Broad-band array design using the asymptotic theory of unequally spaced arrays

The problem of designing broadband linear arrays of omnidirectional sensors is addressed. Attention is restricted to the case of shaded delay-and-sum beamforming. Broadbanding is here defined to mean that the beam-pattern function has little or no frequency dependence of peak response, main-lobe width, plateau sidelobe level, and sinespace separation between the main lobe and the plateau sidelobe. The asymptotic theory of unequally spaced arrays is used to derive relationships between beam-pattern properties and array properties. These relationships are used to translate beam-pattern requirements into functional requirements on sensor spacings and amplitude shadings. The functional requirements are then used to derive a broadband array design. In addition to the design equations, the asymptotic theory is used to derive equations for main-lobe level, sidelobe level, beamwidth, and signal-to-noise ratio (SNR) gain in isotropic noise. A specific example is presented to clarify the concepts and verify that the design procedure actually works