Robust Multi-Antenna Broadcasting with Imperfect Channel State Information

The problem of robust multi-antenna broadcasting is considered in the case of erroneous channel state information (CSI) at the transmitter. The criterion of minimum transmission power is used subject to the constraints guaranteeing that the signal-to-noise ratio (SNR) of each intended receiver satisfies a prescribed quality of service (QoS) requirement for the worst-case norm-bounded CSI mismatch. The resulting robust broadcasting problem is non-convex and, therefore, is difficult to solve. However, a suitable semi-definite relaxation (SDR) of this problem is proposed that enables to transform it to a convex form and to compute the optimal transmitter weight vector.