On the Performance Gain of Integrated Sensing and Communications: A Subspace Correlation Perspective

In this paper, we shed light on the performance gain of integrated sensing and communications (ISAC) from the perspective of channel correlations between radar sensing and communication (S&C), namely ISAC subspace correlation. To begin with, we consider a multi-input multi-output (MIMO) ISAC system and reveal that the optimal ISAC signal is in the subspace spanned by the transmitted steering vectors of the sensing channel and the right singular matrix of the communication channel. By leveraging this result, we study a basic ISAC scenario with a single target and a single-antenna communication user, and derive the optimal waveform covariance matrix for minimizing the estimation error under a given communication rate constraint. To quantify the integration gain of ISAC systems, we define the subspace "correlation coefficient" to characterize the coupling effect between S&C channels. Finally, numerical results are provided to validate the effectiveness of the proposed approaches.