  This paper studies a downlink multiuser transmit beamforming design under
spherical channel uncertainties, using a worst-case robust formulation. This
robust design problem is nonconvex. Recently, a convex approximation
formulation based on semidefinite relaxation (SDR) has been proposed to handle
the problem. Curiously, simulation results have consistently indicated that SDR
can attain the global optimum of the robust design problem. This paper intends
to provide some theoretical insights into this important empirical finding. Our
main result is a dual representation of the SDR formulation, which reveals an
interesting linkage to a different robust design problem, and the possibility
of SDR optimality.
