A Krylov subspace multistage decomposition of the transmit Wiener filter

Besides methods based on eigensubspaces, the reduced-rank multistage Wiener filter (MSWF) is a well-known approach for the approximation of the Wiener filter, the optimum linear receive filter in the minimum mean square error sense, in a lower-dimensional subspace in order to reduce computational complexity and enhance performance in case of low sample support. Analogous, the transmit Wiener filter (TxWF) is the optimum linear filter at the transmitter side where the receiver is kept simple since it applies only a scalar weighting. We use the principles of the MSWF to derive a multistage decomposition of the TxWF which we denote transmit multistage Wiener filter (TxMSWF). In addition, we will show that the reduced-rank TxMSWF can be seen as an approximation of the TxWF in a Krylov subspace. Simulation results reveal that the TxMSWF achieves near optimum performance for relatively low rank. Thus, it is an interesting alternative to low complexity approximations of the TxWF in eigensubspaces.