Least squares approach to the design of frequency invariant beamformer with sensor delay lines in subbands

A least squares approach to the design of frequency invariant beamformers with sensor delay lines (SDL) in subbands is proposed, based on two different types of formulations. One is the constrained least squares (CLS) formulation, which is a much simple and efficient method, but requires potentially unstable matrix reversion. And the other is the constrained total least squares (CTLS) formulation, which is much stable without matrix inversion. CTLS methods´ solutions can be obtained by finding the minimum generalized eigenvector of two matrices. A series of constraint designs with different requirements are presented. To measure the frequency invariant property more critically, the concept of normalized beam pattern variance is raised. Simulation results demonstrate that subband methods exhibit satisfactory frequency invariant property, mainlobe resolution, sidelobe attenuation and interference suppression. Moreover, compared to original fullband method, the subband method can improve beam pattern performance and release the cost of sensors with similar property, efficiently.