Maximin robust design for MIMO communication systems against imperfect CSIT

This paper considers robust transmit strategies, against the imperfectness of CSIT, for MIMO communication systems. Following a deterministic model that assumes the actual channel inside an ellipsoid centered at a nominal channel, we maximize the worst-case received SNR. It is shown that, for a general class of power constraints, the resulting maximin problem can be equivalently transformed into a convex problem, or even further into a semidefinite program. The most important result is that the optimal transmit directions are just the right singular vectors of the nominal channel under some mild conditions. This result reduces the complicated matrix-valued problems to scalar power allocation problems, for which the closed-form solutions are provided.