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In this paper we present how we choose the proper number of virtual array elements from the real array for direction of arrival (DOA) estimation using a conformal hemispherical real array and a single snapshot of the data. The number of virtual array is achieved by using singular value decomposition (SVD) of a real array manifold and the concept of the interpolation techniques. Then, the transformation matrix is generated from both the virtual array manifold and the real array manifold. A numerical simulation has been made to illustrate of the proposed approach. We estimate direction of arrival (DOA) of signals using the matrix pencil method.