Application of the least squares approach to fixed beamformer design with frequency-invariant constraints

An application of the least squares (LS) approach to the design of frequency-invariant beamformers is proposed, based on three different formulations of the problem. The first one is the traditional linearly constrained LS formulation with its solution given by the Lagrange multipliers method. The second and the third ones, which are formulated as an unconstrained LS problem and a constrained total LS problem, respectively, can be considered as extensions of the traditional total LS method and their solutions are obtained by finding the minimum generalised eigenvector of two matrices. Compared with the conventional LS-based methods, a frequency-invariance controlling element is incorporated into the proposed cost functions. Design examples including both broadside and off-broadside main beams are provided with a satisfactory frequency invariant property and sidelobe attenuation. The proposed approach is general and can be applied to different array structures.