  In this paper, an intelligent reflecting surface (IRS)-aided two-way
decode-and-forward (DF) relay wireless network is considered, where two users
exchange information via IRS and DF relay. To enhance the sum rate performance,
three power allocation (PA) strategies are proposed. Firstly, a method of
maximizing sum rate (Max-SR) is proposed to jointly optimize the PA factors of
user U1, user U2 and relay station (RS). To further improve the sum rate
performance, two high-performance schemes, namely maximizing minimum sum rate
(Max-Min-SR) and maximizing sum rate with rate constraint (Max-SR-RC), are
presented. Simulation results show that the proposed three methods outperform
the equal power allocation (EPA) method in terms of sum rate performance. In
particular, the highest performance gain achieved by Max-SR-RC method is up to
45.2% over EPA. Furthermore, it is verified that the total power and random
shadow variable X{\sigma} have a substantial impact on the sum rate
performance.
