New methods of synthesizing Low Sidelobe sum and difference patterns for linear arrays are described. By subarray beam forming, the sum and difference patterns exhibit a common factor, leading to a simple monopulse estimator. A procedure is proposed for the synthesis of the subarray-based sum and difference patterns which approximate a set of reference patterns in least-squares sense. Supervised nulling is incorporated as a means of suppression of strong interference. To further reduce system complexity, we impose the constraint that parts of the beamforming weights are shared by the sum and difference channels. The relationship between the maximum number of common weights allowable and the number of subarrays used is discussed. Numerical results are presented to demonstrate the efficacy of the proposed methods.