Fundamental Limits of MIMO-OTFS and MIMO-OFDM in High-Dynamics ISAC: An Antenna Array Architecture Perspective

Po-Chih Chen, Ming-Chun Lee, Yu-Chih Huang

This paper investigates the fundamental limits of MIMO-OTFS and MIMO-OFDM integrated sensing and communications (ISAC) systems in high-mobility environments, specifically comparing sparse arrays (SA) against conventional uniform linear arrays (ULA). High-dynamics scenarios, such as V2X and satellite networks, suffer from severe Doppler shifts and rapidly time-varying channels, necessitating robust modulation schemes and efficient array geometries. A unified theoretical analysis of ergodic channel capacity and the Cramér$\unicode{x2013}$Rao bound (CRB) for angle estimation is provided. Utilizing the framework of stochastic majorization, the study reveals that SAs consistently outperform ULAs by creating a more $\unicode{x201C}$uniform$\unicode{x201D}$ spatial eigenvalue distribution, which decorrelates the multipath environment and increases communication capacity. For sensing, the paper proves that the angle CRB is inversely proportional to the array's second-order moment of antenna positions asymptotically, demonstrating that SAs achieve superior accuracy$\unicode{x2014}$improving by up to the square of the number of antennas$\unicode{x2014}$due to their increased physical aperture. Notably, the analysis shows that under relatively ideal conditions, MIMO-OTFS and MIMO-OFDM share similar fundamental limits for both capacity and angle estimation, suggesting that spatial geometry, rather than waveform, is the primary driver of fundamental performance gains in the spatial dimension.