  Integrated Sensing and Communications (ISAC) has garnered significant
attention as a promising technology for the upcoming sixth-generation wireless
communication systems (6G). In pursuit of this goal, a common strategy is that
a unified waveform, such as Orthogonal Frequency Division Multiplexing (OFDM),
should serve dual-functional roles by enabling simultaneous sensing and
communications (S&C) operations. However, the sensing performance of an OFDM
communication signal is substantially affected by the randomness of the data
symbols mapped from bit streams. Therefore, achieving a balance between
preserving communication capability (i.e., the randomness) while improving
sensing performance remains a challenging task. To cope with this issue, in
this paper we analyze the ambiguity function of the OFDM communication signal
modulated by random data. Subsequently, a probabilistic constellation shaping
(PCS) method is proposed to devise the probability distributions of
constellation points, which is able to strike a scalable S&C tradeoff of the
random transmitted signal. Finally, the superiority of the proposed PCS method
over conventional uniformly distributed constellations is validated through
numerical simulations.
