Block Krylov methods in time-dispersive MIMO systems

Compared to the conventional full-rank Wiener filter (WF), reduced-rank processing in the minimum mean square error sense is a well-known strategy in order to reduce computational complexity and enhance performance in case of low sample support. In this paper, we reveal the relationship between block Krylov methods and the multi-stage matrix WF (MSMWF) as a reduced-rank matrix WF which estimates a signal vector instead of a scalar. The new insights lead to an implementation of the MSMWF based on Rune´s variant of the block Lanczos algorithm which is more flexible with respect to rank selection compared to existing algorithms. Finally, the application to a time-dispersive multiple-input multiple-output (MIMO) system demonstrates the ability of the new algorithm to lessen receiver complexity while maintaining the same level of system performance or even improve it if second order statistics are not perfectly known. Moreover, the MSMWF outperforms the parallel implementation of multi-stage vector WFs with a comparable computational complexity.