Iterative Inversion of (ELAA-)MIMO Channels Using Symmetric Rank-1 Regularization
CoRR(2024)
摘要
While iterative matrix inversion methods excel in computational efficiency,
memory optimization, and support for parallel and distributed computing when
managing large matrices, their limitations are also evident in multiple-input
multiple-output (MIMO) fading channels. These methods encounter challenges
related to slow convergence and diminished accuracy, especially in
ill-conditioned scenarios, hindering their application in future MIMO networks
such as extra-large aperture array (ELAA). To address these challenges, this
paper proposes a novel matrix regularization method termed symmetric rank-1
regularization (SR-1R). The proposed method functions by augmenting the
channel matrix with a symmetric rank-1 matrix, with the primary goal of
minimizing the condition number of the resultant regularized matrix. This
significantly improves the matrix condition, enabling fast and accurate
iterative inversion of the regularized matrix. Then, the inverse of the
original channel matrix is obtained by applying the Sherman-Morrison transform
on the outcome of iterative inversions. Our eigenvalue analysis unveils the
best channel condition that can be achieved by an optimized SR-1R matrix.
Moreover, a power iteration-assisted (PIA) approach is proposed to find the
optimum SR-1R matrix without need of eigenvalue decomposition. The proposed
approach exhibits logarithmic algorithm-depth in parallel computing for MIMO
precoding. Finally, computer simulations demonstrate that SR-1R has the
potential to reduce iterative iterations by up to 33%, while also
significantly improve symbol error probability by approximately an order of
magnitude.
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