Chance Constrained Robust Downlink Beamforming in Multicell Networks

We introduce a downlink robust optimization approach that minimizes a combination of total transmit power by a multiple antenna base station (BS) within a cell and the resulting aggregate inter-cell interference (ICI) power on the users of the other cells. This optimization is constrained to assure that a set of signal-to-interference-plus-noise ratio (SINR) targets are met at user terminals with certain outage probabilities. The outages are due to the uncertainties that naturally emerge in the estimation of channel covariance matrices between a BS and its intra-cell local users as well as the other users of the other cells. We model these uncertainties using random matrices, analyze their statistical behavior, and formulate a tractable probabilistic approach to the design of optimal robust downlink beamforming vectors. The proposed approach reformulates the original intractable non-convex problem in a semidefinite programming (SDP) form with linear matrix inequality (LMI) constraints. The resulting SDP formulation is convex and numerically tractable under the standard rank relaxation. We compare the proposed chance-constrained approach against two different robust design schemes as well as the worst-case robustness. The simulation results confirm better power efficiency and higher resilience against channel uncertainties of the proposed approach in realistic scenarios.