Matrix formulation for Dolph-Chebyshev beamforming

Several methods have been developed for tapering or shading of line arrays to minimize minor lobes. A method developed by C. L. Dolph makes it possible to optimize the patterns so that 1), for any specified minor lobe, the narrowest possible major lobe is achieved; or 2), for any specified major-lobe width, the lowest possible minor-lobe levels are achieved. The procedure to calculate the required set of shading coefficients involves algebraic manipulation of Chebyshev polynomials. This manipulation becomes increasingly tedious as the array size becomes larger. The letter presents a compact matrix formulation of Dolph-Chebyshev beamforming which can provide additional insight to the general problem of array shading. A special case of this formulation leads to a close-form solution.