Abstract
New deterministic procedures for the design of linear aperiodic arrays are described which permit exploiting, in a combined way, both the positions and the excitation amplitudes of the array elements obtaining a pattern which optimally fits, in terms of a weighted L2 norm, the pattern of a reference linear continuous aperture. A first numerical procedure is based on alternating optimization of positions and amplitudes by means of closed-form convex projectors. Sufficient conditions for the solution to be optimal are established. A second numerical procedure is based on a domino-like sequential determination of the unknowns which can be iterated to convergence. Additionally, analytical asymptotic expressions for the optimal inter-element spacing and amplitude are derived by means of variational techniques. The optimal asymptotic inter-element spacing is demonstrated to be proportional to the reference tapering to the power (-2/3) while the optimal asymptotic array amplitude is proportional to the reference tapering to the power (1/3). For aperiodic arrays with equiamplitude excitation it is proved that the optimal inter-element spacing is proportional to the reference tapering to the power (-1). Based on these asymptotic dependencies, closed-form analytical solutions are obtained for amplitudes and positions of the elements. Several numerical results confirm the effectiveness and accuracy of the new procedures.
Published Version
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