Robust transmit zero-forcing filters

We present linear and non-linear robust transmit zero-forcing filters for the downlink of multi-user multiple-input single-output (MU-MISO) time-division-duplex (TDD) systems which are robust with respect to errors in the channel state information (CSI) arising from channel estimation and time lags in mobile communications. Based on a set of estimated CSI of previous uplink slots, we apply a conditional mean to the cost function underlying the respective filter for the current downlink slot resulting in channel prediction for the CSI and robust filter structures. Thus, the respective transmit filters are less sensitive to imperfect channel knowledge and show dramatic performance improvements compared to their non-robust counterparts. Our approach can be interpreted as a joint optimization of channel prediction and preequalization. Additionally, we point out the relation of the presented approach to another robust technique named stochastic programming and show the analogy to a regularization approach.