form a larger, "virtual," beamforming array.

[0006] Beamforming methods, similar to those used in conventional radar systems and formed by digital post-processing in MIMO systems, utilize wave coherence to manipulate a virtual array to concentrate the energy transmitted or received by each radiating element into a narrow beam, thereby increasing the power in the direction of the beam peak while decreasing power in all other directions. By considering beamforming along only one axis, it can be seen that the larger the array, the better the signal focusing, the narrower the beam, and the higher the array gain.

[0007] MIMO technology, which involves measuring the magnitude and phase of signals received by N receivers (multiple outputs) for each of M transmitters (multiple inputs), can be used to form a "virtual" receiver array larger than the physical receiver array, thereby improving the angular resolution of objects, as is well known to those skilled in the art. Various MIMO modulation schemes exist that aim to orthogonalize these signals so that multiple signals transmitted from individual transmitters can be separated at the receiver. These include, but are not limited to, Time Division Duplex (TDD), Frequency Division Duplex (FDD), and Binary Phase Modulation (BPM). In TDD MIMO, the transmitters transmit signals one by one sequentially. The receiving elements receive the signals from each transmitter sequentially in time, thereby separating the signals according to which transmitter they originated from. When the distance between the transmitting and receiving elements is set appropriately, the signals in each receiver can be re-arranged in accordance with the transmitters from which they were emitted, and the phase difference of each received radiation wave causes an equivalent number of receiving elements to appear that are greater than actually present, resulting in the generation of "virtual" elements.

[0008] Figure 1 shows a virtual array composed of (M × N) elements, but using only (M + N) physical antenna elements, which is far larger than the physical number of transmitters and receivers required. Therefore, the angular resolution of the virtual array is much finer than the angular resolution of the physical array when not used in the MIMO implementation.

[0009] The MIMO array shown in Figure 1 is a Uniform Linear Array (ULA) because the elements are aligned in a straight line along one dimension and have uniform separation. In such a ULA, grating lobes can be prevented within the radar's field of view by selecting the antenna spacing to satisfy the Nyquist spatial sampling criterion. The aperture width or size of a linear sparse array is equal to that of an equivalent packed ULA, but by definition, the elements are sparsely arranged. Because fewer antenna elements are needed to create an equivalent narrow beam than a ULA, it belongs to the general class of Non-Uniform Linear Arrays (NULAs). When the number of elements in the array decreases, "holes" or "empty spaces" occur. These "holes" and "empty spaces" are intentionally created in the design of the sparse array to achieve or maintain certain desirable characteristics. Since ULAs and NULAs can be extended to two dimensions to form rectangular arrays, it will be widely accepted in this field that sparse arrays are equally effective on both axes of a rectangular array.

[0010] Therefore, the main advantage of sparse arrays is that they can reduce hardware costs for a given angular resolution, and when combined with the additional hardware reductions achieved by MIMO systems, such implementations become very attractive. Furthermore, because sparse arrays have larger spacing between elements, they are less affected by mutual coupling between antenna elements (compared to ULAs where elements are closer together), and for a given number of antenna elements, they provide a larger aperture (sum of all spacing between elements) while detecting more source signals by direction of arrival estimation compared to a full ULA of the same number of elements.

[0011] While various types of linear sparse arrays have been developed, this section describes the most common type. A Minimum Redundancy Array (MRA) is a sparse array that covers all possible intervals, or "spatial lag," at least once, but with as few repeated lags as possible. Figure 2 illustrates the calculation of this spatial lag by subtracting all possible sensor positions in a sparse array from each other.

[0012] In another type of sparse array called a Minimum Hole Array (MHA), spatial lags are allowed to appear only once, and the array is optimized to minimize the number of missing lags in the array, or the number of "holes" in a "difference array" formed from spatial lags (differences) that could be generated using sensors available in conventional arrays. However, in practice, perfect MHAs are rare, and the positions of the elements follow the spacing of known Golomb rulers for radio astronomy arrays. It has been shown that MRAs and MHAs are identical when the number of sparse elements is less than 5. Figure 3 shows the difference between a 5-element MRA and a 5-element MHA.

[0013] Figure 4 shows how two different nested array sizes and spacings are combined within a single array to create a hole-free combination array, also known as a supernested array. A supernested array is similar to a nested array, but it combines multiple different arrays.

[0014] Figure 5 shows a coprime array (including an extended coprime array). In a coprime array, subarrays are designed to run concurrently within the combined array, rather than running sequentially as in a nested array. [Overview of the project] [Problems that the invention aims to solve]

[0015] Each type uses proven methods for angle determination, but the radiation pattern determined by the array factor calculation of the array provides insight into how such arrays affect object determination in radar applications. The main problem arising from sparse arrays is that grating lobes resulting from sub-Nyquist spatial sampling can introduce ambiguity into angle detection. In these situations, the key question is how to select the positions of array elements so that the sidelobe level of the sparse array (or the lobes of the array factor that are not the main lobe or beam, i.e., local maximums) is low, minimizing the number of missing spatial lags and minimizing the number of elements required to enable angle detection.

[0016] Figure 6 illustrates this problem by comparing the boresight (0-degree) array factor of 12-element arrays designed using the prior art methods listed above, showing that high side lobes appear in the angular region outside the boresight, often leading to false radar detections, with values ​​much higher than those shown by equivalent ULAs with the same aperture size and separation distance D equal to half a wavelength of the operating frequency. In radar systems, high side lobes can result in the detection of objects as high signal levels appear from the side lobes, but these may be interpreted as appearing on the main beam, or a single object may appear in multiple directions at different angles due to the high side lobe levels. Furthermore, as a result of MIMO virtual array implementation methods, such sparse arrays are difficult to implement because multiple transmitters are multiplexed together to give a larger virtual array, or in the case of nesting, triple-nested arrays and coprime arrays the aperture size of the virtual array is not very large, resulting in reduced angular resolution.

[0017] XP087095549 titled "On design of linear sparse arrays with beampattern shift invariant properties (Regarding the design of linear sparse arrays with invariant properties of beam pattern shift)" shows an algorithm for designing a MIMO array considering sidelobe level and main lobe beam width during design. However, the number of missing spatial lags that can be a reconfiguration issue in the DSP chain is not considered.

[0018] XP033663812 titled "Sparse array design for automotive MIMO radar" independently uses several factors to optimize the sparse array and selects the best result from these independent simulations completed using several different optimization methods. However, the number of missing spatial lags that can also show a reconfiguration issue in the DSP chain is not considered.

[0019] XP031398994 titled "Co-array properties of minimum redundancy linear arrays with minimum sidelobe level" shows a method of selecting the optimal minimum redundancy array by selecting the one with the minimum sidelobe level when several alternative minimum redundancy arrays can be formed. This method is limited in use to the selection of only minimum redundancy arrays and cannot be used for MIMO configurations.

[0020] XP093117636 titled "Non redundant arrays" optimizes the missing lags of the sparse array. However, this optimization cannot be applied to MIMO mapped arrays.

[0021] From the above, there is a need for MIMO sparse array antenna design that simultaneously considers the size of side lobes, the number of missing spatial lags, and the mapping conditions of the MIMO array.

Means for Solving the Problem

[0022] The present invention relates to a sparse MIMO array antenna.

[0023] In one aspect of the present invention, a method for designing a sparse antenna array is provided. The method includes determining a first set of separation distances between a plurality of sparse elements along an axis, the first set having an equivalent aperture size for the sparse antenna array but having more elements than a uniform linear array (ULA) when the beam is directed towards the boresight, and minimizing the maximum radiation power of one or more side lobes. The method further includes determining at least one second set of separation distances between the plurality of sparse elements that minimizes the maximum radiation power of one or more side lobes when the beam is directed in different angular directions, at least one of the different angular directions being at the edge of the field of view of the equivalent ULA, the first set of separation distances and the at least one second set being the same, and being simultaneously optimized to minimize the combined error function of those sets.

[0024] In another aspect of the present invention, a method for designing a sparse MIMO virtual antenna array is provided. The method includes determining the size of an Equivalent Uniform Linear Array (ULA) based on a target number of sparse elements of the sparse MIMO virtual antenna array; setting a first optimization target as the maximum signal level of one or more side lobes of the ULA when the beam is directed toward a boresight; setting a second optimization target as the maximum signal level of one or more side lobes of the ULA when the beam is directed toward the edge of the field of view; determining a set of separation distances between antenna array elements of the sparse MIMO virtual antenna array, wherein simultaneously minimizing the first and second optimization targets, or minimizing the sum of a combination of the first and second optimization targets, wherein minimizing the first optimization target minimizes the maximum radiated power of one or more side lobes, and minimizing the second optimization target minimizes the number of missing spatial lags of the sparse MIMO virtual antenna array; and constructing a sparse MIMO virtual antenna array based on the determined set of separation distances.

[0025] In one embodiment of the present invention, directing the beam to the edge of the field of view involves directing the beam at an angle of 60 degrees outside the boresight.

[0026] In one embodiment of the present invention, directing the beam to the edge of the field of view involves directing the beam at an angle of -60 degrees outside the boresight.

[0027] In one embodiment of the present invention, the set of separation distances includes distances that are multiples of the unit separation distance, where the unit separation distance is equivalent to half a wavelength of the operating frequency of the sparse MIMO virtual antenna array.

[0028] In one embodiment of the present invention, the aperture size of the sparse MIMO virtual antenna array is based on the angular resolution of the sparse MIMO virtual antenna array and the target number of sparse elements, and the aperture size is approximated from the size trend of the minimum redundancy array when the number of sparse elements is less than 12.

[0029] In one embodiment of the present invention, the aperture size of the sparse MIMO virtual antenna array is approximated by the size trend of the minimum Hall array when the number of sparse elements is 12 or more.

[0030] In one embodiment of the present invention, the method further includes applying a first weighting factor to the determination of a set of separation distances in order to minimize one or more sidelobe levels in the boresight.

[0031] In one embodiment of the present invention, the method further includes applying a second weighting factor to the determination of a set of separation distances in order to reduce the number of spatial lags missing in a sparse MIMO virtual antenna array when the beam is directed at an angle of 60 degrees from the boresite.

[0032] In one embodiment of the present invention, the method further includes determining a set of separation distances between a plurality of sparse antenna elements based on a mapping between the positions of a plurality of transmitting elements and a plurality of receiving elements of a sparse MIMO virtual antenna array, and each possible virtual array layout of the MIMO array.

[0033] In one embodiment of the present invention, setting a first optimization target includes selecting positive and negative angles of the nearest minimum from the boresite of the ULA as first optimization angular boundaries for the virtual array element positions of the MIMO sparse array, and setting the maximum signal level of the array factor at all angles outside the region between the first optimization angular boundaries as the first optimization target.

[0034] In one embodiment of the present invention, setting a second optimization target involves setting the positive and negative angles of the nearest minimum around the main beam peak when the beam is directed towards the edge of the field of view as a second optimization angular boundary for the virtual array element positions of the MIMO sparse array, and setting the maximum signal level of the array factor at all angles outside the region between the second optimization angular boundaries as the second optimization target.

[0035] In one embodiment of the present invention, the normalized beamwidth of the main lobe of the array factor of the sparse MIMO antenna array is the same as the beamwidth of a ULA having the same aperture size.

[0036] In another aspect of the present invention, a system for designing a sparse MIMO virtual antenna array is provided. The system includes a memory for storing one or more instructions, and a processor that executes one or more instructions to determine: determine the size of an equivalent uniform linear array (ULA) based on a target number of sparse elements of a sparse MIMO virtual antenna array; set a first optimization target as the maximum signal level of one or more side lobes of the ULA when the beam is directed towards a boresite; set a second optimization target as the maximum signal level of one or more side lobes of the ULA when the beam is directed towards the edge of the field of view; determine a set of separation distances between antenna array elements of a sparse MIMO virtual antenna array, while simultaneously minimizing the first and second optimization targets, or minimizing the sum of a combination of the first and second optimization targets, where minimizing the first optimization target means minimizing the maximum radiated power of one or more side lobes, and minimizing the second optimization target means minimizing the number of missing spatial lags of the sparse MIMO virtual antenna array; and construct a sparse MIMO virtual antenna array based on the determined set of separation distances.

[0037] Various embodiments of the present invention disclose how to design a sparse array with a low sidelobe level while minimizing the number of missing lags in the array or the number of holes in the differential array. As a result, the direction of arrival (DOA) in such an array can be determined with lower computational cost and higher resolution. Furthermore, this method can be used to design a fully virtual MIMO array and is therefore particularly applicable to low-cost, high-performance radar applications by making a compromise between brute-force optimization techniques and DSP techniques.

[0038] The sparse array design of this invention fully utilizes all virtual elements of a MIMO radar sparse array. Reducing array factor sidelobes in a sparse array antenna design reduces false detections in radar systems. This sparse array design improves radar processing speed compared to radars with similar angular resolution implemented with equivalent ULA due to the reduction in the number of channels. Furthermore, this sparse array design reduces the complexity of the DSP in sparse array decoding due to the reduction in the number of holes in the array and the low sidelobe level.

[0039] This approach to designing sparse MIMO antenna arrays simultaneously optimizes the aperture size, sidelobe level (SLL), field of view (FOV), and main lobe width (MLW), which is directly proportional to the number of missing lags. This differs from prior art methods that do not consider the main lobe beam width, or the aperture size and sidelobe level, which can lead to incorrect detection of sidelobes. [Brief explanation of the drawing]

[0040] The present invention will be better understood from the following description of its embodiments, which are given only as examples, with reference to the accompanying drawings. [Figure 1]This document illustrates prior art for a conventional radar system consisting of a single transmit antenna (TX) and receive antenna (RX) array configured as an 8-element ULA, as well as an equivalent MIMO configuration achieved using two transmit antennas and four receive antennas. [Figure 2] A 7-element ULA and its equivalent 4-element sparse array are shown in MRA and MHA configurations. [Figure 3] This shows the main differences between sparse arrays designed for MRA and sparse arrays designed for MHA. [Figure 4] Examples of various types of nested sparse array designs are shown. [Figure 5] An example of a coprime sparse array design is shown. [Figure 6] This shows the predicted array factor of a 12-element array based on the design concepts of ULA, MRA, MHA, coprime, nested, and triple-nested arrays. [Figure 7] The trend line compares the sparse array size with the equivalent ULA size. [Figure 8] This shows a typical example of a MIMO virtual array with two TX antennas and four RX antennas. [Figure 9] This shows an 8-element minimum redundancy array and one latent-mapped MIMO virtual array to partially approximate the minimum redundancy array using 2 transmitting elements and 4 receiving elements. [Figure 10] This is a flowchart showing a method for forming a sparse array antenna according to one embodiment of the present invention. [Figure 11] The optimization domains used in the present invention are shown for the first and second optimization problems of the method in Figure 10. [Figure 12] This shows the layout of an 8-element sparse array using MIMO mapping compared to a conventional 8-element MRA. [Figure 13] This compares the array factor of a conventional MHA layout that is not mapped with the array factor of a MIMO-mapped layout developed using the present invention, as shown in Figure 12. [Figure 14] Figure 12 shows spatial lag charts for an example of an MRA, MIMO array, and a MIMO array optimized only at the boresight. [Figure 15] This shows the effect on the side lobes of a beam scanned outside the boresight when the radiation pattern at the edge of the FOV is not considered during optimization. [Modes for carrying out the invention]

[0041] It has long been said that when high angular resolution is required in radar systems, a narrower beam is needed. Achieving high angular resolution, with or without the additional virtual element gain of MIMO systems, requires the use of larger antenna arrays with additional elements. This means that an additional transmitter (in the case of MIMO systems) and / or receiver (in the case of MIMO or single TX systems) are needed, resulting in increased overall radar cost and size. However, to keep costs down, sparse arrays are often used.

[0042] Based on Figure 1, the shape of the radiation pattern / array factor can be said to be formed due to the time delay between signals reaching each element in the array. The main lobe of the radiation pattern / array factor, or global maximum value, is formed along the spatial direction in which signals are constructively (in phase) added together to produce the maximum value. This direction depends on the angle at which the signal approaches the array (reception) or the phase delay between antenna elements (transmission). In a ULA, the isolation between adjacent elements is the same, and the Nyquist sampling criterion is usually satisfied to prevent the formation of a grating lobe in the radiation pattern / array factor over the desired field of view. However, because the distances between elements in an equivalent sparse array are not identical, the beam pattern changes, and the side lobes increase, which are regions of local maximum values ​​that occur outside the prominent boresight, as defined earlier.

[0043] Here, regarding the mathematical predictions of prior art for the array's radiation pattern, for a wavefront colliding with the receiver's ULA at angle θ, if the receiver spacing is D, the wavefront travels an extra distance of (n-1)Dsin(θ) to reach the nth element of the array compared to the first element. This time delay results in a phase delay of (n-1)φ across the entire array at the nth element. Simultaneous arrival of the signal at each element corresponds to an incident angle of 0 degrees, or boresight. Generally, for a given separation between elements, a larger number of elements in the array results in a narrower beamwidth, and consequently, a higher angular resolution that can be achieved.

[0044] Mathematically, this focusing effect of an array can be expressed as an array factor, which is the complex-valued long-range radiation pattern of an array of isotropic radiators. The one-dimensional array factor of ULA can be neatly expressed as follows, for each discrete angle θ:

number

number

number

[0045] Calculating the array factor using the element positions of a physical array and multiplying it by the radiation pattern of a single physical antenna element within that array provides a good approximation of the radiation pattern of the physical array (excluding influences that can alter the pattern, such as mutual coupling between elements within the physical array). Expressed in decibels, the gain of the array is given by the following equation:

number

[0046] Weighted term w n By changing the phase of the array, the steering angle can be controlled. Furthermore, a weighted term w can be applied to specific elements. n Reducing the amplitude allows the array pattern to be shaped to lower the signal level of the side lobes, but this compromises the overall gain of the antenna.

[0047] While prior art sparse arrays do not simultaneously consider the size of the side lobes, the number of missing spatial lags, or the mapping conditions of the MIMO array, the present invention has been shown to simultaneously consider all of these factors.

[0048] As shown in Figure 7, most prior art sparse array designs do not have a fixed rule for determining the exact reduction in the number of elements obtained from a sparse array with a reduction in elements compared to a typical ULA where D is half a wavelength of the operating frequency. However, there is a tendency to follow for either minimum redundancy or minimum number of holes or missing spatial lags. The optimization region for sparse arrays is typically between the minimum-hole array, which is the most extreme array in terms of the number of elements relative to the array aperture size, and the ULA or "filled array." Comparing this mapping to the equivalent ULA mapping, it is immediately apparent that the array aperture size is larger.

[0049] Furthermore, since most analyses consider the removal of elements from a ULA rather than the expansion of the array from a known number of elements to a larger uniform array, the following equation has been devised based on these trends to give a first-order approximation of this increase when element placement constraints such as MIMO array mapping are applied.

number

[0050] Further examination of this equation reveals that when x < 12, it follows the trend given by the prior art minimum redundant array calculation, and when x > 12, it follows the trend given by the minimum Hall array calculation, where layout mapping constraints have little effect. These trends are plotted in Figure 7, and by reducing the degrees of freedom of the calculation of the present invention by imposing constraints on element placement in the design, most possible equivalent ULA sizes occur in the shaded or optimized region. However, when there are no constraints on element placement, such as when MIMO is not used, the solution will always follow the trend of MHA, and the following equation can be used as the first approximate equivalent ULA size in the present invention.

number

[0051] Various embodiments of the present invention relate to the value of the separation between the nth and (n+1)th elements, D n This allows for calculations that either provide a value that is an integer multiple of the unit separation distance D (generally remaining half a wavelength of the operating frequency), or calculations that give the freedom to find a separation distance that includes real numbers. Setting the former condition when there is no restriction on element placement (i.e., following Equation 7) ultimately allows us to determine the positions of the element placements of the equivalent MHA prior art. Since it is well known in this field that most post-processing techniques prefer to keep the distance D between elements as an integer, we use this condition here. This simplifies the angle of arrival processing of arrays that typically use FFT-based techniques.

[0052] In one embodiment of the present invention, due to the layout limitations caused by MIMO mapping, the previously described prior art coprime and nested array techniques were developed. In a MIMO radar, the mapped position of the virtual element generated by the nth TX and mth RX antenna pair of MIMO is, with M being the total number of RX antennas, (x (m+(n-1)M) , y (m+(n-1)M) ) = (x n , y n ) + (x m , y m ). As an example, the MIMO configurations shown in FIGS. 1 and 8 show that a combination of two TX elements spaced 4D and four RX elements spaced D results in a virtual ULA of eight elements spaced D. However, if all eight virtual elements are mapped to a sparse array, the resulting sparse array aperture size will be equal to that of a 24-element ULA (by Equation (6)). However, due to the fact that the position of the virtual element is the sum of the positions of the TX element and the RX element of each TX-RX pair, the RX element spacing is repeated N times across the entire virtual MIMO array, where N is the number of TX antennas in the MIMO, and it is impossible to arrange the TX and RX antenna elements such that the mapped / virtual MIMO array fits into a sparse array of the same equivalent size as previously reported.

[0053] To further illustrate this, FIG. 9 shows a minimum redundant sparse array having an equivalent ULA size of 24 elements. In many prior art disclosures, the development of these known sparse array types has been discussed, and each sparse array element has its position frequently found using specific optimization algorithms such as genetic optimization, assuming that each sparse array element must be somewhere within a smaller, predefined range. Such techniques are known in the art, but it is clear that such arrays cannot be formed, and such optimization algorithms cannot be used in MIMO virtual array configurations because the element spacing cannot be aligned when mapping the virtual array.

[0054] Figure 9 shows a comparison between MRA and a mapped MIMO configuration using two TX elements and four RX elements, illustrating that only five of the eight elements can be accurately positioned.

[0055] In such MIMO configurations, coprime arrays are often used to form a virtual sparse array because there are formulas that allow for the calculation of element placement. However, the aperture of the coprime array is smaller than that of other sparse array options (closer to the MRA trend line in Figure 7), thus reducing its effectiveness in improving angular resolution. Furthermore, when virtual arrays of such prior art are designed, the focus of the virtual array has been solely on covering spatial lag or reducing the redundancy of spatial lag, while sidelobe levels, if any, have been given only secondary consideration.

[0056] In one embodiment of the present invention, both spatial lag coverage and the side lobe level of the radiation pattern are taken into account for the main beam by focusing on the calculated radiation pattern at both the boresight and simultaneously at the edge of the FOV, with each weighted term w n This is achieved by adding a correction phase, and it is a well-known technique in this field. The phase added to each element in the same plane of the array is expressed by the following equation:

number

[0057] Here, a solution is sought to minimize the level of the array factor's side lobes for both beam conditions, thereby minimizing the physical array emission pattern, by optimizing the isolation between sparse elements and minimizing the potential false detections caused by the sparse array at all angles within the FOV.

[0058] Figure 10 is a flowchart of a method 1000 for forming a sparse array antenna according to an embodiment of the present invention. This method can be carried out by a processor that executes one or more instructions stored in memory. Figure 11 shows the optimization regions used in the present invention for the first and second optimization problems of the method of Figure 10.

[0059] In step 1010, the aperture size of the equivalent uniform linear array (ULA) is determined based on the target number of sparse elements, using equation (5) and the separation distance D. The separation distance D is usually half a wavelength of the operating frequency.

[0060] In step 1020, the positive and negative angles of the nearest minimum (1101,1102) of the array factor relative to this ULA from the boresite are selected, an equal phase is applied to all elements, and these positive and negative angles are set as the first optimized boundary for the virtual array element positions of the sparse array.

[0061] In step 1030, the first optimization goal is set as the maximum signal level of the array factor at all angles outside the region between these first optimization boundaries. That is, we want to minimize the levels of the side lobes within this angular range. This completes the definition of the first problem and essentially describes all the optimization regions 1104 and 1105 outside the main lobe 1103.

[0062] Next, a second problem is defined for the condition (Equation 7) that the phase of the elements is added according to the isolation distance from the first element of the sparse array, and the main beam 1106 is directed towards the edge of the FOV (typically 60 degrees outside the boresite). In one embodiment of the present invention, the second optimization problem may be fixed to solve the condition that the main beam is directed at 60 degrees outside the boresite, defining the problem when an omnidirectional antenna element is used.

[0063] Regarding the second issue, in step 1040, the second optimization boundary for most practical antennas is set based on the nearest minimum 1107 of the array factor around the main beam peak when steered to this end of the FOV, and the FOV angle (60 degrees out of boresite in the example in Figure 11). However, when an omnidirectional antenna element is used, the second optimization boundary is set based on the nearest minimums of both the array factor around the main beam peak when steered to this end of the FOV. The end 1107 is selected to occur closer to the boresite than the beam steering direction, and is usually steered in a positive angular direction from the boresite, but can be steered in a negative direction without limiting or modifying the invention described. In embodiments of the invention, there may be at least two optimization targets. As an example, the optimization target is 0 ° , +60 ° and -60 ° That is the case.

[0064] In step 1050, the second optimization target is set for region 1108 as the maximum signal level of the array factor at all angles outside the second optimization angle boundary, i.e., the sidelobe level is minimized within this angle range, similar to the first optimization target. In embodiments of the present invention, the weighting function may also be applied to this second optimization target by multiplying it by a factor of k, where k=4 is used in the present invention. Any value of k can be adopted and is arbitrarily selected depending on the type of optimization algorithm used. The value of k may be used without limiting or modifying the described invention. In one embodiment of the present invention, the weighting function may be applied to the first optimization target to lower the sidelobe level in favor of detection around the boresight.

[0065] In step 1060, the same distances are linked (due to MIMO virtual array mapping) to simultaneously minimize the sum of the first and second optimization goals, or both of the first and second optimization goals, and the isolation distance between antenna array elements is optimized for both the first and second problems.

[0066] In one embodiment of the present invention, the optimization goal is set to find the minimum of the newly defined combined optimization goals. While the type of optimization algorithm is not limited, the present invention uses a generalized reduction gradient algorithm. The solution is found when a global minimum is found in the combined problems, or when the sidelobe levels are reduced to an acceptable level in both the first and second problems. Optimizing the array factor level reduces the sidelobes resulting from the sparse array. In another embodiment of the present invention, the radiation pattern may be optimized instead of the array factor, which helps reduce the sidelobe level because the optimizer concentrates the gain of a single antenna element in the angular region where the gain is high.

[0067] In one embodiment of the present invention, a generalized shrinking gradient function is used to examine the gradient of the function as the decision variable (or separation distance) changes, and it is determined that the optimal solution has been reached when the partial derivative is equal to zero. By randomly changing the initial or starting value of the decision variable and repeating the process, the global minimum can be reliably found over time, rather than a local minimum that may occur near the starting value. However, the present invention is not dependent on any particular type of solver, and other solvers such as gradient, random, simplex, and Newton-Raphson may be used. Furthermore, by focusing on the signal level of the array factor, side lobes arising from the sparse array are reduced, and by simultaneously combining the problems of the boresight and the main beam focused at the edge of the FOV, a solution that takes into account both the side lobe level (mainly the result of boresight optimization) and the spatial lag (mainly the result of FOV edge scanning angle optimization) can be found.

[0068] The isolation distance is linked during the process according to the designed MIMO-mapped architecture and optimized for all possible isolations within the virtual array configuration, so that all virtual elements can be optimized while reducing the number of missing spatial lags and the level of side lobes in the array factor, thereby maximizing the virtual array size. A further consequence of linking the mapped virtual element spacing (due to the MIMO architecture) is that the number of optimization variables decreases, resulting in a much faster design process compared to one that does not operate with mapped virtual element spacing.

[0069] Considering the previous example of the 8-element array in Figure 9, the present invention relates to the variable D n This is demonstrated by minimizing the array factor outside the main beam, calculated from Equation 4, by simultaneously computing two beams focused at the boresight and 60 degrees (which is typically the edge of the FOV for most planar antennas), while allowing for variations. Due to MIMO layout mapping, the degrees of freedom in the problem are reduced by setting D1=D5, D2=D6, and D3=D7 in a limiting set where D1+D2+D3+D4+D5+D6+D7=11.5 wavelengths (based on 24 elements spaced 0.5 wavelengths apart, obtained when x is set to 8 in Equation 7). Minimizing the array factor with two simultaneously computed beams focused at the boresight and 60 degrees reduces the number of missing lags, which is helpful for later processing of sparse arrays.

[0070] Figure 12 shows a viable MIMO-mapped array 1200 according to an embodiment of the present invention. The array factor of the prior art 8-element MRA and the layout derived from the MIMO-mapped array 1200 of the present invention, compared in Figure 13, show similar sidelobe levels. This MIMO-mapped array 1200 has only three missing holes in the differential array in Figure 14, with lags 17D, 18D, and 20D missing out of all 23 possible combinations (13%). This suggests that although some holes are present, the number of holes is significantly reduced compared to a similar MIMO layout optimized for low sidelobe levels using boresite-only optimization, and the present invention can be considered a type of minimal hole array with reduced aperture size. Comparing the holes appearing in the present invention with those in a similar prior art 8-element equivalent MHA with a slightly larger array aperture, it can be seen that the larger prior art MHA, where the first hole appears at lag 16D, has more than 17% holes. This hole must be recovered by digital signal processing techniques such as an iterative method with adaptive thresholding (IMAT) or matrix interpolation, but also based on a spatial lag (1D to 15D) that is one less than the recovery of lag 17D (1D to 16D) of the described invention. Similar results can be obtained with larger sparse arrays. Thus, the MIMO-mapped array 1200 is derived using novel techniques that enable full control of the MIMO virtual array layout and have performance similar to equivalent prior art MRAs that cannot be configured as a virtual array layout of a MIMO system. The MIMO-mapped array 1200 of the present invention can be used in defense or military systems, but more specifically, it can be applied to automotive applications where low cost is a top priority. Although the MIMO array 1200 is a one-dimensional array, it will be obvious to those skilled in the art that a rectangular array may be formed using the MIMO array 1200.

[0071] As previously mentioned, the number of holes is significantly reduced by including a second optimization problem in which the beam is directed towards the edge of the FOV, which can be seen in the spatial lag chart in Figure 14. A key aspect of the present invention is that when the main lobe is directed towards the edge of the FOV, the optimizer is forced to reduce the size of the grating lobe. These grating lobes are defined as radiation pattern lobes other than the main lobe and occur when the spacing between elements is sufficiently large with added phase, allowing for in-phase summation of radiation fields in multiple directions, and can be ideally avoided as long as the equation d / λ < 1 / (1 + sin θ) is valid, where λ is the wavelength of the operating frequency, d is the distance between elements, and θ is the direction angle in radians. This means that the element positions of sparse arrays are limited by the very large spacing, and consequently, the possibility of eliminating spatial lag is significantly reduced. Figure 14 illustrates this effect by comparing the lag of the MRA, the example of the MIMO array described above, and the example of a MIMO array optimized considering only the first optimization problem at the boresite. Figure 15 further illustrates the need for a second optimization problem, comparing plots of the array factor at the boresight and the edge of the FOV (60 degrees).

[0072] When considering only boresite optimization, i.e., the first optimization problem, we find that the side lobes are kept at a relatively low level relative to the boresite scan angle. However, when we add a phase delay between antenna elements so that the main beam is scanned up to 60 degrees, we find that a large grating lobe exists. This means that, in addition to the complexity of DSP processing for the missing 12 spatial lags, signals arriving from objects near the boresite may be interpreted as arriving from objects at 60 degrees (and vice versa).

[0073] Thus, by simultaneously optimizing the problem for both the boresight and the main beam focused at the edge of the FOV, a solution is found that takes into account both the sidelobe level (primarily the result of boresight optimization) and the spatial lag (primarily the result of FOV edge scan angle optimization). Note that the sidelobe level for a particular beam Pointing angle can be significantly reduced by considering the optimization problem under only one condition, namely when the main beam is directed at either the boresight or the edge of the FOV. However, this worsens the sidelobe level when the main beam is scanned at other angles. In such cases, solutions are found that allow for more holes in the differential array, increasing the complexity of the DSP.

[0074] By forcing the transceiver array elements to be positioned according to the MIMO element mapping of the optimization problem, and thereby positioning the virtual array elements, the entire virtual array is optimized for all possible configurations of transceiver element placement. Furthermore, by using as many virtual elements as possible, the size of the virtual array can be maximized. In addition, by linking the array element spacings according to the MIMO element mapping, the number of variables to be optimized is reduced compared to a sparse array design with the same number of elements but no constraints on element spacing, significantly shortening the design process. Moreover, maximizing the size of the virtual array increases the equivalent ULA size, improving angular accuracy and resolution.

[0075] In this specification, the terms “comprise,” “comprises,” “comprised,” “comprising” or variations thereof, and the terms “include,” “includes,” “included,” “including” or variations thereof are considered interchangeable and are all given the broadest possible interpretation, and vice versa.

[0076] The present invention is not limited to the embodiments described herein and can be modified in both structure and detail.

Claims

1. A method for designing a sparse MIMO virtual antenna array, Based on the target number of sparse elements in the aforementioned sparse MIMO virtual antenna array, the size of the Equivalent Uniform Linear Array (ULA) is determined, When the beam is directed towards the boresite, a first optimization target is set as the maximum signal level of one or more side lobes of the ULA, When the beam is directed towards the edge of the field of view, a second optimization target is set as the maximum signal level of one or more side lobes of the ULA, Determining a set of separation distances between the antenna array elements of the sparse MIMO virtual antenna array, while simultaneously minimizing the first and second optimization objectives, or minimizing the sum of combinations of the first and second optimization objectives, wherein minimizing the first optimization objective means minimizing the maximum radiated power of one or more side lobes, and minimizing the second optimization objective means minimizing the number of missing spatial lags of the sparse MIMO virtual antenna array, A method comprising constructing the sparse MIMO virtual antenna array based on the set of separation distances determined above.

2. The method according to claim 1, wherein directing the beam to the edge of the field of view includes directing the beam at an angle of 60 degrees outside the boresight.

3. The method according to claim 1, further comprising directing the beam to the edge of the field of view at an angle of -60 degrees outside the boresight.

4. The method according to any of the preceding claims, wherein the set of separation distances includes distances that are multiples of a unit separation distance, the unit separation distance being equivalent to half a wavelength of the operating frequency of the sparse MIMO virtual antenna array.

5. The method according to any of the preceding claims, wherein the aperture size of the sparse MIMO virtual antenna array is based on the angular resolution of the sparse MIMO virtual antenna array and the target number of sparse elements, and the aperture size is approximated from the size trend of the minimum redundancy array when the number of sparse elements is less than 12.

6. The method according to any one of the preceding claims, wherein the aperture size of the sparse MIMO virtual antenna array is approximated from the size trend of the minimum Hall array when the number of sparse elements is 12 or more.

7. The method according to any of the prior claims, further comprising applying a first weighting factor to the determination of the set of separation distances in order to minimize the one or more side lobe levels in the boresight.

8. The method according to any of the prior claims, further comprising applying a second weighting factor to the determination of the set of separation distances in order to reduce the number of missing spatial lags in the sparse MIMO virtual antenna array when the beam is directed at an angle of 60 degrees outside the boresite.

9. The method of any of the prior claims, further comprising determining the set of separation distances between the plurality of sparse antenna elements based on a mapping between the positions of a plurality of transmitting elements and a plurality of receiving elements of the sparse MIMO virtual antenna array, and each possible virtual array layout of the MIMO array.

10. Setting the first optimization goal mentioned above is, As a first optimized angular boundary for the virtual array element position of the MIMO sparse array, the positive and negative angles of the nearest minimum from the boresite of the ULA are selected. This includes setting the maximum signal level of the array factor at all angles outside the region between the first optimization angle boundaries as the first optimization target, The method according to claim 1.

11. Setting the second optimization goal mentioned above means As a second optimized angular boundary for the virtual array element positions of the MIMO sparse array, the positive and negative angles of the nearest minimum around the main beam peak when the beam is directed towards the edge of the field of view are selected. This includes setting the maximum signal level of the array factor at all angles outside the region between the second optimization angle boundaries as the second optimization target, The method according to claim 1.

12. The method according to claim 1, wherein the normalized beam width of the main lobe of the array factor of the sparse MIMO antenna array is the same as the beam width of the ULA having the same aperture size.

13. A system for designing sparse MIMO virtual antenna arrays, Memory for storing one or more instructions, A processor that executes one or more instructions, The size of the equivalent uniform linear array (ULA) is determined based on the target number of sparse elements in the aforementioned sparse MIMO virtual antenna array, When the beam is directed towards the boresite, the first optimization target is set as the maximum signal level of one or more side lobes of the ULA, When the beam is directed towards the edge of the field of view, the second optimization target is set as the maximum signal level of one or more side lobes of the ULA, The determination involves determining a set of separation distances between the antenna array elements of the sparse MIMO virtual antenna array, while simultaneously minimizing the first and second optimization objectives, or minimizing the sum of the first and second optimization objectives, where minimizing the first optimization objective means minimizing the maximum radiated power of one or more side lobes, and minimizing the second optimization objective means minimizing the number of missing spatial lags of the sparse MIMO virtual antenna array. A processor that performs the following: constructing the sparse MIMO virtual antenna array based on the set of separation distances determined above, system.

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