On the dimension of the Krylov subspace in low complexity wireless Communications linear receivers


In this paper, we tend to analyse the dimension of the Krylov subspace obtained in Krylov solvers applied to signal detection in low complexity Communication receivers. These receivers are based mostly on the Wiener filter as a pre-processing step for signal detection, requiring the computation of a matrix inverse, which is computationally demanding for massive systems. When applying Krylov solvers to the computation of the Wiener filter, a prescribed variety of iterations is applied to unravel the associated linear system. This allows for obtaining a reduced number of floating point operations. We tend to base our analysis on relating the Krylov subspace with the eigenvalues and therefore 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 have a tendency to show that the actual structure of Communication systems can yield a distinctive Krylov subspace for several right hand sides. Primarily based on the latter, we tend to any extend our findings by solving the multivariate version of the Wiener filter utilising Galerking projections.

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