  Integrated sensing and communication (ISAC) opens up new service
possibilities for sixth-generation (6G) systems, where both communication and
sensing (C&S) functionalities co-exist by sharing the same hardware platform
and radio resource. In this paper, we investigate the waveform design problem
in a downlink multi-user and multi-target ISAC system under different C&S
performance preferences. The multi-user interference (MUI) may critically
degrade the communication performance. To eliminate the MUI, we employ the
constructive interference mechanism into the ISAC system, which saves the power
budget for communication. However, due to the conflict between C&S metrics, it
is intractable for the ISAC system to achieve the optimal performance of C&S
objective simultaneously. Therefore, it is important to strike a trade-off
between C&S objectives. By virtue of the multi-objective optimization theory,
we propose a weighted Tchebycheff-based transformation method to re-frame the
C&S trade-off problem as a Pareto-optimal problem, thus effectively tackling
the constraints in ISAC systems. Finally, simulation results reveal the
trade-off relation between C&S performances, which provides insights for the
flexible waveform design under different C&S performance preferences in
MIMO-ISAC systems.
