Detection-Aware Rate--CRB Characterization for Resource Allocation in ISAC Systems

Integrated sensing and communication (ISAC) performance analysis commonly employs the Cramér–Rao bound (CRB) as the sensing metric. The CRB lower-bounds estimation-error variance under a target-present model but does not characterize the reliability of the energy detection that receivers often use to validate returns against noise and clutter. Considering the range CRB in a single-user, single-target joint power–bandwidth allocation problem, we establish the conditions under which a rate-optimal allocation at a given CRB requirement fails to achieve a given detection probability. We then develop detection-constrained rate–CRB characterizations at two levels: 1) a detection-aware (DA) formulation that treats the CRB and detection probability as parallel requirements, and 2) a detect–then–estimate (DTE) formulation using a $\mathit{\text{detection-gated}}\mathit{\text{CRB}}$ defined on frames that cross an energy threshold. We analyze the resulting changes in the optimal rate and feasible power–bandwidth allocations, and for DTE further show how detection probability and conditional estimation accuracy jointly determine downstream tracking performance. Multi-user, multi-target resource allocation is then formulated under CRB-only, DA, and DTE characterizations. The results show that CRB-only allocation can conceal inadequate detection reliability, and that accounting for detection and receiver architecture materially changes the power–bandwidth allocation and the communication–sensing tradeoff.