Sector sidelobe nulling

The growing interest in adaptive antennas makes it worthwhile to examine the theoretical limits to what can be achieved with reduction of sidelobe levels of array antenna patterns. In this paper we address the problem of determining the minimum possible power that can be present in a specified sidelobe region subject to certain constraints. We consider three different forms of the minimization problem: (1) minimize the ratio of the power in the sidelobe region to the power in the mainbeam region; (2) minimize the ratio of the power in the sidelobe region to the power density in the mainbeam direction; and (3) minimize the power in the specified sidelobe region subject to the constraint that the array response in the mainbeam direction is held constant. It is shown that forms 2 and 3 of the minimization problem lead to identical results, and that the results obtained with form 1 are numerically close to those obtained with forms 2 and 3.