Robust Superdirective Beamforming With Sidelobe Constraints for Circular Sensor Arrays via Oversteering

This article proposes a beamforming method via oversteering for circular sensor arrays, which can synthesize robust superdirective beampatterns with constrained sidelobes. Because the optimal beampattern can be expressed as the sum of finite eigenbeams with different directivities and robustness levels, adjusting the maximum order can achieve beampatterns with a desired robustness level. The sidelobes of these robust beampatterns in azimuth at low frequencies are found to decrease when the optimal weighting vector is oversteered in elevation; thus, robust superdirective beampatterns with constrained sidelobes and robustness can be synthesized by combining the order-adjusting and oversteering techniques; moreover, it is found that only the oversteering amount is required to synthesize desired superdirective beampatterns when robustness and sidelobe constraints are given beforehand. The relationship between the oversteering amount and the frequency can be approximately expressed using a simple neutral network, according to which desired broadband superdirective beampatterns can be readily achieved. Simulations and experimental results show that the performance of the proposed method is like that of the optimization-based method but using a simplified implementation approach rather than a complex numerical algorithm.