Dual-functional radar-communication (DFRC) systems can simultaneously perform both radar and communication functionalities using the same hardware platform and spectrum resource. In this paper, we consider multi-input multi-output (MIMO) DFRC systems and focus on transmit beamforming designs to provide both radar sensing and multi-user communications. Unlike conventional block-level precoding techniques, we propose to use the recently emerged symbol-level precoding approach in DFRC systems, which provides additional degrees of freedom (DoFs) that guarantee preferable instantaneous transmit beampatterns for radar sensing and achieve better communication performance. In particular, the squared error between the designed and desired beampatterns is minimized subject to the quality-of-service (QoS) requirements of the communication users and the constant-modulus power constraint. Two efficient algorithms are developed to solve this non-convex problem on both the Euclidean and Riemannian spaces. The first algorithm employs penalty dual decomposition (PDD), majorization-minimization (MM), and block coordinate descent (BCD) methods to convert the original optimization problem into two solvable sub-problems, and iteratively solves them using efficient algorithms. The second algorithm provides a much faster solution at the price of a slight performance loss, first transforming the original problem into Riemannian space, and then utilizing the augmented Lagrangian method (ALM) to obtain an unconstrained problem that is subsequently solved via a Riemannian Broyden-Fletcher-Goldfarb-Shanno (RBFGS) algorithm. Extensive simulations verify the distinct advantages of the proposed symbol-level precoding designs in both radar sensing and multi-user communications.
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