Large intelligent surfaces (LISs) promise not only to improve the signal-to-noise ratio and spectral efficiency, but also to reduce the energy consumption during the transmission. We consider a base station equipped with an antenna array using the maximum ratio transmission (MRT) and a large reflector array sending signals to a single user. Each subchannel is affected by the Rayleigh flat fading, and the reflecting elements perform imperfect phase correction, which introduces a von Mises distributed phase error. Based on the central limit theorem (CLT), we conclude that the overall channel has an equivalent Gamma fading whose parameters are derived from the moments of the channel fading between the antenna array and LIS and also from the LIS to the single user. Assuming that the equivalent channel can be modeled as a Gamma distribution, we propose very accurate closed-form expressions for the bit error probability and a very tight upper bound. For the case where the LIS is not able to perform perfect phase cancellation, that is under phase errors, it is possible to analyze the system performance considering the analytical approximations and the simulated results obtained using the well-known Monte Carlo method. The analytical expressions for the parameters of the Gamma distribution are very difficult to obtain due to the complexity of the nonlinear transformations of random variables with non-zero mean and correlated terms. Even with perfect phase cancellation, all the fading coefficients are complex due to the link between the user and the base station, which is not neglected in this paper.

中文翻译：

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通过大规模MIMO瑞利衰落信道通信的智能曲面

大型智能表面（LIS）不仅可以提高信噪比和频谱效率，而且还可以减少传输过程中的能耗。我们考虑一个配备有使用最大比率传输（MRT）的天线阵列和向单个用户发送信号的大型反射器阵列的基站。每个子信道均受瑞利平坦衰落影响，并且反射元件执行的相位校正不完美，从而引入了冯·米塞斯（von Mises）分布相位误差。基于中心极限定理（CLT），我们得出结论，整个信道具有等效的Gamma衰落，其参数是从天线阵列和LIS之间的信道衰落的时刻以及从LIS到单个用户的推导得出的。假设可以将等效通道建模为Gamma分布，我们针对误码率和非常严格的上限提出了非常精确的闭式表达式。对于LIS无法执行完美的相位消除的情况，即在相位误差下，可以考虑使用著名的蒙特卡洛方法获得的解析近似值和仿真结果来分析系统性能。由于具有非零均值和相关项的随机变量的非线性变换非常复杂，因此很难获得Gamma分布参数的解析表达式。即使具有完美的相位消除，由于用户与基站之间的链接，所有的衰落系数都很复杂，这在本文中并没有忽略。