Fundamental Limits of MIMO ISAC: An Antenna Array Architecture Perspective

This paper investigates the fundamental limits of MIMO integrated sensing and communications (ISAC) systems, specifically comparing sparse arrays (SAs) against conventional uniform linear arrays (ULAs). A unified theoretical analysis of ergodic channel capacity and the Cram'{e}r$\text{unicode}x2013$Rao bound (CRB) for angle estimation is developed while accounting for the array geometry. Utilizing the framework of stochastic majorization, the study reveals that SAs consistently outperform ULAs by creating a more $\text{unicode}x201C$uniform$\text{unicode}x201D$ 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 central moment of antenna positions asymptotically, demonstrating that SAs achieve superior accuracy$\text{unicode}x2014$improving by up to the square of the number of antennas$\text{unicode}x2014$due to their increased physical aperture. These analyses and conclusions are demonstrated to be also valid for MIMO ISAC systems employed with the modern waveforms OTFS and OFDM, suggesting that spatial geometry, rather than waveform, is the primary driver of fundamental performance gains in the spatial dimension.