Sensing-Constrained Diversity-Multiplexing Tradeoff in MIMO ISAC: A Geometric Approach

Diversity and multiplexing are the two fundamental gains of multiple-input and multiple-output (MIMO) communications, enabling systems to simultaneously achieve increased reliability and higher data rates. The intricate interplay between these two metrics is captured by the celebrated diversity-multiplexing tradeoff (DMT). With the rapid evolution of wireless technologies, low-latency integrated sensing and communication (ISAC) has emerged as a key enabler for 6G applications, including extended reality (XR) and massive digital twins. Consequently, understanding the DMT within MIMO ISAC systems becomes critical. In this paper, we investigate the communication DMT in a mono-static MIMO ISAC system under Rayleigh fading, specifically when the transmitter is constrained to emit sensing-optimal waveforms. By unveiling the geometric properties of generalized Stiefel manifolds and employing large-deviation analysis, we characterize the asymptotic outage probability of this typical ISAC channel. This formulation yields an elegant converse bound on the sensing-constrained DMT. Ultimately, our work provides an answer to a pivotal unanswered question in ISAC system design: How much MIMO gain is fundamentally sacrificed in communication to integrate optimal sensing capabilities?