This paper focuses on multiuser MIMO channel estimation and data transmission at millimeter wave (mmWave) frequencies. The proposed approach relies on the time-divisionduplex (TDD) protocol and is based on two distinct phases. First of all, the Base Station (BS) sends a suitable probing signal so that all the Mobile Stations (MSs), using a subspace tracking algorithm, can estimate the dominant ...

We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the svd of B using an existing subroutine library such as lapack provides the singular values of A. The singular vectors of A are obtained trivially from ...

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...

As illustrated via numerical experiments with an implementation in Spark (the popular platform for distributed computation), randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a full principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a low-rank approximation (in t...

In several dimension reduction techniques, the original variables are replaced by a smaller number of linear combinations. The coefficients of these linear combinations are typically the elements of the left singular vectors of a random matrix. We derive the asymptotic distribution of the left singular vectors of a random matrix that has a normal limit distribution. This result is then used to ...

New perturbation theorems for bases of singular subspaces are proved. These theorems complement the known sinΘ theorems for singular subspace perturbations, taking into account a kind of sensitivity of singular vectors discarded by previous theorems. Furthermore these results guarantee that high relative accuracy algorithms for the SVD are able to compute reliably simultaneous bases of left and...

Consider the SVD X = UDV >, where U is n× n, V is p× p and D is an n× p “diagonal” matrix with entries d1 < . . . < dn. Define two groups of left and right singular vectors associated with the q smallest and n − q largest singular values. Let the groups be defined by Uq, Un−q and Vq, Vn−q . Suppose HJ chooses as its row-basis the n−q largest right singular vectors, Vn−q . Then, from Table 1 of ...

Singular value decomposition is a widely used tool for dimension reduction in multivariate analysis. However, when used for statistical estimation in high-dimensional low rank matrix models, singular vectors of the noise-corrupted matrix are inconsistent for their counterparts of the true mean matrix. In this talk, we suppose the true singular vectors have sparse representations in a certain ba...

We explore a connection between the singular value decomposition (SVD) and functional principal component analysis (FPCA) models in high-dimensional brain imaging applications. We formally link right singular vectors to principal scores of FPCA. This, combined with the fact that left singular vectors estimate principal components, allows us to deploy the numerical efficiency of SVD to fully est...

where U ∈ R is left orthogonal, V ∈ R is orthogonal, and B ∈ R is bidiagonal. When the Lanczos recurrence is implemented in finite precision arithmetic, the columns of U and V tend to lose orthogonality, making a reorthogonalization strategy necessary to preserve convergence of the singular values. A new strategy is proposed for recovering the left singular vectors. When using that strategy, it...