Performance Analysis of Active RIS and Passive RIS-Aided MISO Systems Over Nakagami-$m$ Fading Channel With Imperfect CSI

This paper investigates the performance of active and passive reconfigurable intelligent surface (RIS)-aided multiple-input single-output systems with imperfect channel state information and discrete phase-shift RIS alignment over a generalized Nakagami-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fading channel. Capitalizing on both a direct link and the assistance of an RIS, a source employs a maximum-ratio transmission approach to enhance the channel gains received by the destination. Approximate closed-form expressions for users' outage probability (OP) and ergodic capacity (EC) are respectively derived to capture the main system characteristics and the performance boundaries at high transmit power regimes, thereby providing useful insights involving the diversity order, coding gain, and ergodic slope. Several extensive simulations are presented and reveal some remarkable points: First, active RISs always bring higher EC than passive RISs and have outstanding outage performance in lower and moderate transmit power regimes. Second, active RIS-based systems can achieve a significantly improved performance by either reducing thermal noise or increasing the amplitude gain. Thirdly, the use of a large number of passive RIS elements yields a significant OP improvement when compared to active RIS design. Finally, increasing the number of antennas can achieve the users' OP and EC enhancement for both active and passive RIS-based systems.