Generalized RQ Minimization With Applications in Array Transmit Beamforming
This letter deals with generalized Rayleigh quotient (RQ) minimization with possibly singular matrices in the quadratic forms. An extended theorem providing closed-form analytical solutions for different cases is derived. It is shown that the theorem is an extension of the typical RQ minimization. Next, its applications in array transmit beamforming under the criterion of minimum integrated sidelobe level are illustrated. Finally, theoretical analyses and numerical comparisons are provided to validate both the theorem and the beamformers.