  Integrated sensing and communication (ISAC), which enables hardware,
resources (e.g., spectra), and waveforms sharing, is becoming a key feature in
future-generation communication systems. This paper investigates performance
characterization and waveform design for ISAC systems when the underlying true
communication channels are not accurately known. With uncertainty in a nominal
communication channel, the nominal Pareto frontier of the sensing and
communication performances cannot represent the true performance trade-off of a
real-world operating ISAC system. Therefore, this paper portrays the robust
(i.e., conservative) Pareto frontier considering the uncertainty in the
communication channel. To be specific, the lower bound of the true (but
unknown) Pareto frontier is investigated, technically by studying robust
waveform design problems that find the best waveforms under the worst-case
channels. The robust waveform design problems examined in this paper are shown
to be non-convex and high-dimensional, which cannot be solved using existing
optimization techniques. As such, we propose a computationally efficient
solution framework to approximately solve them. Simulation results show that by
solving the robust waveform design problems, the lower bound of the true but
unknown Pareto frontier, which characterizes the sensing-communication
performance trade-off under communication channel uncertainty, can be obtained.
