Ricardo Coelho Ferreira

Bio: Ricardo Coelho Ferreira is an academic researcher from State University of Campinas. The author has contributed to research in topics: Fading & Nakagami distribution. The author has an hindex of 3, co-authored 4 publications receiving 32 citations.

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

Abstract: 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.

Large Intelligent Surfaces With Discrete Set of Phase-Shifts Communicating Through Double-Rayleigh Fading Channels

Abstract: 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.

Large Intelligent Surfaces Communicating Through Massive MIMO Rayleigh Fading Channels.

Abstract: 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.

Secrecy Analysis and Error Probability of LIS-Aided Communication Systems under Nakagami-m Fading.

Abstract: Large intelligent surfaces (LIS) are a new trend to achieve higher spectral efficiency and signal-to-noise ratio in mobile communications. For this reason, this paper proposes metrics to analyze the performance of systems with multiple antennas aided by LIS and derive the spectral efficiency, secrecy outage probability, and bit error probability in an environment with Nakagami-m distributed fading. In addition to an eavesdropper, there is a single-antenna user, an array of antennas at the transmitter side and the possibility of a direct link between transmitter and receiver. This study assumes that the LIS performs non-ideal phase cancellation leading to a residual phase error that follows a Von Mises distribution, and shows that the resulting channel can be accurately approximated by a Gamma distributed SNR whose parameters are analytically derived. From these formulas, it is possible to evaluate the effect of the strength of the line-of-sight link by varying the Nakagami parameter, m.

On the Performance Analysis of RIS-Empowered Communications Over Nakagami- m Fading

Abstract: In this letter, we study the performance of wireless communications empowered by Reconfigurable Intelligent Surface (RISs) over Nakagami- $m$ fading channels. We consider two phase configuration designs for the RIS, one random and another one based on coherent phase shifting. For both phase configuration cases, we present single-integral expressions for the outage probability and the bit error rate of binary modulation schemes, which can be efficiently evaluated numerically. In addition, we propose accurate closed-form approximations for the ergodic capacity of the considered system. For all considered metrics, we have also derived simple analytical expressions that become tight for large numbers of RIS reflecting elements. Numerically evaluated results compared with Monte Carlo simulations are presented in order to verify the correctness of the proposed analysis and showcase the impact of various system settings.

Accurate Performance Analysis of Reconfigurable Intelligent Surfaces Over Rician Fading Channels

Abstract: We consider in this letter the performance of reconfigurable intelligent surface (RIS)-aided wireless networks over Rician fading channels. We derive new accurate closed-form approximations for several performance measures, including the outage probability, average symbol error probability (ASEP), and the channel capacity. Additionally, to get more insights into the system behavior, we derive asymptotic expression for the outage probability at high signal-to-noise ratio (SNR) values, and provide closed-form expressions for the system diversity order and coding gain. Findings show that the considered RIS scenario can provide a diversity order of $\frac {a+1}{2}$ , where ${a}$ is a function of the Rician channel ${K}$ -factor, Rician channel scale parameter $\boldsymbol{\Omega }$ and the number of reflecting elements ${N}$ .

Performance Analysis of RIS-Aided Systems With Practical Phase Shift and Amplitude Response

Abstract: Reconfigurable intelligent surfaces (RISs) have drawn significant attention due to their capability of controlling the radio environment and improving the system performance. In this paper, we study the performance of an RIS-assisted single-input single-output system over Rayleigh fading channels. Differently from previous works that assume a constant reflection amplitude, we consider a model that accounts for the intertwinement between the amplitude and phase response, and derive closed-form expressions for the outage probability and ergodic capacity. Moreover, we obtain simplified expressions under the assumption of a large number of reflecting elements and provide tight upper and lower bounds for the ergodic capacity. Finally, the analytical results are verified by using Monte Carlo simulations.

Average Rate and Error Probability Analysis in Short Packet Communications over RIS-aided URLLC Systems

Abstract: In this paper, the average achievable rate and error probability of a reconfigurable intelligent surface (RIS) aided systems is investigated for the finite blocklength (FBL) regime. The performance loss due to the presence of phase errors arising from limited quantization levels as well as hardware impairments at the RIS elements is also discussed. First, the composite channel containing the direct path plus the product of reflected channels through the RIS is characterized. Then, the distribution of the received signal-to-noise ratio (SNR) is matched to a Gamma random variable whose parameters depend on the total number of RIS elements, phase errors and the channels' path loss. Next, by considering the FBL regime, the achievable rate expression and error probability are identified and the corresponding average rate and average error probability are elaborated based on the proposed SNR distribution. Furthermore, the impact of the presence of phase error due to either limited quantization levels or hardware impairments on the average rate and error probability is discussed. The numerical results show that Monte Carlo simulations conform to matched Gamma distribution to received SNR for sufficiently large number of RIS elements. In addition, the system reliability indicated by the tightness of the SNR distribution increases when RIS is leveraged particularly when only the reflected channel exists. This highlights the advantages of RIS-aided communications for ultra-reliable and low-latency systems. The difference between Shannon capacity and achievable rate in FBL regime is also discussed. Additionally, the required number of RIS elements to achieve a desired error probability in the FBL regime will be significantly reduced when the phase shifts are performed without error.

Exact Coverage Analysis of Intelligent Reflecting Surfaces With Nakagami- M Channels

Abstract: Intelligent Reflecting Surfaces (IRS) are a promising solution to enhance the coverage of future wireless networks by tuning low-cost passive reflecting elements (referred to as metasurfaces ), thereby constructing a favorable wireless propagation environment. Different from prior works, which assume Rayleigh fading channels and do not consider the direct link between a base station and a user, this article develops a framework based on moment generation functions (MGF) to characterize the coverage probability of a user in an IRS-aided wireless systems with generic Nakagami-m fading channels in the presence of direct links. In addition, we demonstrate that the proposed framework is tractable for both finite and asymptotically large values of the metasurfaces. Furthermore, we derive the channel hardening factor as a function of the shape factor of Nakagami-m fading channel and the number of IRS elements. Finally, we derive a closed-form expression to calculate the maximum coverage range of the IRS for given network parameters. Numerical results obtained from Monte-Carlo simulations validate the derived analytical results.