Optimization method for sparse arrays for MIMO radar

Abstract

A method for designing a sparse MIMO virtual antenna array is disclosed. The method includes determining a 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 to a maximum signal level of one or more sidelobes of the ULA when a beam is pointed to a boresight, setting a second optimization target to a maximum signal level of the one or more sidelobes of the ULA when the beam is pointed to an edge of a field of view, determining a set of spacing distances between antenna array elements of the sparse MIMO virtual antenna array that simultaneously minimizes the first optimization target and the second optimization target or minimizes a sum of the first optimization target and the second optimization target, and constructing the sparse MIMO virtual antenna array based on the determined set of spacing distances.

Description

Technical Field

[0001] This invention relates to an optimization method for an antenna array used in a MIMO radar system, which has a reduced number of elements and optimal performance. Background Technology

[0002] With many countries researching driverless vehicles and the global car fleet exceeding 1.2 billion, autonomous transportation clearly represents a huge emerging market for stakeholders, including governments and private companies. However, affordable sensor systems with high performance and reliability are essential for making autonomous transportation a reality. Technologies including radar, lidar, ultrasound, and camera arrays have been employed, and while each has inherent advantages over others, none is currently sufficient for widespread implementation in complex autonomous driving scenarios, such as driving in busy city centers, due to limitations in resolution, sensitivity, all-weather capability, or cost. Radar technology offers a cheaper solution to most of these problems; however, this excludes angular resolution and sensitivity, both of which can be improved—but at a higher cost.

[0003] The angular resolution or beamwidth of the antenna array aperture is given by the following equation: ..............(1) in φ is the angular resolution, λ is the wavelength, N is the number of antenna elements, d is the spacing between antenna elements, and θ is the transmit or receive angle of the signal. In conventional radar systems, the value of d is typically set to λ / 2 to ensure that the Nyquist sampling criterion for spatial signals at the antenna aperture is met, thereby preventing grating lobes from forming within the field of view. Therefore, this means that for a line-of-sight signal (θ = 0 degrees), the above equation simplifies to an angular resolution equal to 2 / N.

[0004] Therefore, in conventional radar systems, larger antenna arrays (accompanied by an increased number of antenna elements and related hardware) are needed to improve spatial resolution. However, as the antenna array aperture size increases to achieve this, the number of receivers required also increases, which is extremely expensive for applications such as automotive radar. When lower angular resolution is required, a wider beam is sufficient and can be achieved using a small antenna array aperture with a few antenna elements. When higher angular resolution is required, a narrower beam is needed, and a larger antenna array aperture with additional elements must be utilized. This necessitates additional receivers, leading to an increase in the overall cost and size of the radar. This means that for applications requiring low cost (such as automotive radar), conventional architectures are limited to a minimum number of elements and therefore limited to wide beams. However, the general rule largely applies: higher angular resolution requires more antenna elements. Conversely, multiple-input multiple-output (MIMO) radar mitigates this cost increase to some extent.

[0005] MIMO radar is a type of phased array radar. Its transmitter and receiver distribution improves spatial resolution and ranging capability compared to conventional monostatic radars with an equivalent total number of transmit and receive channels. There are two main types of MIMO radar: statistical MIMO, where antennas are placed far apart to provide different "views" of the "scene," and beamforming MIMO, where antennas are placed close together and work together to form a "virtual," larger beamforming array.

[0006] Beamforming methods (such as those used in conventional radar systems, and similar to those achieved through digital post-processing in MIMO systems) manipulate a virtual array to focus the energy emitted or received by each radiating element into a narrow beam using wave coherence. This increases power in the beam peak direction while reducing power in all other directions. Considering beamforming along only one axis, it can be seen that larger arrays achieve narrower beams and increased signal focusing, resulting in higher array gain.

[0007] As is well known to those skilled in the art, MIMO technology can be used to form a "virtual" receiver array larger than the physical receiver array, thereby improving the angular resolution of objects. This MIMO technology involves measuring the amplitude and phase of the signal received at N receivers (multiple outputs) for each of M transmitters (multiple inputs). Various modulation schemes exist for MIMO designed to achieve orthogonality between the signals transmitted by each individual transmitter, allowing these signals to be separated at the receiver side. These schemes include, but are not limited to, Time Division Duplex (TDD), Frequency Division Duplex (FDD), and Binary Phase Modulation (BPM). For TDD MIMO, the transmitters transmit one signal at a time. The receivers then receive the signals originating from each transmitter in chronological order, and thus can separate the signals based on which transmitter they originated from. When the spacing between the transmitters and receivers is appropriately set, the signals at each receiver can be rearranged corresponding to the transmitter from which the signals originated, and the phase difference on each received radiated wave makes the equivalent number of receivers appear to be greater than the actual number of receivers, thus creating "virtual" units.

[0008] Figure 1 A virtual array was demonstrated, consisting of (M × N) elements but utilizing only (M + N) physical antenna elements. This virtual array is significantly larger than the required physical number of transmitters and receivers. Therefore, the angular resolution of the virtual array is much finer than that of a physical array not used in MIMO implementations.

[0009] Figure 1 The MIMO arrangement shown is a uniform linear array (ULA) because the elements are located along a line in one dimension and have uniform spacing. This ULA allows for the prevention of grating lobes within the radar field of view by selecting antenna spacing that satisfies the Nyquist spatial sampling criterion. The aperture width or size of a linear sparse array is equal to its equivalent filled ULA, but by definition, these arrays are sparsely filled. Because linear sparse arrays require fewer antenna elements than ULAs to produce an equivalent narrow beam, they belong to the broader category of non-uniform linear arrays (NULAs). With fewer elements in the array, "holes" or vacancies are intentionally created in the design of sparse arrays to achieve or maintain certain desired characteristics. It is generally accepted in the art that ULAs and NULAs can be extended in two dimensions to form rectangular arrays, and therefore sparse arrays are equally effective on both axes of a rectangular array.

[0010] Therefore, a key advantage of sparse arrays is their lower hardware cost for a given angular resolution; this makes the implementation highly attractive when combined with the additional hardware savings gained from MIMO systems. Furthermore, due to the larger spacing between elements in sparse arrays, they are less susceptible to mutual coupling between antenna elements (compared to ULAs with closer elements), and provide a larger aperture (the sum of the spacing between all elements) for a given number of antenna elements, while detecting more source signals through direction-of-arrival estimation than a complete ULA with the same number of elements.

[0011] Different types of linear sparse arrays have been developed, and the most common type will now be discussed. Minimal Redundancy Array (MRA) is a sparse array in which all possible spacings or "spatial lags" are covered at least once, while the number of repeated lags is minimized. Figure 2 This demonstrates how to achieve spatial hysteresis computation by subtracting each other from all possible sensor locations in a sparse array.

[0012] In another type of sparse array known as the Minimal Hole Array (MHA), spatial hysteresis is allowed to occur only once, and the array is optimized to minimize the number of missing hysteresis in the array, or the number of "holes" in a "differential array," which is formed by spatial hysteresis (differences) generated using available sensors in a conventional array. However, in practice, a perfect MHA is rare, and the cell positions follow the known existing technique of Gronn rod spacing used for radio astronomy arrays. When the number of sparse cells is less than 5, it has been shown that MRA and MHA are identical. Figure 3 The differences between 5-unit MRA and 5-unit MHA are shown.

[0013] Figure 4 This demonstrates combining two different nested array sizes and spacings within a single array to produce a hole-free composite array (also known as a super-nested array). A super-nested array combines multiple different arrays and is similar to a nested array.

[0014] Figure 5 Coprime arrays (including extended coprime arrays) are shown, where subarrays are designed to operate simultaneously in the combined array, rather than sequentially as in nested cases.

[0015] While each type employs proven angle determination methods, the radiation pattern (determined through calculations of the array factor) provides insights into how such an array affects object determination in radar applications. A major problem arising from sparse arrays is that grating lobes generated by sub-Nyquist spatial sampling can introduce ambiguity into angle determination. In this context, the key issue is how to select the positions of array elements such that the sidelobe levels (or lobes in the array factor that are not the main lobe or main beam, i.e., local maxima) of the sparse array are low, thereby minimizing the amount of missing spatial hysteresis and the number of elements required to achieve angle determination.

[0016] Figure 6 This problem is illustrated by comparing the line-of-sight (0-degree) array factor of a 12-element array designed using the previously listed prior art methods, and it is indicated that many of these arrays lead to erroneous radar detections due to high sidelobes in angular regions off the line of sight. These high sidelobes are significantly higher than those that might occur in an equivalent ULA with the same aperture size and a spacing D equal to half the wavelength of the operating frequency. When sidelobes are high in a radar system, objects may be detected due to the higher signal levels emanating from these sidelobes, but these signal levels are interpreted as appearing on the main beam. Alternatively, a single object may be detected multiple times at different angles due to the high sidelobe levels. Furthermore, since the method of implementing MIMO virtual arrays involves multiplexing transmitters together to create a larger virtual array, such sparse arrays are either difficult to implement or, in the case of nested arrays, triple-nested arrays, and coprime arrays, the virtual array aperture size cannot be significantly increased, which in turn reduces angular resolution.

[0017] The paper XP 087095549, titled "On the design of linear sparse arrays with beampattern shift-invariant properties," describes an algorithm for designing MIMO arrays that considers sidelobe levels and main lobe beamwidth during the design process. However, it does not account for the amount of missing spatial hysteresis, which can cause reconstruction difficulties in the DSP chain.

[0018] The paper XP 033663812, titled "Sparse array design for automotive MIMO radar," uses multiple factors to independently optimize the sparse array and selects the best results from these independent simulations performed using various optimization methods. However, it does not consider the number of missing spatial lags, which may cause reconstruction difficulties in the DSP chain.

[0019] The paper XP 031398994, titled "Co-array properties of minimum redundancy linear arrays with minimum sidelobe level," describes a method that selects the optimal minimum redundancy array by choosing the array with the minimum sidelobe level when multiple alternative minimum redundancy arrays can be formed. This limits it to selecting the minimum redundancy array and cannot be used for MIMO configurations.

[0020] The paper XP 093117636, titled "Non-redundant arrays," optimizes sparse arrays for missing hysteresis. However, it cannot be applied to MIMO-mapped arrays.

[0021] Given the above, there is a need for a MIMO sparse array antenna design that simultaneously considers the size of the sidelobes, the number of missing spatial hysteresis, and the MIMO array mapping conditions. Summary of the Invention

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

[0023] In one aspect of the invention, a method for designing a sparse antenna array is provided. The method includes determining a first set of spacing distances between a plurality of sparse elements along an axis, wherein when a beam is directed toward the line of sight of a uniform linear array (ULA) having an equivalent aperture size but a greater number of elements relative to a sparse antenna array, the first set minimizes the maximum radiated power of one or more sidelobes. The method further includes determining at least one second set of spacing distances between the plurality of sparse elements, wherein when the beam is directed toward different angular directions, the at least one second set of spacing distances minimizes the maximum radiated power of one or more sidelobes, wherein at least one of these directions is located at the edge of the field of view of the equivalent ULA, and wherein the first set of spacing distances and the at least one second set of spacing distances are identical and are simultaneously optimized to minimize their combined error function.

[0024] In another aspect of the 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 the target number of sparse elements of the sparse MIMO virtual antenna array; setting a first optimization objective as the maximum signal level of one or more sidelobes of the ULA when the beam is directed toward the line of sight; setting a second optimization objective as the maximum signal level of one or more sidelobes of the ULA when the beam is directed toward the edge of the field of view; determining a set of spacing distances between the antenna array elements of the sparse MIMO virtual antenna array, the set of spacing distances simultaneously minimizing the first optimization objective and the second optimization objective, or minimizing the sum of the first optimization objective and the second optimization objective, wherein minimizing the first optimization objective minimizes the maximum radiated power of one or more sidelobes, and minimizing the second optimization objective minimizes one or more missing spatial hysteresis of the sparse MIMO virtual antenna array; and constructing the sparse MIMO virtual antenna array based on the determined set of spacing distances.

[0025] In an embodiment of the invention, pointing the beam to the edge of the field of view includes pointing the beam at an angle 60 degrees away from the visual axis.

[0026] In an embodiment of the invention, pointing the beam to the edge of the field of view includes pointing the beam at an angle of -60 degrees away from the visual axis.

[0027] In an embodiment of the present invention, the set of interval distances includes multiples of the unit interval distance, wherein the unit interval distance is equal to half the wavelength of the operating frequency of the sparse MIMO virtual antenna array.

[0028] In an 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 number of target sparse elements, wherein when the number of sparse elements is less than 12, the aperture size is approximated by the size trend of the minimum redundancy array.

[0029] In an embodiment of the present invention, when the number of sparse units is equal to or greater than 12, the aperture size of the sparse MIMO virtual antenna array is approximated by the size trend of the minimum aperture array.

[0030] In an embodiment of the invention, the method further includes applying a first weighting factor to the determination of the interval distance set to minimize one or more sidelobe levels at the visual axis.

[0031] In an embodiment of the invention, the method further includes applying a second weighting factor to the determination of the interval distance set to reduce the number of missing spatial hysteresis in the sparse MIMO virtual antenna array when the beam is pointed at an angle 60 degrees away from the line of sight.

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

[0033] In an embodiment of the present invention, setting the first optimization objective includes: selecting the positive and negative angles of the nearest local minimum from the line of sight of the ULA as the first optimization angle boundary for the virtual array cell position 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 angle boundaries as the first optimization objective.

[0034] In an embodiment of the present invention, setting the second optimization objective includes: selecting the positive and negative angles of the nearest local minimum around the peak value of the main beam when the beam is pointed to the edge of the field of view as the second optimization angle boundary for the virtual array cell position 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 angle boundaries as the second optimization objective.

[0035] In an 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 normalized beamwidth of a ULA with the same aperture size.

[0036] In another aspect of the 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 for executing the one or more instructions to: determine the size of an equivalent uniform linear array (ULA) based on a target number of sparse elements of the sparse MIMO virtual antenna array; set a first optimization objective to the maximum signal level of one or more sidelobes of the ULA when the beam is directed toward the line of sight; set a second optimization objective to the maximum signal level of one or more sidelobes of the ULA when the beam is directed toward the edge of the field of view; determine a set of spacing distances between antenna array elements of the sparse MIMO virtual antenna array, the set of spacing distances simultaneously minimizing the first optimization objective and the second optimization objective, or minimizing the sum of the first optimization objective and the second optimization objective, wherein minimizing the first optimization objective minimizes the maximum radiated power of one or more sidelobes, and minimizing the second optimization objective minimizes one or more missing spatial hysteresis of the sparse MIMO virtual antenna array; and construct the sparse MIMO virtual antenna array based on the determined set of spacing distances.

[0037] Various embodiments of the present invention disclose sparse array designs with low sidelobe levels while minimizing the number of missing hysteresis (or holes in differential arrays) in the array. Therefore, the direction of arrival (DOA) in such arrays can be determined with lower computational cost and higher resolution. Furthermore, this method can be used to design complete virtual MIMO arrays and is thus particularly suitable for low-cost, high-performance radar applications by striking a tradeoff between brute-force optimization techniques and DSP techniques.

[0038] The sparse array design of this invention fully utilizes all virtual elements in a MIMO radar sparse array. Reducing array factor sidelobes in the sparse array antenna design reduces false detections in the radar system. Due to the reduced number of channels, the sparse array design achieves higher radar processing speeds than radars with similar angular resolution implemented using equivalent ULAs. Furthermore, due to the reduced number of holes and lower sidelobe levels in the array, this sparse array design exhibits lower DSP complexity in sparse array decoding.

[0039] Unlike existing methods that do not consider main lobe beamwidth, or aperture size and sidelobe level (which means that incorrect points may be detected on the sidelobes), this method for designing sparse MIMO antenna arrays optimizes the main lobe width (MLW), which is proportional to the aperture size, sidelobe level (SLL), field of view (FOV), and the number of missing hysteresis. Attached Figure Description

[0040] The present invention will be more clearly understood through the following description of its embodiments in conjunction with the accompanying drawings, which are given by way of example only, in which: - Figure 1 A conventional radar system comprising a single transmit antenna (TX) and a receive antenna (RX) array configured as an 8-element ULA is shown, along with prior art for an equivalent MIMO configuration using 2 transmit antennas and 4 receive antennas. Figure 2 The equivalent 4-cell sparse arrays of the 7-cell ULA and its MRA and MHA configurations are shown; Figure 3 The main differences between sparse arrays designed for MRA and MHA are shown; 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 The predicted array factor of a 12-cell array based on the design concepts of ULA, MRA, MHA, coprime, nested, and triple nested arrays is shown. Figure 7The trend line is shown comparing the sparse array size to its equivalent ULA size; Figure 8 A typical example of a MIMO virtual array consisting of 2 TX antennas and 4 RX antennas is shown; Figure 9 An 8-cell minimum redundancy array is shown, along with a potential mapped MIMO virtual array that partially approximates this minimum redundancy array using 2 transmit cells and 4 receive cells. Figure 10 This is a flowchart illustrating a method for forming a sparse array antenna according to an embodiment of the present invention; Figure 11 The invention is shown for use in this invention. Figure 10 The optimization regions of the first and second optimization problems of the method; Figure 12 The layout of an 8-cell sparse array with MIMO mapping is shown, which is compared with a conventional 8-cell MRA. Figure 13 The array factor of the unmapped MHA layout in the prior art was compared with... Figure 12 The diagram shows a MIMO mapping layout developed using this invention; Figure 14 MRA was shown. Figure 12 Spatial hysteresis diagrams of the MIMO array shown, and an example of a MIMO array optimized only at the line of sight; and Figure 15 The effect of sidelobes on beams that deviate from the line of sight is shown when the radiation pattern at the edge of the field of view is not considered during optimization. Detailed Implementation

[0041] As previously noted, when radar systems require higher angular resolution, narrower beams are needed. To achieve this, regardless of whether the additional virtual cell gain of a MIMO system is utilized, a larger antenna array with additional cells must be used. This means that additional transmitters (in the case of MIMO systems) and / or receivers (in the case of MIMO or single TX systems) will be required, leading to an increase in overall radar cost and size. However, to maintain low cost, sparse arrays are often used.

[0042] based on Figure 1The shape of the radiation pattern / array factor is formed because of the time delay between signals arriving at each element within the array. The main lobe, or global maximum, of the radiation pattern / array factor is formed along the spatial direction in which the signals constructively (in phase) combine to produce the maximum value. Furthermore, this direction depends on the angle at which the signal approaches the array (receive) or the phase delay between antenna elements (transmit). In a ULA, the spacing between adjacent elements is uniform and typically satisfies the Nyquist sampling criterion to prevent the formation of grating lobes 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 uniform, the beam pattern will change, and sidelobes (as previously defined, are regions of local maxima that occur off-axis, where the signal level is significant) will increase.

[0043] We now discuss the prior art mathematical prediction of the radiation pattern of the array, where, for a wavefront striking the ULA of a receiver at an angle θ, where the receiver spacing is D, the wavefront travels an additional distance (n-1)D sin(θ) to reach the nth cell in the array compared to reaching the 1st cell. This time delay causes an asymptotic phase delay across the entire array, which is (n-1)Φ at the nth cell. When the signal arrives at each cell simultaneously, it will correspond to the angle of incidence at 0 degrees or the line of sight. Typically, for a given cell spacing, the more cells in the array, the finer the beamwidth, and therefore the finer the angular resolution that can be achieved.

[0044] Mathematically, this focusing effect of the array can be expressed as an array factor, which is the complex-valued far-field radiation pattern of the isotropic radiator array. At each discrete angle θ, the one-dimensional array factor of the ULA can be elegantly expressed as follows: ......................(2) Among them, w n It is the complex weighted sum of the nth element in the array (with amplitude and phase), and D is the element spacing. Those skilled in the art will understand that for ULA, term D is typically the distance at the lower half-wavelength of the operating frequency and remains constant between elements; however, the equation can be rewritten in terms of the distance relative to the first element: ......................(3) Where D0 is the distance from the first cell to itself, and is therefore 0. This equation can then be used to determine the array factor of a sparse array.

[0045] To convert array factors to decibels, use the LOG function, which makes: .....................(4) When the array factor is calculated using the cell locations of the physical array and multiplied by the radiation pattern of a single physical antenna cell in the array, the resulting radiation pattern provides a good approximation of the radiation pattern of the physical array (excluding effects such as mutual coupling between cells in the physical array that may alter the radiation pattern). The array gain, in decibels, is given by the following formula: .....................(5) Among them, G E The gain of a single unit.

[0046] The array's steering angle can be adjusted by changing the weighting term w. n The phase is controlled. Furthermore, the weighting term w at a specific unit is reduced. n The amplitude can be adjusted to reduce the signal level of the sidelobes by adjusting the array pattern, but this is detrimental to the overall antenna gain.

[0047] It has been previously shown that existing sparse arrays do not simultaneously consider the size of side lobes, the number of missing spatial lags, or MIMO array mapping conditions, while the present invention considers all of these factors simultaneously.

[0048] according to Figure 7 For most existing sparse array designs, there are no fixed rules to determine the exact number of cell reductions that can be achieved from a sparse array with a reduced cell count relative to a typical ULA, where D is half the wavelength of the operating frequency. However, there are trends to follow for minimum redundancy, minimum number of holes, or missing space hysteresis. The sparse array optimization region typically lies between a minimum-hole array (which is most extreme in terms of the number of cells relative to the array aperture size) and a ULA, or "filled array." By comparing this mapping with the equivalent ULA mapping, the increase in array aperture size can be readily observed.

[0049] Furthermore, since most analyses consider removing cells from the ULA rather than extending an array of known numbers of cells to a larger uniform array, equations have been developed based on these trends to give a first-order approximation of this increase when cell placement constraints are applied (such as MIMO array mapping): Equivalent ULA cell number (constrained) ≈ .................(6) in x It represents the number of sparse array cells.

[0050] By further examining the equation, it can be seen that the equation is... x When the value is less than 12, it follows the trend given by the minimum redundancy array calculation in the existing technology. x For values ​​≥ 12, a trend is observed that is derived from the minimum hole array calculation, where layout mapping constraints have a relatively small impact. These trends are plotted on... Figure 7 In this context, when the computational degrees of freedom of the invention are reduced by imposing cell placement constraints in the design, the most likely equivalent ULA size will appear in the shaded or optimized regions. However, if cell placement constraints are not required, such as in the case of not using MIMO, the solution always follows the MHA trend, and the following equation can be used as the first approximate equivalent ULA size in the invention.

[0051] Equivalent ULA cell number (unconstrained) ≈ ...(7) in x It is still the number of sparse array cells.

[0052] Various embodiments of the present invention enable calculations to give the interval D between the nth unit and the (n+1)th unit. n The values ​​of these values ​​are integer multiples of the unit spacing distance D (which is typically still half the wavelength of the operating frequency), or give the calculation degrees of freedom to find spacing distances containing real numbers. When the aforementioned conditions are set for cases where no cell placement restrictions are required (i.e., when Equation 7 is followed), prior art cell placement locations are ultimately found for the equivalent MHA. It is well known in the art that most post-processing techniques preferably maintain an integer distance D between cells, hence this condition is used here. This simplifies array angle-of-arrival processing, which typically uses FFT-based techniques.

[0053] In embodiments of the present invention, layout constraints caused by MIMO mapping are considered, which is the reason for developing the previously mentioned prior art coprime array and nested array techniques. In MIMO radar, the mapping position of the virtual cell generated by the nth TX antenna and the mth RX antenna in the MIMO is determined by... Given, where M is the total number of RX antennas. For example, Figure 1 and Figure 8The illustrated MIMO configuration shows that a combination of two TX elements with a spacing of 4D and four RX elements with a spacing of D produces a virtual ULA with eight elements of spacing D. However, if all eight virtual elements could be mapped into a sparse array, the aperture size of the resulting sparse array would be equal to the aperture size of a ULA with 24 elements (according to Equation 6). However, since the virtual element positions are the sum of the TX and RX element positions for each TX-RX pair, the RX element spacing is repeated N times throughout the virtual MIMO array (where N is the number of TX antennas in the MIMO), and it is impossible to place the TX and RX antenna elements such that the mapped / virtual MIMO array conforms to any previously reported sparse array with a similar equivalent size.

[0054] To explain this further, now in Figure 9 The diagram illustrates a minimal redundant sparse array with an equivalent ULA size of 24 cells. Many prior art disclosures have discussed the development of these well-known types of sparse arrays, where cell locations are often found using specific optimization algorithms (such as genetic optimization) that assume each sparse array cell must be located somewhere within a small, predefined range. Such techniques are well-known in the art; however, it is clear and apparent that such arrays cannot be formed, and such optimization algorithms cannot be used in MIMO virtual array configurations because cell spacing cannot be aligned when mapping the virtual array.

[0055] Figure 9 This is illustrated graphically by comparing MRA with a mapped MIMO arrangement using 2 TX cells and 4 RX cells, which can only correctly locate 5 out of 8 cells.

[0056] In such MIMO scenarios, coprime arrays are typically used to form virtual sparse arrays because there exists an equation for the placement of computational cells; however, these coprime arrays have smaller apertures (closer to) than other sparse array options. Figure 7 The MRA trend lines in the model (and therefore their effectiveness in improving angular resolution are also reduced). Furthermore, when such existing virtual arrays have been designed, their focus has been solely on spatial hysteresis coverage, or alternatively, on reducing spatial hysteresis redundancy, with only secondary consideration given to sidelobe levels (if they were indeed given consideration).

[0057] In embodiments of the invention, both spatial lag coverage and radiation pattern sidelobe levels have been considered by focusing on the radiation pattern calculated for the main beam at both the line of sight and the edge of the field of view (FOV). This is achieved by applying a weighting element w to each weighting unit. nThis is achieved by adding the correct phase, and is a well-known technique in the art, wherein the phase added at each cell in the same plane of the array is: Degree........................(8) and θ It is the angle at which the edge of the field of view (FOV) appears.

[0058] Here, a solution is sought to minimize the array factor sidelobe level by optimizing the spacing between sparse elements and minimizing any possible false detections that the sparse array may introduce at all angles within the FOV, and thereby minimize the physical array radiation pattern for both beam conditions.

[0059] Figure 10 This is a flowchart illustrating a method 1000 for forming a sparse array antenna according to an embodiment of the present invention. The method can be implemented by a processor that executes one or more instructions stored in memory. Figure 11 The invention is shown for use in this invention. Figure 10 The optimization regions of the first and second optimization problems of the method.

[0060] At step 1010, the size of the equivalent uniform linear array (ULA) aperture is determined based on the target number of sparse cells using equation (5) and the spacing distance D. The spacing distance D is typically half the wavelength of the operating frequency.

[0061] At step 1020, for this ULA, the positive and negative angles of the nearest local minimum (1101, 1102) of the array factor from the view axis are selected, the same phase is applied to all cells, and these angles are set as the first optimization boundary for the virtual array cell positions of the sparse array.

[0062] At step 1030, the first optimization objective 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 sidelobe level within that angular range. This completes the definition of the first problem and essentially considers all optimization regions 1104 and 1105 outside the main lobe 1103.

[0063] Then, a second problem is defined with respect to the condition that the element phase is added based on the spacing distance relative to the first element in the sparse array (Equation 7), where the main beam 1106 points to the edge of the FOV (typically 60 degrees off the line of sight). In embodiments of the invention, the second optimization problem can be fixed as solving for the condition that the main beam points 60 degrees off the line of sight to define the problem when using omnidirectional antenna elements.

[0064] Regarding the second question, at step 1040, the nearest minimum value of the array factor 1107 around the main beam peak when the main beam is turned to this edge of the FOV, and the FOV angle (in...) Figure 11 In the example, a 60-degree offset from the line of sight is used to set the second optimization boundary for most practical antennas. However, when using omnidirectional antenna elements, the second optimization boundary is set based on the two nearest minimum values ​​of the array factor around the main beam peak when the main beam is turned to this edge of the FOV. Edge 1107 is selected as an edge closer to the line of sight than the beam turning direction, which typically turns in a positive angular direction from the line of sight, but can turn in a negative direction without limiting or changing the described invention. In embodiments of the invention, at least two optimization targets can exist. In the example, the optimization targets can be at 0°, +60°, and -60°.

[0065] At step 1050, for region 1108, the second optimization objective is set to the maximum signal level of the array factor at all angles outside the second optimization angle boundary; that is, similar to the first optimization objective, minimizing the sidelobe level within this angle range. In embodiments of the invention, this can be achieved by multiplying the second optimization objective by a factor. k To apply a weighting function to the second optimization objective, wherein, in this invention, the value is used k = 4 . k Any value can be used, and the value can be arbitrarily chosen depending on the type of optimization algorithm used. k The value can be used without limiting or changing the described invention. In embodiments of the invention, a weighting function can be applied to the first optimization objective to prioritize detection around the viewing axis to reduce sidelobe levels.

[0066] At step 1060, the spacing between antenna array elements is optimized for both the first and second problems, wherein identical distances are linked together (due to MIMO virtual array mapping) to simultaneously minimize the first optimization objective and the second optimization objective, or the sum of the first optimization objective and the second optimization objective.

[0067] In embodiments of the invention, the optimization objective is set to minimize the newly defined combined optimization objective. Any type of optimization algorithm can be used, but a generalized reduced gradient type is used in this invention. A solution is found when the global minimum of the combined problem is found in the first and second problems, or when the sidelobe level has been reduced to an acceptable level. By optimizing the array factor level, sidelobes generated by the sparse array are reduced. In another embodiment of the invention, the radiation pattern can be optimized instead of the array factor to help reduce the sidelobe level, because the optimizer focuses on the angular regions with higher gain for individual antenna elements.

[0068] In embodiments of the invention, the generalized reduced gradient function is used to calculate the gradient of the function as the decision variable (or interval distance) changes, and when the partial derivative is equal to zero, it is determined that the optimal solution has been reached. By randomly changing the initial or starting value of the decision variable and repeating this process, it is possible to ensure, over time, that a global minimum is found rather than a local minimum, which may occur near the starting value. However, the invention does not rely on any particular type of solver and other types of solvers, such as gradient solvers, stochastic solvers, simplex solvers, or Newton-Raphson solvers, can be used. Furthermore, by focusing the signal level of the array factor, sidelobes generated from the sparse array are reduced, and by combining the problem of focusing the main beam at the line of sight and the edge of the field of view, a solution considering both sidelobe levels (mainly due to line-of-sight optimization) and spatial lag (mainly due to edge optimization of the FOV scanning angle) is found.

[0069] Because the spacing is linked together according to the designed MIMO mapping architecture and optimized for all possible spacings in the virtual array configuration, all virtual cells can be optimized, allowing for maximization of the virtual array size while reducing the number of missing spatial hysteresis and array factor sidelobe levels. A further consequence of linking the mapped virtual cell spacing (due to the MIMO architecture) is a reduction in the number of optimization variables, and therefore, a faster design process compared to one that does not manipulate the mapped virtual cell spacing.

[0070] By considering Figure 9 The previous example of an 8-element array illustrates the invention by minimizing the array factor outside the main beam, calculated by Equation 4, where two beams focused on the line of sight and at 60 degrees (which is typically the edge of the FOV for most planar antennas) are calculated simultaneously, while allowing the variable D... n Changes were made. Due to the MIMO layout mapping, with the constraint set to D1+D2+D3+D4+D5+D6+D7=11.5 wavelengths (based on 24 elements spaced at 0.5 wavelengths, and derived when x is set to 8 in Equation 7), the degrees of freedom of the problem were reduced by setting D1=D5, D2=D6, and D3=D7. The array factor was minimized by utilizing two beams simultaneously calculated and focused on the line of sight and at 60 degrees, reducing the number of missing hysteresis, which is helpful for later processing of sparse arrays.

[0071] Figure 12 A feasible MIMO mapping array 1200 according to an embodiment of the present invention is shown. When in... Figure 13When compared, the array factor of the prior art 8-cell MRA and the array factor of the layout obtained from the MIMO mapping array 1200 of the present invention show similar sidelobe levels. This MIMO mapping array 1200 in differential array ( Figure 14 Only three holes are missing in the array, meaning that 17D, 18D, and 20D hysteresis (13%) are missing in all 23 possible combinations. This indicates that although some holes exist, their number is significantly reduced compared to similar MIMO layouts optimized for low sidelobe levels using only line-of-sight optimization, and the present invention can be considered a minimal hole array type with reduced aperture size. By comparing the holes appearing in the present invention with those in a prior art 8-element equivalent MHA with similar but slightly larger array apertures, it can be seen that more than 17% of the holes exist in the larger prior art MHA, with the first hole appearing at hysteresis 16D. This hole must be recovered using digital signal processing techniques, such as an iterative method with adaptive thresholding (IMAT) or matrix completion, but the recovery of this hole must be based on one less spatial hysteresis (1D to 15D) compared to the spatial hysteresis (1D to 16D) used in the described invention for recovering hysteresis 17D. Similar results can be seen for larger sparse arrays. Therefore, the MIMO mapping array 1200 is obtained using a novel technique that allows for complete control over the MIMO virtual array layout and has performance similar to that of equivalent prior art MRAs that cannot be configured as virtual array layouts in MIMO systems. The MIMO mapping array 1200 of this invention can be used in defense or war systems, but is more specifically suitable for automotive applications where lower costs are preferred. Although the MIMO array 1200 is a one-dimensional array, it will be apparent to those skilled in the art that the MIMO array 1200 can be used to form a rectangular array.

[0072] As previously mentioned, by including a second optimization problem in which the beam is directed to the edge of the FOV, the number of holes is significantly reduced, which can... Figure 14 This is evident in the spatial hysteresis diagram. This is a key aspect of the invention, where the optimizer is forced to reduce the size of the grating lobes when the main lobe is pointed towards the edge of the FOV. These grating lobes are defined as radiation pattern lobes other than the main lobe, which have sufficiently large inter-cell spacing and added phase to allow radiation fields to be added in phase in more than one direction, and only if the equation... By maintaining an effective grating (where λ is the wavelength of the operating frequency, d is the distance between elements, and θ is the directional angle in radians), these grating lobes can be ideally avoided. This, in turn, means that the positions of the sparse array elements are constrained to not have very large spacing, and consequently, the possibility of eliminating spatial lag is significantly reduced. Figure 14This effect is demonstrated by comparing the hysteresis of MRA, the previously described MIMO array example, and an example of a MIMO array optimized solely using the first optimization problem at the line of sight. Figure 15 The text further indicates the need for a second optimization problem, which compares the array factor plots at the view axis and the edge of the FOV (60 degrees).

[0073] When considering optimization only at the line of sight (i.e., for the first optimization problem), it can be seen that the sidelobes remain at a relatively low level for the line-of-sight scanning angle. However, when a phase delay is added between the antenna elements to make the main beam scan to 60 degrees, large grating lobes can be seen. This means that, in addition to the complexity of DSP processing due to the 12 missing spatial lags, signals from objects near the line of sight may be interpreted as coming from objects at 60 degrees (and vice versa).

[0074] Therefore, by simultaneously optimizing the problem for the main beam focused on both the line of sight and the edge of the field of view (FOV), a solution was found that considers both sidelobe levels (primarily due to line-of-sight optimization) and spatial lag (primarily due to edge optimization of the FOV scanning angle). It should be noted that if the optimization problem is considered only for one condition (i.e., the main beam points to the line of sight or the edge of the FOV), the sidelobe level at a specific beam pointing angle can be significantly reduced. However, this degrades the sidelobe level when the main beam is scanned to other angles. In these cases, solutions were found that allow for more holes in the differential array, thus increasing DSP complexity.

[0075] The overall virtual array is optimized for all possible configurations of transmit and receive unit placement by forcing the transmit and receive array elements to be placed according to the MIMO element mapping in the optimization problem and thus according to the placement of the virtual array elements. The maximum number of possible virtual elements is also used, allowing the virtual array size to be maximized. Furthermore, by linking the array element spacing together according to the MIMO element mapping, the number of optimization variables is reduced compared to a sparse array design with the same number of elements but no constraints on their spacing, and the design process becomes faster. Moreover, by maximizing the size of the virtual array, the equivalent ULA size increases, which translates to increased angular accuracy and resolution.

[0076] In the specification, the terms “comprise (comprise, comprises, comprised, and comprising)” or any variations thereof, and the terms “include (includes, included, included, and including)” or any variations thereof, are considered to be interchangeable and should be provided with the broadest possible interpretation, and vice versa.

[0077] The present invention is not limited to the embodiments described above, but may vary in both construction and details.

Claims

1. A method for designing a sparse MIMO virtual antenna array, the method comprising: The size of the equivalent uniform linear array (ULA) is determined based on the target number of sparse elements in the sparse MIMO virtual antenna array. The first optimization objective is set as the maximum signal level of one or more sidelobes of the ULA when the beam is pointed at the line of sight; The second optimization objective is set as the maximum signal level of one or more sidelobes of the ULA when the beam is pointed at the edge of the field of view; Determine the set of spacing distances between the antenna array elements of the sparse MIMO virtual antenna array, the set of spacing distances simultaneously minimizing the first optimization objective and the second optimization objective, or minimizing the sum of the first optimization objective and the second optimization objective, wherein minimizing the first optimization objective minimizes the maximum radiated power of one or more sidelobes, and minimizing the second optimization objective minimizes one or more missing spatial hysteresis of the sparse MIMO virtual antenna array; as well as The sparse MIMO virtual antenna array is constructed based on the determined set of interval distances.

2. The method of claim 1, wherein: Pointing the beam to the edge of the field of view includes pointing the beam at an angle 60 degrees away from the visual axis.

3. The method of claim 1, further comprising: Pointing the beam to the edge of the field of view includes pointing the beam at an angle of -60 degrees away from the visual axis.

4. The method as claimed in any of the preceding claims, wherein, The set of interval distances includes multiples of the unit interval distance, wherein the unit interval distance is equal to half the wavelength of the operating frequency of the sparse MIMO virtual antenna array.

5. The method as claimed in 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 number of the target sparse elements, wherein when the number of sparse elements is less than 12, the aperture size is approximated by the size trend of the minimum redundancy array.

6. The method as claimed in any of the preceding claims, wherein, When the number of sparse units is equal to or greater than 12, the aperture size of the sparse MIMO virtual antenna array is approximated by the size trend of the minimum aperture array.

7. The method of any of the preceding claims, further comprising applying a first weighting factor to the determination of the set of interval distances to minimize one or more sidelobe levels at the visual axis.

8. The method of any of the preceding claims, further comprising applying a second weighting factor to the determination of the set of interval distances to reduce the number of missing spatial hysteresis in the sparse MIMO virtual antenna array when the beam is pointed at an angle 60 degrees away from the line of sight.

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

10. The method of claim 1, wherein, Setting the first optimization objective includes: The positive and negative angles of the nearest local minimum from the line of sight of the ULA are selected as the first optimized angular boundaries for the virtual array cell positions of the MIMO sparse array; and Set 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.

11. The method of claim 1, wherein, Setting the second optimization objective includes: The positive and negative angles around the nearest local minimum value around the main beam peak when the beam is pointed to the edge of the field of view are selected as the second optimized angular boundary for the virtual array cell position of the MIMO sparse array; and The maximum signal level of the array factor at all angles outside the region between the second optimization angle boundaries is set as the second optimization target.

12. The method of claim 1, wherein, The normalized beamwidth of the main lobe of the array factor of the sparse MIMO antenna array is the same as the normalized beamwidth of a ULA with the same aperture size.

13. A system for designing sparse MIMO virtual antenna arrays, the system comprising: The memory is used to store one or more instructions; as well as A processor, the processor being configured to execute the one or more instructions to perform the following operations: The size of the equivalent uniform linear array (ULA) is determined based on the target number of sparse elements in the sparse MIMO virtual antenna array. The first optimization objective is set as the maximum signal level of one or more sidelobes of the ULA when the beam is pointed at the line of sight; The second optimization objective is set as the maximum signal level of one or more sidelobes of the ULA when the beam is pointed at the edge of the field of view; Determine the set of spacing distances between the antenna array elements of the sparse MIMO virtual antenna array, the set of spacing distances simultaneously minimizing the first optimization objective and the second optimization objective, or minimizing the sum of the first optimization objective and the second optimization objective, wherein minimizing the first optimization objective minimizes the maximum radiated power of one or more sidelobes, and minimizing the second optimization objective minimizes one or more missing spatial hysteresis of the sparse MIMO virtual antenna array; as well as The sparse MIMO virtual antenna array is constructed based on the determined set of interval distances.

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