采用Lanczos算法快速估計(jì)噪聲子空間
Fast Noise Subspace Estimation via the Lanczos Algorithm
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摘要: 提出一種采用Lanczos算法估計(jì)噪聲子空間的新方法。該方法采用傳統(tǒng)的空間平滑技術(shù)解相干，然后由多級維納濾波器的預(yù)濾波器的性質(zhì)可知，多級維納濾波器的冗余分解級的預(yù)濾波器可以構(gòu)成一個噪聲子空間。由此可以采用Lanczos算法快速估計(jì)到噪聲子空間。由于不需要對協(xié)方差矩陣作特征值分解，而且所要求的冗余分解的級數(shù)較少，其運(yùn)算量比基于特征值分解方法要小得多。此外，采用Lanczos算法計(jì)算降維矩陣和冗余矩陣只構(gòu)成多級維納濾波器的前向遞推，從而使得算法的復(fù)雜度大大降低。最后，計(jì)算機(jī)仿真驗(yàn)證了該方法的有效性。
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關(guān)鍵詞:
- Lanczos算法;降維;多級維納濾波器;空間譜
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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