An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non-unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal-based reduced-order model of the system. Copyright (C) 2012 John Wiley & Sons, Ltd.

Subspace Pursuit Embedded in Orthogonal Matching Pursuit

Orthogonal Matching Pursuit (OMP) is a popular greedy pursuit algorithm widely used for sparse signal recovery from an undersampled measurement system. However, one of the main shortcomings of OMP is its irreversible selection procedure of columns of measurement matrix. i.e., OMP does not allow removal of the columns wrongly estimated in any of the previous iterations. In this paper, we propose a modification in OMP, using the well known Subspace Pursuit (SP), to refine the subspace estimated by OMP at any iteration and hence boost the sparse signal recovery performance of OMP. Using simulations we show that the proposed scheme improves the performance of OMP in clean and noisy measurement cases.

Antenna selection for time-varying channels based on slepian subspace projections

Single receive antenna selection (AS) allows single-input single-output (SISO) systems to retain the diversity benefits of multiple antennas with minimum hardware costs. We propose a single receive AS method for time-varying channels, in which practical limitations imposed by next-generation wireless standards such as training, packetization and antenna switching time are taken into account. The proposed method utilizes low-complexity subspace projection techniques spanned by discrete prolate spheroidal (DPS) sequences. It only uses Doppler bandwidth knowledge, and does not need detailed correlation knowledge. Results show that the proposed AS method outperforms ideal conventional SISO systems with perfect CSI but no AS at the receiver and AS using the conventional Fourier estimation/prediction method. A closed-form expression for the symbol error probability (SEP) of phase-shift keying (MPSK) with symbol-by-symbol receive AS is derived.