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A method of synthesizing aperture antenna excitations to obtain optimum performance in the presence of aperture blockage is presented. The problem of optimizing the performance indices such as directivity and angular sensitivity is formulated as an -dimensional minimization problem, with constraint on the sidelobe level. In most cases, the objective function is nonlinear with multiple minima which does not yield readily to gradient methods. A simplex search method is used in the study for optimizing the performance index. The sidelobe level (SLL) constraint has been incorporated using the penalty function method. The method is applied to circular monopulse aperture distribution with circular blockage to obtain maximum directivity factor (DF) in the sum mode and maximum angular sensitivity factor (ASF) in the difference mode, with sidelobe level constraint. The effect of blockage on the maximum directivity and maximum angular sensitivity is studied for various sidelobe level constraints.