Robust Tomlinson–Harashima Precoding for the Wireless Broadcast Channel

Previous designs of Tomlinson–Harashima precoding (THP) for the broadcast channel with multiple (cooperative) transmitters and noncooperative (decentralized) scalar receivers assume complete channel state information (CSI) at the transmitter. Due to its nonlinearity, THP is more sensitive to errors in CSI at the transmitter than linear precoding, which may be large in wireless communications. Thus, THP performance degrades severely—and it is even outperformed by corresponding linear precoders. We propose a novel robust optimization for THP with partial CSI based on mean-square error (MSE), which performs a conditional mean (CM) estimate of the cost function including a novel model of the receivers. This enables a smooth transition of robust THP from complete, via partial, to statistical CSI. The performance is now always superior or in the worst case equal to corresponding linear precoding techniques. With these features, the proposed robust THP is very attractive for application in the wireless broadcast channel.