A new backward recursion for the multi-stage nested Wiener filter employing Krylov subspace methods

The multi-stage nested Wiener filter (MSNWF) can be identified to be the solution of the Wiener-Hopf equation in the Krylov subspace of the covariance matrix of the observation and the crosscorrelation vector of the observation and the desired signal. Therefore, the Arnoldi algorithm which arises from the MSNWF development can be replaced by the Lanczos algorithm leading to a simpler computation of the Krylov subspace basis. Moreover, the foundation in the Krylov subspace framework helps to derive an order-recursive representation of the MSNWF which generates the filter for rank D in terms of the filter for rank D-1. The new backward recursion is used to design a linear equalizer filter in an enhanced data rates for GSM evolution (EDGE) system. Simulation results show the ability of the MSNWF to reduce the receiver complexity while the system performance is unchanged.