Analysis of non-periodic antenna arrays : an accelerated Macro Basis Function approach
(2012)
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- Authors
- Supervisors
- Craeye, Christophe
- Abstract
- (en) Antenna array design has recently focused on non-periodic structures. The possibility of having arbitrary antenna positions provides additional degrees of freedom that allow one to achieve radiation characteristics that would not be possible with periodic arrays made of the same number of elements. The sparse nature of non-periodic arrays avoids the overlap of effective areas at lower frequencies (and, hence, coupling efficiency issues) and the non-periodicity discards the presence of eigenmodes. This type of array can be used for imaging, radioastronomy, telemetry and defense applications. This calls for the development of efficient numerical methods for the analysis of non-periodic antenna arrays. In this dissertation, an efficient Method of Moments solution of non-periodic arrays has been addressed using a class of non-iterative methods that reduce the effective number of unknowns. The reduction of unknowns is achieved assuming that the currents on one of the antennas in the array can be decomposed in terms of a limited number of current distributions or Macro Basis Functions (MBFs). Then, one may perform an LU decomposition of the reduced system of equations and solve for multiple right-hand sides. This is useful as it provides a complete description of the array, i.e., the array impedance matrix and all the embedded element patterns. For most practical cases, the reduction of the MoM system of equations using MBFs becomes the dominant contribution to computation time. Two novel methods have been developed to overcome this limitation. The first one exploits multipole expansions to compute the reaction integral between MBFs. The reaction integral between two MBFs is efficiently obtained integrating over the unit sphere the scalar product between the (pre-computed) far-field patterns of these MBFs multiplied by a translation operator. In the second method, the reaction integrals between MBFs are fitted, after three physically-based transformations, to a low-order harmonic-polynomial form, using a small number of sampling points. Then, while filling the reduced MoM impedance matrix, the computational complexity devoted to obtain the interaction between two MBFs is completely independent from the number of elementary basis functions per antenna. This process is independent of the array geometry, which enables the optimization of the antennas' positions at a very low computational cost, while taking into account mutual coupling. The aforementioned methods can also be applied to the case of antenna arrays in a planar layered medium. This is possible after expressing the spatial-domain Green's function in closed-form as a finite sum of cylindrical waves and one spherical wave. In the multipole-based method, the computation of the reaction integrals is dominated by the operations associated with the spherical wave term. Thus, the presence of a planar layered medium can be accounted for without significantly increasing the computational complexity one would have in the case of a homogeneous medium. Regarding the second method, the number of harmonic-polynomial expressions that need to be evaluated is higher than in the homogeneous medium case. However, this method remains competitive and is more efficient than the one based on multipole expansions, after the fitting process. Finally, the efficient calculation of the array factors and the radiation patterns of non-periodic antenna arrays has been also addressed. First, the Non-uniform Fast Fourier Transform (NFFT) is used to evaluate array factors. Second, it is shown how the NFFT can be combined with the Macro Basis Function method to express the embedded element patterns as a series of pattern multiplication problems, each term being related to a macro basis function. The proposed formulation leads to the efficient calculation of the array factors and the array patterns of non-periodic antenna arrays.
- Affiliations
Citations
Gonzalez Ovejero, D. (2012). Analysis of non-periodic antenna arrays : an accelerated Macro Basis Function approach. https://hdl.handle.net/2078.5/158044