Precoding for the multiantenna downlink: Multiuser SNR gap and optimal user ordering

This paper develops a practical design method for implementing Tomlinson-Harashima precoding (THP) in a downlink channel with multiple antennas at the transmitter and a single antenna at each receiver. A two-step design process is proposed for minimizing the total transmit power while satisfying every user's minimum data rate and maximum bit-error rate (BER) requirements. First, the BER and rate requirements are converted to "virtual rate" requirements, which account for the gap-to-capacity introduced by practical quadrature amplitude modulation (QAM) and THP. The second step is to determine the transmit covariance matrices (which specify the entire THP system) that will provide these virtual rates at the minimum total transmit power. As one of the main features in the proposed scheme, an algorithm for finding the optimal user encoding (or presubtraction) order in polynomial time is proposed. In addition, we also propose an algorithm that finds a near-optimal order, but which is much less complex. The proposed method outperforms existing zero-forcing-based THP systems in term of power efficiency.