In this article, a new noniterative beam shaping method is introduced to synthesise array factor (AF) of an unequally spaced linear array (UESLA). The proposed method is based on eigenvector decomposition of sampled data matrix of a given pattern. Using matrix analysis, the eigenvalues and their corresponding eigenvectors of the sampled matrix are determined. It is shown that the eigenvalues and eigenvectors of the sampled matrix are related to the locations and complex excitation coefficients of the array elements. According to the concept of generalized eigenvalue concept, the solution of locations and excitation coefficients is derived using least square method. In order to reduce the number of array elements, singular value decomposition is applied to obtain a low ranked matrix using rejection of nonzero eigenvalues. Using the approximated sampled matrix, the excitation and locations of the optimized array elements are calculated. A few comprehensive examples are investigated to verify the accuracy of the proposed method and the obtained results are compared with those of an equally spaced linear array (ESLA). It is shown that the total number of array elements in an UESLA is less than that of ESLA, which is the most advantage of the introduced method in AF synthesis.

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