Subspace Geometry of Pareto-Optimal ISAC

Integrated sensing and communications (ISAC) unifies radar-style sensing and wireless data transmission on a shared spectral and hardware platform. While its empirical motivations are well documented, rigorous design requires a geometric understanding of the tradeoff between sensing performance and communication reliability. This paper develops a theoretical ISAC framework based on a dual-functional MIMO transmitter and focuses on the geometry of covariance (second-order) design. A unified baseband signal model is introduced together with canonical metrics for sensing and communication expressed through Fisher information and achievable rates. Using information-theoretic and estimation-theoretic arguments, we characterize the Pareto-optimal tradeoff surface and show that optimal transmit covariances concentrate on low-dimensional informative subspaces. The resulting geometric interpretation provides a clear view of ISAC tradeoffs and complements existing RadCom studies.