Given the high spectral efficiency, holographic multiple-input multiple-output (MIMO) technology holds promise for enhancing both sensing and communication capabilities. However, accurately characterizing its performance poses a challenge due to the spatial correlation induced by densely spaced antennas. In this paper, a holographic MIMO (HMIMO) based integrated sensing and communications (ISAC) framework is proposed for both downlink and uplink scenarios. The spacial correlation is incorporated in the communication channel modeling, while an accurate spherical wave-based model is utilized to characterize sensing link. By considering both instantaneous channel state information (CSI) and statistical CSI, closed-form expressions are derived for sensing rates (SRs), communication rates (CRs), and outage probabilities under different ISAC designs to investigate the theoretical performance limits of the proposed HISAC framework. Further insights are gained by examining high signal-to-noise ratio slopes and diversity orders. Specifically, i) for the downlink case, a sensing-centric (S-C) design and a communications-centric (C-C) design are investigated based on different beamforming strategies, and a Pareto optimal design is proposed to characterize the attainable SR-CR region; ii) for the uplink case, the S-C design and the C-C design are distinguished by the interference cancellation order of the communication signal and the sensing signal, and the rate region is obtained through a time-sharing strategy. Numerical results reveal that HMIMO based ISAC (HISAC) systems outperform both conventional MIMO based ISAC systems and HMIMO based frequency-division sensing and communications systems, underscoring the superior performance of HISAC.

翻译：鉴于全息多输入多输出（MIMO）技术具有高频谱效率，有望增强感知和通信能力。然而，由于天线密集排列引起的空间相关性，精确表征其性能构成挑战。本文针对下行和上行场景，提出了基于全息MIMO（HMIMO）的集成感知与通信（ISAC）框架。在通信信道建模中引入空间相关性，并采用精确的球面波模型表征感知链路。通过同时考虑瞬时信道状态信息（CSI）和统计CSI，推导出不同ISAC设计下感知速率、通信速率和中断概率的闭式表达式，以探究所提HISAC框架的理论性能极限。通过分析高信噪比斜率和分集阶数进一步获得洞察。具体而言：i) 在下行场景中，基于不同波束赋形策略研究了感知中心设计与通信中心设计，并提出了帕累托最优设计以表征可达的SR-CR区域；ii) 在上行场景中，通过通信信号与感知信号的干扰消除顺序区分S-C设计与C-C设计，并采用时分共享策略获取速率区域。数值结果表明，基于HMIMO的ISAC系统不仅优于传统MIMO ISAC系统，也优于基于HMIMO的频分感知与通信系统，凸显了HISAC的优越性能。