A direct robust supergain method in mode space for the circular array mounted on an infinite rigid cylinder was proposed,and then it was also applied to the circular array mounted on a finite rigid cylinder which is more practical.According to the concept of phase modes,the beam pattern is expanded into a series of eigen-beams multiplying by modal coefficients. The modal noise cross spectral matrix is calculated from sound scattering theory.In the original modal robust supergain method,the coefficient vector in mode space is transformed indirectly from the weighting vector in sensor space.The method presented here gives the most suitable modal coefficient vector directly under the related constraint conditions based on the second-order cone programming.The results of simulation show that the direct modal robust supergain method can not only improve robustness using the white noise gain constraint, but also change the mode orders to provide compromise between array gain and robustness in low frequencies.Beam performance measures such as sidelobe level can be optimized as well as array gain,so this method can give more effective schemes for designing practical robust supergain beamformers.
