Min-max robust transmit beamforming for power efficient quality of service guarantee

We consider the problem of power-efficient transmit beamforming design at multi-antenna base stations (BSs) of a multicell network, when the channel state information (CSI) at both transceiver ends are imperfect. We introduce an optimization problem that accounts for robustness at, both, the constraints and the objective function. The robust constraints guarantee the quality of service (QoS) at mobile users (MUs) by ensuring that a set of signal-to-interference-plus-noise ratio (SINR) targets are met, despite the presence of erroneous CSI at both the BS and the MU sides. The robust objective function minimizes a linear combination of total transmit power at each BS and the overall inflicted interference power on the other users of the other cells under the worst-case of channel uncertainties. As the proposed problem is NP-hard, in general, we reformulate the problem into a semidefinite programming (SDP) with linear matrix inequality (LMI) constraints using the standard rank relaxation and the S-procedure. The simulation results confirm the effectiveness of the proposed robust beamforming design in terms of power efficiency at BSs and QoS guarantee at MUs, when compared with the conventional method in the presence of imperfect CSI.