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Conjugate gradient adaptive matched filter

机译:共轭梯度自适应匹配滤波器

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摘要

We consider an adaptive reduced-rank detector, referred to as the CG-AMF detector, which is obtained by using the conjugate gradient (CG) algorithm to solve for the weight vector of the adaptive matched filter (AMF). The CG is a computationally efficient iterative algorithm, which finds the projection of the AMF weight vector to the Krylov subspace with a dimension growing with the CG iterations. This effectively leads to a family of reduced-rank detectors indexed by the number of CG iterations. The main purpose of this paper is to examine the output signal-to-interference-and-noise ratio (SINR) of the CG-AMF detector in the presence of strong clutter/interference. Specifically, by exploiting a connection between the CG algorithm and the Lanczos algorithm, we show the output SINR can be asymptotically expressed in a simple form involving a Ritz vector of the sample covariance matrix. The probability density function (pdf) and expected value of the output SINR are then obtained based on this approximation. Our theoretical analysis of the CG-AMF detector is verified by computer simulation. Numerical comparisons are also made with several popular reduced-rank detectors using either data-independent or data-dependent rank reduction approaches. Our results show that for a fixed training size, the CG-AMF detector often reaches its peak output SINR with a lower rank compared with the other reduced-rank detectors, which implies that the CG-AMF detector has lower computational complexity and less training requirement.
机译:我们考虑了一种自适应降秩检测器,称为CG-AMF检测器,它是通过使用共轭梯度(CG)算法求解自适应匹配滤波器(AMF)的权重向量而获得的。 CG是一种计算效率很高的迭代算法,该算法可找到AMF权重矢量到Krylov子空间的投影,并且其尺寸随CG迭代的增长而增大。这有效地导致了一系列由CG迭代次数索引的降秩检测器。本文的主要目的是检查在存在强杂波/干扰的情况下CG-AMF检测器的输出信噪比(SINR)。具体来说,通过利用CG算法和Lanczos算法之间的联系,我们显示了可以以简单形式渐近表示输出SINR,该简单形式涉及样本协方差矩阵的Ritz向量。然后根据该近似值获得概率密度函数(pdf)和输出SINR的期望值。通过计算机仿真验证了我们对CG-AMF检测器的理论分析。还使用几种独立于数据或依赖于数据的秩降低方法,与几种流行的降秩检测器进行了数值比较。我们的结果表明,对于固定的训练大小,CG-AMF检测器通常以比其他降低秩的检测器更低的等级达到其峰值输出SINR,这意味着CG-AMF检测器具有更低的计算复杂度和更少的训练需求。

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