Optimised array antenna nulling with phase-only control

The pointing direction gain of a linear phased array antenna is maximised with the constraints of phase-only control at the N antenna elements and the imposition of J nulls at angles θ₁, θ₂. . ., θ_J from the array normal. The specification of J nulling angles requires the a priori knowledge of the directions of the emitter sources. This maximisation problem with constraints is reduced to 2J +2 nonlinear equations which can be solved via a vector Newton algorithm to yield the N complex antenna weights in terms of the 2J+2 unknowns. Examples are given for a 20 element array with uniform and Hamming amplitude weighting and the imposition of as many as five nulling angles. Examples of mainbeam nulling are also given