  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.
