[Paper Review] On the Fundamental Tradeoff of Integrated Sensing and Communications Under Gaussian Channels

Yifeng Xiong, Fan Liu+4 more|arXiv (Cornell University)|Apr 14, 2022

Radar Systems and Signal Processing4 citations

TL;DR

This paper establishes the fundamental tradeoff between communication rate and sensing accuracy in integrated sensing and communication (ISAC) systems over Gaussian channels by introducing a Cramér-Rao bound (CRB)-rate region framework. It characterizes two corner points—$P_{\rm SC}$ (max rate under min CRB) and $P_{\rm CS}$ (min CRB under max rate)—and proves that these are achieved via Gaussian signaling and uniform distribution over the Stiefel manifold, respectively, revealing a dual tradeoff between subspace allocation and deterministic-random waveform design.

ABSTRACT

ISAC is recognized as a promising technology for the next-generation wireless networks, which provides significant performance gains over individual S&C systems via the shared use of wireless resources. The characterization of the S&C performance tradeoff is at the core of the theoretical foundation of ISAC. In this paper, we consider a point-to-point ISAC model under vector Gaussian channels, and propose to use the CRB-rate region as a basic tool for depicting the fundamental S&C tradeoff. In particular, we consider the scenario where a unified ISAC waveform is emitted from a dual-functional ISAC Tx, which simultaneously performs S&C tasks with a communication Rx and a sensing Rx. In order to perform both S&C tasks, the ISAC waveform is required to be random to convey communication information, with realizations being perfectly known at both the ISAC Tx and the sensing Rx as a reference sensing signal as in typical radar systems. As the main contribution of this paper, we characterize the S&C performance at the two corner points of the CRB-rate region, namely, $P_{SC}$ indicating the max. achievable rate constrained by the min. CRB, and $P_{CS}$ indicating the min. achievable CRB constrained by the max. rate. In particular, we derive the high-SNR capacity at $P_{SC}$, and provide lower and upper bounds for the sensing CRB at $P_{CS}$. We show that these two points can be achieved by the conventional Gaussian signaling and a novel strategy relying on the uniform distribution over the Stiefel manifold, respectively. Based on the above-mentioned analysis, we provide an outer bound and various inner bounds for the achievable CRB-rate regions. Our main results reveal a two-fold tradeoff in ISAC systems, consisting of the subspace tradeoff (ST) and the deterministic-random tradeoff (DRT) that depend on the resource allocation and data modulation schemes employed for S&C, respectively.

Motivation & Objective

• To establish a theoretical foundation for the performance tradeoff between sensing and communication in ISAC systems.
• To model a unified ISAC waveform that supports both communication and sensing with known reference signals.
• To characterize the fundamental limits of ISAC performance using the Cramér-Rao bound (CRB) and mutual information (rate) as metrics.
• To identify the two extreme operating points of the CRB-rate region: $P_{\rm SC}$ and $P_{\rm CS}$, representing the best tradeoff between rate and sensing accuracy.
• To reveal two intrinsic tradeoffs: subspace tradeoff (ST) and deterministic-random tradeoff (DRT), governed by resource and modulation design.

Proposed method

• Proposes a CRB-rate region framework to jointly analyze sensing and communication performance in ISAC systems under vector Gaussian channels.
• Treats the ISAC waveform as a random but known nuisance parameter in the sensing model, enabling a Miller-Chang type CRB for sensing estimation.
• Derives the high-SNR communication capacity at $P_{\rm SC}$ and provides lower and upper bounds for the sensing CRB at $P_{\rm CS}$.
• Identifies Gaussian signaling as optimal for achieving $P_{\rm SC}$, and a novel strategy based on uniform distribution over the Stiefel manifold (semi-unitary matrices) for achieving $P_{\rm CS}$.
• Establishes outer and inner bounds for the achievable CRB-rate region using time-sharing and convex optimization techniques.
• Analyzes the tradeoffs through Lagrangian duality and asymptotic analysis, showing that the semi-unitary inner bound outperforms the pentagon inner bound due to superior slope behavior at corner points.

Experimental results

Research questions

• RQ1 What is the fundamental tradeoff between communication rate and sensing accuracy in ISAC systems over Gaussian channels?
• RQ2 How can the performance limits of ISAC be characterized when both sensing and communication are performed via a single waveform?
• RQ3 What signaling strategies achieve the optimal performance at the two corner points of the CRB-rate region: $P_{\rm SC}$ and $P_{\rm CS}$?
• RQ4 What are the intrinsic tradeoffs governing ISAC waveform design, and how do they depend on resource allocation and modulation schemes?
• RQ5 Can tighter inner bounds be derived for the CRB-rate region by combining semi-unitary and Gaussian signaling strategies?

Key findings

• The high-SNR communication capacity at $P_{\rm SC}$ is characterized and shown to be achievable via conventional Gaussian signaling.
• The sensing CRB at $P_{\rm CS}$ is bounded by lower and upper expressions, with the lower bound derived from the semi-unitary waveform strategy.
• The point $P_{\rm CS}$ is achieved by a novel waveform design based on uniform distribution over the Stiefel manifold, which outperforms standard schemes in sensing accuracy.
• The two corner points $P_{\rm SC}$ and $P_{\rm CS}$ are shown to be achievable via distinct signaling strategies, revealing a fundamental duality in ISAC waveform design.
• The outer bound of the CRB-rate region is derived, and it is shown that the semi-unitary–Gaussian inner bound strictly dominates the pentagon inner bound due to superior slope behavior at the corner points.
• The analysis reveals a two-fold tradeoff: subspace tradeoff (ST) related to resource allocation and deterministic-random tradeoff (DRT) tied to modulation and waveform randomness.