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

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.