Construction of 1-Bit Transmit Signal Vectors for Downlink MU-MISO Systems: QAM Constellations

In this paper, we investigate the construction of a transmit signal for downlink multiuser multiple-input single-output (MU-MISO) systems under the cost-effective 1-bit digital-to-analog converters (DACs). Due to the coarse nonliner property, conventional precoding methods, developed under infinite-resolution DACs, could not yield an attractive performance having a severe error-floor. Finding an optimal transmit signal, moreover, is computationally implausible due to its combinatorial nature. This challenging problem has been partially solved in our earlier work focusing on phase-shift-keying constellations. Our major contribution is to extend it into more practical quadrature-amplitude-modulation constellations in a non-trivial way. We first derive the so-called feasibility condition to guarantee that every user's noiseless received signal belongs to a desired decision region, and then transform it as linear constraints. Taking the robustness to an additive noise into account, the proposed construction method is formulated as a mixed integer linear programming problem. We construct an efficient algorithm to solve it (equivalently, to generate an 1-bit transmit signal). Via simulation results, we demonstrate the superiority of the proposed method with respect to a computational complexity and detection performance.