Robust Downlink Transmit Optimization Under Quantized Channel Feedback via the Strong Duality for QCQP

Consider a robust multiple-input single-output downlink beamforming optimization problem in frequency division duplexing system. The base station (BS) sends training signals to the users, and every user estimates channel coefficients, quantizes gain direction of estimated them back BS. Suppose that state information at transmitter is imperfectly known mainly due quantization errors, estimation errors outdated effects. actual modeled as an uncertainty set composed two inequality homogeneous one equality inhomogeneous quadratic constraints, order account for aforementioned Then transmit power minimization formulated subject signal-to-noise-plus-interference ratio constraints. Each constraint transformed equivalently into matrix (QMI) with respect vectors. transformation accomplished by equivalent phase rotation process strong duality result quadratically constrained program. accordingly turned QMI problem, solved restricted linear relaxation additional valid convex Simulation results are presented demonstrate performance proposed method, show efficiency relaxation.