Synthesis of Optimal Narrow Beam Low Sidelobe Linear Array With Constrained Length

Abstract

Abstract-The synthesis of optimal narrow beam low sidelobe linear array is addressed. Only the length of the array is constrained. The number, the positions and the weightings of the elements are left free. It is proven, that the optimal design is always an array with a small number of elements. One first demonstrates that among equally spaced linear arrays of given length, the sparsest Dolph-Chebyshev design, i.e., the one with the largest admissible inter-element distance, is the optimal one. Then, the restriction to equally spaced elements is removed, and the general problem is solved and discussed. It is shown that the sparsest Dolph-Chebyshev designs are optimal for array lengths in given specified intervals and close to optimal for all other lengths.

Experimental Validation of Linear Aperiodic Array for Grating Lobe Suppression

“…A n e jkx n sin(θ) (2) where θ is the observation angle, k the free space propagation constant, A n and x n are respectively the complex amplitude and the position of the nth element, with x 1 = −a for simplicity (see Figure 1). So, x N + a can be considered as the total size of the aperture array.…”

“…In particular, works on array synthesis methods, based on deterministic procedures [1,2] or on heuristic search methods [3,4], are addressed. Usually, these techniques are focused on the array factor synthesis, assuming ideal isotropic radiators separated a distance close to half of a wavelength.…”

Comparison Guidelines and Benchmark Procedure for Sparse Array Synthesis

“…This synthesis problem can be solved by means of the classical solution from Dolph-Chebyshev [14] to achieve the minimum beamwidth for the chosen SLL; this kind of excitation, together with equal spacing among elements, has previously shown to provide almost optimal patterns [18]. For a Dolph-Chebyshev excitation, in the case of d E = λ/2, the value of u 1 can be calculated as:…”