  In this paper, we focus on 1-bit precoding for large-scale antenna systems in
the downlink based on the concept of constructive interference (CI). By
formulating the optimization problem that aims to maximize the CI effect
subject to the 1-bit constraint on the transmit signals, we mathematically
prove that, when relaxing the 1-bit constraint, the majority of the obtained
transmit signals already satisfy the 1-bit constraint. Based on this important
observation, we propose a 1-bit precoding method via a partial branch-and-bound
(P-BB) approach, where the BB procedure is only performed for the entries that
do not comply with the 1-bit constraint. The proposed P-BB enables the use of
the BB framework in large-scale antenna scenarios, which was not applicable due
to its prohibitive complexity. Numerical results demonstrate a near-optimal
error rate performance for the proposed 1-bit precoding algorithm.
