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In this paper, we focus on 1-bit precoding approaches for downlink massivemultiple-input multiple-output (MIMO) systems, where we exploit the concept ofconstructive interference (CI). For both PSK and QAM signaling, we firstlyformulate the optimization problem that maximizes the CI effect subject to therequirement of the 1-bit transmit signals. We then mathematically prove that,when employing the CI formulation and relaxing the 1-bit constraint, themajority of the transmit signals already satisfy the 1-bit formulation.Building upon this important observation, we propose a 1-bit precoding approachthat further improves the performance of the conventional 1-bit CI precodingvia a partial branch-and-bound (P-BB) process, where the BB procedure isperformed only for the entries that do not comply with the 1-bit requirement.This operation allows a significant complexity reduction compared to thefully-BB (F-BB) process, and enables the BB framework to be applicable to thecomplex massive MIMO scenarios. We further develop an alternative 1-bit schemethrough an `Ordered Partial Sequential Update' (OPSU) process that allows anadditional complexity reduction. Numerical results show that both proposed1-bit precoding methods exhibit a significant signal-to-noise ratio (SNR) gainfor the error rate performance, especially for higher-order modulations.

Interference Exploitation 1-Bit Massive MIMO Precoding: A Partial Branch-and-Bound Solution with Near-Optimal Performance