Bit Error Probability for Large Intelligent Surfaces Under Double-Nakagami Fading Channels

In this work, we investigate the probability distribution function of the channel fading between a base station, an array of intelligent reflecting elements, known as large intelligent surfaces (LIS), and a single-antenna user. We assume that both fading channels, i.e., the channel between the base station and the LIS, and the channel between the LIS and the single user are Nakagami-m distributed. Additionally, we derive the exact bit error probability considering quadrature amplitude (M-QAM) and binary phase-shift keying (BPSK) modulations when the number of LIS elements, n, is equal to 2 and 3. We assume that the LIS can perform phase adjustment, but there is a residual phase error modeled by a Von Mises distribution. Based on the central limit theorem, and considering a large number of reflecting elements, we also present an accurate approximation and upper bounds for the bit error rate. Through several Monte Carlo simulations, we demonstrate that all derived expressions perfectly match the simulated results.