Application of Second-Order Cone Programming Theory to Robust Adaptive Beamforming
Application of Second-Order Cone Programming Theory to Robust Adaptive Beamforming
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DOI：
10.1007/978-3-662-46469-4_43
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发表时间：
2015
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影响因子：
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通讯作者：
Rong Zhang;Haiyan Song
中科院分区：
文献类型：
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作者：
Rong Zhang;Haiyan Song
由于阵列导向矢量误差和小样本误差等原因，在实际工程应用中，标准Capon波束形成器（SCB）的性能可能会比传统Capon波束形成器（CBF）差。目前，几乎所有提高SCB鲁棒性的算法都采用了最陡下降法、共轭梯度法、最小均方法等。但大多数算法存在收敛速度慢、计算效率低的问题。针对上述问题，本文提出了一种采用二阶锥规划（SOCP）理论统一求解的方法，既提高了收敛速度，又提高了计算精度，从而有效地克服了以往优化方案的不足。结果表明，大多数自适应波束形成算法都涉及一个非凸问题，即在无限多个非凸二次约束下求二次函数的最小化问题。本文证明了该算法可以以凸形式重新表述为所谓的SCOP，并使用已建立的内点法有效地（在多项式时间内）求解。最后，通过计算机仿真算例，与现有的自适应波束形成算法相比，表明了该算法的优异性能。
Due to the array steering vector errors and small-sample errors and so on, the performance of the Standard Capon Beamformer (SCB) may become worse than that of the Conventional Beamformer (CBF) in practical engineering applications. Nowadays, almost all existing algorithms to improve the robustness of SCB utilize the steepest descent method, conjugate gradient method, least mean squares (LMS) method and so on. However, most of them have the slow convergence and inefficient computation. Aiming at the above problems, this paper presents a unified process to solve them by the second-order cone programming (SOCP) theory, which can not only enhance the convergence speed but also improve the calculation accuracy so as to overcome the shortcomings of the previous optimization solutions effectively. It turns out that most adaptive beamforming algorithms involve a non-convex problem which is minimization of a quadratic function subject to infinitely many non-convex quadratic constraints. In this paper, it is shown that the proposed algorithm can be reformulated in a convex form as the so-called SCOP and solved efficiently (in polynomial time) using the well-established interior point method. Finally, computer simulations show the algorithm’s excellent performance as compared with existing adaptive beamforming algorithms via the computer simulation examples.