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In this article, we combine two new technologies [full-duplex (FD) transmission and intelligent reflecting surface (IRS)] in a wireless communication system for investigation. Specifically, we evaluate the performance of an IRS-aided bidirectional FD communication system in a practical scenario where imperfect self-interference (SI) cancellation and hardware impairments (HIs) are taken into consideration. We successfully derive the closed-form expressions of ergodic capacity (EC) and symbol error rate (SER) of the IRS-aided FD-HI system over Rayleigh fading channels. We confirm the correctness of the derived expressions via Monte-Carlo simulations. To clarify the effects of residual SI and HIs, we compare the performance of the IRS-aided FD-HI system with that of the IRS-aided FD-ideal hardware (ID), half-duplex (HD)-HI, and HD-ID systems. Numerical results clarify a strong impact of residual SI and HIs on the …