Order calibrated functional beamforming for constant mainlobe width

This paper introduces a beamformer with constant mainlobe width over a given frequency range based on the well-known Functional Beamforming. In fact, one of the main issues with Conventional and Functional Beamforming is the worsening of spatial resolution towards lower frequencies. The idea presented here is to exploit the order (exponent in its typical formulation) of Functional Beamforming as a leverage to maintain the same mainlobe width for different analysis frequencies. A strategy for accurately measure the mainlobe size is described and exploited for characterizing any array used in the beamforming analysis. An order calibration procedure, which boils down to the estimation of two fitting coefficients describing the proper beamformer order, is proposed. The procedure resulted useful to achieve a constant mainlobe size across a given frequency range. The validity of the whole approach is demonstrated on both synthesized and experimental data.