Cramér-Rao Bound Optimization for Massive MIMO DFRC Systems with 1-Bit DACs and ADCs

In this paper, we investigate the dual-function radar-communication (DFRC) design for massive multiple-input multiple-output (MIMO) systems equipped with 1-bit digital-to-analog converters (DACs) at the transmitter and 1-bit analog-to-digital converters (ADCs) at the receiver, motivated by the need for low-cost and power-efficient implementations of massive MIMO systems. We consider a downlink scenario where the transmit signal matrix is optimized to enhance sensing performance while satisfying communication quality of service (QoS) requirements. Specifically, the objective is to minimize the 1-bit Cramér-Rao bound (CRB) for estimating the azimuth angle of a point-like target under symbol-level constructive interference (CI) constraints. We conduct an asymptotic analysis of the 1-bit Fisher information, revealing its nonmonotonicity with the signal-to-noise ratio (SNR), and introduce amplitude constraints to exclude regions where the objective function value is clearly suboptimal and facilitate convergence to high-quality solutions. The resulting problem is a nonconvex optimization challenge with coupled binary and linear constraints. We transform the discrete problem into a continuous constrained one, characterize its global and local minima, and tackle it via the augmented Lagrangian method (ALM) and a spectral projected gradient (SPG) method combined with nonmonotone line search. The solution is further refined via local search and cutting-plane techniques. Extensive numerical experiments verify our analysis, showing that the proposed approach exhibits promising DFRC performance compared to benchmark schemes.