A unified framework for regularized linear estimation in communication systems

Two concerns often arise simultaneously when applying linear estimation in communication systems: the computational complexity can be prohibitively high when the system size is large, and the performance may degrade dramatically when the presumed model is mismatched with the actual system. In this paper, we introduce a subspace expansion framework to jointly address these concerns, in which the observation is first projected onto a lower-dimensional subspace and then the solution of the projected problem is regularized. We discuss two projection methods based on eigensubspace and Krylov subspace expansions. We show that the Krylov subspace projection provides an economical solution to regularized linear estimation. We also compare different regularization methods, such as principal components and diagonal loading. We show that diagonal loading generally outperforms other alternatives and that Krylov subspace rank reduction can yield a regularization effect close to diagonal loading. Finally, we investigate the impact of preconditioning on the performance and complexity for mismatched modeling and propose a loaded preconditioner, which can reduce complexity as well as preserve the regularization effect. Under the proposed framework, various regularization schemes are studied and some guidelines for choosing the right scheme are provided.