  In this letter, we study the outage probability of intelligent reflecting
surface (IRS) assisted full duplex two-way communication systems, which
characterizes the performance of overcoming the transmitted data loss caused by
long deep fades. To this end, we first derive the probability distribution of
the cascaded end-to-end equivalent channel with an arbitrarily given IRS
beamformer. Our analysis shows that deriving such probability distribution in
the considered case is more challenging than the case with the phase-matched
IRS beamformer. Then, with the derived probability distribution of the
equivalent channel, we obtain the closed-form expression of the outage
probability performance. It theoretically shows that the reflecting element
number has a conspicuous effect on the improvement of the system reliability.
Extensive numerical results verify the correctness of the derived results and
confirm the superiority of the considered IRS assisted two-way communication
system comparing to the one-way counterpart.
