  This paper investigates the issues of the hybrid beamforming design for the
orthogonal frequency division multiplexing dual-function radar-communication
(DFRC) system in multiple task scenarios involving the radar scanning and
detection task and the target tracking task. To meet different task
requirements of the DFRC system, we introduce two novel radar beampattern
metrics, the average integrated sidelobe to minimum mainlobe ratio (AISMMR) and
average peak sidelobe to integrated mainlobe ratio (APSIMR), to characterize
the space-frequency spectra in different scenarios. Then, two HBF design
problems are formulated for two task scenarios by minimizing the AISMMR and
APSIMR respectively subject to the constraints of communication
quality-of-service (QoS), power budget, and hardware. Due to the non-linearity
and close coupling between the analog and digital beamformers in both the
objective functions and QoS constraint, the resultant formulated problems are
challenging to solve. Towards that end, a unified optimization algorithm based
on a consensus alternating direction method of multipliers (CADMM) is proposed
to solve these two problems. Moreover, under the unified CADMM framework, the
closed-form solutions of primal variables in the original two problems are
obtained with low complexity. Numerical simulations are provided to demonstrate
the feasibility and effectiveness of the proposed algorithm.
