Transmit processing in MIMO wireless systems

By restricting the receive filter to be scalar, we derive the optimizations for linear transmit processing from the respective joint optimizations of transmit and receive filters. We can identify three filter types similar to receive processing: the transmit matched filter (TxMF), the transmit zero-forcing filter (TxZF), and the transmit Wiener filter (TxWF). The TxWF has similar convergence properties as the receive Wiener filter, i.e. it converges to the matched filter and the zero-forcing filter for low and high signal to noise ratio, respectively. Additionally, the mean square error (MSE) of the TxWF is a lower bound for the MSEs of the TxMF and the TxZF. The optimizations for the linear transmit filters are extended to obtain the respective Tomlinson-Harashima preceding (THP) solutions. The new formulation of the THP optimizations directly leads to an algorithm to compute the preceding order. We also discuss the reasons why the linear transmit filters are outperformed by the respective THP schemes.