Minor subspace tracking using MNS technique

Abstract

This paper introduces new minor (noise) subspace tracking (MST) algorithms based on the minimum noise subspace (MNS) technique. The latter has been introduced as a computationally efficient subspace method for blind system identification. We exploit here the principle of the MNS, to derive the most efficient algorithms for MST. The proposed method joins the advantages of low complexity and fast convergence rate. Moreover, this method is highly parallelizable and hence its computational cost can be easily reduced to a very low level when parallel architectures are available. Different implementations are proposed for different contexts and they are compared via numerical simulations.

Generalized Minimum Noise Subspace For Array Processing

“…, and thus (18). The above biased and unbiased algorithms are referred to as GMNS-N-PSA (N stands for non-overlapping) and GMNS-NU-PSA (NU stands for non-overlapping and unbiased), respectively.…”

“…MNS is much more efficient because it avoids large-scale EVD/SVD computation in the standard subspace method. MNS has been applied to blind system identification [15], source localization [16], array calibration [16], multichannel blind image deconvolution [17], and adaptive subspace tracking [18]. However, the number of parallel computing units based on which MNS is implemented is the same as the dimension of the noise subspace and is, generally not equal to the actually available number of computing units (K) of the parallel computing architecture in use.…”

“…As will be shown, our GMNSbased adaptive algorithms have advantages in terms of computational complexity and convergence rate. It should be noted that some adaptive algorithms for MNS have already been proposed in [20] but they are limited to least minor subspace analysis. 4) We further propose efficient GMNS-based adaptive algorithms for principal eigenvector tracking (PET) from the corresponding GMNS-based PST algorithms.…”