Spherical Mode Expansion Research Articles

Spherical Fourier-Transform-Based Real-TimeNear-Field Shaping and Focusing in Beyond-5G Networks

For ultra-reliable high-data-rate communication, the beyond fifth generation (B5G) and the sixth generation (6G) wireless networks will heavily rely on beamforming, with mobile users often located in the radiative near-field of large antenna systems. Therefore, a novel approach to shape both the amplitude and phase of the electric near-field of any general antenna array topology is presented. Leveraging on the active element patterns generated by each antenna port, the beam synthesis capabilities of the array are exploited through Fourier analysis and spherical mode expansions. As a proof-of-concept, two different arrays are synthesized from the same active antenna element. These arrays are used to obtain 2D near-field patterns with sharp edges and a 30 dB difference between the fields' magnitudes inside and outside the target regions. Various validation and application examples demonstrate the full control of the radiation in every direction, yielding optimal performance for the users in the focal zones, while significantly improving the management of the power density outside of them. Moreover, the advocated algorithm is very efficient, allowing for a fast, real-time modification and shaping of the array's radiative near-field.

Stellar Speckle and Correlation Derived From Classical Wave Expansions for Spherical Antennas

Michelson phase and Hanbury Brown-Twiss intensity stellar interferometry require expressions for the first-and second-order correlation functions, respectively, of the fields radiated by stars in terms of their diameters and measured quasi-monochromatic wavelengths. Although our sun and most other stars are spherical in shape at optical wavelengths, previous determinations of speckle and correlation functions have modeled stars as circular disks rather than spheres because of the mathematical tools available for partially coherent fields on planar surfaces. However, with the incentive that most stars are indeed shaped like spheres and not disks, this article models a star as a spherical antenna composed of a random distribution of uncorrelated volume sources within a thin surface layer (photosphere). Working directly with the time-domain fields, a self-contained, straightforward, detailed derivation of speckle patterns and correlation functions is given based on a novel, angularly symmetric, spherical mode expansion with coefficients determined by the assumed Lambertian nature of the star's radiation and the uniform asymptotic behavior of the spherical Hankel functions. First-order spatially averaged and temporally averaged correlation functions are proven to be identical, and the normalized second-order correlation function is shown to equal one plus the square of the first-order correlation function. The direct time-domain approach reveals explicit expressions for the quasi-monochromatic wave-packet fields of stellar radiation as well as new criteria for the validity of the far-field approximation for the fields of incoherent sources that are much less restrictive than the Rayleigh-distance criterion for coherent sources.

Element phase centre and orientation compensation in conformal arrays during continuous deformations based on spherical mode expansion

Radiation field of conformal arrays can be obtained by simulation computation. There must be a trade-off between computation accuracy and complexity. With respect to applications where both high efficiency or even real-time applications and accuracy are required, such as adaptive beamformers together with time-varying array structures due to deformations or vibrations, more effective methodologies have to be employed for precise mainlobe direction maintenance and rigorous suppression of existing interferences. A method combining spherical mode expansion, rotation and translation of spherical waves, spatial displacement phase compensation, and approximations of constant element radiation patterns in local coordinate systems is proposed here, featuring one-time numerical effort for isolated element radiation patterns, fast coupling matrix calculation based on updated array configuration, and analytical radiation field expressions with limited eigenmode expansion coefficients storage requirements. Adaptive beamformers are utilised to validate the effects of remaining approximations including constant element patterns in local coordinate systems and constant mutual coupling matrix, proving the proposed method has the potential for aircraft-borne conformal antenna array radiation field analysis where deformations and vibrations occur continuously.

A Compact Ultrawideband Reflector Antenna: Using a Wide-Band Omnidirectional Antenna with a Mechanically Steerable Endfire Beam to Illuminate a Half-Cut Paraboloid Reflector

An ultrawideband, compact, paraboloid reflector antenna with a mechanically steerable endfire beam is presented, with its performance evaluated in frequency, time, and power domains. A fixed, omnidirectional monocone feed, engineered to maintain the same illumination of the reflector during its rotation, is used to facilitate scanning. Moreover, the omnidirectional mode of the antenna system can be enabled by recessing the reflector. A monocone feed is designed using the spherical mode expansion (SME) technique to achieve consistent monopole-like patterns over a wide bandwidth. To achieve the small group delay variation at a reduced size, the reflector is placed close to the monocone. The nearfield paraboloid can still produce a planar wavefront without destructive interference despite this proximity; therefore, the destructive interference is avoided. The reflector is designed based on a multidimensional parametric study to accomplish a reduced size and reasonable performance in both frequency and time domains.

Synthesis of coupled antenna arrays using digital phase control via integer programming

A pattern synthesis technique for real and coupled antenna arrays by using digital phase-only excitation weights is introduced here. The method is formulated as an integer linear programming problem incorporating a fast full-wave analysis of the array, based on the finite element method and spherical mode expansions. The method achieves radiation patterns with specified pointing directions, main lobe widths, minimum sidelobe level, and prescribed nulls, controlled by digital phase shifters.

A First-Order Model of the Multiple-Feed Toroidal Magneto-Dielectric Antenna

A model of the input impedance of the toroidal permeable antenna, which is the dual of the conventional metal loop antenna, is derived, starting from Schelkunoff’s transmission line description of the loop antenna instead of the electrically small limit model. This antenna operates in both the monopole mode and circularly polarized dipole mode and is constructed from a torus of high permeability material. Since the ultimate goal is to obtain an impedance model from which to derive the best matching network; the input impedance is expressed in a form that has a frequency independent resistor terminating a reactive network which is called the Darlington form. Because such a circuit mimics closely the input impedance of the dipole modes of the spherical mode expansion, it is a much better model of the antennas as we go beyond the electrically small limit. The feed loop contribution is explicitly accounted for and the results are compared with fullwave simulations of a typical toroidal antenna operating in both monopole and circularly polarized dipole modes which show a good agreement well beyond the electrically small limit.

Gradient-Based Aperiodic Array Synthesis of Real Arrays With Uniform Amplitude Excitation Including Mutual Coupling

This paper proposes the synthesis of aperiodic arrays of realistic antennas excited with uniform amplitude, where the mutual coupling between elements is rigorously taken into account. A cost function that involves the expression of the radiated field of the coupled array is obtained and its gradient is evaluated in order to move the elements in the corresponding direction at each iteration. The synthesis method involves the calculation of the gradient of the field radiated by the coupled array, which is obtained analytically by using a full-wave method based on the generalized scattering matrix, spherical mode expansions and rotation, and translation properties of spherical waves.

Optimal Design Method of MIMO Antenna Directivities and Corresponding Current Distributions by Using Spherical Mode Expansion

This paper proposes a new methodology to design optimal antennas for MIMO (Multi-Input Multi-Output) communication systems by using spherical mode expansion. Given spatial channel properties of a MIMO channel, such as the angular profile at both sides, the optimal MIMO antennas should provide the largest channel capacity with a constraint of the limited implementation space (volume). In designing a conventional MIMO antenna, first the antenna structure (current distribution) is determined, second antenna directivity is calculated based on the current distribution, and thirdly MIMO channel capacity is calculated by using given angular profiles and obtained antenna directivity. This process is repeated by adjusting the antenna structure until the performance satisfies a predefined threshold. To the contrary, this paper solves the optimization problem analytically and finally gives near optimal antenna structure (current distribution) without any greedy search. In the proposed process, first the optimal directivity of MIMO antennas is derived by applying spherical mode expansion to the angular profiles, and second a far-near field conversion is applied on the derived optimal directivity to achieve near optimal current distributions on a limited surface. The effectiveness of the proposed design methodology is validated via numerical calculation of MIMO channel capacity as in the conventional design method while giving near optimal current distribution with constraint of an antenna structure derived from proposed methodology.

Miniaturization of TEM Horn Using Spherical Modes Engineering

The spherical mode expansion is exploited to miniaturize a transverse electromagnetic (TEM) horn antenna and achieve good frequency and time domain performances. To adjust the radiated powers of fundamental transverse electric and transverse magnetic modes, the combined loop and TEM horn antenna is engineered. The constructive combination of the two modes below the horn’s turn-on frequency miniaturizes the antenna and improves its gain. The magnitude and phase tuning of the desired modes is achieved by modifying the loop’s geometry. The spherical modal spectrum at higher frequencies is also studied and the antenna’s geometry is further modified to maintain constructive interference between the higher order spherical modes. A prototype with electrical size of $0.188~\lambda ~\times0.145\lambda ~\times0.087\lambda $ (length $\times $ width $\times $ height) at the turn-on frequency is fabricated over a ground plane. Over three times lower turn-on frequency is obtained compared to a conventional TEM horn with up to 9 dB improvement in the realized gain at the low end and better radiation characteristics over more than 5:1 bandwidth (from 0.87 to 4.5 GHz). Unidirectional operation with front to back ratio >9 dB and excellent time-domain performance with fidelity factor >95% over wide field of view are also demonstrated.

Modal‐matching‐based analysis for axially corrugated dielectric‐rod‐loaded horn

AbstractAn efficient design procedure based on modal‐matching method for axially corrugated dielectric‐rod‐loaded horns of complicated geometries is proposed in this paper. Calculation of the generalized scattering matrix of individual module, which is obtained by dividing the complex horn into simple sections, is carried out. Analytic expressions of power‐coupling integrals between different kinds of waveguides are presented, including those derived initially, which greatly shorten the calculation time. Techniques including the field equivalence principle and the spherical mode expansion are further implemented for radiation pattern prediction. A rexolite‐loaded axially corrugated horn antenna is finally investigated as a numerical experiment, with the frequency range of 17–33 GHz. The results obtained by our method and by commercial full‐wave simulation software are in excellent agreement, but our method is more efficient.

Analysis and Demonstration of Two Spherical Mode Expansion Resolution Algorithms

The measured radiation field of an antenna may be expanded in a series of vector spherical modes in a specified spherical coordinate system. Such an expansion may be resolved, by means of an iterative algorithm, into two constituent vector spherical mode expansions in two other specified spherical coordinate systems. The sum of these constituent expansions is equal to the original total radiation field. The purpose of such a resolution is to separate the radiation fields due to two identified parts of the original antenna which together constitute the entire radiating structure. Once the resolution has been accomplished, one may study the radiation from the currents on the two parts of the antenna individually including mutual interaction to all orders. This is to be distinguished from measurement of the radiation fields of the two parts individually because that measurement does not include the mutual interaction. A demonstration measurement of a two antenna system is described and iterative postmeasurement processing is employed to identify the radiation from currents on the two constituent antennas of the overall radiating structure. The results are compared with those of an earlier approximate noniterative algorithm developed for the same purpose and the differences are discussed.

Mutual Coupling Compensation Matrices for Transmitting and Receiving Arrays

A general method to obtain a matrix which allows the compensation of mutual coupling effects in transmitting arrays for the total field in all directions is introduced. This method is independent of the numerical method used in the analysis and it can include the effect of the antenna platform. The starting point can be the active element patterns or the spherical mode expansion from spherical near-field antenna measurements. Additionally, the spherical mode expansion is also used to find a matrix which allows the compensation of mutual coupling effects in receiving arrays. Through this theory, a simple relation between the compensation matrices of the transmitting and the receiving arrays is found. As a consequence, the scattering matrix of a circuit that allows the simultaneous compensation of mutual coupling effects for the transmission and the reception problem can be easily defined. Finally, it will be shown how the capabilities of the compensation in all directions depend strongly on the array element.

MATRIX METHOD FOR FAR-FIELD CALCULATION USING IRREGULAR NEAR-FIELD SAMPLES FOR CYLINDRICAL AND SPHERICAL SCANNING SURFACES

—A matrix method which takes into account the probe positioning errors in cylindrical and spherical near-field (NF) measurement techniques is proposed. The near-field irregularities made impossible the determination of the cylindrical or spherical wave expansion from the measured data using classical techniques based on 2D Discrete Fourier Transformation (2D-DFT) in cylindrical case (CC) and orthogonality properties in spherical case (SC). The irregularities can be randomly distributed but known and the matrix method expresses the linear relation between the measured near-field and the corresponding cylindrical or spherical modal expansion coefficients. Once the coefficients of the cylindrical and the spherical wave expansions are known the far-field of the antenna under test (AUT) is easily determined. Accuracy of the matrix method is numerically studied as a function of the irregularities magnitude and for different noise levels (data Signal to Noise Ratio). Also, experimental results have shown the efficiency of the proposed technique.

A survey of the application of the spherical vector wave mode expansion approach to antenna-channel interaction modeling

This paper provides an overview of recent advances in the modeling, analysis, and measurements of interactions between antennas and the propagation channel in multiple antenna systems based on the spherical vector wave mode expansion of the electromagnetic field and the antenna scattering matrix. It demonstrates the importance and usefulness of this approach to gain further insights into a variety of topics such as physics-based propagation channel modeling, mean effective gain, channel correlation, propagation channel measurements, antenna measurements and testing, the number of degrees of freedom of the radio propagation channel, channel throughput, and diversity systems. The paper puts particular emphasis on the unified approach to antenna-channel analysis at the same time as the antenna and the channel influence are separated. Finally, the paper provides the first bibliography on the application of the spherical vector wave mode expansion of the electromagnetic field to antenna-channel interactions.

Efficient Combined Array Thinning and Weighting for Pattern Synthesis With a Nested Optimization Scheme

A novel procedure to thin an antenna array which synthesizes a desired pattern with the minimum number of active elements is introduced. The proposed method yields both the active elements and their corresponding excitations of a thinned array having the minimum number of active elements needed to meet several prescribed design specifications of the radiated far-field pattern. Specifications such as achieving a minimum gain, obtaining a pattern with a maximum allowable sidelobe level or synthesizing a shaped beam pattern confined into a mask are considered. Null field directions can also be added. In order to carry out the thinning, a genetic algorithm is used, while computing the excitations is carried out through linear or quadratic programming. The procedure incorporates the generalized scattering matrix analysis of an array made up of elements whose radiated field can be expressed as a spherical mode expansion, thus taking all electromagnetic effects inherently into account. Therefore, since the presence of an element can substantially alter the array features because of mutual coupling, two types of thinning are considered: removing elements or turning them off. Numerical results of arrays made up of isotropic sources, dielectric resonator antennas and microstrip patch antennas are presented.

Planar ESPAR Array Design with Nonsymmetrical Pattern by Means of Finite-Element Method, Domain Decomposition, and Spherical Wave Expansion

The application of a 3D domain decomposition finite-element and spherical mode expansion for the design of planar ESPAR (electronically steerable passive array radiator) made with probe-fed circular microstrip patches is presented in this work. A global generalized scattering matrix (GSM) in terms of spherical modes is obtained analytically from the GSM of the isolated patches by using rotation and translation properties of spherical waves. The whole behaviour of the array is characterized including all the mutual coupling effects between its elements. This procedure has been firstly validated by analyzing an array of monopoles on a ground plane, and then it has been applied to synthesize a prescribed radiation pattern optimizing the reactive loads connected to the feeding ports of the array of circular patches by means of a genetic algorithm.

Relation Between the Array Pattern Approach in Terms of Coupling Coefficients and Minimum Scattering Antennas

The well-known approach for the calculation of the radiation pattern of a finite array from the scattering parameters between the array feeding ports (coupling coefficients) is connected to the theory of minimum-scattering antennas (MS antennas) by making use of spherical mode expansions. It is shown how this approach for array radiation patterns involves an MS Antenna approximation in the first order of reflections (mutual coupling) between the elements in the array. For this purpose the generalized scattering matrix (GSM) formalism for a finite array in terms of spherical modes is used. Finally, the MS antenna theory is applied to estimate the radiation pattern of an array of waveguide-fed apertures.

Analysis of Circular Microstrip Patch Antenna Using Spherical Modal Expansion Technique

icrostrip antennas are finding increasing popularity by using their advantages in size, cost and conformity to supporting structure and easy of fabrication. In this paper analysis of circular patch, using Spherical modal Expansion technique (SM E) and design of circular patch at 8.2GHz using IE3D simulator is presented. The solution provided by SM E is analytical and therefore more efficient and accurate than numerical and ray tracing techniques. The properties of SM E are exploited to perform a precision calculation. A sample computation on circular patch is performed to demonstrate validity of this approach and is supported by experimental results.

Phaseless spherical near-field antenna measurements for low and medium gain antennas

Abstract. The characterisation of antenna radiation patterns by measurements in the near-field and a following near-field far-field transformation require accurate amplitude and phase data. Especially at higher frequencies phase measurements are demanding in terms of instrumentation and measurement accuracy. Phaseless techniques which require amplitude only data on one or more measurement surfaces are therefore of special interest. In this paper a phaseless spherical algorithm based on spherical modal expansion is presented. The algorithm works with amplitude only near-field data measured on two spheres of different radii and is therefore not restricted to certain types of antennas as for planar measurements for example. Simulated as well as measured results of low and medium gain antennas are shown.

Spherical Vector Wave Expansion of Gaussian Electromagnetic Fields for Antenna-Channel Interaction Analysis

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we introduce an approach to analyze the interaction between antennas and the propagation channel. We study both the antennas and the propagation channel by means of the spherical vector wave mode expansion of the electromagnetic field. Then we use the expansion coefficients to study some properties of general antennas in those fields by means of the antenna scattering matrix. The focus is on the spatio-polar characterization of antennas, channels and their interactions. We provide closed form expressions for the covariance of the field multimodes as function of the power angle spectrum (PAS) and the channel cross-polarization ratio (XPR). A new interpretation of the mean effective gains (MEG) of antennas is also provided. The maximum MEG is obtained by conjugate mode matching between the antennas and the channel; we also prove the (intuitive) results that the optimum decorrelation of the antenna signals is obtained by the excitation of orthogonal spherical vector modes. </para>