A Taylor synthesis for principal solution patterns of multiplicative antenna systems

A multiplicative (cross-correlation) receiving antenna system with a linear aperture can have a power pattern P₀(u ) (the so-called principal-solution power pattern) whose spatial frequency transfer function (SFTF) is uniform over the entire spatial frequency (SF) bandwidth. A modified principal solution system which retains the uniform SFTF except for smooth transitions at the ends of the SF passband is described. The transitions are due to a change in the original pattern P₀(u), which suffers from high sidelobes, to a Taylor (1955) synthesis pattern P_T (u) which involves a slowly varying envelope pattern. All of the slowly varying envelope sidelobes of P_T(u ) are set at the same appropriate low level, e.g. -30 dB. The aperture weighting distributions are free of singularities, unlike those for P₀(u), and can be sampled to provide the current weightings for a linear multiplicative array