General radiation-pattern synthesis technique for array antennas of arbitrary configuration and element type

General radiation-pattern synthesis technique for array antennas of arbitrary configuration and element type.

Abstract: An interactive iterative-synthesis technique is presented, which is of particular use for far-field patterns defined in terms of power only. The method is applied in general to three-dimensional array configurations composed of different element types, with the required far-field defined over large angular regions. Suggestions for extending the method to near-field, simultaneous multiparameter or constrained synthesis are also given. The description of the method is presented for three different conditions, depending on whether both the array amplitude and the phase or just the amplitude or the phase are variable. Examples of the method, applied to various practical synthesis problems, and comparisons to other techniques are also given.

1    l.itroduction

Antenna design is an optimisation problem with a large number of variables and constraints. Initial design relies on good engineering and economic judgement, and results in reducing the choice of antenna types to a small number. Closer analysis usually reduces these types further to a specific set of antennas with bounds on size, cost, weight, etc.

A radiation-pattern synthesis technique is then used to obtain an approximation to an 'ideal' far-field pattern. In general his problem is ill-defined, and choices need to be made; hence a synthesis technique should perform two functions:

(a) It should enable a good compromise between conflicting performance parameters to be achieved.

(b) It should obtain the array amplitude and phase distribution.

The method given here endeavours to meet these requirements by combining flexibility and efficiency.

2   Review of previous work

The subject of radiation-pattern synthesis is extensive. The following is not intended to be a comprehensive review, but should serve as a guide to the extent of previous work. It has been divided into five subsections. These indicate the type of far-field requirements or the constraints on the aperture distribution.

2.1 Pencil beams

The relation between the array far-field pattern and its aperture distribution, in terms of a truncated Fourier expansion, was first pointed out by Wolff [1] and was investigated further by Schelkunoff [2]. Using Chebyshev methods, a minimum deviation fit was proposed by Dolph [3] and extended to continuous sources by Taylor [4]. The problem of physically achieving the synthesised distribution was also addressed in this paper, and the superdirective ratio was defined.

Synthesis of pencil-beam type patterns was subsequently considered by many authors, and various procedures were proposed. Ma [5] introduced the use of Bernstein polynomials and also extended the synthesis of Chebyshev-type patterns to nonuniformly spaced arrays [6]. The use of element position as a third variable was also addressed by Tseng and Cheng [7], and Bayliss [8] extended the work to difference patterns. Hyneman [9] proposed a method for controlling the sidelobe topography of an array within specified limits, and Stutzman [10] suggested an iterative sampling method to control the sidelobe level. Atwood [11] used a method applicable to nonisotropic sources. Goto [12] used Gegenbauer polynomials to reach a compromise between directivity and sidelobe level. Perini [13] proposed an iterative steepest-descent method to take advantage of all the available parameters such as element spacing, amplitude, phase and frequency. Elliott [14] gave a method of syn-thesising a pencil beam with given sidelobe topography while Lopez [15] looked at maximising the difference slope with given sidelobe level. Haupt [16] proposed a method whereby both sum and difference patterns could be simultaneously synthesised with nulls in prescribed directions.

22 Performance indices

Optimisation, with respect to given performance indices such as efficiency, signal-to-noise ratio, Q, etc., was addressed by Butler et al. [17, 18, 19]. Kurth [20] proposed a method which could be applied to power patterns while Sarkar [21] gave a method which could be applied to arbitrarily oriented arrays.

The fact that, in general, radiation pattern synthesis is ill-posed was recognised by Deschamps and Cabayan [22] and was treated again by Nashed [23].

byR>»Qdes [28], [29]. Morrison [30] and Steyskal [31] addressed the problem of power synthesis, Morrison using a varia^-Mial method. Stutzman [32] extended the iterative sampling >a;:thod to shaped beams from planar arrays. Mautz and Har^n^ton [33] used a different iterative procedure in order lo synthesise power patterns. Evans [34] and Lopez [35] lookc-1 at the synthesis of sector patterns. Prasad [36] used the nxihod of alternating orthagonal projections, and Pozar [37 j as'-d ?r.'»gaki Modes. Elliott [38] adapted his method for pencil beaiiia to synthesise shaped beams.

2.4 Contoured beams

Satellite applications have provided the need to generate contoured beams: in this field Galindo-Israel [39], and Klein [40] used an array-fed reflector and adopted a minimax optimisation procedure, while Wood [41] used spherical wave expansion to obtain global coverage from a front-fed reflector. Jorgensen [42] used the method of aperture field synthesis to provide contoured beams. Bor-nemann [43] uses a method similar to Woodward's, applied to a planar array, to achieve various complex beamshapes.

2.5 Phase only

Phase-only synthesis was first addressed by Chu [44]. Fong and Birgenheier [45] later proposed a 'steepest ascent' method. Baird and Rassweiler [46] used phase-only synthesis to produce nulls in prescribed directions while Steyskal [47] proposed another method to produce nulls. Giusto and Vincenti [48] used a random search and simplex method to generate nulls. Shore [49] used nonlinear programming techniques, again to produce nulls. Chakraborty [50] applied phase-only synthesis to the more general problem of pattern shaping.