Performance Analysis of Superdirectivity of Circular Arrays and Implications for Sonar Systems

Superdirective beamforming (SDB) has received a lot of interest recently since by this technique a small circular array, i.e., small <inline-formula><tex-math notation="LaTeX">$ka$</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">$a$</tex-math></inline-formula> is the radius and <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> is the wave number, can achieve small beamwidth, and high directivity factor (DF) as offered by a large circular array using conventional beamforming (CBF). However, the nice features derived theoretically are difficult to achieve in practice since SDB is highly sensitive to signal mismatch, such as errors in array configuration, incorrect signal model, etc. Many methods have been proposed to balance the performance (beamwidth and DF) against the sensitivity. The tradeoff analyses are application and data dependent and computationally intensive. We show in this paper, by deconvolving the CBF beam output using the known beam pattern, that the deconvolved beam output can achieve a narrower beamwidth, higher DF, and lower sidelode level than the SDB, and offers the same robustness as CBF. The performance of the various beamforming methods are quantitatively analyzed and systematically compared in this paper for a wide range of <inline-formula><tex-math notation="LaTeX">$ka$</tex-math></inline-formula> and input signal level. Deconvolution takes negligible processing time and can be applied to existing systems where the beam data are often the only data available.