  Intelligent reflecting surface (IRS) is envisioned as a promising hardware
solution to hardware cost and energy consumption in the fifth-generation (5G)
mobile communication network. It exhibits great advantages in enhancing data
transmission, but may suffer from performance degradation caused by inherent
hardware impairment (HWI). For analysing the achievable rate (ACR) and
optimizing the phase shifts in the IRS-aided wireless communication system with
HWI, we consider that the HWI appears at both the IRS and the signal
transceivers. On this foundation, first, we derive the closed-form expression
of the average ACR and the IRS utility. Then, we formulate optimization
problems to optimize the IRS phase shifts by maximizing the signal-to-noise
ratio (SNR) at the receiver side, and obtain the solution by transforming
non-convex problems into semidefinite programming (SDP) problems. Subsequently,
we compare the IRS with the conventional decode-and-forward (DF) relay in terms
of the ACR and the utility. Finally, we carry out simulations to verify the
theoretical analysis, and evaluate the impact of the channel estimation errors
and residual phase noises on the optimization performance. Our results reveal
that the HWI reduces the ACR and the IRS utility, and begets more serious
performance degradation with more reflecting elements. Although the HWI has an
impact on the IRS, it still leaves opportunities for the IRS to surpass the
conventional DF relay, when the number of reflecting elements is large enough
or the transmitting power is sufficiently high.
