Simple direction finding of noncircular signals using the centro-Hermitian property

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In the direction estimation of noncircular signals, the sensor array can be virtually extended by adding its complex conjugated version. Exploiting the centro-Hermitian of the extended signal vector without specific requirements of array geometry, we present a computationally efficient method for direction estimation based on the multiple signal classification (MUSIC) principle. When the MUSIC-like estimation is formulated in the virtually extended array, the resulting objective function includes the variable of the phase of a noncircular signal as well as the variable of its direction. The minimum of the two-variable function with respect to the phase is shown to be the same as double the smallest eigenvalue of a 2 x 2 matrix involved in it. Accordingly the estimation for directions of arrival is carried out by calculating the minimum eigenvalue, rather than the determinant of the matrix that conventional methods have usually employed. The eigenvalue-based method (EBM) can be efficiently implemented through real number computation utilizing the centro-Hermitian property. Simulation results demonstrate the superiority of EBM over the determinant-based conventional one.