Stability analysis in Gram-Schmidt QR decomposition

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.