Large Intelligent Surfaces With Discrete Set of Phase-Shifts Communicating Through Double-Rayleigh Fading Channels

It is known that the Central Limit Theorem (CLT) is not always the most appropriate tool for deriving closed-form expressions. We evaluate a Single-Input Single-Output (SISO) system performance in which the Large Intelligent Surface (LIS) acts as a scatterer. The direct link between the transmitting and receiving devices is negligible. Quantization phase errors are considered since the high precision configuration of the reflection phases is not always feasible. We derive exact closed-form expressions for the spectral efficiencies, outage probabilities, and average symbol error rate (SER) of different modulations. We assume a more comprehensive scenario in which $b$ bits are dedicated to the LIS elements' phase adjustment. From Monte Carlo simulations, we prove the excellent accuracy of our approach and investigate the behavior of power scaling law and power required to reach a specific capacity, depending on the number of reflecting elements. We show that the LIS with approximately fifty elements and four dedicated bits for phase quantization outperforms the conventional system performance without LIS.