Large Intelligent Surfaces Communicating Through Massive Mimo Rayleigh Fading Channels

Large intelligent surfaces (LIS) promises 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 non-perfect 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 be obtained 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 that is not neglected in this paper.