Downlink precoding for multiuser MISO systems with imperfect channel knowledge

It is well-known that the downlink beamforming problem of minimizing the total transmit power under users' signal-to-interference- plus-noise ratio (SINR) constraints can be reformulated as a conic quadratic optimization problem and efficiently solved, if the transmitter is provided with the perfect information about the channel. In this work, we study the robust counterpart of the latter, convex problem. By robustness it is meant that the base station knows only uncertainty regions where the exact channels lie, and that it is supposed to satisfy the conic quadratic constraints for all channels that belong to these regions. We provide a direct optimal solution for this problem, based on the ellipsoid method from convex optimization theory. By exploiting the structure of the problem, we define also a virtual robust mean square error optimization problem, that can be solved by semidefinite programming methods in a much more efficient manner, and which presents (at least) a tight conservative approximation of the main problem.