On the radiation pattern of a multibeam antenna

The optimum radiation of a lens antenna with an array feed ofMelements is desired, which will exhibit maximum gain in a number (k) of specified directions and nulls in other (j) specified directions. This optimum is not derived; however, a condition for the optimum is shown to be some superposition of just (k + j) individual radiation patterns where each individual pattern is obtained by a separate excitation set of allMfeed elements such that the gain is maximized in each of the (k + j) directions. (The feed array excitation set for each of the (k + j) maximum gain individual patterns is derived.) Thus the number of unknown feed excitation coefficients is reduced fromMto (k + j).