  We consider a cognitive radio-based Internet-of-Things (CR-IoT) network
consisting of one primary IoT (PIoT) system and one secondary IoT (SIoT)
system. The IoT devices of both the PIoT and the SIoT respectively monitor one
physical process and send randomly generated status updates to their associated
access points (APs). The timeliness of the status updates is important as the
systems are interested in the latest condition (e.g., temperature, speed and
position) of the IoT device. In this context, two natural questions arise: (1)
How to characterize the timeliness of the status updates in CR-IoT systems? (2)
Which scheme, overlay or underlay, is better in terms of the timeliness of the
status updates. To answer these two questions, we adopt a new performance
metric, named the age of information (AoI). We analyze the average peak AoI of
the PIoT and the SIoT for overlay and underlay schemes, respectively. Simple
asymptotic expressions of the average peak AoI are also derived when the PIoT
operates at high signal-to-noise ratio (SNR). Based on the asymptotic
expressions, we characterize a critical generation rate of the PIoT system,
which can determine the superiority of overlay and underlay schemes in terms of
the average peak AoI of the SIoT. Numerical results validate the theoretical
analysis and uncover that the overlay and underlay schemes can outperform each
other in terms of the average peak AoI of the SIoT for different system setups.
