Optimized CSI Feedback for Robust THP Design

In the broadcast channel (BC), the signals of the multiple users can be separated by means of preceding. For the design of precoding, channel state information (CSI) is necessary at the transmitter side. In many cases (e.g., for frequency division duplex (FDD) systems), the transmitter cannot estimate this information and the CSI has to be communicated from the receivers to the transmitter via a feedback channel that is assumed to be error-free but introduces a delay. Every user estimates the channel and reduces it to a low-dimensional representation for data compression that is possible due to the channel correlations. Before the feedback, the CSI is quantized and only the index of the codebook entry is sent to the transmitter, since the data rate of the feedback channel is limited. We propose a joint MSE optimization of the channel estimation and the rank reduction basis, where the quantizer is modeled as a data independent additive noise source. Based on the fed back codebook index, robust multi-user precoding schemes, viz., linear precoding and Tomlinson Harashima precoding (THP), are designed that clearly outperform non-robust schemes.