Generalized Dolph–Chebyshev Pencil-Beam Synthesis with an Analytically Parameterized Sidelobe Envelope

Pencil-beam synthesis often requires precise sidelobe control while maintaining a low dynamic range ratio (DRR) of the excitation coefficients. This paper presents a generalized Dolph–Chebyshev method for pencil-beam synthesis based on a new class of Chebyshev-type polynomials with an analytically parameterized oscillation envelope. The proposed formulation introduces a free parameter that provides an additional degree of freedom beyond conventional Dolph–Chebyshev synthesis. This parameter enables direct shaping of the sidelobe envelope while maintaining a relatively low DRR. Moreover, it can be optimized to minimize the DRR for a prescribed sidelobe level. To enable fast pencil-beam synthesis, particular attention is paid to computational efficiency through analytical formulations and an optimized numerical implementation. Numerical results demonstrate that the proposed method provides improved far-out sidelobe suppression over a broad angular range and generally lower relative sidelobe power compared with the Dolph–Chebyshev, Gegenbauer, conventional Taylor n-bar, and generalized Taylor n-bar methods, while maintaining comparable beamwidths and directivity and a relatively low DRR. By combining analytical formulations, one-dimensional DRR optimization, and parameterized sidelobe shaping, the proposed approach provides a computationally efficient and scalable framework for low-DRR pencil-beam synthesis.