  In conventional joint communications and sensing (JCAS) designs for
multi-carrier multiple-input multiple-output (MIMO) systems, the
dual-functional waveforms are often optimized for the whole frequency band,
resulting in limited communications--sensing performance tradeoff. To overcome
the limitation, we propose employing a subset of subcarriers for JCAS, while
the communications function is performed over all the subcarriers. This offers
more degrees of freedom to enhance the communications performance under a given
sensing accuracy. We first formulate the rate maximization under the sensing
accuracy constraint to optimize the beamformers and JCAS subcarriers. The
problem is solved via Riemannian manifold optimization and closed-form
solutions. Numerical results for an 8x4 MIMO system with 64 subcarriers show
that compared to the conventional subcarrier sharing scheme, the proposed
scheme employing 16 JCAS subcarriers offers 60% improvement in the achievable
communications rate at the signal-to-noise ratio of 10 dB. Meanwhile, this
scheme generates the sensing beampattern with the same quality as the
conventional JCAS design.
