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It's a difficult problem to optimize a sparse planar array for narrow main lobe width (MLW) and low peak side lobe level (PSLL) simultaneously. In this paper, the matrix pencil method (MPM) is applied to synthesize a sparse planar array. The sparse planar array is designed to a separable planar array by a product of two orthogonal linear sparse arrays. In order to obtain these two orthogonal sparse linear arrays, firstly two desired radiation patterns are designed according to the demands. Then the two desired patterns are sampled and reconstructed by using the MPM. Due to the advantages of the MPM, the element positions and excitations can be optimized simultaneously. And very low computational cost is needed for this process. A min-max criterion is also proposed for calculating the weights in the MPM. The method for planar array optimization addressed in this paper is easy to be implemented and has low computational cost. Several simulation cases demonstrate the effectiveness of the method.