How Much do Hardware Imperfections Affect the Performance of Reconfigurable Intelligent Surface-Assisted Systems?

In the present work, we investigate the impact of transceiver hardware imperfection on reconfigurable intelligent surface (RIS)-assisted wireless systems. In this direction, first, we present a general model that accommodates the impact of the transmitter (TX) and receiver (RX) radio frequency impairments. Next, we derive novel closed-form expressions for the instantaneous end-to-end signal-to-noise-plus-distortion-ratio (SNDR). Building upon these expressions, we extract an exact closed-form expression for the system's outage probability, which allows us not only to quantify RIS-assisted systems' outage performance but also reveals that the maximum allowed spectral efficiency of the transmission scheme is limited by the levels of the transceiver hardware imperfection. Likewise, a diversity analysis is provided. Moreover, in order to characterize the capacity of RIS-assisted systems, we report a new upper-bound for the ergodic capacity, which takes into account the number of the RIS's reflective units (RUs), the level of TX and RX hardware imperfection, as well as the transmission signal-to-noise-ratio (SNR). Finally, two insightful ergodic capacity ceilings are extracted for the high-SNR and high-RUs regimes. Our results highlight the importance of accurately modeling the transceiver hardware imperfection and reveals that they significantly limit the RIS-assisted wireless system performance.