Open AccessStability analysis in Gram‐Schmidt QR decomposition
Author(s) -
Kobayashi Ricardo Tadashi,
Abrão Taufik
Publication year - 2016
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2016.0123
Subject(s) - qr decomposition , mathematics , stability (learning theory) , mimo , moment (physics) , gaussian , gramian matrix , matrix (chemical analysis) , random matrix , gram , limit (mathematics) , condition number , algorithm , eigenvalues and eigenvectors , computer science , mathematical analysis , statistics , beamforming , physics , materials science , classical mechanics , quantum mechanics , machine learning , biology , bacteria , composite material , genetics
In this study, important aspects concerning the stability of the QR decomposition (QRD) through the modified Gram‐Schmidt (GS) orthogonalisation procedure with application in multiple‐input–multiple‐output (MIMO) detection are investigated. In particular, the numerical stability of GS‐QRD is analysed through the condition number, considering a matrix with Gaussian entries, which is a very special class of matrix, especially for telecommunication systems in general and for MIMO system in particular. The condition number is analysed in the average sense, aided by random processes theory, including in special the central limit theorem, random variable transformation and moment generating functions. An analytical bound for the condition number is found and corroborated by numerical simulations.