A method for optimizing MIMO radar antenna position for three-dimensional imaging of space targets

Abstract

The present disclosure provides a MIMO radar antenna position optimization method for three-dimensional imaging of space targets, which decomposes a two-dimensional array composed of ground-based radars into two orthogonal one-dimensional arrays; for each one-dimensional array, the theoretical maximum grating lobe is calculated according to the number of transceiver antennas and the radar operating frequency; if the theoretical maximum grating lobe meets the maximum grating lobe index requirement of the imaging area, only the imaging resolution is used as an index to allocate the position of the one-dimensional array within the equivalent aperture length range; otherwise, the one-dimensional array position optimization is performed with the imaging area maximum grating lobe and the imaging resolution as joint indexes; the optimization results of the azimuth array and the height array are combined to obtain the array position optimization result. The present application decouples the azimuth and height directions, optimizes and combines them respectively, reduces the optimization complexity, effectively solves the contradiction between the high grating lobe energy and the azimuth resolution when the sparse MIMO radar performs three-dimensional imaging of space targets, and improves the space target imaging quality.

Description

Technical Field

[0001] This invention relates to the field of space target radar imaging, and more particularly to a method for optimizing the position of a MIMO radar antenna for three-dimensional imaging of space targets. Background Technology

[0002] Geostationary orbit (GEO) targets are satellites or other space objects located above the Earth's equator, synchronized with the Earth's rotation. The altitude of a GEO target is approximately 35,768 kilometers. Geostationary orbit satellites are characterized by their relative stationary position relative to the Earth, wide coverage area, and high application benefits, making them widely used in military, civilian, and commercial fields and highly valued by various countries. If high-resolution imaging of geostationary orbit targets can be achieved, information such as the satellite's structure and the type and size of its onboard equipment can be obtained, and further analysis of its operating frequency band, imaging capabilities, and mission objectives can be performed.

[0003] Because GEO targets are stationary relative to the ground, existing ground-based radars cannot image them in two or three dimensions, only acquiring one-dimensional range images. However, if multiple radars distributed across the Earth's surface are networked into a sequential transmit-simultaneous receive (MIMO) radar system, the azimuth resolution of geostationary orbit targets can be obtained using the equivalent azimuth aperture formed by the networked radars, thus enabling imagery of space targets. When MIMO radars are distributed along a linear array, two-dimensional imaging results of space targets can be obtained; when MIMO radars are distributed across the Earth's surface to form an array, three-dimensional imaging results of space targets can be obtained.

[0004] Ground-based radars capable of detecting GEO targets are large, expensive, and have long construction periods, thus their numbers are limited. Networking a limited number of radars to detect GEO targets is a typical imaging problem under sparse observation conditions. The number of transmit / receive elements and the antenna placement of a MIMO radar determine its spatial sampling capability for the target, and therefore determine the imaging performance, including azimuth resolution, sidelobe level, and maximum grating lobe.

[0005] Array configuration is essentially an array optimization problem for a specific application. The key to optimization is determining the objective function and then implementing array optimization using an optimization algorithm. MIMO radar array optimization typically involves both element position and element excitation amplitude. While optimization algorithms can simultaneously optimize both element position and amplitude using weighted methods, a significant drawback of amplitude weighting is that it doesn't fully utilize signal energy, leading to a lower signal-to-noise ratio, reduced beamforming quality, and increased optimization complexity. Therefore, for GEO target MIMO radar imaging array configuration, a primary focus should be on optimizing element position.

[0006] For MIMO radar imaging of space targets, the system imaging performance requirements are met by optimizing the MIMO radar antenna position. Unlike traditional MIMO array design, the constraints and optimization targets for MIMO arrays used for space target detection are different.

[0007] For ground-based radar imaging of space targets, the equivalent array length determines the azimuth resolution. To achieve higher azimuth resolution, MIMO radar requires a longer equivalent array length. However, the number of ground-based radars is limited, which leads to excessively large antenna array spacing. Sparse arrays cause high grating lobes during imaging, resulting in strong false targets at the true target locations within a certain range in the azimuth direction. Therefore, it is essential to improve the grating lobe suppression capability of the imaging radar system.

[0008] Therefore, position optimization for MIMO radar requires consideration of targets such as maximum grating lobe, azimuth resolution, and elevation resolution within the imaging area. The optimization problem can be described as: given some parameters, finding the antenna position that satisfies the resolution and maximum grating lobe requirements of the imaging area. Classical optimization algorithms such as Particle Swarm Optimization (PSO) and genetic algorithms can be used to solve this type of problem.

[0009] The basic idea of ​​the Particle Swarm Optimization (PSO) algorithm is to find the optimal solution through cooperation and information sharing among individuals in a swarm. PSO consists of a particle swarm, where each particle represents a solution. The particle swarm searches and aggregates throughout the solution space, finding the optimal solution by remembering the local optima of the particles and being guided by the global optima. Since the transmitting and receiving antennas are arbitrarily distributed, only the back projection imaging (BP) algorithm in the time domain can be used for radar imaging. However, the time complexity of the BP imaging algorithm is related to the number of transmitting and receiving antennas and the size of the imaging grid. When optimizing using the PSO algorithm, each particle in each iteration requires an imaging process, therefore, directly using a two-dimensional array to perform three-dimensional imaging to optimize the array position has extremely high time complexity. Summary of the Invention

[0010] In view of this, the present invention provides a MIMO radar antenna position optimization method for three-dimensional imaging of space targets, which decouples the azimuth and altitude directions, optimizes the one-dimensional array in each direction separately and then combines them, thereby reducing the complexity of optimizing the array position.

[0011] To solve the above-mentioned technical problems, the present invention is implemented as follows.

[0012] A method for optimizing the antenna position of a MIMO radar for three-dimensional imaging of space targets includes: Step 1: Decompose the two-dimensional array of ground-based radar into two orthogonal one-dimensional arrays, namely the azimuth array and the elevation array; Step 2: For each of the two one-dimensional arrays, calculate the theoretical maximum grating lobe based on the number of transmitting and receiving antennas and the radar operating frequency. If the theoretical maximum grating lobe meets the maximum grating lobe index requirement for the imaging region, no imaging processing is required; the position of the one-dimensional array is allocated within the equivalent aperture length range based solely on the imaging resolution. If the theoretical maximum grating lobe does not meet the maximum grating lobe index requirement for the imaging region, the position of the one-dimensional array is optimized based on the two-dimensional imaging of the one-dimensional array, using the maximum grating lobe of the imaging region and the imaging resolution as joint indices. Step 3: Combine the optimization results of the azimuth array and the elevation array to obtain the array position optimization result of the MIMO radar antenna.

[0013] Preferably, in step 1, before decomposing the azimuth array and the elevation array, an imaging coordinate system is established to determine the range, azimuth, and elevation directions of the imaging, such that the azimuth resolution and maximum grating lobe are only related to the array distribution along the azimuth direction, and the elevation resolution and maximum grating lobe are only related to the array distribution along the elevation direction. A three-dimensional imaging coordinate system is established based on the location of the spatial target. Assuming the Earth is an ideal sphere, the X-axis is the distance from the Earth's center of mass to the center of the target, and the XY plane is the equatorial plane. The three-dimensional spatial coordinate system is established and is a right-handed system. The Z-axis is perpendicular to the equatorial plane and points to the North Pole. The Y-axis is in the equatorial plane and is perpendicular to the X-axis. The X-direction is defined as the distance direction, the Y-direction as the azimuth direction, and the Z-direction as the altitude direction.

[0014] Preferably, in step 2, the theoretical maximum grating lobe is calculated as follows: ;in, This represents the maximum frequency of the transmitted signal from the transmitting radar in the one-dimensional array. This refers to the number of channels formed by the transmitting and receiving antennas in a one-dimensional array. This refers to the bandwidth of the transmitted signal.

[0015] Preferably, in step 2, the allocation of the position of the one-dimensional array based solely on imaging resolution is as follows: Calculate the equivalent aperture length of the one-dimensional array based on its imaging resolution specifications. ; Based on the number of transmitting antennas and the equivalent aperture length Assign the positions of the transmitting antennas and transmitting antennas in the one-dimensional array: When the number of transmitting antennas is 1, the receiving antenna is arranged at a point centered on the nadir point with a length of [missing information] on the Earth's surface. The array can meet the imaging resolution requirements; among them, two receiving antennas are located at a length of... At both ends of the array, the remaining receiving and transmitting antennas are located at... Randomly distributed within a range; When the number of transmitting antennas is greater than or equal to 2, the transmitting and receiving antennas are arranged with the nadir point as the center and a ground length of [missing information]. In the array; among them, two transmitting antennas are located at a length of At both ends of the array, the remaining transmitting antennas and all receiving antennas are located at... Random distribution within the range can meet the requirements of imaging resolution.

[0016] Preferably, in step 2, the two-dimensional imaging based on a one-dimensional array, using the maximum raster lobe of the imaging region and the imaging resolution as joint indicators, specifically includes optimizing the position of the one-dimensional array: Calculate the equivalent aperture length of the one-dimensional array based on its imaging resolution specifications. ; Determine the antenna to be optimized: When the number of transmitting antennas is 1, there are two receiving antennas located centered at the nadir point, with a ground length of... At both ends of the array, the remaining receiving and transmitting antennas are distributed at... Within the length array range, the specific location needs to be optimized; when the number of transmitting antennas is greater than or equal to 2, the transmitting antennas are located centered on the nadir point, with a ground length of [missing information]. At both ends of the array, the remaining transmitting antennas and all receiving antennas are distributed at... Within the length array range, the specific location needs to be optimized; The position allocation scheme of the antenna to be optimized is used to form particles; the particle swarm algorithm is used to obtain the optimal position of the antenna to be optimized, and combined with the determined antennas at both ends of the array, the position optimization result of the one-dimensional array is obtained. The fitness calculation method of the particle swarm optimization algorithm is as follows: For the array position allocation scheme corresponding to the particles, a two-dimensional imaging result is obtained through backpropagation (BP) imaging. The two-dimensional imaging result is projected onto the corresponding direction to obtain the peak amplitude radiation pattern (PAD). The main lobe region is determined based on known imaging resolution indicators, and the largest grating lobe in the grating lobe region outside the main lobe region is extracted from the PAD. Calculate the maximum grating lobe fitness based on the maximum grating lobe Maximum grid lobe The smaller the value, the greater the maximum grid lobe fitness. The higher the value, the better; particle fitness is determined based on the maximum grid lobe fitness.

[0017] Preferably, in the particle swarm optimization, a penalty factor is further designed based on the antenna position spacing constraint and the array boundary constraint; the particle fitness is equal to the maximum grating lobe fitness minus the penalty factor.

[0018] Preferably, the calculation of the equivalent aperture length of the one-dimensional array... for: The known imaging resolution index is The cumulative angle of the one-dimensional antenna array relative to the space target is calculated using formula (I). : (I) in, The wavelength corresponding to the center frequency of the radar transmitted signal; The cumulative angle Substituting into formula (II), we obtain the angle between the one-dimensional antenna array and the center of the Earth. : (II) in, The sum of the length of the Earth's radius and the altitude of its geosynchronous orbit. The radius of the Earth; The equivalent aperture length of a one-dimensional array for: .

[0019] Preferably, in step 3, when combining the optimization results of the azimuth array and the altitude array, the Latin hypercube sampling technique is used to divide the one-dimensional array into intervals, select interval values, and shuffle and pair them to combine the two one-dimensional arrays into two-dimensional coordinates.

[0020] Beneficial effects: (1) This invention provides a method for optimizing the position of a MIMO radar antenna for three-dimensional imaging of space targets. It decouples the azimuth and elevation directions, optimizes the one-dimensional array in each direction separately and then combines them, thereby reducing the complexity of optimizing the array position.

[0021] (2) When optimizing, the theoretical maximum grating lobe is given priority. Based on the ideal maximum grating lobe, the position of the one-dimensional array is allocated only within the equivalent aperture length range based on the imaging resolution. No imaging processing is required, thereby reducing unnecessary calculations and lowering the optimization difficulty.

[0022] (3) If the theoretical maximum grating lobe does not meet the requirements, the position optimization is carried out based on the two-dimensional imaging of the one-dimensional array using the maximum grating lobe of the imaging area and the imaging resolution as joint indicators. Since it is two-dimensional imaging, the array position optimization can be completed with limited computation.

[0023] (4) The present invention can effectively solve the contradiction between the high grating lobe energy and the azimuth resolution when sparse MIMO radar performs three-dimensional imaging of space targets, thereby improving the imaging quality of space targets. Attached Figure Description

[0024] Figure 1 This is a flowchart of the present invention.

[0025] Figure 2 This is an XOZ profile of the imaging scene.

[0026] Figure 3 The result is the antenna position optimization in the height direction.

[0027] Figure 4 This is the result of the azimuth antenna position optimization.

[0028] Figure 5 This shows the antenna location distribution results.

[0029] Figure 6 This is the imaging result. Detailed Implementation

[0030] The purpose of this invention is to reduce the extremely high complexity caused by the need for three-dimensional imaging during MIMO radar antenna position optimization. To address this problem, the solution proposed in this invention is as follows: Firstly, it is necessary to determine reasonable optimization objectives; Secondly, it avoids 3D imaging calculations, reducing computational load and complexity; Thirdly, we should try to determine the parameters by direct calculation using known parameters, and try to avoid the computational burden of joint optimization algorithms such as particle swarm optimization.

[0031] Regarding the first solution mentioned above, based on the analysis of the background technology, this invention selects improving the grating lobe suppression capability of the imaging radar system and satisfying the azimuth and altitude resolution as the objectives that antenna position optimization needs to meet. Regarding the second solution mentioned above, this invention reduces processing difficulty by decomposing the two-dimensional array of ground-based radars into two orthogonal one-dimensional arrays, simplifying three-dimensional imaging into two-dimensional imaging. Regarding the third solution mentioned above, given the limited number of ground-based radars and the predetermined number of transmitting and receiving antennas, coupled with the generally known radar operating frequency, this invention designs parameter calculation methods based on known quantities such as the number of transmitting and receiving antennas, the center frequency of the radar signal, and bandwidth, avoiding complex calculations.

[0032] Based on the above considerations, this invention provides a MIMO radar antenna position optimization method for three-dimensional imaging of space targets, comprising: Step 1: Decompose the two-dimensional array of ground-based radar into two orthogonal one-dimensional arrays, namely the azimuth array and the elevation array.

[0033] Step 2: For each of the two one-dimensional arrays, calculate the theoretical maximum grating lobe based on the number of transmitting and receiving antennas and the radar operating frequency. If the theoretical maximum grating lobe meets the maximum grating lobe index requirement of the imaging region, no imaging processing is required, and the position of the one-dimensional array is allocated within the equivalent aperture length range based solely on the imaging resolution. If the theoretical maximum grating lobe does not meet the maximum grating lobe index requirement of the imaging region, the position of the one-dimensional array is optimized based on the two-dimensional imaging of the one-dimensional array, using the maximum grating lobe of the imaging region and the imaging resolution as joint indices.

[0034] Step 3: Combine the optimization results of the azimuth array and the elevation array to obtain the array position optimization result of the MIMO radar antenna.

[0035] As can be seen, this invention decouples the azimuth and height directions, optimizing the one-dimensional array separately for each direction before combining them, thus reducing the complexity of optimizing the array position. Simultaneously, the optimization prioritizes the theoretical maximum grating lobe. Based on the ideal maximum grating lobe, the position of the one-dimensional array is allocated solely based on the imaging resolution within the equivalent aperture length, eliminating the need for imaging processing and reducing unnecessary computation, thereby lowering the optimization difficulty. If the theoretical maximum grating lobe does not meet the requirements, the position optimization is then performed based on two-dimensional imaging of the one-dimensional array, using the maximum grating lobe of the imaging region and the imaging resolution as joint indicators. Because it is two-dimensional imaging, array position optimization can be completed with limited computational resources.

[0036] The implementation process of the above solution will be described in detail below with reference to the accompanying drawings and examples.

[0037] Step 1: Decompose the two-dimensional array of ground-based radar into two orthogonal one-dimensional arrays, namely the azimuth array and the elevation array.

[0038] In this step, the imaging coordinate system is first established to determine the range, azimuth, and height directions of the image.

[0039] A three-dimensional imaging coordinate system is established based on the GEO target location. Assuming the Earth is an ideal sphere, the X-axis is defined as the distance from the Earth's center of mass to the target's center, and the XY plane is defined as the equatorial plane. A three-dimensional spatial coordinate system (right-handed system) is established, with the Z-axis perpendicular to the equatorial plane and pointing towards the North Pole, and the Y-axis lying in the equatorial plane and perpendicular to the X-axis. The X-direction is defined as the range direction, the Y-direction as the azimuth direction, and the Z-direction as the altitude direction.

[0040] In a three-dimensional coordinate system, three-dimensional imaging needs to consider the resolution in the azimuth and height directions. Due to their independence, they need to be processed separately.

[0041] Here, we take the height dimension as an example. Let the target center point be P, and the XOZ profile of the three-dimensional coordinate system be as follows. Figure 2As shown in the diagram, the center of the sphere is O, the target in geostationary orbit is point P, and the line connecting OP intersects the Earth's surface at point Q. In the two-dimensional plane, two tangent lines passing through point P and tangent to the Earth intersect the Earth at points T1 and T2 respectively. Therefore, the arc segment from Earth that allows observation of target P is T1-Q-T2. The distances OT1 and OT2 are both Earth radii. The distance to OP is the sum of the Earth's radius and the altitude of the geosynchronous orbit. The distribution range of the antenna array along this arc is... ,in Symmetric about point Q. Let... The cumulative angle is the angle between the ground-based radar antenna array and the target P. Let be the angle between the ground-based radar array and the origin O. Then, in the triangle... Middle, Angle for ,horn for .

[0042] Then in the triangle In the middle, according to the sine theorem of a triangle, the angle is obtained. and The relationship is as follows.

[0043] (1) in, The length of the Earth's radius plus the target's altitude, The radius of the Earth, i.e. .

[0044] Step 2: For each of the two one-dimensional arrays, calculate the theoretical maximum grating lobe based on the number of transmitting and receiving antennas and the radar operating frequency.

[0045] Theoretically, the first grating lobe The amplitude at that point is:

[0046] in, The frequency of the transmitted signal. This represents the total number of transmit and receive antenna channels. This refers to the bandwidth of the transmitted signal.

[0047] This allows us to obtain the maximum amplitude at the first grating lobe. for:

[0048] in, This represents the maximum frequency of the transmitted signal. The further away from the main lobe, the lower the grating lobe.

[0049] For example, for an X-band radar, assuming the transmitted signal frequency range is 9GHz~11GHz, the bandwidth is 2GHz, and the radar antenna has 2 transmitters and 40 receivers, then... =20log10(11 / 80 / 2)=-23.25dB. For a Ka-band radar, assuming the transmitted signal frequency range is 34GHz~36GHz, the bandwidth is 2GHz, and the radar antenna has 2 transmits and 40 receives, then... =20log10(36 / 80 / 2)=-12.96 dB.

[0050] If the theoretical maximum value of the grating lobe meets the index requirement of the maximum grating lobe in the imaging area, that is, all grating lobes in the entire imaging space meet the imaging requirements, then the influence of the grating lobe does not need to be considered, and no imaging processing is required. The antenna position can be obtained by theoretical analysis based on the array length.

[0051] If the theoretical maximum value of the grating lobe does not meet the requirements for the maximum grating lobe in the imaging region, in order to make the grating lobe located outside the imaging region, it is necessary to consider joint optimization with resolution and the maximum grating lobe in the imaging region as objective functions.

[0052] Step 3: Determine whether the theoretical maximum grating lobe meets the maximum grating lobe index requirements of the imaging region; if yes, proceed to step 4; otherwise, proceed to step 5.

[0053] Step 4: Without imaging processing, allocate the position of the one-dimensional array within the equivalent aperture length range based solely on the imaging resolution. Then proceed to Step 6.

[0054] In this step, the equivalent aperture length of the one-dimensional array is first calculated based on the imaging resolution specifications of the one-dimensional array. Then, based on the number of transmitting antennas and the equivalent aperture length... Assign the positions of the transmitting antennas and transmitting antennas in the one-dimensional array.

[0055] Equivalent aperture length The method for determining it is as follows: In near-field conditions, due to spatial invariance, for a given array equivalent aperture, the resolution changes with the target position. The resolution of the target along the perpendicular bisector of the array's equivalent aperture is typically used as the resolution metric. Figure 3 Point P in the equation has the following relationship: (2) in, To accumulate angles, It is an oblique perspective. For height resolution, The wavelength corresponds to the center frequency of the radar transmitted signal.

[0056] Consider oblique angle If the value is 0, the above equation simplifies to: (3) So, given the resolution specifications At that time, the accumulated angle can be obtained from equation (3). The value of can be obtained from formula (1). The value of . In the XOZ plane, The value can be used to calculate the surface aperture length. The value is , For the Earth's radius, equal to .based on The array length can be determined, and the array of this length is arranged at a position centered on the sub-satellite point, with the direction corresponding to that of a one-dimensional array.

[0057] The spatial wave vector of a MIMO array target is composed of the sum of the transmitted wave vector and the received wave vector. The following discussion will focus on the different numbers of transmitting and receiving antennas.

[0058] Taking altitude as an example, when the number of transmitting antennas is 1, based on the relationship between the equivalent aperture of the MIMO array and SAR, the receiving antenna is arranged at a point centered on the nadir point with a ground length of [missing information]. The array can meet the requirements for imaging height resolution. Two receiving antennas are located in... At both ends of the array, the remaining receiving and transmitting antennas are randomly distributed within this range. When the number of transmitting antennas is greater than or equal to 2, the transmitting and receiving antennas are arranged in an area centered on the nadir point with a ground length of [missing information]. In the array; among them, two transmitting antennas are located at a length of At both ends of the array, the remaining transmitting antennas and all receiving antennas are within this range. Random distribution within the height dimension can meet the requirements for altitude resolution. Identical positional allocation in the azimuth dimension means changing the resolution to azimuth resolution.

[0059] Step 5: Joint optimization based on resolution and maximum raster lobe of imaging region.

[0060] Taking altitude as an example, this step mainly includes the following steps: (1) Calculate the equivalent aperture length of the height array based on the height imaging resolution index. The calculation method is the same as in step four.

[0061] (2) Determine the antenna to be optimized: There are two receiving antennas located at a distance of [missing information] centered on the nadir point, with a ground length of [missing information]. At both ends of the array, the remaining receiving and transmitting antennas are distributed at... Within the length array range, the specific location needs to be optimized; when the number of transmitting antennas is greater than or equal to 2, the transmitting antennas are located centered on the nadir point, with a ground length of [missing information]. At both ends of the array, the remaining transmitting antennas and all receiving antennas are distributed at... Within the length array range, the specific locations need to be optimized. The range of values ​​for the distribution of these antenna locations to be optimized is centered on the nadir point and extends over a distance of [missing information - likely a length value]. / The array region.

[0062] (3) The positions of all antennas to be optimized form an allocation scheme corresponding to one particle. Based on the distribution range of the antenna positions to be optimized, the positions and velocities of the particles in the population are initialized.

[0063] (4) Calculate the fitness of each particle in the swarm. For an array with arbitrary distribution, a two-dimensional imaging result in the range-height direction must be obtained through backpropagation (BP). The maximum value in the range direction is used as the projection value in the height direction, thus projecting the two-dimensional imaging result onto the height direction to obtain the Peak Amplitude Pattern (PAP). Therefore, the two-dimensional image can be simplified to a one-dimensional function, and the peak amplitude pattern is defined as follows: (4) Where x is the elevation coordinate and y is the range coordinate. These are pixels in the two-dimensional imaging result.

[0064] The raster lobe region is selected from the area outside a certain range to the left and right of the main lobe peak. The maximum raster lobe can typically be defined as: (5) in, This represents the theoretical high-resolution aspect ratio.

[0065] Therefore, based on the known imaging resolution specifications The main lobe region is determined, and the grating lobe region outside the main lobe region is extracted from the peak amplitude pattern (PAP). The maximum grating lobe is obtained using formula (5). The maximum grid lobe fitness is calculated according to formula (6). : (6) in, C It is a positive constant greater than 1, because SL A negative value indicates the maximum grid lobe fitness. It is a positive value, and the value of the maximum grating lobe. The smaller the value, the greater the maximum grid lobe fitness. The larger.

[0066] Finally, based on the maximum grating lobe fitness Determine the particle fitness. The maximum grid lobe fitness can be directly used. As a particle fitness metric, a penalty factor can be designed based on antenna spacing constraints and array boundary constraints. The particle fitness is equal to the maximum grating lobe fitness. Subtract the penalty factor. Use a constant. C Adjust the maximum lobe fitness to match the magnitude of the penalty factor.

[0067] When designing the penalty factor based on antenna position spacing constraints and array boundary constraints, the spacing between each pair of antennas is calculated. If it is less than a set threshold, it is recorded as antenna spacing being too small. The more cases of antenna spacing being too small, the larger the penalty factor. At the same time, it is calculated whether each antenna is within the array boundary range. If it is outside the range, it is recorded as antenna exceeding the boundary. The more cases of antenna exceeding the boundary, the larger the penalty factor.

[0068] (5) For each particle, compare its fitness with the fitness of its individual history best (local optimum). If it is better, then take it as the current individual history best for that particle.

[0069] (6) For each particle, compare its fitness with the fitness of the swarm best (global optimal solution), and if it is better, then take it as the current swarm best.

[0070] (7) Adjust the particle speed and position.

[0071] (8) If the iteration termination condition is met, the population optimum obtained is the final optimization result; otherwise, go to (4). The iteration termination condition can usually be selected as the maximum number of iterations or the maximum number of grating lobes meeting the index requirements during the search iteration process.

[0072] The final optimized transmit antenna position coordinates are as follows: The position coordinates of the receiving antenna are .

[0073] Assuming the MIMO radar has 2 transmitting antennas and 40 receiving antennas, a center frequency of 35 GHz, a bandwidth of 2 GHz, a height resolution requirement of better than 0.2 m, an imaging area ranging from -10 m to 10 m from the target center, and a maximum grating lobe better than -16 dB, the theoretical maximum grating lobe is -12.96 dB, which does not meet the requirement for the maximum grating lobe within the imaging area. Therefore, joint optimization of the radar antennas and target position is required. Assuming the number of particles is 30 and the number of iterations is 100, the final optimization result is as follows: Figure 3 As shown, the transmitting antenna has a range of 750 km on the Earth's surface, corresponding to a latitude range of (-3.36°, 3.36°) (negative values ​​are located in the Southern Hemisphere).

[0074] To optimize the azimuth antenna position, the number of transmitting and receiving antennas remains the same as in the altitude direction. Based on the imaging area range and maximum grating lobe index in the azimuth direction, the above steps are repeated to obtain the optimized azimuth result. Let the optimized transmitting antenna position coordinates be... The position coordinates of the receiving antenna are Assuming the radar parameters are set as above, the azimuth resolution is required to be better than 0.2m, the imaging area is from -6m to 6m from the target center, and the maximum grating lobe is better than -16dB. The optimized antenna position results are as follows: Figure 4 As shown.

[0075] Step 6: Combine the optimization results of the azimuth array and the elevation array to obtain the array position optimization result of the MIMO radar antenna.

[0076] When combining data, the transmitting and receiving antennas are distributed across the entire two-dimensional space as much as possible. For example, Latin hypercube sampling techniques can be used to divide a one-dimensional array into intervals, select values ​​for each interval, and shuffle and pair them, combining two one-dimensional arrays into a two-dimensional coordinate system. Specifically: First, sort the optimized one-dimensional array coordinates in the height and azimuth directions respectively. Then, divide the intervals according to the frequency, select the elements belonging to the interval, and ensure that each interval has one and only one element and the elements are not repeated. Then, keeping the element order of the height (or azimuth) interval unchanged, the element order of the azimuth (or height) interval is randomly shuffled to break the association between the height and azimuth, thus achieving two-dimensional dispersion; finally, the shuffled height and azimuth elements are paired one by one to obtain the optimized two-dimensional coordinates.

[0077] Antenna position distribution of a certain combination form as follows Figure 5 As shown, the antenna obtains the following three-dimensional imaging results of the target: Figure 6 As shown. Calculations from the imaging results show that, at this array position, the azimuth resolution of the point target imaging is 0.192m, the elevation resolution is 0.189m, the maximum grating lobe in the azimuth is -16.2dB, and the maximum grating lobe in the elevation is -16.9dB, which meets the system design requirements.

[0078] This concludes the process.

[0079] In summary, this invention addresses the problem of ground-based radar imaging of space targets by using parameters such as the number of transmitting antennas, the number of receiving antennas, the center frequency of the radar signal, and the bandwidth as known parameters, and using azimuth and altitude resolution and the maximum grating lobe of the imaging area as optimization indicators to optimize the antenna position.

[0080] The antenna position optimization method proposed in this invention can effectively solve the contradiction between excessively high grating lobe energy and azimuth resolution when sparse MIMO radar performs three-dimensional imaging of space targets, thereby improving the imaging quality of space targets.

[0081] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the position of a MIMO radar antenna for three-dimensional imaging of space targets, characterized in that, include: Step 1: Decompose the two-dimensional array of ground-based radar into two orthogonal one-dimensional arrays, namely the azimuth array and the elevation array; Step 2: For each of the two one-dimensional arrays, calculate the theoretical maximum grating lobe based on the number of transmitting and receiving antennas and the radar operating frequency. If the theoretical maximum grating lobe meets the maximum grating lobe index requirement for the imaging region, no imaging processing is required; the position of the one-dimensional array is allocated within the equivalent aperture length range based solely on the imaging resolution. If the theoretical maximum grating lobe does not meet the maximum grating lobe index requirement for the imaging region, the position of the one-dimensional array is optimized based on the two-dimensional imaging of the one-dimensional array, using the maximum grating lobe of the imaging region and the imaging resolution as joint indices. Step 3: Combine the optimization results of the azimuth array and the elevation array to obtain the array position optimization result of the MIMO radar antenna.

2. The method as described in claim 1, characterized in that, In step 1, before decomposing the azimuth array and the elevation array, an imaging coordinate system is established to determine the range, azimuth, and elevation directions of the imaging. This ensures that the azimuth resolution and maximum raster lobe are only related to the array distribution along the azimuth direction, and the elevation resolution and maximum raster lobe are only related to the array distribution along the elevation direction. A three-dimensional imaging coordinate system is established based on the location of the spatial target. Assuming that the Earth is an ideal sphere, the X-axis is the distance from the Earth's center of mass to the center of the target, and the XY plane is the equatorial plane. The three-dimensional spatial coordinate system is established and is a right-handed system. The Z-axis is perpendicular to the equatorial plane and points towards the North Pole; the Y-axis lies in the equatorial plane and is perpendicular to the X-axis; the X-direction is defined as the distance direction, the Y-direction as the azimuth direction, and the Z-direction as the altitude direction.

3. The method as described in claim 1, characterized in that, In step 2, the theoretical maximum grating lobe is calculated as follows: ;in, This represents the maximum frequency of the transmitted signal from the transmitting radar in the one-dimensional array. This refers to the number of channels formed by the transmitting and receiving antennas in a one-dimensional array. This refers to the bandwidth of the transmitted signal.

4. The method as described in claim 1, characterized in that, In step 2, the allocation of the one-dimensional array position based solely on imaging resolution is as follows: Calculate the equivalent aperture length of the one-dimensional array based on its imaging resolution specifications. ; Based on the number of transmitting antennas and the equivalent aperture length Assign the positions of the transmitting antennas and transmitting antennas in the one-dimensional array: When the number of transmitting antennas is 1, the receiving antenna is arranged with the nadir point as the center and a length of [missing information] on the ground. The array can meet the imaging resolution requirements; among them, two receiving antennas are located at a length of... At both ends of the array, the remaining receiving and transmitting antennas are located at... Randomly distributed within a range; When the number of transmitting antennas is greater than or equal to 2, the transmitting and receiving antennas are arranged with the nadir point as the center and a ground length of [missing information]. In the array; among them, two transmitting antennas are located at a length of At both ends of the array, the remaining transmitting antennas and all receiving antennas are located at... The random distribution within the range can meet the requirements of imaging resolution.

5. The method as described in claim 1, characterized in that, In step 2, the two-dimensional imaging based on a one-dimensional array, using the maximum raster lobe of the imaging region and the imaging resolution as joint indicators, specifically includes the following: Calculate the equivalent aperture length of the one-dimensional array based on its imaging resolution specifications. ; Determine the antenna to be optimized: When the number of transmitting antennas is 1, there are two receiving antennas located centered at the nadir point, with a ground length of... At both ends of the array, the remaining receiving and transmitting antennas are distributed at... Within the length array range, the specific location needs to be optimized; when the number of transmitting antennas is greater than or equal to 2, the transmitting antennas are located centered on the nadir point, with a ground length of [missing information]. At both ends of the array, the remaining transmitting antennas and all receiving antennas are distributed at... Within the length array range, the specific location needs to be optimized; The position allocation scheme of the antenna to be optimized is used to form particles; the particle swarm algorithm is used to obtain the optimal position of the antenna to be optimized, and combined with the determined antennas at both ends of the array, the position optimization result of the one-dimensional array is obtained. The fitness calculation method of the particle swarm optimization algorithm is as follows: For the array position allocation scheme corresponding to the particles, a two-dimensional imaging result is obtained through backpropagation (BP) imaging. The two-dimensional imaging result is projected onto the corresponding direction to obtain the peak amplitude radiation pattern (PAD). The main lobe region is determined based on known imaging resolution indicators, and the largest grating lobe in the grating lobe region outside the main lobe region is extracted from the PAD. Calculate the maximum grating lobe fitness based on the maximum grating lobe Maximum grid lobe The smaller the value, the greater the maximum grid lobe fitness. The higher the value, the better; particle fitness is determined based on the maximum grid lobe fitness.

6. The method as described in claim 5, characterized in that, In the particle swarm optimization, a penalty factor is further designed based on the antenna position spacing constraints and array boundary constraints; the particle fitness is equal to the maximum grating lobe fitness minus the penalty factor.

7. The method as described in claim 4 or 5, characterized in that, The calculation of the equivalent aperture length of the one-dimensional array for: The known imaging resolution index is The cumulative angle of the one-dimensional antenna array relative to the space target is calculated using formula (I). : （I） in, The wavelength corresponding to the center frequency of the radar transmitted signal; The cumulative angle Substituting into formula (II), we obtain the angle between the one-dimensional antenna array and the center of the Earth. : (II) in, The sum of the length of the Earth's radius and the altitude of its geosynchronous orbit. The radius of the Earth; The equivalent aperture length of a one-dimensional array for: .

8. The method as described in claim 1, characterized in that, In step 3, when combining the optimization results of the azimuth array and the elevation array, the Latin hypercube sampling technique is used to divide the one-dimensional array into intervals, select interval values, and shuffle and pair them to combine the two one-dimensional arrays into two-dimensional coordinates.

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