Age of Incorrect Information in Semantic Communications for NOMA Aided XR Applications

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 article, 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.