Design of Linear Arrays Forming Pencil Beams Based on Derivatives of Chebyshev Polynomials

Polynomial approximation of pencil beam allows the analytical design of linear arrays with a direct control of the sidelobe level. The most popular polynomial approximation is Dolph-Chebyshev. It brings the beam with equiripple sidelobes and, consequently, high power in the sidelobe region. The sidelobe power can be reduced by using the arrays with decaying sidelobes. Such an array is obtained by employing a polynomial with nonequiripple behavior. In this paper, we propose a straightforward method for the design of uniform linear arrays forming narrow beams with decaying sidelobes. The method is based on the polynomial approximation in which an arbitrary order derivative of the Chebyshev polynomial is used. For the given sidelobe level, increasing the order causes a reduction in sidelobe power. A significant reduction is achieved for the derivatives up to the fifth order. However, such behavior deteriorates beamwidth, directivity, and dynamic range ratio.