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. INDEX TERMS Bit error rate, large intelligent surfaces, massive MIMO, Nakagami-m fading, von Mises circular distribution.

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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.

Despite many studies already published on large intelligent surfaces (LIS), there are still some gaps in mathematical models in the face of possible scenarios. In this work, we evaluate the performance of a single-input single-output (SISO) system in which an LIS acts as a controllable scatterer. We consider that the direct link between the transmitting and receiving devices is non-existent due to a blockage. Quantization phase errors at the LIS are considered since a 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 schemes. We assume a more comprehensive scenario in which b bits are dedicated to the phase adjustment of the LIS' elements. Based on Monte Carlo simulations, we prove the excellent accuracy of our approach and investigate the behavior of the power scaling law and the power required to reach a specific capacity, depending on the number of reflecting elements. We show that an LIS with approximately fifty elements and four dedicated bits for phase quantization outperforms the conventional system without LIS.INDEX TERMS Large Intelligent Surface, outage probability, quantization phase errors, spectral efficiency, symbol error rate.

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.