US 12,266,859 B2
Eigen decomposition by gradient ascent
Sivarama Venkatesan, West Orange, NJ (US); Jaakko Eino Ilmari Vihriälä, Oulu (FI); Olli Juhani Piirainen, Oulu (FI); and Markus Myllylä, Oulu (FI)
Assigned to Nokia Solutions and Networks Oy, Espoo (FI)
Filed by Nokia Solutions and Networks Oy, Espoo (FI)
Filed on Dec. 3, 2021, as Appl. No. 17/457,486.
Claims priority of application No. 20206276 (FI), filed on Dec. 9, 2020.
Prior Publication US 2022/0181791 A1, Jun. 9, 2022
Int. Cl. H01Q 21/06 (2006.01); H01Q 1/24 (2006.01)
CPC H01Q 21/06 (2013.01) [H01Q 1/246 (2013.01)] 14 Claims
OG exemplary drawing
 
1. An apparatus comprising:
one or more processors;
an antenna array; and
a memory comprising computer readable instructions that, when executed by the one or more processors, cause the apparatus at least to:
receive one or more initial signals;
receive an input covariance matrix, wherein the input covariance matrix is a channel covariance matrix;
determine one or more eigenvalues and eigenvectors of the input covariance matrix iteratively using gradient ascent, wherein each iteration of the gradient ascent has a step size, μ, that maximises a Rayleigh quotient along the gradient;
generate one or more transformed signals by applying a transform to the one or more initial signals, wherein based on the determination of one or more eigenvectors of the input covariance matrix the transform comprises a matrix of eigenvectors of the input covariance matrix; and
transmit, by the antenna array, the transformed signal, wherein the computer readable instructions, when executed by the one or more processors, further cause the apparatus at least to:
determine a first eigenvector of the input covariance matrix iteratively using gradient ascent;
update the input covariance matrix using matrix deflation;
determine one or more eigenvectors of the input covariance matrix iteratively using gradient ascent based on the updated input covariance matrix; and
determine a first eigenvalue of the input covariance matrix associated with the first eigenvector by taking a trace of an intermediate matrix, wherein updating the input covariance matrix using matrix deflation comprises:
generating the intermediate matrix comprising a product of a product vector and the first eigenvector, wherein the product vector comprises a product of the input covariance matrix and the first eigenvector; and
subtracting the intermediate matrix from the input covariance matrix to determine the updated input covariance matrix.