Low-Complexity Hybrid Beamforming for MMSE-Based Symbol-Level Precoding in Multi-User MISO System

Data-aided symbol-level precoding can exploit constructure interference for improving the energy and system efficiency in the multiantenna downlink channel, where multiple users are simultaneously served over the same channel resources. This article attempts at the end-to-end joint design of hybrid symbol-level precoder, which deals with a flexible form of constructive interference region, while allowing for multi-level constellations mixed among the different users. It considers the minimum mean square error-based optimization problem to ensure the minimum required gain under a fixed total-power constraint, which involves critical implementation issues regarding the computational complexity. An iterative closed-form solution has been presented while deriving the optimum solution in a closed form for a digital precoder subject to a fixed analog beam, serving as a key implementation block for low-complexity implementation. Furthermore, a mathematical framework is developed for employing the different number of radio frequency chains dynamically for the analog precoder as an efficient means of achieving a tradeoff between the power consumption and the performance in practice. It is shown that the performance of our proposed algorithm is similar to that of the fully-digital precoder within approximately 1 dB, suggesting that its implementation complexity can be overcome, even for numerous antenna elements, in practice.