  Joint communications and sensing (JCAS) systems have recently emerged as a
promising technology to utilize the scarce spectrum in wireless networks and to
reuse the same hardware to save infrastructure costs. In practical JCAS
systems, dual functional constant-modulus waveforms can be employed to avoid
signal distortion in nonlinear power amplifiers. However, the designs of such
waveforms are very challenging due to the nonconvex constant-modulus
constraint. The conventional branch-and-bound (BnB) method can achieve optimal
solution but at the cost of exponential complexity and long run time. In this
paper, we propose an efficient deep unfolding method for the constant-modulus
waveform design in a multiuser multiple-input multiple-output (MIMO) JCAS
system. The deep unfolding model has a sparsely-connected structure and is
trained in an unsupervised fashion. It achieves good communications-sensing
performance tradeoff while maintaining low computational complexity and low run
time. Specifically, our numerical results show that the proposed deep unfolding
scheme achieves a similar achievable rate compared to the conventional BnB
method with 30 times faster execution time.
