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

TL;DR

This paper analyzes the performance improvements of integrated sensing and communications (ISAC) systems through a subspace correlation perspective, revealing optimal signal structures and quantifying the integration gain.

Contribution

It introduces the concept of subspace correlation in ISAC, derives optimal waveform covariance for a basic scenario, and validates the approach with numerical results.

Findings

Optimal ISAC signals lie in the subspace spanned by sensing and communication channels.

The subspace correlation coefficient quantifies the coupling effect between S&C channels.

Numerical results confirm the effectiveness of the proposed waveform design.

Abstract

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.