Transmit Signal Design for Large-Scale MIMO System With 1-bit DACs

Deploying low-resolution (e.g. one-bit) digital-toanalog converters (DACs) is of great importance in the multiple-input multiple-output (MIMO) system equipped with a large-scale antenna array since such a hardware architecture brings low-cost and circuit power saving for each antenna. In this paper, the problem of transmit signal design in a large-scale MIMO system with 1-bit DACs is investigated. To ensure directional transmission, we propose to design the transmit signal by minimizing the weighted mean-squared error (MSE) between the formed beampattern and a given one. The resulting design problem, which involves a nonconvex fourth-order objective and a set of nonconvex discrete constraints, is NP-hard, and therefore, an alternating minimization (AM) method is devised. In order to obtain a high-quality 1-bit solution, we propose a continuous and differentiable function to approximate the 1-bit signal, such that the problem with discrete 1-bit constraint is recast to an unconstrained optimization problem with a penalty term, which can be effectively solved via the limited-memory Broyden, Fletcher, Goldfarb, and Shanno (L-BFGS) approach. Moreover, it is found that a closed-form solution can be obtained when equal weights are applied. In addition, low-complexity schemes are developed based on the fast Fourier transform (ITT). The numerical simulations are conducted to demonstrate the effectiveness and superiority of the proposed method.