Symbol error probability of mmWave communications with transmit antenna selection and RISs under the impacts of hardware impairments

Summary In practice, hardware impairments (HIs) often exist in wireless devices, especially in low‐cost device systems. However, previous reports usually ignored HIs due to the computational complexity in mathematical derivations, particularly in millimeter‐wave (mmWave) communications. This article proposes the usage of transmit antenna selection (TAS) and multiple reconfigurable intelligent surfaces (RISs) to address HIs in mmWave communications. In particular, TAS is utilized at the source to increase the received signal power at the destination and reduce the effects of HIs. Multiple channel gains from RISs are combined with the classical source‐destination channel gain at the destination. The symbol error probability (SEP) expression of the mmWave communications with TAS and RISs under the effects of HIs (shortened as the TAS‐RISs‐HIs communications) is formulated over Nakagami‐ channels and verified through Monte Carlo simulations. The effects of HIs on the SEP of TAS‐RISs‐HIs communications are demonstrated through numerical illustrations. Specifically, the SEP of the TAS‐RISs‐HIs communications is significantly higher than the SEP of the ideal hardware communications with TAS and RISs, especially in the high transmit power regime. As a result, ignoring HIs when evaluating the SEP of the mmWave communications can result in some inappropriate conclusions. Moreover, the joint and separate advantages of TAS and RISs are thoroughly analyzed when comparing the SEPs in the cases with and without TAS, with and without RISs.