A novel Gamma-distributed geometric constellation design framework for integrated sensing and communication (ISAC) is proposed in this paper. In this framework, constellation points are modeled as samples drawn from a parameterized two-dimensional distribution, with a Gamma distribution for the amplitude and a uniform distribution for the phase. End-task performance metrics, namely, the probability of detection for sensing and mutual information for communication, are used as objective functions of the optimization problem, and the problem is solved via particle swarm optimization. We further derive analytical performance bounds for the proposed design, including the union bound on the symbol error rate for communication and the Cramer--Rao bound for sensing parameter estimation. The proposed method is compared with constellations obtained via end-to-end neural network design, demonstrating competitive performance while requiring significantly fewer parameters and no training data. Moreover, the proposed geometric constellation is more compatible with conventional system architectures than probabilistic or neural network-based designs.

翻译：本文提出了一种新颖的Gamma分布几何星座设计框架，用于集成感知与通信（ISAC）。在该框架中，星座点被建模为从参数化二维分布中抽取的样本，其中幅度服从Gamma分布，相位服从均匀分布。以任务终端性能指标——感知检测概率与通信互信息——作为优化目标函数，并采用粒子群优化算法求解。我们进一步推导了所提设计的分析性能界，包括通信符号错误率的联合界和感知参数估计的克拉美-罗界。通过与端到端神经网络设计的星座进行对比，该方法在保持竞争性能的同时，所需参数显著更少且无需训练数据。此外，相较于基于概率或神经网络的设计，所提几何星座与传统系统架构具有更好的兼容性。