Analysis of Pareto Boundary in MIMO ISAC: From the Perspective of Instantaneous Covariance Mismatch

Integrated sensing and communications (ISAC) is emerging as one of the six application scenarios for future wireless networks. Characterizing the Pareto boundary is an urgent issue in multiple-input multiple-output (MIMO) ISAC systems. The lack of unified sensing metrics and the neglect of the instantaneous worst-case sensing requirement in the existing works present challenges to this issue. In this paper, we propose a more universal and operable theoretical limit analysis framework where the high-signal-to-noise ratio (SNR) channel capacity is characterized under instantaneous covariance mismatch constraint. We use the covariance mismatch that implies the distance to optimal covariance as the sensing metric. The optimal covariance can be computed by optimizing any key sensing metric. An MIMO ISAC Pareto boundary can be obtained by computing channel capacity under fine-grained sensing thresholds, below which the mismatch must be constrained. In the experiments, three radar modes are considered, and the results show that different radar modes affect capacity performance and a trade-off exists between communication and sensing. In addition, pure communication capacity is the upper bound of the communication capacity in ISAC. Moreover, capacity under instantaneous constraint approaches that under average one in pure MIMO communications when signal length approaches infinity.