Robust Adaptive Beamforming Design Based On Worst-case Optimization

In recent years,with the development trend of wireless communication,the importance of adaptive beamforming technology has become more and more obvious,and the application scenarios are also more extensive.The beamforming method aims to design the beamformer weights according to a certain criterion to achieve the goal of optimizing the output performance.Nowadays,the complex and diverse signal transmission scenarios mean that there are unavoidable error factors in practical applications.Due to the high dependence of traditional beamforming algorithms on precise prior information,the actual steering vector mismatches will cause the performance of the beamformer to decline seriously.Therefore,the robust beamforming method under steering vector mismatch becomes the focus of the researches.This paper proposes two uncertain sets of steering vectors based on the worst-case performance.Under such imprecise prior information,the robust adaptive beamforming method is discussed.In this paper,we maximize the output signal-to-noise-plus-interference ratio of the beamformer as the optimization goal.The first uncertainty set consists of a similarity constraint and a nonconvex double-sided ball constraint.For this nonconvex set of actual steering vectors,we use the form of an optimization problem to describe the constraint model in the worst-case performance.Equivalently,we use the duality and relaxation of the optimization problem to transform the constraints of the optimization problem and extract the hidden convexity of the constraint so that it can be brought back to the problem model of the beamformer weights then the quadratic matrix inequality(QMI)problem is formulated.In order to be able to effectively solve this kind of problem,the QMI problem is rewritten as a linear matrix inequality(LMI)problem by using semidefifinite program relaxation.In order to make the relaxation reach ‘tight' state by obtaining a rank-one solution.we impose an additional effective linear constraint to the LMI problem to strengthen the elimination of high-rank optimal solutions and improve the possibility of obtaining rank-one solution.This paper analyzes the mathematical expression of rank-one,and further processes the LMI problem model.An iterative algorithm is proposed to obtain the optimal or approximate solution of the beamformer weights.The simulation examples show a higher signal-to-interference-to-noise ratio performance than some existing robust beamformers.The second uncertainty set proposed in this paper is based on the prior information of the direction of arrival sector.The correlation between the actual steering vector and the newly constructed feature space integral matrix is used to restrict the steering vector.The received signal is still within the angle range of the a priori information,and we still use the signal-to-noise-plus-interference ratio under the worst-case performance as the goal to construct the optimization problem.We obtain the beamformer weights under such models by following the method proposed in first case.To validate our results,simulation examples are presented and demonstrate the improved performance of the proposed robust beamformers in terms of the array output SINR,compared with other traditional algorithms.