Beam scanning with null and excitation constraints for linear arrays of antennas

We describe a synthesis technique that allows to scan the radiation pattern of a linear antenna array within a wide angular sector, in presence of null constraints and excitation constraints. In particular, the method allows the beam scanning with null constraints and phase-only control. The algorithm yields a number Q of array patterns approximating Q desired patterns close to each other in the scan sector, while satisfying the assigned constraints. The solution, that is, the sequence consisting of the Q synthesized patterns and of the corresponding excitation vectors, can be seen as the point of intersection between two sets of sequences, Y and Z. The points of Y satisfy a part of the design requirements, while the points of Z satisfy the remaining requirements. If the set is empty, the solution is found as a point of one of the two sets minimizing a suitable distance from the other. This point is determined by the method of projections