Performance analysis for IRS-aided communication systems with composite fading/shadowing direct link and discrete phase shifts

Intelligent reflecting surface (IRS) is an emerging technology and serves as a key component of any smart radio environment. In this article, we consider an IRS that assists communication of a direct link between a single-antenna transmitter and a receiver. It is assumed that a direct link experiences composite fading/shadowing and is modeled by Generalized-K distribution. Moreover, IRS has line-of-sight (LoS) paths, therefore, Rician distribution is used to characterize the fading for these paths. We also consider phase errors that exist due to discrete number of phase shifts. We derive an approximation for the end-to-end signal-to-noise ratio (SNR) which shows that an amplitude of the direct link is increased by a positive offset because of the presence of IRS. Based on this SNR approximation, a new statistical framework that includes cumulative distribution function (CDF), probability density function (PDF), and moment generating function (MGF) is developed. Leveraging this statistical framework, we derive new and accurate closed-form approximations for the outage probability, average error probability, ergodic capacity and generalized moments. It is shown that the considered IRS-aided system (IAS) achieves much better performance even with a few numbers of phase shifts as compared to other baseline systems. Simulations are also provided which verify the tightness of our derived approximations.