  This paper studies the fair transmission design for an intelligent reflecting
surface (IRS) aided rate-splitting multiple access (RSMA). IRS is used to
establish a good signal propagation environment and enhance the RSMA
transmission performance. The fair rate adaption problem is constructed as a
max-min optimization problem. To solve the optimization problem, we adopt an
alternative optimization (AO) algorithm to optimize the power allocation,
beamforming, and decoding order, respectively. A generalized power iteration
(GPI) method is proposed to optimize the receive beamforming, which can improve
the minimum rate of devices and reduce the optimization complexity. At the base
station (BS), a successive group decoding (SGD) algorithm is proposed to tackle
the uplink signal estimation, which trades off the fairness and complexity of
decoding. At the same time, we also consider robust communication with
imperfect channel state information at the transmitter (CSIT), which studies
robust optimization by using lower bound expressions on the expected data
rates. Extensive numerical results show that the proposed optimization
algorithm can significantly improve the performance of fairness. It also
provides reliable results for uplink communication with imperfect CSIT.
