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.
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