基于并行次梯度投影和Krylov子空间技术的鲁棒降秩自适应处理
Robust Reduced-Rank Adaptive Processing Based on Parallel Subgradient Projection and Krylov Subspace Techniques
摘要：
在本文中，我们提出了一种新的降秩自适应滤波算法的Krylov子空间方法的思想与集合论自适应滤波框架相结合。与现有的基于Krylov子空间的降秩方法不同，所提出的算法在最小化Krylov子空间中的\sinq{true}均方误差（MSE）的意义上跟踪最优点，即使当估计的统计量变得错误时（例如，由于环境的突然变化）。因此，与现有的方法相比，该算法更适合自适应滤波应用。该算法分析的基础上的自适应投影次梯度法（APSM）的修改版本。数值算例表明，对于码分多址（CDMA）系统中的干扰抑制问题以及简单的系统辨识问题，该算法具有比现有方法更好的跟踪性能。
英文摘要：
In this paper, we propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework. Unlike the existing Krylov-subspace-based reduced-rank methods, the proposed algorithm tracks the optimal point in the sense of minimizing the \sinq{true} mean square error (MSE) in the Krylov subspace, even when the estimated statistics become erroneous (e.g., due to sudden changes of environments). Therefore, compared with those existing methods, the proposed algorithm is more suited to adaptive filtering applications. The algorithm is analyzed based on a modified version of the adaptive projected subgradient method (APSM). Numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for the interference suppression problem in code-division multiple-access (CDMA) systems as well as for simple system identification problems.
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