Robust supergain beamforming for circular array via second-order cone optimization

The phenomenon of supergain for a circular array and its robust version are presented. The superdirective array gain for the circular array, although it is not so extreme as an endfire line array, outperforms a lot over that of a conventional beamformer in isotropic noise fields when the interelement spacings are less than one-half wavelength. However, optimum beamforming algorithms can be extremely sensitive to slight errors in array characteristics. The performance are known to degrade if some of underlying assumptions on the sensor array violated. Therefore white noise gain constraint (WNC) is used to increase the robustness of supergain beamforming against random errors. We show that the robust supergain beamforming can be reformulated in a form of second-order cone programming and resolved easily. Some computer simulations are also given to illustrate the presented approach.