Second-order cone programming for robust downlink beamforming with imperfect CSI

In this paper, we study the problem of downlink multicell processing (MCP) when a channel state information is used to design transmit beamforming. This kind of design entails the complexity that requires extra signalling overhead. However, the channel state information (CSI) may be subjected to estimation and quantization errors. To acquire reduction in signalling overhead, we propose a robust multicell downlink beamforming that minimizes a combination of the sum-power, used by each base station (BS) to transmit data to its local users, and the worst-case of the resulting overall interference induced on the other users of the adjacent cells in the presence of imperfect channel state information, whilst also guaranteeing that the worst-cases of the signal-to-interference-plus-noise ratio (SINR) remains above the required level. We consider a spherical uncertainty set to model the imperfection in CSI between the true and the estimated channel coefficients. The original non-convex problem is formulated as the second-order cone programming (SOCP) and then recast the convex constraints in linear matrix inequality (LMI) form. Also, we reformulate a coordinated beamforming with imperfect instantaneous CSI based on spherical uncertainty set using the standard semidefinite relaxation (SDR). Simulation results confirm the efficiency of the proposed method at BSs, compared with the conventional method in the presence of imperfect CSI to validate the theoretical analysis.