  Millimeter-wave (mmWave) joint communication-radar (JCR) will enable high
data rate communication and high-resolution radar sensing for applications such
as autonomous driving. Prior JCR systems that are based on the mmWave
communications hardware, however, suffer from a limited angular field-of-view
and low estimation accuracy for radars due to the employed directional
communication beam. In this paper, we propose an adaptive and fast combined
waveform-beamforming design for the mmWave automotive JCR with a phased-array
architecture that permits a trade-off between communication and radar
performances. To rapidly estimate the mmWave automotive radar channel in the
Doppler-angle domain with a wide field-of-view, our JCR design employs a few
circulant shifts of the transmit beamformer and apply two-dimensional partial
Fourier compressed sensing technique. We optimize these circulant shifts to
achieve minimum coherence in compressed sensing. We evaluate the JCR
performance trade-offs using a normalized mean square error (MSE) metric for
radar estimation and a distortion MSE metric for data communication, which is
analogous to the distortion metric in the rate distortion theory. Additionally,
we develop a MSE-based weighted average optimization problem for the adaptive
JCR combined waveform-beamforming design. Numerical results demonstrate that
our proposed JCR design enables the estimation of short- and medium-range radar
channels in the Doppler-angle domain with a low normalized MSE, at the expense
of a small degradation in the communication distortion MSE.
