  In this letter, we consider hybrid beamforming for millimeter wave (mmWave)
MIMO integrated sensing and communications (ISAC). We design the transmit beam
of a dual-functional radar-communication (DFRC) base station (BS), aiming at
approaching the objective radar beam pattern, subject to the constraints of the
signal to interference-plus-noise ratio (SINR) of communication users and total
transmission power of the DFRC BS. To provide additional degree of freedom for
the beam design problem, we introduce a phase vector to the objective beam
pattern and propose an alternating minimization method to iteratively optimize
the transmit beam and the phase vector, which involves second-order cone
programming and constrained least squared estimation, respectively. Then based
on the designed transmit beam, we determine the analog beamformer and digital
beamformer subject to the constant envelop constraint of phase shifter network
in mmWave MIMO, still using the alternating minimization method. Simulation
results show that under the same SINR constraint of communication users, larger
antenna array can achieve better radar beam quality.
