The inherent randomness of communication symbols creates a fundamental tension in Integrated Sensing and Communications (ISAC). On the one hand, they enable data transmission while allowing sensing to fully reuse communication resources. On the other hand, their randomness induces waveform-dependent fluctuations that directly affect sensing accuracy. This paper investigates a foundational question arising from this tradeoff: \textit{How does the modulation waveform affect the ranging Cramér--Rao Bound (CRB) when sensing reuses random data symbols?} We address this question by revealing a structural factorization of the Fisher information matrix (FIM) for joint delay-amplitude estimation, which separates the deterministic Jacobian of the target geometry from the random frequency-domain signal power induced by the data symbols. This structure yields a Jensen-type universal lower bound on the CRB, which is exactly attained by CP-OFDM under PSK constellations. For QAM and broader sub-Gaussian constellations, we develop an asymptotic perturbation analysis of the inverse FIM and prove that, when the number of transmitted symbols $N$ grows large, CP-OFDM achieves a lower ranging CRB than any frequency-spread orthogonal waveform over the almost-sure event where the random FIM is invertible. This superiority is further extended to amplitude estimation and full joint delay-amplitude estimation. We also characterize the local geometry of the stochastic CRB minimization problem over the unitary group. The analysis reveals that CP-OFDM is a stationary point for finite $N$, and its Riemannian Hessian is positive semidefinite for sufficiently large $N$, establishing its asymptotic local optimality. Numerical results confirm that OFDM outperforms representative waveforms including SC, OTFS, and AFDM.

翻译：通信符号的固有随机性在集成感知与通信（ISAC）中产生了根本性矛盾。一方面，通信符号使数据传输成为可能，同时允许感知功能完全复用通信资源；另一方面，其随机性会诱发依赖波形的波动，直接影响感知精度。本文研究了这一权衡衍生出的基础性问题：当感知复用随机数据符号时，调制波形如何影响测距克拉美-罗界（CRB）？为回答该问题，我们揭示了联合时延-幅度估计的费舍尔信息矩阵（FIM）的结构性分解，该分解将目标几何的确定性雅可比矩阵与数据符号引起的随机频域信号功率分离。这一结构推导出CRB的Jensen型通用下界，且PSK星座下CP-OFDM可精确达到该下界。针对QAM及更广泛的亚高斯星座，我们发展了逆FIM的渐近扰动分析，并证明当传输符号数$N$增大时，在随机FIM可逆的几乎必然事件上，CP-OFDM实现的测距CRB低于任意频率扩展正交波形。该优势进一步扩展至幅度估计及完整联合时延-幅度估计。我们还刻画了酉群上随机CRB最小化问题的局部几何特征。分析表明，CP-OFDM在有限$N$时是驻点，且当$N$足够大时其黎曼海森矩阵为半正定，从而确立了其渐近局部最优性。数值结果证实OFDM性能优于SC、OTFS、AFDM等代表性波形。