  As a cost-effective alternative, hybrid analog and digital beamforming
architecture is a promising scheme for millimeter wave (mmWave) system. This
paper considers two hybrid beamforming architectures, i.e. the
partially-connected and fully-connected structures, for mmWave dual-function
radar communication (DFRC) system, where the transmitter communicates with the
downlink users and detects radar targets simultaneously. The optimization
problems are formulated by minimizing a weighted summation of radar and
communication performance, subject to constant modulus and power constraints.
To tackle the non-convexities caused by the two resultant problems, effective
Riemannian optimization algorithms are proposed. Specifically, for the
fully-connected structure, a manifold algorithm based on the alternating
direction method of multipliers (ADMM) is developed. While for the
partially-connected structure, a low-complexity Riemannian product manifold
trust region (RPM-TR) algorithm is proposed to approach the near-optional
solution. Numerical simulations are provided to demonstrate the effectiveness
of the proposed methods.
