采用Lanczos算法快速估计噪声子空间
Fast Noise Subspace Estimation via the Lanczos Algorithm
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摘要: 提出一种采用Lanczos算法估计噪声子空间的新方法。该方法采用传统的空间平滑技术解相干，然后由多级维纳滤波器的预滤波器的性质可知，多级维纳滤波器的冗余分解级的预滤波器可以构成一个噪声子空间。由此可以采用Lanczos算法快速估计到噪声子空间。由于不需要对协方差矩阵作特征值分解，而且所要求的冗余分解的级数较少，其运算量比基于特征值分解方法要小得多。此外，采用Lanczos算法计算降维矩阵和冗余矩阵只构成多级维纳滤波器的前向递推，从而使得算法的复杂度大大降低。最后，计算机仿真验证了该方法的有效性。Abstract: A novel method is proposed for estimating the noise subspace in the case where the signals are coherent. The characters of MultiStage Wiener Filter (MSWF) show that the pre-filters of redundant stages of the MSWF can create an orthonormal basis for the noise subspace, then with the classical spatial smoothing technique and the Lanczos algorithm, the noise subspace can be quickly obtained even under the condition that coherent signals exist. The new method outperforms the eigendecomposition based method in terms of computational complexity. Finally, simulation results are presented to illustrate the performance of the proposed method for the noise subspace via the classical MUSIC estimator.
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