On Unified CRLB Framework from Generic Signals to ISAC Waveforms with Virtual Array Sensing

Abstract: This paper presents a unified Cramér-Rao lower bound (CRLB) framework for signal-level parameters in integrated sensing and communications (ISAC)-enabled radar systems. Starting from the generic signal model, we analyze the coupling between delay and Doppler in the Fisher information matrix (FIM), which is unsolved and often overlooked in relevant studies. Addressing this issue, we derive the conditions under which the coupling terms can be eliminated and demonstrate that these conditions are typically satisfied for ISAC-enabled waveforms. Afterward, the CRLBs of representative ISAC waveforms are derived within the unified framework, enabling consistent and comparable analysis across the waveforms and avoiding model-dependent discrepancies. Further, the framework is extended to virtual array (VA) sensing systems, where the impact of different multiplexing schemes is analyzed. Simulation results demonstrate the consistency between the CRLBs derived from the proposed framework and those obtained from waveform-specific analyses. The proposed framework shows strong generality, waveform-compatibility, and flexibility, offering a versatile tool for the CRLB analysis of various waveforms, including those lacking existing analytical results.