Closed-Form Design of Optimum Linear Arrays Based on Raised-Cosine Beampattern

Linear arrays forming pencil beams with slowly decaying sidelobes make a good trade-off among excitation dynamic range ratio, beam efficiency, directivity, sidelobe level, and beamwidth. Popular arrays with such sidelobe behavior are Taylor, Gauss, Gegenbauer, and second-kind Chebyshev. In this paper, we propose a closed-form method for the design of pencil-beam arrays with a prescribed sidelobe level. The method exploits the leastsquares approximation of a raised cosine function in the azimuth domain, thus bringing the beampattern with slowly decaying sidelobes. For common numbers of excitation coefficients and sidelobe levels, the proposed arrays simultaneously exhibit the optimum beamwidth, dynamic range ratio, and directivity.