Phase-only pattern nulling with reduced degrees of freedom

It is noted that, in some cases, it is desirable to synthesize pattern nulls by perturbing the phases of small sub-areas of the aperture or a small number of array elements or subarray blocks of elements. This approach would be required, for example, to provide a null in the sidelobe region of a shaped-beam pattern adaptively; attempting this using all the available degrees of freedom (i.e. with full phase control) would present the difficulty of ensuring that in addition to minimizing the pattern gain at the nulling angle, a high-gain beam of the desired shape is maintained. An additional benefit of nulling using only a small subset of the available degrees of freedom would be that such a system would in practice be simpler and cheaper, and should allow more rapid convergence. It is concluded that, compared to synthesizing the null with full phase control, using phase control on pairs of elements produces slightly inferior but generally quite usable patterns, provided the elements in the pair are chosen appropriately.<>