Reduced complexity transmit Wiener filter based on a Krylov subspace multi-stage decomposition

The multi-stage transmit Wiener filter (MSTxWF) is presented, an approach to reducing the complexity of the transmit Wiener filter (TxWF). The MSTxWF is found by applying the multi-stage decomposition known from the receive multi-stage Wiener filter (MSWF) to the TxWF. Complexity reduction is achieved by truncating the decomposition. We show that the resulting reduced rank MSTxWF can be interpreted as an approximation of the TxWF in a Krylov subspace, allowing for an efficient computation of the MSTxWF with the Lanczos algorithm. The reduced rank MSTxWF shows near-optimum performance for relatively low rank, making it an interesting alternative to eigenspace-based methods for complexity reduction.