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A space domain optimal beamforming approach for spherical microphone arrays is presented, which is based on original microphone signals rather than spherical harmonics. A simple correlated multipath signal model is employed. The beamforming optimization criteria, including adaptive beamforming, multi-beam steering, sidelobe control, correlated interference cancellation and robustness control, are proposed and reformulated in a convex form of second order cone programming, which is computationally tractable. Using the spherical harmonics framework, we also prove that, given a perfect spatial sampling scheme, the conventional plan-wave decomposition (PWD) beamformer can be interpreted as a space domain minimum variance distortionless response (MVDR) beamformer under the condition of a spherically isotropic sound field.