  In this paper, we investigate an amplify-and-forward (AF) based two-way
cooperative status update system, where two sources aim to exchange status
updates with each other as timely as possible with the help of a relay.
Specifically, the relay receives the sum signal from the two sources in one
time slot, and then amplifies and forwards the received signal to both the
sources in the next time slot. We adopt a recently proposed concept, the age of
information (AoI), to characterize the timeliness of the status updates.
Assuming that the two sources are able to generate status updates at the
beginning of each time slot (i.e., generate-at-will model), we derive a
closed-form expression of the expected weighted sum AoI of the considered
system. We further minimize the expected weighted sum AoI by optimizing the
transmission power at each node under the peak power constraints. Simulation
results corroborate the correctness of our theoretical analysis.
