  This paper studies the application of cognitive radio inspired non-orthogonal
multiple access (CR-NOMA) to reduce age of information (AoI) for uplink
transmission. In particular, a time division multiple access (TDMA) based
legacy network is considered, where each user is allocated with a dedicated
time slot to transmit its status update information. The CR-NOMA is implemented
as an add-on to the TDMA legacy network, which enables each user to have more
opportunities to transmit by sharing other user's time slots. A rigorous
analytical framework is developed to obtain the expressions for AoIs achieved
by CR-NOMA with and without re-transmission, by taking the randomness of the
status update generating process into consideration. Numerical results are
presented to verify the accuracy of the developed analysis. It is shown that
the AoI can be significantly reduced by applying CR-NOMA compared to TDMA.
Moreover, the use of re-transmission is helpful to reduce AoI, especially when
the status arrival rate is low.
