  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.
