TY - JOUR
T1 - On the dimension of the Krylov subspace in low complexity wireless communications linear receivers
AU - Carvajal, Rodrigo
AU - Aguero, Juan Carlos
N1 - Funding Information:
El trabajo de R. Carvajal fue financiado por el Fondo Nacional de Desarrollo Cient?fico y Tecnol?gico (FONDECYT)-Chile, a trav?s de su programa de postdoctorado 2014, proyecto No. 3140054. El trabajo de J. C. Agu?ro fue parcialmente financiado por FONDECYT-Chile a trav?s del proyecto No. 1150954. Este trabajo fue parcialmente financiado por el Centro Avanzado de Ingenieri? El?ctrica y Electr?nica (AC3E, Proyecto Basal FB0008), Chile.
Publisher Copyright:
© 2016 IEEE.
PY - 2016/3
Y1 - 2016/3
N2 - In this paper, we analyse the dimension of the Krylov subspace obtained in Krylov solvers applied to signal detection in low complexity communication receivers. These receivers are based on the Wiener filter as a pre-processing step for signal detection, requiring the computation of a matrix inverse, which is computationally demanding for large systems. When applying Krylov solvers to the computation of the Wiener filter, a prescribed number of iterations is applied to solve the associated linear system. This allows for obtaining a reduced number of floating point operations. We base our analysis on relating the Krylov subspace with the eigenvalues and the eigenvectors of the received covariance matrix, and on the the cross-covariance matrix between the received and the transmitted signals. In our analysis, we show that the particular structure of communication systems can yield a unique Krylov subspace for several right hand sides. Based on the latter, we further extend our findings by solving the multivariate version of the Wiener filter utilising Galerking projections.
AB - In this paper, we analyse the dimension of the Krylov subspace obtained in Krylov solvers applied to signal detection in low complexity communication receivers. These receivers are based on the Wiener filter as a pre-processing step for signal detection, requiring the computation of a matrix inverse, which is computationally demanding for large systems. When applying Krylov solvers to the computation of the Wiener filter, a prescribed number of iterations is applied to solve the associated linear system. This allows for obtaining a reduced number of floating point operations. We base our analysis on relating the Krylov subspace with the eigenvalues and the eigenvectors of the received covariance matrix, and on the the cross-covariance matrix between the received and the transmitted signals. In our analysis, we show that the particular structure of communication systems can yield a unique Krylov subspace for several right hand sides. Based on the latter, we further extend our findings by solving the multivariate version of the Wiener filter utilising Galerking projections.
KW - Krylov subspace
KW - Low complexity receivers
KW - Wiener filter
UR - http://www.scopus.com/inward/record.url?scp=84968796796&partnerID=8YFLogxK
U2 - 10.1109/TLA.2016.7459598
DO - 10.1109/TLA.2016.7459598
M3 - Article
AN - SCOPUS:84968796796
VL - 14
SP - 1192
EP - 1198
JO - IEEE Latin America Transactions
JF - IEEE Latin America Transactions
SN - 1548-0992
IS - 3
M1 - 7459598
ER -