  Integrated sensing and communication (ISAC) has emerged as a key technology
for future communication systems. In this paper, we provide a general framework
to reveal the fundamental tradeoff between sensing and communication in OFDM
systems, where a unified ISAC waveform is exploited to perform both tasks. In
particular, we define the Capacity-Bayesian Cramer Rao Bound (BCRB) region in
the asymptotically case when the number of subcarriers is large. Specifically,
we show that the asymptotically optimal input distribution that achieves the
Pareto boundary point of the Capacity-BCRB region is Gaussian and the entire
Pareto boundary can be obtained by solving a convex power allocation problem.
Moreover, we characterize the structure of the sensing-optimal power allocation
in the asymptotically case. Finally, numerical simulations are conducted to
verify the theoretical analysis and provide useful insights.
