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.

中文翻译：

---

双Nakagami衰落信道下大型智能表面的误码率

在这项工作中，我们研究了基站，一组称为大智能表面（LIS）的智能反射元件和一个单天线用户之间信道衰落的概率分布函数。我们假设两个衰落信道，即基站和LIS之间的信道，以及LIS和单个用户之间的信道都是Nakagami- $ m $ 分散式。此外，我们得出精确 考虑正交幅度（ $ M $ -QAM）和二进制相移键控（BPSK）调制（当LIS元素数量增加时， $ n $ ，等于2和3。我们假设LIS可以执行相位调整，但是存在一个由冯·米塞斯分布建模的残留相位误差。基于中心极限定理，并考虑大量反射元素，我们还提供了误码率的精确近似值和上限。通过几个蒙特卡洛模拟，我们证明了所有导出的表达式都与模拟结果完全匹配。