Numerically stable method of signal subspace estimation based on multistage Wiener filter

Abstract

In this paper, a numerically stable method of signal subspace estimation based on Householder multistage Wiener filter (HMSWF) is proposed. Numerical stability of the method lies on the fact that the Householder matrix in HMSWF ensures the unitary blocking operation and significantly strengthens the orthogonality of basis vectors, especially in the finite-precision implementation. In the following, we analyze the numerical stability of HMSWF and MSWF based on the correlation subtractive structure (CSS-MSWF) by establishing the equivalence between the forward recursion of MSWF and the Arnoldi algorithm in numerical linear algebra. Besides, the equivalence between HMSWF and the Householder QR decomposition (QRD) on the Krylov matrix underlying in MSWF is directly established. Based on the relationship, two theoretical upper bounds of the orthogonality error of basis vectors in signal subspace are obtained and it is demonstrated that the orthogonality of basis vectors based on HMSWF is perfectly preserved by the numerically well-behaved Householder matrix, and the corresponding signal subspace estimation is much more numerically stable than that based on CSS-MSWF. Simulations show the numerical stability of the proposed method of signal subspace estimation by HMSWF. CitationZhuang X B, Cui X W, Lu M Q, et al. Numerically stable method of signal subspace estimation based on multistage Wiener filter.

Reduced-rank space-time adaptive detection for airborne radar

“…For airborne radar, there is an inherent need for minimal sample support methodologies, mainly because of clutter nonstationarity and computation complexity [1][2][3][4][5]. The reduced-rank technique is a simple but effective approach to cope with the low sample support problem [4,[6][7][8][9][10][11][12][13][14][15][16]. There are three key procedures: i) find a subspace within which the received signal can be processed, ii) project the received signal onto the above subspace, and iii) calculate the weight vector (for filters) or the test statistic (for detectors).…”

“…Statistically optimum reduced-rank filters can improve performance compared to the above beamforming-type reduced-rank approaches [14]. The principalcomponents (PC) technique [17], minimum power eigencanceler (MPE) [8], minimum norm eigencanceler (MNE) approach [8], cross-spectral metric (CSM) approach [9], multistage Wiener filter (MWF) [10][11][12], auxiliary-vector filter (AVF) [13,15], indirect dominant mode rejection (IDMR) approach [16], and joint iterative optimization filters [14] are all of this type.…”

Adaptive detectors in the Krylov subspace

“…The rank reduction is an important technique in signal processing, and it is widely adopted in radar, sonar, communication, global positioning system (GPS) and so on. As a kind of reduced rank method, the Krylov subspace technique [1][2][3][4][5] requires neither eigenvalue decomposition (EVD) nor matrix inversion operation, and has superior performance to the EVD-based methods, such as the principal component (PC) [6] and the cross spectral metric (CSM) [7].…”