Linear equalization in communications with mismatched modeling using Krylov subspace expansion

Linear equalization can be applied to combat intersymbol interference (ISI) and cross-antenna interference (CAI) for communication systems over multipath channels. If the channel estimation is imperfect, the receiver uses a mismatched model of the system. Regularized equalization based on Krylov subspace expansion can be applied to improve robustness and reduce complexity for large systems. In this paper, we study the convergence behavior, stopping criteria, and preconditioner design for Krylov subspace methods. We show that the optimal rank can be chosen using a decision-aided estimate of the mean-squared error (MSE). However, due to the semi-convergence behavior, conventional preconditioners may fail to provide gains. To overcome this issue, we introduce regularized preconditioners, which cluster only the largest eigenvalues of the system matrix in Krylov subspace methods.