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In this paper, we consider the one-bit precoding problem for the multiuserdownlink massive multiple-input multiple-output (MIMO) system with phase shiftkeying (PSK) modulation. We focus on the celebrated constructive interference(CI)-based problem formulation. We first establish the NP-hardness of theproblem (even in the single-user case), which reveals the intrinsic difficultyof globally solving the problem. Then, we propose a novel negative $\ell_1$penalty model for the considered problem, which penalizes the one-bitconstraint into the objective by a negative $\ell_1$-norm term, and show theequivalence between (global and local) solutions of the original problem andthe penalty problem when the penalty parameter is sufficiently large. Wefurther transform the penalty model into an equivalent min-max problem andpropose an efficient alternating proximal/projection gradient descent ascent(APGDA) algorithm for solving it, which performs a proximal gradient decentover one block of variables and a projection gradient ascent over the otherblock of variables alternately. The APGDA algorithm enjoys a low per-iterationcomplexity and is guaranteed to converge to a stationary point of the min-maxproblem and a local minimizer of the penalty problem. To further reduce thecomputational cost, we also propose a low-complexity implementation of theAPGDA algorithm, where the values of the variables will be fixed in lateriterations once they satisfy the one-bit constraint. Numerical results showthat, compared to the state-of-the-art CI-based algorithms, both of theproposed algorithms generally achieve better bit-error-rate (BER) performancewith lower computational cost.

Efficient CI-Based One-Bit Precoding for Multiuser Downlink Massive MIMO Systems with PSK Modulation