Spherical Bessel function based deterministic beam-forming for sphericalsurfaced apertures

A deterministic beam-forming approach aiming at synthesising differently shaped beams for a partial, spherical-surfaced conformal aperture is presented. It is mathematically shown that current distribution on such an aperture can be expanded into a Fourier series, and its far-field radiation pattern can be further expressed in a concise closed form. If the aperture distribution satisfies a weighted zeroth-order or first-order spherical Bessel function, one can easily achieve various shaped beams such as pencil, flat-topped and bimodal beams by simply tuning a single weighting coefficient of the Bessel function. The proposed approach is deterministic and intuitive, making it possible to achieve fast, real-time beam-forming for spherical conformal arrays.