# A singular value decomposition updating algorithm for subspace tracking

*12-Nov-2019 23:54*

An alternative MIMO transmission techniques commonly referred to as V-BLAST uses a cancellation and nulling scheme requiring multiple instances of Moore-Penrose pseudo-inverses of a modified channel matrix H This approach is described e.g.

Instead, the method uses the received vector r and the signal vector s or its estimate to update initial estimates of a) the left and right *singular* vectors, and b) the corresponding *singular* *values*, and to output the updated estimates thereof; the initial estimates are provided to the method as an input or are otherwise known.

It is our hope that developers of new **algorithms** and perturbation theories will benefit from the theory, methods, and examples in this paper.

Citation Context ..compute all eigenvectors and eigenvalues, resulting in superfluous computations.

A summary of the **subspace** **tracking** techniques is given in H.

Viberg, in an article entitled “Two decades of array signal processing research,” IEEE Signal Processing Mag., vol.

In accordance with the invention, a method is provided for **updating** **singular** **values** and **singular** vectors in a **singular** **value** **decomposition** (SVD) of a matrix transfer function relating an output vector to an input vector, the method comprising the steps of: a) obtaining initial estimates of the **singular** **values** and **singular** vectors; b) providing the output vector and the input vector; c) projecting the output vector and the input vector onto the initial estimates of the **singular** vectors to obtain orthogonal projections of the output and input vectors; and, d) determining updated estimates of the **singular** **values** and **singular** vectors from the orthogonal projections of the input and output vectors and the initial estimates of the **singular** **values** and the **singular** vectors.Diagnosing anomalies is critical for both network operators and end users.It is a difficult problem because one must extract and interpret anomalous patterns from large amounts of ..." Anomalies are unusual and significant changes in a network's traffic levels, which can often span multiple links.These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..." In this paper we develop new Newton and conjugate gradient **algorithms** on the Grassmann and Stiefel manifolds.

These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing.

with frequency, the SVD needs to be periodically updated to maintain channel orthogonality and avoid inter-channel interference.