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A spherical harmonics domain microphone array beamforming approach is proposed. It unifies 3D multi-beam forming with tractable mainlobe levels, automatic multi-null steering, sidelobe control, and robustness control into one optimization framework, using a single spherical microphone array. The optimum array weights are designed by maintaining distortionless responses in multiple mainlobe directions and guaranteeing all sidelobes below given threshold values, while minimizing the beamformer output power. A weight vector norm constraint is also employed to improve the robustness of the beamformer. A convex optimization formulation is derived, and implemented by the second order cone programming (SOCP) method. Design examples demonstrate a satisfactory performance.