Synthesis of maximally sparse conformal circular arc array with a required beam pattern by unitary matrix pencil method

This paper extends the unitary matrix pencil (UMP) method to synthesize maximally sparse conformal circular-arc array with a required beam pattern. Due to the nonlinearity between the circular-arc array pattern and its element pattern, Fourier transform preprocessing for the required beam pattern is introduced to achieve a mathematical expression, i.e., sum of a series of undamped complex exponentials , which is related to array element positions and their excitations. Then, the UMP method is used to determine the reduced number of elements and their position distributions. Moreover, the complex excitations of array elements are reconstructed by obtaining the least-square solution of an over-determined equation. A set of examples for synthesizing sparse conformal circular-arc arrays with different desired patterns and E-type patch element including the mutual coupling are conducted. Results show that the proposed UMP method can achieve a considerably lower pattern reconstruction error with a reduced number of elements than results in the literature, which demonstrates its effectiveness and robustness.