Fast Evaluation of the Radiation Patterns of True Time Delay Arrays With Beam Steering

A multilevel algorithm for the computation of the transient radiation patterns of true time delay (TTD) conformal arrays over a range of observation and beam steering directions is presented. The multilevel algorithm is based on hierarchical decomposition of the array into smaller sub-arrays of elements. At the finest level of decomposition, the angular-temporal radiation patterns of single-element sub-arrays are obtained over a sparse angular grid of directions and short temporal duration, by either measurement or calculation. Subsequent steps of the algorithm comprise multilevel aggregation of delayed sub-array contributions. This process continues until the transient radiation pattern of the whole array is obtained. At each level, the radiation pattern is interpolated to a finer angular grid of observations and steering directions followed by temporal delay compensation. The multilevel array decomposition algorithm attains a computational complexity substantially lower than that of the direct evaluation. Furthermore, the algorithm is particularly efficient for large arrays with large numbers of elements.     

Multilevel fast physical optics algorithm for radiation from non-planar apertures

A novel multilevel algorithm for computing the radiation patterns of nonplanar aperture antennas over a range of observation angles is presented. The proposed technique is directly applicable to reflector and lens antennas as well as to radomes. The multilevel computational sequence is based on a hierarchical decomposition of the radiating aperture and comprises two main steps. First, computation of the radiation patterns of all subapertures of the finest level over a very coarse angular grid. Second, multilevel aggregation of the radiation patterns of neighboring subapertures into the final pattern of the whole aperture via a phase compensated interpolation. The multilevel algorithm attains computational complexity comparable to that of the fast Fourier transform based techniques while avoiding their limitations.     

Near-field far-field transformation in time domain from optimalplane-polar samples

This paper presents a new approach to the time-domain near-field far-field transformation technique introduced by Hansen and Yaghijan (1994) and is based either on a time-domain or frequency-domain scheme. The approach presented here attempts to overcome the main drawbacks of this technique related to the computer time and memory requirements, which could make unrealistic the application of the technique to cases of practical interest. To this end, the advanced representation of the (time and frequency domain) near field previously introduced by the authors, which requires a minimum number of nonequispaced field samples, are exploited. This leads to new relationship between the near-field measured samples and the far field, which requires a minimal set of time-space measurements. Various computational schemes are considered and compared showing that the presented algorithm requires a reduced measurement effort, computer time, and memory occupancy, while allowing a lower far-field reconstruction error for a fixed number of measurements     

基于未知源域重构的无相位近场测量技术

天线的远场对于研究天线辐射特性具有重大意义,由于远场的直接测量有着诸多限制,近场测量技术计算远场因其简洁准确的特点得到广泛应用. 然而,传统的近场测量技术要求获取近场区的幅度和相位分布才能发挥作用,随着天线频率的升高,人们想要在近场区获取准确的相位信息变得十分困难. 为了解决该技术难题,文中提出一种无相位近场测量技术. 利用一个封闭面上的幅度信息重建或猜测出包围待测天线的球面切向电场分布,并采用遗传算法进行全局优化,其最初为四组随机数据,经过数次优化后将逐渐接近准确结果. 仿真结果表明,本文方法能够在忽略相位信号的前提下,计算出准确的远场辐射特性.     

Statistical modal analysis applied to near-field measurements of random emissions

The problem of near-field to far-field transformation of narrow-band incoherent electromagnetic fields is analyzed. The coherence matrix of signals sampled in the time domain on a surface enclosing incoherent sources is derived. Two equivalent formulations based on the processing of the coherence matrix are introduced: The signal subspace analysis and the bimodal transformation. In the signal-subspace approach, the coherence matrix is processed using a method based on singular value decomposition, giving rise to a set of functions on the surface enclosing the incoherent sources. Each of these functions is individually transformed to the far field via a modal decomposition and the sum of the transformed functions gives the total far field. In the second formulation, the bimodal transformation is used to transform the near field coherence matrix into the far field coherence matrix from which the far-field pattern is derived. The applications of the proposed transformations in the presence of noise are illustrated. A numerical example using incoherent radiating dipoles inside a leaking wire-grid enclosure validates the two formulations of near-field to far-field transformation. The proposed methodology gives the mathematical foundation for designing a compact time domain measurement facility well suited to incoherent electromagnetic radiation.     

Spatial sampling and filtering in near-field measurements

A sample spacing criterion and a data minimization technique for measurements made over the surface of a plane in the near field of an antenna are presented. The sample spacing is shown to depend on the distance from the antenna to the measurement plane, and on the extent to which evanescent waves can be neglected. The near-field data minimization technique utilizes two-dimensional spatial filtering to effect a significant reduction in computational effort required to calculate selected portions of the far-field pattern. Far-field patterns of anXband antenna calculated from near-field measurements are presented and compared with those measured on a standard far-field range. The far-field calculations are repeated for several near-field sample spacings and for various post-filter sample rates.     

A sparse data fast Fourier transform (SDFFT)

A multilevel algorithm that efficiently Fourier transforms sparse spatial data to sparse spectral data with controllable error is presented. The algorithm termed "sparse data fast Fourier transform" (SDFFT) is particularly useful for signal processing applications where only part of the k-space is to be computed - regardless of whether it is a regular region like an angular section of the Ewald sphere or it consists of completely arbitrary points scattered in the k-space. In addition, like the various nonuniform fast Fourier transforms, the O(NlogN) algorithm can deal with a sparse, nonuniform spatial domain. In this paper, the parabolic reflector antenna problem is studied as an example to demonstrate its use in the computation of far-field patterns due to arbitrary aperture antennas and antenna arrays. The algorithm is also promising for various applications such as backprojection tomography, diffraction tomography, and synthetic aperture radar imaging.     

Multilevel Plane Wave Based Near-Field Far-Field Transformation for Electrically Large Antennas in Free-Space or Above Material Halfspace

A recently presented fully probe-corrected near-field far-field transformation employing plane wave expansion and diagonal translation operators enables near-field far-field transformation for arbitrary measurement contours and arbitrary antennas. A multilevel extension, inspired by the multilevel fast multipole method, is presented that is suitable for the efficient transformation of electrically large antennas with a size of tens or even hundreds of wavelengths. The measurement points are grouped in a multilevel fashion and translations are carried out to the box centers on the highest level only. The plane waves are processed through the different levels to the measurement points using a disaggregation and anterpolation procedure resulting in a reduced overall complexity. In the second part of this paper, the influence of perfectly conducting ground planes and dielectric halfspaces, as an approximation for ground effects in a real measurement setup, is investigated. As such ground reflected waves are assumed, which propagate from the investigated antenna to the field probe and add to the direct wave contributions. The far-field conditions required for these assumptions are achieved by a source box grouping scheme. By this extension ground effects are directly considered within the near-field far-field transformation. Transformation results using simulated and measured near-field data are shown.      

A multilevel matrix decomposition algorithm for analyzingscattering from large structures

A multilevel algorithm is presented for analyzing scattering from electrically large surfaces. The algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics. The algorithm permits a fast matrix-vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks, with each describing the interaction between distant scatterers. The multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast Fourier transform (FFT) and that only relies on well-known algebraic techniques. The computational complexity and the memory requirements of the proposed algorithm are O(N log² N)     

FFT applications to plane-polar near-field antenna measurements

The four-point bivariate Lagrange interpolation algorithm was applied to near-field antenna data measured in a plane-polar facility. The results were sufficiently accurate to permit the use of the FFT (fast Fourier transform) algorithm to calculate the far-field patterns of the antenna. Good agreement was obtained between the far-field patterns as calculated by the Jacobi-Bessel and the FFT algorithms. The significant advantage in using the FFT is in the calculation of the principal plane cuts, which may be made very quickly. Also, the application of the FFT algorithm directly to the near-field data was used to perform surface holographic diagnosis of a reflector antenna. The effects due to the focusing of the emergent beam from the reflector, as well as the effects of the information in the wide-angle regions, are shown. The use of the plane-polar near-field antenna test range has therefore been expanded to include these useful FFT applications     

Far-field patterns of spaceborne antennas from plane-polar near-field measurements

Certain unique features of a recently constructed plane-polar near-field measurement facility for determining the far-field patterns of large and fragile spaceborne antennas are described. In this facility, the horizontally positioned antenna rotates about its axis while the measuring probe is advanced incrementally in a fixed radial direction. The near-field measured data is then processed using a Jacobi-Bessel expansion to obtain the antenna far fields. A summary of the measurement and computational steps is given. Comparisons between the outdoor far-field measurements and the constructed far-field patterns from the near-field measured data are provided for different antenna sizes and frequencies. Application of the substitution method for the absolute gain measurement is discussed. In particular, results are shown for the 4.8-m mesh-deployable high-gain antenna of the Galileo spacecraft which has the mission of orbiting Jupiter in 1988.     

The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems

This paper presents the adaptive cross approximation (ACA) algorithm to reduce memory and CPU time overhead in the method of moments (MoM) solution of surface integral equations. The present algorithm is purely algebraic; hence, its formulation and implementation are integral equation kernel (Green's function) independent. The algorithm starts with a multilevel partitioning of the computational domain. The interactions of well-separated partitioning clusters are accounted through a rank-revealing LU decomposition. The acceleration and memory savings of ACA come from the partial assembly of the rank-deficient interaction submatrices. It has been demonstrated that the ACA algorithm results in O(NlogN) complexity (where N is the number of unknowns) when applied to static and electrically small electromagnetic problems. In this paper the ACA algorithm is extended to electromagnetic compatibility-related problems of moderate electrical size. Specifically, the ACA algorithm is used to study compact-range ground planes and electromagnetic interference and shielding in vehicles. Through numerical experiments, it is concluded that for moderate electrical size problems the memory and CPU time requirements for the ACA algorithm scale as N/sup 4/3/logN.     

Fast radiation pattern evaluation for lens and reflector antennas

A novel algorithm referred to as the fast physical optics (FPO) for computing the radiation patterns of nonplanar aperture antennas over a range of observation angles is presented. The computation is performed in the framework of the conventional physical optics approximation appropriate for the high frequency regime. The proposed algorithm is directly applicable to reflector and lens antennas as well as to radomes. The method comprises two steps. First, a decomposition of the aperture into subdomains and computation of the pertinent radiation pattern of each subdomain. Second, interpolation, phase-correction and aggregation of the radiation patterns into the final pattern of the whole aperture. A multilevel algorithm is formulated via a recursive application of the domain decomposition and aggregation steps. The computational structure of the multilevel algorithm resembles that of the FFT while avoiding its limitations.     

Time domain adaptive integral method for surface integral equations

An efficient marching-on-in-time (MOT) scheme is presented for solving electric, magnetic, and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium. The proposed scheme is the extension of the frequency-domain adaptive integral/pre-corrected fast-Fourier transform (FFT) method to the time domain. Fields on the scatterer that are produced by space-time sources residing on its surface are computed: 1) by locally projecting, for each time step, all sources onto a uniform auxiliary grid that encases the scatterer; 2) by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global, multilevel/blocked, space-time FFTs; 3) by locally interpolating these fields back onto the scatterer surface. As this procedure is inaccurate when source and observer points reside close to each other; and 4) near fields are computed classically, albeit (pre-)corrected, for errors introduced through the use of global FFTs. The proposed scheme has a computational complexity and memory requirement of O(N/sub t/N/sub s/log/sup 2/N/sub s/) and O(N/sub s//sup 3/2/) when applied to quasiplanar structures, and of O(N/sub t/N/sub s//sup 3/2/log/sup 2/N/sub s/) and O(N/sub s//sup 2/) when used to analyze scattering from general surfaces. Here, N/sub s/ and N/sub t/ denote the number of spatial and temporal degrees of freedom of the surface current density. These computational cost and memory requirements are contrasted to those of classical MOT solvers, which scale as O(N/sub t/N/sub s//sup 2/) and O(N/sub s//sup 2/), respectively. A parallel implementation of the scheme on a distributed-memory computer cluster that uses the message-passing interface is described. Simulation results demonstrate the accuracy, efficiency, and the parallel performance of the implementation.     

时域近场测量的间接频域算法和直接时域算法研究

时域近远场变换是时域近场天线测量的关键技术。本文对时域近远场变换的间接频域算法和直接时域算法进行了数值模拟和分析。针对开口矩形波导天线的时域近场测量 ,选取时空采样参数和内插公式 ,用两种算法计算时域远场方向图 ,分析周期性、时域混叠问题和扫描面截断效应 ,在相互比较和验证的基础上 ,指出两者的优、缺点及适用的情况。     

A Hardware Acceleration Platform for Digital Holographic Imaging

This paper presents a hardware acceleration platform for image reconstruction in digital holographic imaging. The hardware accelerator executes a computationally demanding reconstruction algorithm which transforms an interference pattern captured on a digital image sensor into visible images. Focus in this work is to maximize computational efficiency, and to minimize the external memory transfer overhead, as well as required internal buffering. The paper presents an efficient processing datapath with a fast transpose unit and an interleaved memory storage scheme. The proposed architecture results in a speedup with a factor 3 compared with the traditional column/row approach for calculating the two-dimensional FFT. Memory sharing between the computational units reduces the on-chip memory requirements with over 50%. The custom hardware accelerator, extended with a microprocessor and a memory controller, has been implemented on a custom designed FPGA platform and integrated in a holographic microscope to reconstruct images. The proposed architecture targeting a 0.13 µm CMOS standard cell library achieves real-time image reconstruction with 20 frames per second.     

Planar near-field to far-field transformation using an equivalentmagnetic current approach

An alternative method is presented for computing far-field antenna patterns from near-field measurements. The method utilizes the near-field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna, and these currents are used to ascertain the far fields. Under certain approximations, the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near-field measurements are made. An electric field integral equation (EFIE) is developed to relate the near fields to the equivalent magnetic currents. The method of moments is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient method, and in the case of a rectangular matrix, a least-squares solution for the currents is found without explicitly computing the normal form of the equation. Near-field to far-field transformation for planar scanning may be efficiently performed under certain conditions. Numerical results are presented for several antenna configurations     

Far-field predictions from near-field measurements using an exactintegral equation solution

This paper presents a new approach to derive far-field data needed in antenna and EMI/EMC testing from near-field measurements. An exact integral equation solution to the wave propagation problem is used to transform the near-field data to the far field. The method requires near-field measurements on two closed surfaces enclosing all sources and inhomogeneities. The approach is validated with numerical simulation of measurements of fields radiated from a known antenna     

Far-field pattern determination from the near-field amplitude ontwo surfaces

The possibility of determining the far field of radiating systems by measuring only the near-field amplitude is investigated. The main difficulties of the problem are examined in some detail and a new near-field/far-field transformation technique is developed, based on the measurement of the near-field amplitude over two surfaces surrounding the antenna under test. The accuracy of the far-field reconstruction results are related both to the distance between such surfaces and to some a priori information concerning the near-field phase and/or the radiating system. The information on the radiating system allows relaxation of the need for any information on the near-field phase provided that the distance between the measurement surfaces is high enough. Conversely, the knowledge of a more or less corrupted near-field phase allows reduction of such distances without affecting the accuracy of the far-field reconstruction. Numerical examples validating the effectiveness of the developed algorithm are provided for the planar scanning case     

基于重加权?1范数惩罚的远近场混合源定位算法

现有信源定位方法大多假定信源是远场源或近场源,而实际定位系统中往往存在远场源和近场源共存的情况。为实现远、近场源分离及高精度信源定位,本文在稀疏信号重构理论框架下提出了一种新的远近场混合源定位算法。该算法利用阵列协方差矩阵反对角线元素和重加权l1范数惩罚获得所有信源的到达角（Direction Of Arrival, DOA）估计。在DOA估计的基础上,根据远场与近场源距离参数位于不同区间的特点利用一维搜索实现远、近场源分离以及近场源距离参数的估计。从理论角度分析了重加权l1范数惩罚算法的重构性能。本文所提算法不仅同时适用于高斯和非高斯信号,而且无需多维搜索和参数配对,也无需信源数的先验信息,同时还可以获得较好的定位精度。计算机仿真结果验证了所提算法的有效性。