In the low-altitude wireless networks, the simultaneous sensing data acquisition and sharing (SDAS) through an ISAC signaling strategy becomes a typical application scenario. In this paper, we mainly investigate three primary aspects of the SDAS system, namely, the information-theoretic framework, the optimal distribution of channel input, and the optimal waveform design for Gaussian signaling. First, we establish the information-theoretic framework and develop a modified source-channel separation theorem (MSST) tailored for the SDAS systems. The proposed MSST elucidates the relationship between achievable distortion, coding rate, and communication channel capacity in cases where the distortion metric is separable for sensing and communication (S\&C) processes. Second, we present an optimal channel input design for dual-functional signaling, which aims to minimize SDAS distortion under the constraints of the MSST and resource budget. We then conceive a two-step Blahut-Arimoto (BA)-based optimal search algorithm to numerically solve the functional optimization problem. Third, to provide practical design insights, we further propose an optimal waveform design for Gaussian signaling in multi-input multi-output (MIMO) SDAS systems. The associated covariance matrix optimization problem is addressed using a successive convex approximation (SCA)-based waveform design algorithm. Finally, we provide numerical simulation results to demonstrate the effectiveness of the proposed algorithms, which characterize the unique performance tradeoff between S&C processes.

翻译：在低空无线网络中，通过通感一体化（ISAC）信令策略实现的同时感知数据获取与共享（SDAS）成为典型应用场景。本文主要研究SDAS系统的三个核心问题：信息论框架、信道输入的最优分布，以及高斯信令下的最优波形设计。首先，我们建立信息论框架，并提出适用于SDAS系统的改进源信道分离定理（MSST）。该定理在感知与通信（S&C）过程的失真度量可分离的情况下，阐明了可达失真、编码速率与通信信道容量之间的关系。其次，针对双功能信令设计最优信道输入，旨在满足MSST约束与资源预算的条件下最小化SDAS失真。我们提出基于两步Blahut-Arimoto（BA）的最优搜索算法，以数值求解该泛函优化问题。第三，为提供实用设计依据，我们进一步提出多输入多输出（MIMO）SDAS系统中高斯信令的最优波形设计。相关协方差矩阵优化问题通过基于逐次凸近似（SCA）的波形设计算法求解。最后，通过数值仿真验证所提算法的有效性，并揭示S&C过程间独特的性能权衡特性。