Simplified transmit covariance optimization and user ordering algorithm for successive zero-forcing precoding

In this paper we consider transmit covariance matrix optimization and user ordering problem for successive zero-forcing (SZF) precoding for multiuser multiple-input multiple-output (MIMO) downlink, where base station as well as the mobile receivers are equipped with multiple antennas. With SZF, an optimization of sum rate maximizing transmit covariance matrices is necessary. A dirty paper coding (DPC) based transmit covariance matrix optimization algorithm has been recently proposed in [1]. The algorithm involves three steps: the dual multiple access channel (MAC) covariance optimization using sum power iterative water-filling [2], the MAC to broadcast channel (BC) covariance transformation [3] for DPC, and transformation of the DPC downlink covariance matrices to SZF matrices. Hence, that algorithm is computationally very complex, and may not be realizable in practice. In this paper, we propose a suboptimal but much simplified algorithm, which employs an iterative procedure similar to the MAC covariance optimization technique of [2], but does not involve multiple levels of covariance matrix transformations. Additionally, the optimized algorithm requires the optimization to be applied to all possible user orders. Hence, we propose a heuristic user ordering algorithm based on previously proposed user selection algorithms, so that the exhaustive search through all possible user orders is avoided without significant performance penalty. Simulation results show that proposed algorithm performs very close to the algorithm of [1] in low SNR regime.