Uplink-downlink bidirectional training of multiuser MIMO filters and precoders

Joint optimization of linear and nonlinear precoders and receive filters is considered for both the uplink/downlink in a single cell. The users and base station have multiple antennas and channel state information is initially unknown and not explicitly estimated. In the nonlinear case, for the uplink we assume successive interference cancellation at the base station, and for the downlink we assume that the base station pre-compensates for the interference with Tomlinson-Harashima precoding (THP). We assume time-division duplex with channel reciprocity, and estimate the filters directly with bidirectional training: the uplink feedforward/feedback filters at the base station are estimated via uplink training and are used as interference pre-compensation filters for downlink training of the mobile receivers. The filters are updated using a sum least squares criterion. We prove convergence of related iterative schemes in which the filters are updated according to a minimum mean squared error (MMSE) criterion, subject to different power constraints. Numerical results show that nonlinear filters can provide substantial gains relative to linear filters when the forward-backward iterations are limited.