Nulling limitations for a multiple-beam antenna

Some fundamental limitations on radiation pattern nulling inherent in any multiple-beam antenna system are derived. The specific case of a satellite multiple-beam antenna at synchronous altitude operating over the earth field of view is considered in detail, although the general results are presented so as to be applicable to an arbitrary planar aperture such as a phased array. The multiple-beam antenna offers the large aperture needed for good nulling resolution, while keeping the number of signal ports utilized in any nulling algorithm at a tractable number. Two specific modes of operation are considered: an earth-coverage mode, in which one desires to null a number of interfering sources while realizing the best possible earth-coverage communications link over the remaining earth field of view; and a maximum signal mode, where one desires only to maximize the signal to a specified number of users while nulling the interfering sources. Both cases are treated in detail. Optimum results are derived for an arbitrary planar aperture and compared to what can be accomplished with a fixed set of beams (the case of 7 and 19 beams are considered). For the earth-coverage mode, the quality of the earth-coverage radiation pattern versus beam position must be traded off with the optimum beam position for good nulling-i.e., it will be shown that the set of beams which gives the flatest earth-coverage radiation pattern with no prescribed nulls is not optimum when nulls are to be formed. The optimum beam positioning is determined using the results of two-dimensional sampling theory. Furthermore, the earth-coverage constraint is seen to severely limit the gain available to a signal source near the null, relative to the maximum signal mode. The maximum directivity available to a user in the maximum signal mode is also shown to be a function of beam position. For signal sources close to the edge of the field of view, the directivity available to the source can be significantly less than optimum.