On the Fundamental Tradeoff of Integrated Sensing and Communications Under Gaussian Channels

• Published in: IEEE transactions on information theory Vol. 69; no. 9; pp. 5723 - 5751
• Main Authors: Xiong, Yifeng, Liu, Fan, Cui, Yuanhao, Yuan, Weijie, Han, Tony Xiao, Caire, Giuseppe
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Channels; Communication; Covariance matrices; Cramer-Rao bounds; CRB-rate region; deterministic-random tradeoff; Gaussian channels; Integrated sensing and communication; Manifolds (mathematics); Mathematical models; Radar equipment; Receivers; Resource allocation; Sensors; Signaling; subspace tradeoff; Symbols; Task analysis; Tradeoffs; Upper bounds; Waveforms; Wireless networks
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2023.3284449

Integrated Sensing and Communication (ISAC) is recognized as a promising technology for the next-generation wireless networks, which provides significant performance gains over individual sensing and communications (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 (P2P) ISAC model under vector Gaussian channels, and propose to use the Cramér-Rao bound (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 transmitter (Tx), which simultaneously communicates information to a communication receiver (Rx) and senses targets with the help of 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. In this context, we treat the ISAC waveform as a random but known nuisance parameter in the sensing signal model, and define a Miller-Chang type CRB for the analysis of the sensing performance. As the main contribution of this paper, we characterize the S&C performance at the two corner points of the CRB-rate region, namely, <inline-formula> <tex-math notation="LaTeX">P_{\mathrm{ SC}} </tex-math></inline-formula> indicating the maximum achievable communication rate constrained by the minimum CRB, and <inline-formula> <tex-math notation="LaTeX">P_{\mathrm{ CS}} </tex-math></inline-formula> indicating the minimum achievable CRB constrained by the maximum communication rate. In particular, we derive the high-SNR communication capacity at <inline-formula> <tex-math notation="LaTeX">P_{\mathrm{ SC}} </tex-math></inline-formula>, and provide lower and upper bounds for the sensing CRB at <inline-formula> <tex-math notation="LaTeX">P_{\mathrm{ CS}} </tex-math></inline-formula>. We show that these two points can be achieved by the conventional Gaussian signalling and a novel strategy relying on the uniform distribution over the set of semi-unitary matrices, i.e., 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. Within this framework, we examine the state-of-the-art ISAC signalling strategies and study a number of illustrative examples, which are validated through numerical simulations.