  Dual function radar communications (DFRC) systems are attractive technologies
for autonomous vehicles, which utilize electromagnetic waves to constantly
sense the environment while simultaneously communicating with neighbouring
devices. An emerging approach to implement DFRC systems is to embed information
in radar waveforms via index modulation (IM). Implementation of DFRC schemes in
vehicular systems gives rise to strict constraints in terms of cost, power
efficiency, and hardware complexity. In this paper, we extend IM-based DFRC
systems to utilize sparse arrays and frequency modulated continuous waveforms
(FMCWs), which are popular in automotive radar for their simplicity and low
hardware complexity. The proposed FMCW-based radar-communications system (FRaC)
operates at reduced cost and complexity by transmitting with a reduced number
of radio frequency modules, combined with narrowband FMCW signalling. This is
achieved via array sparsification in transmission, formulating a virtual
multiple-input multiple-output array by combining the signals in one coherent
processing interval, in which the narrowband waveforms are transmitted in a
randomized manner. Performance analysis and numerical results show that the
proposed radar scheme achieves similar resolution performance compared with a
wideband radar system operating with a large receive aperture, while requiring
less hardware overhead. For the communications subsystem, FRaC achieves higher
rates and improved error rates compared to dual-function signalling based on
conventional phase modulation.
