CN114740277B - Method and system for correcting radiation characteristics of curved surface array - Google Patents
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Abstract
Description
技术领域Technical Field
本发明属于天线信号处理技术领域,涉及一种曲面阵列的辐射特性校正方法与系统。The invention belongs to the technical field of antenna signal processing, and relates to a radiation characteristic correction method and system for a curved array.
背景技术Background Art
随着天线技术的不断发展,不同类型的天线层出不穷并广泛应用于各高新技术领域。共形阵列天线(Conformal Antenna Array,CAA)是指与物体外形保持一致的天线阵,也即各阵列单元分布于电子系统载体的表面并使阵列表面与载体平台外形相贴合,此种天线也称共形阵。相比传统平面阵列天线,共形阵列天线在满足天线本身性能要求的基础上,还可兼顾载体的气动特性,且由于天线安装的位置特殊,在一定程度上提高了载体内的空间利用率。此外,共形阵列天线分布在三维空间内,相应地提高了空域覆盖范围等。共形阵列天线的诸多优势使得其成为天线领域的研究热点,在雷达、通信及导航等相关领域得到了广泛关注,是未来天线发展的主要方向。With the continuous development of antenna technology, different types of antennas emerge in an endless stream and are widely used in various high-tech fields. Conformal Antenna Array (CAA) refers to an antenna array that is consistent with the shape of an object, that is, each array unit is distributed on the surface of the electronic system carrier and the array surface is in line with the shape of the carrier platform. This type of antenna is also called a conformal array. Compared with traditional planar array antennas, conformal array antennas can not only meet the performance requirements of the antenna itself, but also take into account the aerodynamic characteristics of the carrier. In addition, due to the special location of the antenna installation, the space utilization rate in the carrier is improved to a certain extent. In addition, conformal array antennas are distributed in three-dimensional space, which correspondingly improves the airspace coverage range. The many advantages of conformal array antennas have made it a research hotspot in the antenna field. It has received widespread attention in related fields such as radar, communication and navigation, and is the main direction of future antenna development.
共形阵列天线的辐射特性校正(阵列流形误差校正)是共形阵列天线应用发展的关键技术基础,目前,通常采用相位补偿的方法进行校正,包括阵元连线相位补偿法、径向相位补偿法和Z向相位补偿法等,其中Z向相位补偿法应用最为广泛,Z向相位补偿法又称投影法。曲面阵列天线属于一种典型的共形阵列天线,然而,在实现本发明的过程中,发明人发现传统的投影法面对曲面阵列天线的辐射特性校正问题,仍存在着相位补偿效果差的技术问题。The radiation characteristic correction (array manifold error correction) of conformal array antennas is the key technical foundation for the application and development of conformal array antennas. At present, phase compensation methods are usually used for correction, including array element connection phase compensation method, radial phase compensation method and Z-direction phase compensation method, among which Z-direction phase compensation method is the most widely used, and Z-direction phase compensation method is also called projection method. Curved array antenna is a typical conformal array antenna. However, in the process of realizing the present invention, the inventor found that the traditional projection method still has the technical problem of poor phase compensation effect in the face of the radiation characteristic correction problem of curved array antennas.
发明内容Summary of the invention
针对上述传统方法中存在的问题,本发明提出了一种曲面阵列的辐射特性校正方法与一种曲面阵列的辐射特性校正系统,还提供了一种信号处理设备和一种计算机可读存储介质,可显著提升对曲面阵列天线的相位补偿效果。In response to the problems existing in the above-mentioned traditional methods, the present invention proposes a radiation characteristic correction method for a curved array and a radiation characteristic correction system for a curved array, and also provides a signal processing device and a computer-readable storage medium, which can significantly improve the phase compensation effect of the curved array antenna.
为了实现上述目的,本发明实施例采用以下技术方案:In order to achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:
一方面,提供一种曲面阵列的辐射特性校正方法,包括步骤:On the one hand, a method for calibrating radiation characteristics of a curved array is provided, comprising the steps of:
将曲面阵列上最接近阵列中心的两个阵元确定为校正基点;Determine the two array elements closest to the center of the curved array as calibration base points;
基于校正基点计算投影后曲面阵列上各阵元的阵元投影位置;投影后曲面阵列上的阵元间距与等长均匀平面阵上的阵元间距相同;The projection position of each array element on the curved array after projection is calculated based on the correction base point; the array element spacing on the curved array after projection is the same as the array element spacing on the uniform plane array of equal length;
获取曲面阵列上各阵元的阵元真实位置;Obtain the true position of each array element on the curved array;
通过计算各阵元真实位置与相应阵元投影位置之差,得到曲面阵列上各阵元的投影位置误差;By calculating the difference between the real position of each array element and the projection position of the corresponding array element, the projection position error of each array element on the curved array is obtained;
利用各阵元的投影位置误差对曲面阵列的方向图进行相位补偿处理,得到曲面阵列经辐射特性校正后的方向图。The projection position error of each array element is used to perform phase compensation processing on the directional pattern of the curved array to obtain the directional pattern of the curved array after the radiation characteristics are corrected.
另一方面,还提供一种曲面阵列的辐射特性校正系统,包括:On the other hand, a radiation characteristic correction system for a curved array is also provided, comprising:
基点确定模块,用于将曲面阵列上最接近阵列中心的两个阵元确定为校正基点;A base point determination module is used to determine two array elements on the curved array that are closest to the array center as calibration base points;
投影位置模块,用于基于校正基点计算投影后曲面阵列上各阵元的阵元投影位置;投影后曲面阵列上的阵元间距与等长均匀平面阵上的阵元间距相同;A projection position module is used to calculate the projection position of each array element on the curved array after projection based on the correction base point; the array element spacing on the curved array after projection is the same as the array element spacing on the uniform plane array of equal length;
阵元位置模块,用于获取曲面阵列上各阵元的阵元真实位置;An array element position module is used to obtain the true position of each array element on the curved array;
投影误差模块,用于通过计算各阵元真实位置与相应阵元投影位置之差,得到曲面阵列上各阵元的投影位置误差;A projection error module is used to obtain the projection position error of each array element on the curved array by calculating the difference between the real position of each array element and the projection position of the corresponding array element;
补偿处理模块,用于利用各阵元的投影位置误差对曲面阵列的方向图进行相位补偿处理,得到曲面阵列经辐射特性校正后的方向图。The compensation processing module is used to perform phase compensation processing on the directional pattern of the curved array by using the projection position error of each array element to obtain the directional pattern of the curved array after the radiation characteristics are corrected.
又一方面,还提供一种信号处理设备,包括存储器和处理器,存储器存储有计算机程序,处理器执行计算机程序时实现上述曲面阵列的辐射特性校正方法的步骤。On the other hand, a signal processing device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above-mentioned method for correcting the radiation characteristics of the curved array when executing the computer program.
再一方面,还提供一种计算机可读存储介质,其上存储有计算机程序,计算机程序被处理器执行时实现上述曲面阵列的辐射特性校正方法的步骤。On the other hand, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned method for correcting the radiation characteristics of a curved array are implemented.
上述技术方案中的一个技术方案具有如下优点和有益效果:One of the above technical solutions has the following advantages and beneficial effects:
上述曲面阵列的辐射特性校正方法与系统,通过采用一种改进投影法,也即将靠近曲面阵列中心的阵元位置作为校正基准,通过阵元间隔计算得到其余阵元的阵元投影位置,然后计算曲面阵列上各阵元的阵元真实位置与采用改进投影法投影后的相应阵元的阵元投影位置之间的位置差,最后利用得到的投影位置误差对曲面阵列的方向图进行相位补偿处理,得到经辐射特性校正后的方向图。如此,使得上述方案在均匀曲面阵列中具有应用范围更为广泛、相位补偿效果更为优秀等特点,能够实现对任意曲率弯曲的均匀曲面阵列进行相位补偿,以得到接近于平面阵列性能的阵列方向图,从而显著提升对曲面阵列天线的相位补偿效果。The above-mentioned method and system for correcting the radiation characteristics of the curved array adopts an improved projection method, that is, the array element position close to the center of the curved array is used as the correction reference, and the array element projection position of the remaining array elements is calculated by the array element spacing, and then the position difference between the actual array element position of each array element on the curved array and the array element projection position of the corresponding array element after projection using the improved projection method is calculated, and finally the obtained projection position error is used to perform phase compensation processing on the directional pattern of the curved array to obtain the directional pattern after the radiation characteristics are corrected. In this way, the above-mentioned scheme has the characteristics of a wider application range and better phase compensation effect in uniform curved arrays, and can realize phase compensation of uniform curved arrays with arbitrary curvature to obtain an array directional pattern close to the performance of a planar array, thereby significantly improving the phase compensation effect of the curved array antenna.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为一个实施例中阵列信号发射图;FIG1 is a diagram of array signal transmission in one embodiment;
图2为一个实施例中曲面阵列的辐射特性校正方法的流程示意图;FIG2 is a schematic flow chart of a method for calibrating radiation characteristics of a curved array in one embodiment;
图3为一个实施例中曲面阵列上阵元m与曲率角度关系示意图;FIG3 is a schematic diagram showing the relationship between array element m and curvature angle on a curved array in one embodiment;
图4为传统投影法的阵元投影示意图;FIG4 is a schematic diagram of array element projection of a traditional projection method;
图5为一个实施例中改进投影法与传统投影法的阵元投影对比示意图;FIG5 is a schematic diagram showing a comparison of array element projections between an improved projection method and a traditional projection method in one embodiment;
图6为一个实施例中M=64,q=π/2时曲面阵相位补偿前后的方向图示意;FIG6 is a schematic diagram of the directional diagram of the curved array before and after phase compensation when M=64 and q=π/2 in one embodiment;
图7为一个实施例中M=64,q=2*π/3时曲面阵相位补偿前后方向图示意;FIG7 is a schematic diagram of the front and rear directional diagrams of the curved array phase compensation when M=64 and q=2*π/3 in one embodiment;
图8为一个实施例中M=64,q=π时曲面阵相位补偿前后方向图示意;FIG8 is a schematic diagram of the front and rear directional diagrams of the curved array phase compensation when M=64 and q=π in one embodiment;
图9为一个实施例中不同曲率下各状态积分旁瓣比值示意图;FIG9 is a schematic diagram of the integrated sidelobe ratios of various states under different curvatures in one embodiment;
图10为一个实施例中两种方法随着曲率增加的RMSE变化曲线示意图;FIG10 is a schematic diagram of RMSE variation curves of two methods as curvature increases in one embodiment;
图11为一个实施例中曲面阵列的辐射特性校正系统的模块结构示意图。FIG. 11 is a schematic diagram of the module structure of a radiation characteristic correction system for a curved array in one embodiment.
具体实施方式DETAILED DESCRIPTION
为了使本申请的目的、技术方案及优点更加清楚明白,以下结合附图及实施例,对本申请进行进一步详细说明。应当理解,此处描述的具体实施例仅仅用以解释本申请,并不用于限定本申请。In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.
除非另有定义,本文所使用的所有的技术和科学术语与属于本申请的技术领域的技术人员通常理解的含义相同。本文中在本申请的说明书中所使用的术语只是为了描述具体的实施例的目的,不是旨在于限制本申请。本文所使用的术语“和/或”包括一个或多个相关的所列项目的任意的和所有的组合。Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art to which the present application belongs. The terms used herein in the specification of the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application. The term "and/or" used herein includes any and all combinations of one or more related listed items.
下面将结合本发明实施例图中的附图,对本发明实施方式进行详细说明。The following will describe the implementation of the present invention in detail with reference to the accompanying drawings in the embodiment diagram of the present invention.
曲面阵列天线属于一种典型的共形阵列天线。当采用均匀平面阵列天线时,各阵元与阵列中心的收发波程差为一等比数列,在空间叠加可形成聚焦性能良好的主瓣波束;而对于曲面阵列天线而言,各阵元收发波程差不再保持为等比关系,使得其方向图的主瓣性能产生严重恶化。在实际工程应用中,为使曲面阵列天线的辐射特性接近平面阵列天线的辐射特性,避免阵列形变对方向图性能产生影响,需要对共形阵列天线的形变进行校正,这是一个具有重要研究意义的技术问题,也是制约共形阵列天线发展应用的一个关键因素。Curved array antennas are a typical conformal array antenna. When a uniform planar array antenna is used, the transmit and receive path difference between each array element and the center of the array is a geometric series, which can form a main lobe beam with good focusing performance when superimposed in space; but for curved array antennas, the transmit and receive path difference between each array element is no longer in a geometric relationship, which causes the main lobe performance of its radiation pattern to deteriorate seriously. In actual engineering applications, in order to make the radiation characteristics of the curved array antenna close to those of the planar array antenna and avoid the influence of array deformation on the radiation pattern performance, it is necessary to correct the deformation of the conformal array antenna. This is a technical issue with important research significance and a key factor restricting the development and application of conformal array antennas.
然而,分析发现当曲面阵列天线的弯曲度过高时,传统投影法的相位补偿效果会变得较差,无法满足实际应用要求。因此,本申请针对传统的投影法面对曲面阵列天线的辐射特性校正时,仍存在着的相位补偿效果差的技术问题,提供了一种新的校正方法(也称改进投影法),通过将曲面阵列靠近阵列中心的阵元位置作为校正基准,利用阵元间隔计算得到其余阵元位置,进而得到校正后的阵列方向图,使其在均匀曲面阵列中具有应用范围更为广泛、相位补偿效果更为优秀等特点,可实现对任意曲率弯曲的均匀曲面阵列进行相位补偿,以得到接近于平面阵列性能的阵列方向图。However, analysis has found that when the curvature of the curved array antenna is too high, the phase compensation effect of the traditional projection method will become poor and cannot meet the requirements of practical applications. Therefore, this application provides a new correction method (also called improved projection method) to address the technical problem of poor phase compensation effect when the traditional projection method is used to correct the radiation characteristics of the curved array antenna. The position of the array element close to the center of the curved array is used as the correction reference, and the positions of the remaining array elements are calculated using the array element spacing, thereby obtaining the corrected array pattern, so that it has a wider range of applications and better phase compensation effects in uniform curved arrays. It can realize phase compensation for uniform curved arrays with arbitrary curvatures to obtain an array pattern close to the performance of a planar array.
为便于对下文方法进行直观与详细说明,下面在直角坐标系中展开说明。本领域技术人员可以理解,下文方法也可以在其他坐标系中应用,只需对相关参量进行坐标关系(坐标系之间)变换即可同理应用,因此下文方法并不仅限于在直角坐标系中应用。In order to facilitate the intuitive and detailed description of the following method, the following method is described in a rectangular coordinate system. Those skilled in the art can understand that the following method can also be applied in other coordinate systems, and the method can be applied in the same way by simply transforming the coordinate relationship (between coordinate systems) of the relevant parameters. Therefore, the following method is not limited to application in a rectangular coordinate system.
如图1所示,为阵列信号发射示意图,图1中阵元数为M,其中均匀平面阵列各阵元间隔记为l,以等间距形式分布在x轴上,与传统平面阵列不同的是,当阵列基底采用柔性可变材料时,平面阵列可形变为任意曲率的曲面阵列,分别如图1中的曲面阵1和曲面阵2所示,假设该两个曲面阵的曲率分别为q1和q2(q1>q2),曲率q越大,表示曲面阵的弯曲程度越大。当方位角为θ时,各阵元在空间中叠加形成的阵列方向图分布可表示为:As shown in Figure 1, it is a schematic diagram of array signal transmission. In Figure 1, the number of array elements is M, where the interval between each array element of the uniform planar array is denoted as l, and they are distributed on the x-axis in an equidistant manner. Different from the traditional planar array, when the array substrate adopts a flexible variable material, the planar array can be deformed into a curved array with any curvature, as shown in curved array 1 and curved array 2 in Figure 1, respectively. Assuming that the curvatures of the two curved arrays are q 1 and q 2 (q 1 >q 2 ), the larger the curvature q, the greater the curvature of the curved array. When the azimuth angle is θ, the array pattern distribution formed by the superposition of each array element in space can be expressed as:
其中,xm和ym分别为第m个阵元所对应的x轴坐标和y轴坐标,m=1,2,...,M;k=2πf/c为波数,f为发射信号频率,c为光速。Wherein, xm and ym are the x-axis coordinate and y-axis coordinate corresponding to the m-th array element, respectively, m=1,2,...,M; k=2πf/c is the wave number, f is the frequency of the transmitted signal, and c is the speed of light.
对于平面阵列,各阵元坐标ym全部置为零,式(1)可改写为:For a planar array, the coordinates ym of each array element are all set to zero, and equation (1) can be rewritten as:
请参阅图2,本申请实施例提供了一种曲面阵列的辐射特性校正方法,包括以下步骤S12至S20:Referring to FIG. 2 , an embodiment of the present application provides a method for calibrating radiation characteristics of a curved array, comprising the following steps S12 to S20:
S12,将曲面阵列上最接近阵列中心的两个阵元确定为校正基点。S12, determining two array elements on the curved array that are closest to the array center as calibration base points.
可以理解,阵列中心是指曲面阵列的圆弧中点,因此,校正基点也即曲面阵列的圆弧中点两侧距离该中点最近的两个阵元(位置)。It can be understood that the array center refers to the midpoint of the arc of the curved array. Therefore, the correction base point is the two array elements (positions) on both sides of the midpoint of the arc of the curved array that are closest to the midpoint.
S14,基于校正基点计算投影后曲面阵列上各阵元的阵元投影位置;投影后曲面阵列上的阵元间距与等长均匀平面阵上的阵元间距相同。S14, calculating the projection position of each array element on the curved array after projection based on the correction base point; the array element spacing on the curved array after projection is the same as the array element spacing on the uniform plane array of equal length.
可以理解,等长均匀平面阵是指阵列长度与曲面阵列的阵列长度相同的均匀平面阵,在该阵列长度内两种阵列上可分布相同数量的阵元。因此,可以将曲面阵列的投影平面设为等长均匀平面阵所在平面或x轴平面。It can be understood that the uniform plane array of equal length refers to a uniform plane array with the same array length as the curved array, and the same number of array elements can be distributed on the two arrays within the array length. Therefore, the projection plane of the curved array can be set to the plane where the uniform plane array of equal length is located or the x-axis plane.
S16,获取曲面阵列上各阵元的阵元真实位置。S16, obtaining the true position of each array element on the curved array.
可以理解,各阵元的阵元真实位置是指曲面阵列上各阵元在当前坐标系中的位置坐标。各阵元的阵元真实位置可以预先提供,也可以由载体设备从坐标系中直接测量读取或者通过其他方式获得。It can be understood that the real position of each element refers to the position coordinate of each element on the curved array in the current coordinate system. The real position of each element can be provided in advance, or can be directly measured and read from the coordinate system by the carrier device or obtained by other means.
在一个实施例中,关于上述的步骤S16,包括:In one embodiment, the above step S16 includes:
获取曲面阵列的曲率和阵列长度,对曲率进行等间距分割处理;Obtain the curvature and array length of the curved array, and perform equal-interval segmentation processing on the curvature;
根据分割后的曲率确定曲面阵列上各阵元对应的元方位角;Determine the element azimuth corresponding to each array element on the curved array according to the segmented curvature;
根据曲率、阵列长度和元方位角计算得到各阵元的阵元真实位置。The true position of each array element is calculated based on the curvature, array length and element azimuth.
可以理解,对于曲面阵列,采用圆弧模型来拟合阵列曲率及对应各阵元位置坐标xm和ym,如图3所示,设定好曲面阵列对应的曲率值q,由于是均匀曲面阵列(对于非均匀曲面阵列也可以通过分割为多个均匀曲面阵列来处理),将曲率等间距分为M份,则阵元m对应的角度(也即上述的元方位角)可记为:It can be understood that for the curved array, the arc model is used to fit the array curvature and the corresponding position coordinates xm and ym of each array element, as shown in FIG3. The curvature value q corresponding to the curved array is set. Since it is a uniform curved array (a non-uniform curved array can also be processed by dividing it into multiple uniform curved arrays), the curvature is divided into M parts with equal spacing, and the angle corresponding to the array element m (that is, the element azimuth angle mentioned above) can be recorded as:
α=q/M*m-q/2 (3)α=q/M*m-q/2 (3)
在一个实施例中,阵元真实位置通过如下公式计算得到:In one embodiment, the true position of the array element is calculated by the following formula:
其中,xm表示曲面阵列上各阵元在直角坐标系中的x轴坐标,ym表示曲面阵列上各阵元在直角坐标系中的y轴坐标,r表示曲面阵列所在圆的半径,α表示元方位角,m=1,2,...,M,M表示曲面阵列的阵元数。Wherein, xm represents the x-axis coordinate of each element on the curved array in the rectangular coordinate system, ym represents the y-axis coordinate of each element on the curved array in the rectangular coordinate system, r represents the radius of the circle where the curved array is located, α represents the element azimuth, m=1,2,...,M, and M represents the number of elements in the curved array.
具体的,曲面阵列产生形变时,阵列长度始终保持不变,1为L1=(M-1)*l,L1即为图2中弧长,圆的半径记为r=L1/q,则可以通过式(4)计算得到xm和ym的值。Specifically, when the curved array is deformed, the array length remains unchanged, 1 is L 1 =(M-1)*l, L 1 is the arc length in Figure 2, and the radius of the circle is recorded as r=L 1 /q, then the values of x m and y m can be calculated by formula (4).
如图4所示,可以看出,平面阵列曲面化程度越高,发生曲面畸变越大,形变后的曲面阵列上各个阵元与平面阵列相对应阵元的位置差愈大,如小曲率的曲面阵对应的位置差X'和大曲率的曲面阵对应的位置差X”所示;而平面阵列曲面化后普遍靠近阵列中心的两个阵元位置与原始位置差距相对较小,因此,将靠近阵列中心的阵元位置作为校正基准,可通过阵元间隔l计算得到其余阵元位置,进而得到校正后的阵列方向图。其中,阵元n为阵列中的阵元。As shown in FIG. 4 , it can be seen that the higher the curvature of the planar array, the greater the surface distortion, and the greater the position difference between each element on the deformed curved array and the corresponding element in the planar array, as shown by the position difference X' corresponding to the curved array with a small curvature and the position difference X" corresponding to the curved array with a large curvature; and after the planar array is curved, the positions of the two elements close to the center of the array are generally relatively small compared with the original positions. Therefore, the position of the element close to the center of the array is used as the correction reference, and the positions of the remaining elements can be calculated by the element interval l, thereby obtaining the corrected array pattern. Among them, element n is the element in the array.
在一个实施例中,投影后曲面阵列上各阵元的阵元投影位置通过如下公式计算得到:In one embodiment, the projection position of each array element on the curved array after projection is calculated by the following formula:
其中,m表示曲面阵列上最接近阵列中心的左侧校正基点,m+1表示曲面阵列上最接近阵列中心的左侧校正基点,l表示阵元间距。Wherein, m represents the left correction base point closest to the array center on the curved array, m+1 represents the left correction base point closest to the array center on the curved array, and l represents the array element spacing.
具体的,选取最靠近曲面阵列的阵列中心的两个阵元为基点,如图5中所示,假设最靠近阵列中心的两个阵元分别为阵元m和阵元m+1,采用改进投影法处理时,保持投影后的各阵元间距(阵元距离)与均匀平面阵相同,则其余阵元的阵元投影位置坐标可通过上述式(5)计算得到。如图5中所示,给出了投影后与阵元m相邻的阵元m-1、阵元m+1、阵元m+2的位置示意图。Specifically, the two array elements closest to the center of the curved array are selected as base points, as shown in FIG5 , assuming that the two array elements closest to the center of the array are array element m and array element m+1, respectively, when the improved projection method is used, the spacing between the array elements (array element distance) after projection is kept the same as that of the uniform plane array, then the array element projection position coordinates of the remaining array elements can be calculated by the above formula (5). As shown in FIG5 , a schematic diagram of the positions of array element m-1, array element m+1, and array element m+2 adjacent to array element m after projection is given.
S18,通过计算各阵元真实位置与相应阵元投影位置之差,得到曲面阵列上各阵元的投影位置误差。S18, obtaining the projection position error of each array element on the curved array by calculating the difference between the actual position of each array element and the projection position of the corresponding array element.
可以理解,在得到曲面阵列上每个阵元的真实位置及其投影后的阵元投影位置后,即可分别计算每个阵元的投影位置误差。It can be understood that after obtaining the true position of each array element on the curved array and the projection position of the array element after projection, the projection position error of each array element can be calculated respectively.
在一个实施例中,曲面阵列上各阵元的投影位置误差通过如下公式计算得到:In one embodiment, the projection position error of each array element on the curved array is calculated by the following formula:
其中,m表示曲面阵列上第m个阵元,表示阵元m对应的阵元投影位置在直角坐标系中的x轴坐标。Where m represents the mth array element on the curved array. Represents the x-axis coordinate of the projection position of the array element corresponding to the array element m in the rectangular coordinate system.
由于投影部分可以不考虑y轴方向的位置坐标,因此通过上述位置误差计算方式即可快速获得各阵元的投影位置误差数据。Since the projection part does not need to consider the position coordinates in the y-axis direction, the projection position error data of each array element can be quickly obtained through the above position error calculation method.
S20,利用各阵元的投影位置误差对曲面阵列的方向图进行相位补偿处理,得到曲面阵列经辐射特性校正后的方向图。S20, performing phase compensation processing on the directional pattern of the curved array using the projection position error of each array element, to obtain the directional pattern of the curved array after the radiation characteristic is corrected.
可以理解,在得到各阵元的投影位置误差后,可以利用该误差数据作为相位补偿项用于曲面阵列的方向图计算中,得到校正后的方向图。It can be understood that after the projection position error of each array element is obtained, the error data can be used as a phase compensation item for calculating the directivity pattern of the curved array to obtain a corrected directivity pattern.
在一个实施例中,曲面阵列经辐射特性校正后的方向图通过如下公式计算得到:In one embodiment, the radiation pattern of the curved array after radiation characteristic correction is calculated by the following formula:
其中,Pimprove表示曲面阵列经辐射特性校正后的方向图,M表示曲面阵列的阵元数,k表示波数,xm表示曲面阵列上各阵元在直角坐标系中的x轴坐标,ym表示曲面阵列上各阵元在直角坐标系中的y轴坐标,θ表示方位角,D表示投影位置误差。Wherein, P improve represents the radiation pattern of the curved array after radiation characteristic correction, M represents the number of array elements of the curved array, k represents the wave number, x m represents the x-axis coordinate of each array element on the curved array in the rectangular coordinate system, y m represents the y-axis coordinate of each array element on the curved array in the rectangular coordinate system, θ represents the azimuth, and D represents the projection position error.
具体的,利用计算得到各阵元位置误差通过上述式(7)对曲面阵列方向图进行相位补偿处理。Specifically, the position error of each array element is calculated and then phase compensation is performed on the curved array pattern through the above formula (7).
如图5所示,实线箭头为改进投影法所对应的阵元位置变化轨迹,虚线箭头为传统投影法对应的阵元位置变化轨迹,传统投影法进行相位补偿是通过将曲面阵上各阵元在y轴方向上的坐标直接置零,则此时目标位置P处接收到的来自曲面阵列的方向图计算公式为:As shown in Figure 5, the solid arrow is the trajectory of the array element position change corresponding to the improved projection method, and the dotted arrow is the trajectory of the array element position change corresponding to the traditional projection method. The traditional projection method performs phase compensation by directly setting the coordinates of each array element on the curved array in the y-axis direction to zero. At this time, the calculation formula for the directional pattern received from the curved array at the target position P is:
可见,与本申请采用的改进投影法下的相位补偿方式本质有别。It can be seen that the phase compensation method under the improved projection method adopted in this application is essentially different.
上述曲面阵列的辐射特性校正方法,通过采用一种改进投影法,也即将靠近曲面阵列中心的阵元位置作为校正基准,通过阵元间隔计算得到其余阵元的阵元投影位置,然后计算曲面阵列上各阵元的阵元真实位置与采用改进投影法投影后的相应阵元的阵元投影位置之间的位置差,最后利用得到的投影位置误差对曲面阵列的方向图进行相位补偿处理,得到经辐射特性校正后的方向图。如此,使得上述方案在均匀曲面阵列中具有应用范围更为广泛、相位补偿效果更为优秀等特点,能够实现对任意曲率弯曲的均匀曲面阵列进行相位补偿,以得到接近于平面阵列性能的阵列方向图,从而显著提升对曲面阵列天线的相位补偿效果。The above-mentioned method for correcting the radiation characteristics of the curved array adopts an improved projection method, that is, the array element position close to the center of the curved array is used as the correction reference, and the array element projection position of the remaining array elements is calculated by the array element spacing, and then the position difference between the actual array element position of each array element on the curved array and the array element projection position of the corresponding array element after projection using the improved projection method is calculated, and finally the obtained projection position error is used to perform phase compensation processing on the directional pattern of the curved array to obtain the directional pattern after the radiation characteristics are corrected. In this way, the above-mentioned scheme has the characteristics of a wider application range and better phase compensation effect in uniform curved arrays, and can realize phase compensation of uniform curved arrays with arbitrary curvature to obtain an array directional pattern close to the performance of a planar array, thereby significantly improving the phase compensation effect of the curved array antenna.
在一个实施例中,为了更直观且全面地说明上述曲面阵列的辐射特性校正方法,下面是以某型曲面阵列为例,对本发明提出的曲面阵列的辐射特性校正方法进行仿真应用与对比说明的示例。In one embodiment, in order to more intuitively and comprehensively illustrate the radiation characteristic correction method of the curved array mentioned above, the following is an example of simulation application and comparative explanation of the radiation characteristic correction method of the curved array proposed in the present invention, taking a certain type of curved array as an example.
需要说明的是,本说明书中给出的实施案例仅为示意性的,并非为本发明具体实施案例的唯一限定,本领域技术人员可以在本发明提供的实施案例的示意下,同理采用上述提供的曲面阵列的辐射特性校正方法,实现对不同曲面阵的仿真应用。It should be noted that the implementation cases given in this specification are only for illustration and are not the sole limitation for the specific implementation cases of the present invention. Those skilled in the art can, under the guidance of the implementation cases provided by the present invention, adopt the radiation characteristic correction method of the curved array provided above to realize the simulation application of different curved arrays.
设置阵元数为M=64,发射信号频率为f=5.68GHz,阵元间距为l=λ/2,λ=c/f为波长,方向图角度范围θ∈[-90°,90°]。对曲面阵列方向图仿真时,曲率分别为q=π/2、q=2*π/3和q=π,其中q=0代表此时阵列处于平面阵列状态,其余依次递增的q数值分别表示弯曲程度越来越严重的三种曲面阵列。Set the number of array elements to M = 64, the frequency of the transmitted signal to f = 5.68 GHz, the array element spacing to l = λ/2, λ = c/f is the wavelength, and the angular range of the pattern θ∈[-90°, 90°]. When simulating the curved array pattern, the curvatures are q = π/2, q = 2*π/3, and q = π, respectively, where q = 0 represents that the array is in a planar array state, and the other q values that increase in sequence represent three types of curved arrays with increasingly severe curvature.
如图6-图8所示,画出了M=64,l=0.05时不同q值时平面阵列方向图、原始曲面阵列方向图以及两种相位补偿方法(传统的与本申请上述方法的)进行补偿后的阵列方向图。如图6所示,当q的值较小时,即曲面阵相较于平面阵列的弯曲程度较小时,主瓣及相邻几个旁瓣两种投影法的补偿效果有差别但不大,对于远离主瓣的旁瓣补偿效果改进投影法优于传统投影法,因此,在低曲率情况下,对曲面阵列进行相位补偿投影法与传统改进投影法二者皆可。As shown in Figures 6 to 8, the planar array pattern, the original curved array pattern, and the array pattern after compensation by two phase compensation methods (the traditional method and the above method of the present application) at different q values when M = 64 and l = 0.05 are drawn. As shown in Figure 6, when the value of q is small, that is, when the curvature of the curved array is smaller than that of the planar array, the compensation effects of the two projection methods for the main lobe and several adjacent side lobes are different but not large. For the side lobe compensation effect far away from the main lobe, the improved projection method is better than the traditional projection method. Therefore, in the case of low curvature, both the phase compensation projection method and the traditional improved projection method can be used for the curved array.
如图7所示,本申请提出的改进投影法的优势逐渐显现,尤其在图6至图8三图的对比中,可以明显的看出随着曲率的增大,改进投影法的相位补偿效果明显优于传统投影法,传统投影法进行相位补偿后其方向图较平面阵列方向图波形旁瓣差距较大,而改进投影法相位补偿后的曲面阵列方向图与平面阵列波形基本还能保持一致。因此,在高曲率的曲面状态下,使用改进投影法进行相位补偿是较好的选择。As shown in Figure 7, the advantages of the improved projection method proposed in this application gradually emerge, especially in the comparison of Figures 6 to 8, it can be clearly seen that as the curvature increases, the phase compensation effect of the improved projection method is significantly better than the traditional projection method. After the traditional projection method performs phase compensation, its directional pattern is much different from the waveform sidelobes of the planar array directional pattern, while the curved array directional pattern after phase compensation of the improved projection method is basically consistent with the planar array waveform. Therefore, in the case of a high curvature curved surface, using the improved projection method for phase compensation is a better choice.
为进一步比较本申请提出的改进投影法与传统投影法的性能,对阵列方向图的积分旁瓣比(ISLR)和均方根误差(RMSE)进行了计算:In order to further compare the performance of the improved projection method proposed in this application with the traditional projection method, the integrated sidelobe ratio (ISLR) and root mean square error (RMSE) of the array pattern were calculated:
ISLR和RMSE对比结果分别如图9和图10所示,从图9可以发现,不同曲率下,改进投影法补偿后的方向图积分旁瓣比值与原始平面阵列十分接近,而传统投影法进行相位补偿后的方向图积分旁瓣比值随着曲率越大,与平面阵列的差距逐渐加大。从图10中可以看到投影法随着曲率的增加,RMSE整体趋势朝着越来越大的走向,但改进投影法RMSE数值仍然处于很小的范围内,因此,改进投影法的效果优于传统投影法,且随着曲率越来越大,传统投影法的补偿效果迅速劣化。The comparison results of ISLR and RMSE are shown in Figures 9 and 10 respectively. From Figure 9, it can be found that under different curvatures, the integral sidelobe ratio of the directional pattern after compensation by the improved projection method is very close to the original planar array, while the integral sidelobe ratio of the directional pattern after phase compensation by the traditional projection method gradually increases with the curvature. From Figure 10, it can be seen that as the curvature increases, the overall trend of RMSE of the projection method is getting larger and larger, but the RMSE value of the improved projection method is still in a very small range. Therefore, the effect of the improved projection method is better than that of the traditional projection method, and as the curvature increases, the compensation effect of the traditional projection method rapidly deteriorates.
将ISLR和RMSE的分析结果结合起来可以得出结论:当曲率增大后,虽然主瓣聚焦性能差不多,但传统投影法旁瓣性能恶化较严重,导致相位补偿后曲面阵列方向图ISLR值与平面阵列差距变大,且RMSE值也不断增加,相比而言,改进投影法能够同时保证良好的主瓣性能和旁瓣性能,方向图补偿效果明显优于传统投影法。Combining the analysis results of ISLR and RMSE, it can be concluded that: when the curvature increases, although the main lobe focusing performance is similar, the side lobe performance of the traditional projection method deteriorates seriously, resulting in a larger gap between the ISLR value of the curved array pattern and that of the planar array after phase compensation, and the RMSE value also continues to increase. In comparison, the improved projection method can simultaneously guarantee good main lobe performance and side lobe performance, and the pattern compensation effect is significantly better than the traditional projection method.
应该理解的是,虽然图1流程图中的各个步骤按照箭头的指示依次显示,但是这些步骤并不是必然按照箭头指示的顺序依次执行。除非本文中有明确的说明,这些步骤的执行并没有严格的顺序限制,这些步骤可以以其它的顺序执行。而且图1的至少一部分步骤可以包括多个子步骤或者多个阶段,这些子步骤或者阶段并不必然是在同一时刻执行完成,而是可以在不同的时刻执行,这些子步骤或者阶段的执行顺序也不必然是依次进行,而是可以与其它步骤或者其它步骤的子步骤或者阶段的至少一部分轮流或者交替地执行。It should be understood that, although the various steps in the flowchart of FIG. 1 are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear description in this article, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps of FIG. 1 may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the sub-steps or stages of other steps.
请参阅图11,在一个实施例中,还提供一种曲面阵列的辐射特性校正系统100,包括基点确定模块11、投影位置模块13、阵元位置模块15、投影误差模块17和补偿处理模块19。其中,基点确定模块11用于将曲面阵列上最接近阵列中心的两个阵元确定为校正基点。投影位置模块13用于基于校正基点计算投影后曲面阵列上各阵元的阵元投影位置;投影后曲面阵列上的阵元间距与等长均匀平面阵上的阵元间距相同。阵元位置模块15用于获取曲面阵列上各阵元的阵元真实位置。投影误差模块17用于通过计算各阵元真实位置与相应阵元投影位置之差,得到曲面阵列上各阵元的投影位置误差。补偿处理模块19用于利用各阵元的投影位置误差对曲面阵列的方向图进行相位补偿处理,得到曲面阵列经辐射特性校正后的方向图。Please refer to FIG. 11. In one embodiment, a radiation characteristic correction system 100 for a curved array is also provided, comprising a base point determination module 11, a projection position module 13, an array element position module 15, a projection error module 17, and a compensation processing module 19. The base point determination module 11 is used to determine the two array elements closest to the center of the curved array as the correction base points. The projection position module 13 is used to calculate the array element projection position of each array element on the curved array after projection based on the correction base points; the array element spacing on the curved array after projection is the same as the array element spacing on the uniform plane array of equal length. The array element position module 15 is used to obtain the true array element position of each array element on the curved array. The projection error module 17 is used to obtain the projection position error of each array element on the curved array by calculating the difference between the true position of each array element and the projection position of the corresponding array element. The compensation processing module 19 is used to perform phase compensation processing on the directional pattern of the curved array using the projection position error of each array element to obtain the directional pattern of the curved array after the radiation characteristic correction.
上述曲面阵列的辐射特性校正系统100,通过各模块的协作,采用一种改进投影法,也即将靠近曲面阵列中心的阵元位置作为校正基准,通过阵元间隔计算得到其余阵元的阵元投影位置,然后计算曲面阵列上各阵元的阵元真实位置与采用改进投影法投影后的相应阵元的阵元投影位置之间的位置差,最后利用得到的投影位置误差对曲面阵列的方向图进行相位补偿处理,得到经辐射特性校正后的方向图。如此,使得上述方案在均匀曲面阵列中具有应用范围更为广泛、相位补偿效果更为优秀等特点,能够实现对任意曲率弯曲的均匀曲面阵列进行相位补偿,以得到接近于平面阵列性能的阵列方向图,从而显著提升对曲面阵列天线的相位补偿效果。The above-mentioned curved array radiation characteristic correction system 100, through the cooperation of various modules, adopts an improved projection method, that is, the array element position close to the center of the curved array is used as the correction reference, and the array element projection position of the remaining array elements is obtained by calculating the array element spacing, and then the position difference between the actual array element position of each array element on the curved array and the array element projection position of the corresponding array element after projection using the improved projection method is calculated, and finally the obtained projection position error is used to perform phase compensation processing on the directional pattern of the curved array to obtain the directional pattern after radiation characteristic correction. In this way, the above-mentioned scheme has the characteristics of a wider application range and better phase compensation effect in uniform curved arrays, and can realize phase compensation of uniform curved arrays with arbitrary curvature to obtain an array directional pattern close to the performance of a planar array, thereby significantly improving the phase compensation effect of the curved array antenna.
在一个实施例中,阵元位置模块15包括阵列参数子模块、阵元方位子模块和阵元位置子模块。其中,阵列参数子模块用于获取所述曲面阵列的曲率和阵列长度,对所述曲率进行等间距分割处理。阵元方位子模块用于根据分割后的曲率确定所述曲面阵列上各阵元对应的元方位角。阵元位置子模块用于根据所述曲率、所述阵列长度和所述元方位角计算得到各阵元的所述阵元真实位置。In one embodiment, the array element position module 15 includes an array parameter submodule, an array element orientation submodule and an array element position submodule. The array parameter submodule is used to obtain the curvature and array length of the curved array and perform equal-interval segmentation processing on the curvature. The array element orientation submodule is used to determine the element azimuth angle corresponding to each array element on the curved array according to the segmented curvature. The array element position submodule is used to calculate the true array element position of each array element according to the curvature, the array length and the element azimuth angle.
关于曲面阵列的辐射特性校正系统100的具体限定,可以参见上文中曲面阵列的辐射特性校正方法的相应限定,在此不再赘述。上述曲面阵列的辐射特性校正系统100中的各个模块可全部或部分通过软件、硬件及其组合来实现。上述各模块可以硬件形式内嵌于或独立于具体数据处理功能的设备中,也可以软件形式存储于前述设备的存储器中,以便于处理器调用执行以上各个模块对应的操作,前述设备可以是但不限于本领域已有的各型天线信号处理设备或机载系统。For the specific definition of the radiation characteristic correction system 100 for curved arrays, please refer to the corresponding definition of the radiation characteristic correction method for curved arrays above, which will not be repeated here. Each module in the above-mentioned radiation characteristic correction system 100 for curved arrays can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of a device with a specific data processing function in the form of hardware, or can be stored in the memory of the aforementioned device in the form of software, so that the processor can call and execute the operations corresponding to the above modules. The aforementioned device can be, but is not limited to, various types of antenna signal processing devices or airborne systems already available in the art.
又一方面,还提供一种信号处理设备,包括存储器和处理器,存储器存储有计算机程序,处理器执行计算机程序时实现如下处理步骤:将曲面阵列上最接近阵列中心的两个阵元确定为校正基点;基于校正基点计算投影后曲面阵列上各阵元的阵元投影位置;投影后曲面阵列上的阵元间距与等长均匀平面阵上的阵元间距相同;获取曲面阵列上各阵元的阵元真实位置;通过计算各阵元真实位置与相应阵元投影位置之差,得到曲面阵列上各阵元的投影位置误差;利用各阵元的投影位置误差对曲面阵列的方向图进行相位补偿处理,得到曲面阵列经辐射特性校正后的方向图。On the other hand, a signal processing device is also provided, including a memory and a processor, the memory storing a computer program, and the processor implementing the following processing steps when executing the computer program: determining the two array elements on the curved array closest to the array center as correction base points; calculating the array element projection position of each array element on the curved array after projection based on the correction base points; the array element spacing on the curved array after projection is the same as the array element spacing on the equal-length uniform plane array; obtaining the true array element position of each array element on the curved array; obtaining the projection position error of each array element on the curved array by calculating the difference between the true position of each array element and the projection position of the corresponding array element; and performing phase compensation processing on the directional pattern of the curved array using the projection position error of each array element to obtain the directional pattern of the curved array after the radiation characteristics are corrected.
需要说明的是,上述信号处理设备可以是本领域中各型天线信号处理设备,包括机载和非机载设备,其除了包括上述存储器和处理器等核心部件外,本领域技术人员可以理解其还可以包括其他本说明书未详尽列出的其他组成部件,具体可以视具体设备型号确定。It should be noted that the above-mentioned signal processing device can be various types of antenna signal processing devices in the field, including airborne and non-airborne devices. In addition to the core components such as the above-mentioned memory and processor, technical personnel in this field can understand that it can also include other components not listed in detail in this specification, which can be determined according to the specific device model.
在一个实施例中,处理器执行计算机程序时还可以实现上述曲面阵列的辐射特性校正方法各实施例中增加的步骤或者子步骤。In one embodiment, when the processor executes the computer program, the processor may also implement the steps or sub-steps added in the above-mentioned embodiments of the method for correcting the radiation characteristics of the curved array.
再一方面,还提供一种计算机可读存储介质,其上存储有计算机程序,其特征在于,计算机程序被处理器执行时实现如下处理步骤:将曲面阵列上最接近阵列中心的两个阵元确定为校正基点;基于校正基点计算投影后曲面阵列上各阵元的阵元投影位置;投影后曲面阵列上的阵元间距与等长均匀平面阵上的阵元间距相同;获取曲面阵列上各阵元的阵元真实位置;通过计算各阵元真实位置与相应阵元投影位置之差,得到曲面阵列上各阵元的投影位置误差;利用各阵元的投影位置误差对曲面阵列的方向图进行相位补偿处理,得到曲面阵列经辐射特性校正后的方向图。On the other hand, a computer-readable storage medium is provided, on which a computer program is stored, characterized in that when the computer program is executed by a processor, the following processing steps are implemented: two array elements on the curved array closest to the center of the array are determined as correction base points; the array element projection position of each array element on the curved array after projection is calculated based on the correction base points; the array element spacing on the curved array after projection is the same as the array element spacing on the uniform plane array of equal length; the array element true position of each array element on the curved array is obtained; the projection position error of each array element on the curved array is obtained by calculating the difference between the true position of each array element and the projection position of the corresponding array element; and the projection position error of each array element is used to perform phase compensation processing on the directional pattern of the curved array to obtain the directional pattern of the curved array after the radiation characteristics are corrected.
在一个实施例中,计算机程序被处理器执行时,还可以实现上述曲面阵列的辐射特性校正方法各实施例中增加的步骤或者子步骤。In one embodiment, when the computer program is executed by a processor, it can also implement the steps or sub-steps added in the above-mentioned embodiments of the method for correcting the radiation characteristics of a curved array.
本领域普通技术人员可以理解实现上述实施例方法中的全部或部分流程,是可以通过计算机程序来指令相关的硬件来完成的,计算机程序可存储于一非易失性计算机可读取存储介质中,该计算机程序在执行时,可包括如上述各方法的实施例的流程。其中,本申请所提供的各实施例中所使用的对存储器、存储、数据库或其它介质的任何引用,均可包括非易失性和/或易失性存储器。非易失性存储器可包括只读存储器(ROM)、可编程ROM(PROM)、电可编程ROM(EPROM)、电可擦除可编程ROM(EEPROM)或闪存。易失性存储器可包括随机存取存储器(RAM)或者外部高速缓冲存储器。作为说明而非局限,RAM以多种形式可得,诸如静态RAM(SRAM)、动态RAM(DRAM)、同步DRAM(SDRAM)、双数据率SDRAM(DDRSDRAM)、增强型SDRAM(ESDRAM)、同步链路(Synchlink)DRAM(SLDRAM)、存储器总线式动态随机存储器(Rambus DRAM,简称RDRAM)以及接口动态随机存储器(DRDRAM)等。Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and/or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus dynamic random access memory (Rambus DRAM, referred to as RDRAM) and interface dynamic random access memory (DRDRAM).
以上实施例的各技术特征可以进行任意的组合,为使描述简洁,未对上述实施例中的各个技术特征所有可能的组合都进行描述,然而,只要这些技术特征的组合不存在矛盾,都应当认为是本说明书记载的范围。The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
以上实施例仅表达了本申请的几种实施方式,其描述较为具体和详细,但并不能因此而理解为对发明专利范围的限制。应当指出的是,对于本领域的普通技术人员来说,在不脱离本申请构思的前提下,还可做出若干变形和改进,都属于本申请保护范围。因此本申请专利的保护范围应以所附权利要求为准。The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and all of them belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.
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