  In millimeter-wave (mmWave) dual-function radar-communication (DFRC) systems,
hybrid beamforming (HBF) is recognized as a promising technique utilizing a
limited number of radio frequency chains. In this work, in the presence of
extended target and clutters, a HBF design based on the subarray connection
architecture is proposed for a multiple-input multiple-output (MIMO) DFRC
system. In this HBF, the double-phase-shifter (DPS) structure is embedded to
further increase the design flexibility. We derive the communication spectral
efficiency (SE) and radar signal-to-interference-plus-noise-ratio (SINR) with
respect to the transmit HBF and radar receiver, and formulate the HBF design
problem as the SE maximization subjecting to the radar SINR and power
constraints. To solve the formulated nonconvex problem, the joinT Hybrid
bRamforming and Radar rEceiver OptimizatioN (THEREON) is proposed, in which the
radar receiver is optimized via the generalized eigenvalue decomposition, and
the transmit HBF is updated with low complexity in a parallel manner using the
consensus alternating direction method of multipliers (consensus-ADMM).
Furthermore, we extend the proposed method to the multi-user multiple-input
single-output (MU-MISO) scenario. Numerical simulations demonstrate the
efficacy of the proposed algorithm and show that the solution provides a good
trade-off between number of phase shifters and performance gain of the DPS HBF.
