Structure-Aware Sparse Bayesian Learning-Based Channel Estimation for Intelligent Reflecting Surface-Aided MIMO

This paper presents novel cascaded channel estimation techniques for an intelligent reflecting surface-aided multiple-input multiple-output system. Motivated by the channel angular sparsity at higher frequency bands, the channel estimation problem is formulated as a sparse vector recovery problem with an inherent Kronecker structure. We solve...

Structured matrices for predictive control of large and multi-dimensional systems

The extremely large telescopes that should see first light in coming years demand so-called adaptive optics systems to overcome the devastating effect of the atmospheric turbulence on the image quality. A sensor measures the incoming distortion of the light and is used for reshaping the latter using a deformable mirror. Processing the large...

Recursive Kronecker-based Vector AutoRegressive identification for large-scale adaptive optics

This brief presents an algorithm for the recursive identification of Vector AutoRegressive (VAR) models of large dimensions. We consider a VAR model where the coefficient matrices can be written as a sum of Kronecker products. The algorithm proposed consists of recursively updating the Kronecker factor matrices at each new time step using...

Exploiting Kronecker Structures: With applications to optimization problems arising in the field of adaptive optics

We study the important mathematical problem of approximating the inverse of low Kronecker-rank matrices in this same form. A traditional alternating least squares (ALS) scheme for solving such problems is presented, and we discuss two efficient solutions to the subproblems arising in the corresponding iterations. The first relies on a least...

Recursive Kronecker-based Vector Auto-Regressive identification for large-scale Adaptive Optics systems

Adaptive Optics (AO) play an essential role in the field of astronomical seeing for ground-based telescopes, providing a corrected image from the disturbance caused by the light having to travel through the turbulent atmosphere of our Earth. To provide us with more detailed images, the sizes of these telescopes are getting increasingly larger....

Kronecker-ARX models in identifying (2D) spatial-temporal systems

In this paper we address the identification of (2D) spatial-temporal dynamical systems governed by the Vector Auto-Regressive (VAR) form. The coefficient-matrices of the VAR model are parametrized as sums of Kronecker products. When the number of terms in the sum is small compared to the size of the matrix, such a Kronecker representation...