Bit Error Probability for Large Intelligent Surfaces Under Double-Nakagami Fading Channels
25 May 2020-Vol. 1, pp 750-759
TL;DR: This work presents an accurate approximation and upper bounds for the bit error rate of 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.
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.
Citations
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TL;DR: This letter studies the performance of wireless communications empowered by Reconfigurable Intelligent Surface (RISs) over Nakagami- $m$ fading channels and proposes accurate closed-form approximations for the ergodic capacity of the considered system.
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.
66 citations
TL;DR: The performance of reconfigurable intelligent surface (RIS)-aided wireless networks over Rician fading channels is considered, and new accurate closed-form approximations for several performance measures are derived, including the outage probability, average symbol error probability, and the channel capacity.
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 ${N}$ .
63 citations
Cites background from "Bit Error Probability for Large Int..."
...Most recently, [15] provided closed-form expressions for the bit error probability of RIS-assisted network over Nakagami-m fading channels....
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TL;DR: This paper considers 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 of an RIS-assisted single-input single-output system over Rayleigh fading channels.
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.
47 citations
Cites methods from "Bit Error Probability for Large Int..."
...In [14], exact and accurate approximated expressions for the bit error rate (BER) were derived over a Nakagami-m fading channel....
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TL;DR: In this article, the authors developed 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.
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.
40 citations
TL;DR: In this article, the performance of a single-input single-output (SISO) system in which an LIS acts as a controllable scatterer is evaluated.
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.
35 citations
References
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Book•
01 Jan 1970
17,608 citations
Book•
01 Jan 1965
TL;DR: This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory.
Abstract: Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory
13,886 citations
4,028 citations
"Bit Error Probability for Large Int..." refers background in this paper
...Since C and S are uncorrelated (see Appendix C), for the Gaussian case, this condition implies that they are also independent random variables [31], and therefore their joint distribution can be given as...
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...Therefore, the variance of the product is given by var(uv) = var(u)var(v) + var(u)E[v]2 + var(v)E[u]2 [31]....
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...where ρ is defined as [31] ρ = E[CS] − E[C]E[S] σCσS (51)...
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TL;DR: Simulation results demonstrate that an IRS-aided single-cell wireless system can achieve the same rate performance as a benchmark massive MIMO system without using IRS, but with significantly reduced active antennas/RF chains.
Abstract: Intelligent reflecting surface (IRS) is a revolutionary and transformative technology for achieving spectrum and energy efficient wireless communication cost-effectively in the future. Specifically, an IRS consists of a large number of low-cost passive elements each being able to reflect the incident signal independently with an adjustable phase shift so as to collaboratively achieve three-dimensional (3D) passive beamforming without the need of any transmit radio-frequency (RF) chains. In this paper, we study an IRS-aided single-cell wireless system where one IRS is deployed to assist in the communications between a multi-antenna access point (AP) and multiple single-antenna users. We formulate and solve new problems to minimize the total transmit power at the AP by jointly optimizing the transmit beamforming by active antenna array at the AP and reflect beamforming by passive phase shifters at the IRS, subject to users’ individual signal-to-interference-plus-noise ratio (SINR) constraints. Moreover, we analyze the asymptotic performance of IRS’s passive beamforming with infinitely large number of reflecting elements and compare it to that of the traditional active beamforming/relaying. Simulation results demonstrate that an IRS-aided MIMO system can achieve the same rate performance as a benchmark massive MIMO system without using IRS, but with significantly reduced active antennas/RF chains. We also draw useful insights into optimally deploying IRS in future wireless systems.
3,045 citations
"Bit Error Probability for Large Int..." refers background in this paper
...A LIS, which is an array composed of a massive number of low-cost reflecting elements, is capable of reflecting the incident signals with adjustable phase-shifts [2]....
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01 Jan 1960
TL;DR: In this article, the authors summarized the principal results of a series of statistical studies in the last seven years on the intensity distributions due to rapid fading, and presented an extremely simplified method for estimating the improvement available from various systems of diversity reception.
Abstract: This paper summarizes the principal results of a series of statistical studies in the last seven years on the intensity distributions due to rapid fading The method of derivation and the principal characteristics of the m-distribution, originally found in our hf experiments and described by the author, are outlined Its applicability to both ionospheric and tropospheric modes of propagation is fairly well confirmed by some observations Its theoretical background is also discussed in detail A theoretical interpretation of the log-normal distribution is given on the basis of this formula An extremely simplified method is presented for estimating the improvement available from various systems of diversity reception The mutual dependences between the m-formula and other basic distributions are fully discussed Some generalized forms of the basic distributions are also investigated in relation to the m-formula Two methods of approximating a given function with the m-distribution are shown The joint distribution of two variables, each of which follows the m-distribution, is derived in two different ways Based on this, some useful associated distributions are also discussed
2,441 citations