Robust Optimal Downlink Beamforming Based On QCQP Strong Duality Under Quantized Channel Feedback

In recent years,with the development of wireless communication network,the number of network devices is increasing.For a base station,how to serve more devices while ensuring the quality of communication has become an urgent problem.Over the past decade,driven by advances in wireless communications,researchers have been interested in beamforming.In wireless communication,multi-antenna technology has become one of the key technologies to adapt to the explosive growth of the number of users and meet the demand of high data rate service.One advantage of multiple-antenna technology is that the base station can beamform the signals which it needs to transmit,also known as beamforming.Beamforming technology is a spatially selective way to receive,transmit or relay signal of interest in channels with interference and noise.The technology assigns a weight value to each antenna so as to directionally send the desired signals to the user,thus improving the quality of service.In this thesis,an optimization problem of robust beamforming with multiple input single output downlink is studied in a communication system with frequency division duplex mode between base station and users.In this system,the base station sends training signals to the users,through which each user estimates the channel coefficients,quantifies the gain and direction of the channel,and sends it back to the base station.It is assumed that the channel state information from the base station to the user is not completely known to the base station,which is mainly caused by quantization error of channel direction and channel estimation error and influence of outdated channel.In order to consider the influence of the above errors,the disturbance of the actual channel is modeled as an uncertain set composed of two homogeneous quadratic inequalities and a non-homogeneous quadratic equality constraint.Then,under the constraint of the robust signal-to-noise ratio for each user,the optimization problem of minimizing the transmitted power of the base station is obtained.For the optimization problem to design robust beamforming vector,this thesis uses the equivalent phase rotation method and the strong duality of quadratic constraint quadratic programming to transform the robust signal-to-noise ratio constraint for each user to a quadratic matrix inequality constraint.In this method,the robust minimization problem is transformed into a quadratic matrix inequality problem,and its relaxation is transformed into a convex linear matrix inequality optimization problem to solve it.Meanwhile,a rank-one strengthening constraint condition is proposed to improve the rank-one rate of the optimal solution from the relaxed linear matrix inequality optimization problem.Finally,the effectiveness of the proposed method and the rank-one strengthening constraint is verified by simulation results.