Robust beamforming with magnitude response constraints using iterative second-order cone programming

The problem of robust beamforming for antenna arrays with arbitrary geometry and magnitude response constraints is one of considerable importance. Due to the presence of the non-convex magnitude response constraints, conventional convex optimization techniques cannot be applied directly. A new approach based on iteratively linearizing the non-convex constraints is then proposed to reformulate the non-convex problem to a series of convex subproblems, each of which can be optimally solved using second-order cone programming (SOCP). Moreover, in order to obtain a more robust beamformer against array imperfections, the proposed method is further extended by optimizing its worst-case performance using again SOCP. Different from some conventional methods which are restricted to linear arrays, the proposed method is applicable to arbitrary array geometries since the weight vector, rather than its autocorrelation sequence, is used as the variable. Simulation results show that the performance of the proposed method is comparable to the optimal solution previously proposed for uniform linear arrays, and it also gives satisfactory results under different array specifications and geometries tested. © 2006 IEEE.published_or_final_versio

A new method for robust beamforming using iterative second-order cone programming

This paper addresses the problem of beamforming for antenna arrays in the presence of mismatches between the true and nominal steering vectors. A new method for robust beamforming is proposed by minimizing the array output power while controlling the array mainlobe response. Due to the presence of the non-convex response constraints, a new approach based on iteratively linearizing the non-convex constraints is proposed to reformulate the non-convex problem to a series of second-order cone programming (SOCP) subproblems, each of which can be optimally solved by well-established convex optimization techniques. Simulation results show that the proposed method offers better performance than conventional methods tested. © 2012 IEEE.published_or_final_versionThe 2012 IEEE International Symposium on Circuits and Systems (ISCAS), Seoul, Korea, 20-23 May 2012. In IEEE International Symposium on Circuits and Systems Proceedings, 2012, p. 2569-257

Steering vector estimation and beamforming under uncertainties

In this paper, we propose a new method for estimating the steering vector under uncertainties, which is utilized for improving the robustness of beamforming. We show that the desired steering vector can be estimated in closed form from a convex optimization problem by making use of the subspace principle. As this method is developed based on an extended version of the orthonormal PAST (OPAST), the steering vector can be recursively estimated with very low complexity and moving sources can be handled. To further improve the performance of beamforming, the uncertainty of the array covariance matrix is taken into account. Numerical results demonstrate that the proposed method performs well in the presence of uncertainties. © 2012 IEEE.published_or_final_versio