Antenna Pattern Synthesis Research Articles

Quality factor constrained, antenna pattern synthesis using a restricted class of aperture functions

The quality factor [Q] for the E-plane strip source antenna is minimized with respect to a class of aperture functions for which the [Q] converges. A complete basis for the above class of functions is constructed for the first time and this basis is used to minimize the above mentioned [Q]. The functions which minimize the above [Q] turn out to be doubly orthogonal and are used to implement a constrained aperture synthesis procedure. New results concerning the maximum bandwidth (or minimum [Q]) of the E-plane strip source antenna are given.

Generalized array pattern synthesis by the method of alternating orthogonal projections

A geometric formulation of the null-steering array antenna pattern synthesis problems for arbitrary array geometries is proposed. The formulation allows the use of some simple intuitive techniques for the construction of the array weights. In particular it is shown that the optimum vector can be obtained in an appropriately selected weight vector subspace via a recursive projection algorithm starting from its known projection on the vector lying in the constrained look direction. The algorithm is computationally very simple and can be used for on-line solution of synthesis problems for complex array geometries.

Pattern synthesis of cylindrical slot antenna

A constrained synthesis procedure is applied to the cylindrical slot antenna. Sets of orthogonal eigenfunctions are generated to represent the aperture and radiation fields. The error criterion is that of the minimum mean-square match and the super-gain ratio represents the source constraint. The method is illustrated for the cosecant pattern.

Pattern synthesis of spherical circular array antenna by conjugate gradient method

AbstractIn this paper, the spherical circular array antenna pattern is synthesized and the results are compared with the planar circular array. Since the pattern function is complicated, analysis of pattern syntheses of solid surface arrays such as the spherical array becomes difficult. Herein, pattern synthesis is done numerically by minimizing the mean‐square‐error between the desired and synthesized power patterns using the conjugate gradient method. This method is found to be effective in the pattern synthesis of the spherical array. Calculations show that when elements with sharp patterns are used in the array, phase control is more advantageous in practice than amplitude control. Also shown here is the excitation method by which a circularly polarized pattern along the apex direction can be obtained when turnstile antennas are arrayed conformally on the sphere. With this excitation method, the pattern is synthesized and the axial ratio of polarization for main‐beam scan degrades less for spherical than planar array. Furthermore, for spherical array the axial ratio can be improved by placing the elements on a conducting sphere.

Synthesis of equiripple sector antenna patterns

A tutorial description is given of a procedure for synthesizing equiripple approximations to a sector pattern which is constant over the coverage region and zero elsewhere. This procedure, which represents a generalization of Dolph-Chebyshev synthesis, can be used to synthesize both zero phase and minimum phase approximations (with the latter yielding a better approximation to the desired magnitude function). Theoretical considerations and comparisons of recently constructed arrays suggest that the synthesized patterns have maximum rolloff at the coverage region boundary given constraints on the maximum allowable deviations from the desired pattern and the number of array elements. Extension to synthesis of more complex desired functions is discussed.

Radiation pattern synthesis of planar antennas using the iterative sampling method

A synthesis method is presented for determining an excitation of an arbitrary (but fixed) planar source configuration. The desired radiation pattern is specified over all or part of the visible region. It may have multiple and/or shaped main beams with low sidelobes. The iterative sampling method is used to find an excitation of the source which yields a radiation pattern that approximates the desired pattern to within a specified tolerance. In this paper the method is used to calculate excitations for line sources, linear arrays (equally and unequally spaced), rectangular apertures, rectangular arrays (arbitrary spacing grid), and circular apertures. Examples using these sources to form patterns with shaped main beams, multiple main beams, shaped sidelobe levels, and combinations thereof are given.

Computational methods for antenna pattern synthesis

Some general numerical methods for antenna pattern synthesis, with and without constraints, are developed. Particular cases considered are 1) field pattern specified in amplitude and phase, 2) field pattern specified in amplitude only, and 3) these two cases with a constraint on the source norm. Both the source and the field are discretized at the beginning, and the methods of finite dimensional vector spaces are used for the computations. The theory is general, but is applied only to point sources arbitrarily distributed in a plane, and to pattern synthesis in this plane. Some numerical examples are given for ten sources approximately equispaced on one-half of an ellipse, with the desired field pattern chosen to be the csc <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi</tex> pattern in the first quadrant.

Antenna pattern synthesis based on optimization in a probabilistic sense

Antenna optimization theory is usually formulated on the premise that all parameters could be adjusted with unlimited accuracy. Since no practical antenna can be built with absolute precision, only optimization in some probabilistic sense of a random performance index appears to be meaningful. The method also generalizes and gives meaning to the concept of regularization used by others. An approximate solution to the probability distribution of the random performance index is obtained. From this several possible senses of optimization may be defined. Several examples in the synthesis of a two-dimensional secant pattern are studied in detail. In general, it may be impractical to build an array with deterministically optimum currents but also next to impossible to even compute the currents accurately. A detailed numerical analysis is given to show possible sources of errors.

A synthesis of array antennas for high directivity and low sidelobes

By application of a Gegenbauer polynomial, pattern synthesis of array antennas which have high directivity and low sidelobe level is investigated. A Chebyshev or uniform-amplitude array is included as a special case of the result obtained. The current amplitudes of the array elements are represented by a Jacobi polynomial and are easily calculated. It is shown by numerical calculations for a linear array and a hexagonal planar array that there is an optimum directivity for a specified sidelobe level within a class of Gegenbauer-polynomial patterns.

Antenna synthesis and solution of inverse problems by regularization methods

Antenna pattern synthesis is discussed as an example of problems. This serves the purpose of introducing a concept that is useful in many other applications: remote sensing, inverse scattering, etc. It also suggests that regulation methods that have been devised to solve improperly posed problems can be applied to antenna synthesis and the aforementioned problems. This gives systematic methods for solving the pattern synthesis problem even when the element patterns are arbitrary.

Method of Conjugate Gradients for Antenna Pattern Synthesis

The computational method of conjugate gradients for linear operator equations is given. This technique is applied to the solution of the integral equation that relates the aperture distribution and the far‐field pattern. This problem is treated from the variational setting by minimizing an error functional. In searching for the solution, a sequence of expanding subspaces in a function space is generated via the Frechet differential of the error functional. The error functional is minimized in each of the subspaces and thus forms a sequence of approximating solutions. This iterative procedure may be conveniently implemented on a computer. Two synthesis problems are treated using this technique, and the results are discussed.

Antenna pattern synthesis with an imaging optical heterodyne receiver

A system is proposed and discussed which would allow rapid direct synthesis and steering of far-field antenna patterns for optical heterodyne receivers. The system produces an antenna pattern which is the image of a spatial filter in the reference beam.

A Technique for the Synthesis of Line-Source Antenna Patterns Having Specified Sidelobe Behavior

A new method for the synthesis of line.source antenna patterns having prescribed sidelobe envelope functions is discussed. The patterns obtained are inherently nonsupergained and, in the sense of Taylor patterns, approach the narrowest beamwidth for the given sidelobe behavior. Sample patterns and corresponding aperture distributions, together with required design parameters, are given. The sidelobe envelope functions for those patterns having maximum gain for a given maximum sidelobe level are also presented.

An Axial Form of the Sampling Theorem and its Application to Optical Diffraction

The sampling theorem is used to obtain expressions for the diffracted amplitude G(y, z) at any point in space, once the distribution along the axis G(y, 0) is known at the sampling points. In the case of a circular symmetrical pupil, G(y, 0) is simply the Fourier transform of the pupil function. The real or imaginary parts of G(y, z) may be obtained either from the real or from the imaginary part of G(y, 0). By suitable oversampling, the real part of G(y, z) may be found from its imaginary part, and vice versa. A technique for the synthesis of antenna patterns is suggested.

Resolution limitations of a finite aperture

Methods of increasing antenna resolution by data processing are of interest in radio astronomy and radiometric mapping applications. This paper deals with the fundamental limitations of such operations. Communication theory techniques using prolate spheroidal wave functions have already been applied to antenna pattern synthesis. These techniques are applied to the problem of reconstituting an observed temperature distribution. The manner in which noise limits this reconstitution process is clearly shown. A least expected mean square error reconstitution process is also detailed. An interesting analogy between data processing and supergaining is noted. Finally, the limitation set by noise on the resolution of a data processed finite aperture is concluded.

On the problem of optimum antenna aperture distribution

The antenna pattern synthesis problem for a finite line source is formulated and treated in the space of absolutely square-integrable functions. An examination is made of the condition that must be imposed on the desired radiation pattern so that the problem is solvable. The optimum aperture distribution is determined by the variational technique, subject to the requirement that the approximating radiation patterns should have a superdirective ratio less than or equal to some fixed positive value. The optimality of the solution is demonstrated by considering the sufficient condition. The error criterion is measured in the mean-square sense.

Application of periodic functions approximation to antenna pattern synthesis and circuit theory

Recently, mathematicians gave results on the approximation of periodic functions f(x) by trigonometric sums P_{n}(x) . These results can be useful for antenna radiation and circuit theory problems. Rather than the least mean-square criterion which leads to Gibbs' phenomenon, it has been adopted that the maximum in the period of the error, | f - P_{n} | , is to be minimized. By linear transformation of the Fourier sum, a P_{n} sum can be obtained to give an error of the order 1/n^{p} . The Fourier sum would give \Log n/n^{p} . Limitations on the maximum of P_{n} derivatives are introduced allowing one to obtain the order of maximum error. Antenna power diagram synthesis is then looked at with these results. The power radiation v^{2} of an array of n isotropic independent sources equally spaced can always be written under the form of a P_{n} sum. Thus it is possible to give general limitations for the derivatives of v^{2} in the broadside case and the endfire case. These limitations depend upon the over-all antenna dimension vs wavelength a/\lambda and the maximum error. A practical problem of shaped beam antenna is examined. It is shown that, by using the mathematical theory, improvements can be made on the diagram from what is usually obtained. For circuit theory, physically evident limitations in time T and spectrum F allow one to write the most general function under the form of a P_{n} sum, and thus to apply the mathematical results to that field. Formal analogy allows comparison of antenna pattern and circuit theories.