As an evolving successor to the mobile Internet, the extended reality (XR) devices can generate a fully digital immersive environment similar to the real world, integrating integrating virtual and real-world elements. However, in addition to the difficulties encountered in traditional communications, there emerge a range of new challenges such as ultra-massive access, real-time synchronization as well as unprecedented amount of multi-modal data transmission and processing. To address these challenges, semantic communications might be harnessed in support of XR applications, whereas it lacks a practical and effective performance metric. For broadening a new path for evaluating semantic communications, in this paper, we construct a multi-user uplink non-orthogonal multiple access (NOMA) system to analyze its transmission performance by harnessing a novel metric called age of incorrect information (AoII). First, we derive the average semantic similarity of all the users based on DeepSC and obtain the closed-form expressions for the packets' age of information (AoI) relying on queue theory. Besides, we formulate a non-convex optimization problem for the proposed AoII which combines both error-and AoI-based performance under the constraints of semantic rate, transmit power and status update rate. Finally, in order to solve the problem, we apply an exact linear search based algorithm for finding the optimal policy. Simulation results show that the AoII metric can beneficially evaluate both the error- and AoI-based transmission performance simultaneously.

翻译：作为移动互联网的演进替代，扩展现实设备能够生成与真实世界相似的全数字沉浸式环境，融合虚拟与真实世界元素。然而，除传统通信中遇到的困难外，还涌现出超大规模接入、实时同步以及前所未有的大量多模态数据传输与处理等一系列新挑战。为应对这些挑战，可利用语义通信支持扩展现实应用，但缺乏实用且有效的性能指标。为开辟评估语义通信的新路径，本文构建了一个多用户上行非正交多址接入系统，通过采用称为错误信息年龄的新颖指标分析其传输性能。首先，基于深度语义通信模型推导所有用户的平均语义相似度，并利用排队论获得数据包信息年龄的闭式表达式。此外，针对所提出的结合误差与基于信息年龄性能的错误信息年龄指标，在语义速率、发射功率和状态更新速率约束下，建立了一个非凸优化问题。最后，为求解该问题，应用基于精确线性搜索的算法寻找最优策略。仿真结果表明，错误信息年龄指标能同时有效评估基于误差和基于信息年龄的传输性能。