Article

Beamforming Through Reconfigurable Intelligent Surfaces in Single-User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise

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Abstract

We consider a fading channel in which a multi-antenna transmitter communicates with a multi-antenna receiver through a reconfigurable intelligent surface (RIS) that is made of N reconfigurable passive scatterers impaired by phase noise. The beamforming vector at the transmitter, the combining vector at the receiver, and the phase shifts of the N scatterers are optimized in order to maximize the signal-to-noise-ratio (SNR) at the receiver. By assuming Rayleigh fading (or line-of-sight propagation) on the transmitter-RIS link and Rayleigh fading on the RIS-receiver link, we prove that the SNR is a random variable that is equivalent in distribution to the product of three (or two) independent random variables whose distributions are approximated by two (or one) gamma random variables and the sum of two scaled non-central chi-square random variables. The proposed analytical framework allows us to quantify the robustness of RIS-aided transmission to fading channels. For example, we prove that the amount of fading experienced on the transmitter-RIS-receiver channel linearly decreases with N1. This proves that RISs of large size can be effectively employed to make fading less severe and wireless channels more reliable.

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... Moreover, the authors in [11] derived the outage probability as well as the spectral efficiency in the scenario where two users communicated with the aid of RIS. In addition, the capacity of an RIS-aided singleuser MIMO system was analyzed in [12], and the capacity of RIS-aided multi-pair communication systems was analyzed in [13]. However, all of these existing contributions only consider the maximal achievable rate under infinite codelength, while the analysis under finite codelength remains blank. ...
... and the channel dispersion V = Var[i X;Y (x; y)|X] can be expressed as (12), where H = N j=1 X j . Lemma 1 derives the exact achievable rate of a general RIS-aided SISO system. ...
... Lemma 2 is provided below to give some simplification and approximation of the mean and variance items in (12). ...
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The ideal Shannon channel capacity can only be achieved by infinite codelength, so it is not accurate for practical finite codelength. The codelength of channel coding schemes heavily affects the performance of communication systems, but it cannot be too long to ensure affordable decoding complexity and latency. Unfortunately, existing performance analysis for systems aided by reconfigurable intelligent surface (RIS) only focus on the ideal channel capacity and neglect the achievable rate loss caused by finite codelength. To fill in this gap, this paper analyzes the achievable rate under finite codelength in a time-coherent RIS-aided systems, and gives an approximate analytic solution based on Taylor expansion and multi-dimensional central limit theorem. To be more specific, the closed form approximated achievable rate is given based on Taylor expansion, and it is shown that the required codelength decreases superlinearly with the increase of the number of RIS elements. Simulation results verify the analysis, and demonstrate the advantage of RIS-aided systems over the traditional large antenna array schemes.
... By appropriately configuring the electronic circuits, different wave transformations can be realized. Recent research works have shown that RISs whose geometric size is sufficiently large can outperform other technologies, e.g., relays, at a reduced hardware and signal processing complexity [2], and can enhance the reliability of wireless links by reducing the fading severity [3]. In addition, the achievable performance of RIS-assisted systems has been proved to be robust to various hardware impairments, e.g., the phase noise, which may further reduce the implementation cost [4]. ...
... This completes the proof. Remark 2: The optimization of RIS-assisted systems based on (1) is different from, e.g., [3] and [8]. From (10), we observe that: (i) the amplitude and the phase of the tunable load impedances are not independent of each other; and (ii) the internal losses (through R 0 ) of the tunable circuits are explicitly taken into account along with the self impedance of the radiating elements (through Z SS ) of the RIS. ...
... Remark 3: From (15), we evince that, in the far-field region, the received power after optimizing the RIS scales with the square of the number of elements, i.e., |H E2E | 2 ∝ |F (θ)| 2 ∝ N 2 RIS . This is in agreement with conventional communication models for RISs, e.g., [3] and [8]. In addition, the power of the signal scattered by an RIS scales with the reciprocal of the product of the square of the transmission distances between the transmitter and the mid-point of the RIS, and the mid-point of the RIS and the receiver. ...
Preprint
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Reconfigurable intelligent surfaces (RISs) are an emerging technology for enhancing the performance of wireless networks at a low and affordable cost, complexity, and power consumption. We introduce an algorithm for optimizing a single-input single-output RIS-assisted system in which the RIS is modeled by using an electromagnetic-compliant framework based on mutual impedances. More precisely, we provide the following new contributions: (i) in the absence of mutual coupling among the scattering elements of the RIS, we derive a closed-form expression for the optimal tunable impedances, which inherently accounts for the interplay between the amplitude and phase of the lumped loads of the RIS; and (ii) in the presence of mutual coupling, we introduce an iterative algorithm for optimizing the tunable impedances of the RIS. The algorithm is proved to be convergent by showing that the objective function is non-decreasing and upper bounded. Numerical results reveal that the mutual coupling among the scattering elements of the RIS significantly affects the end-to-end signal-to-noise ratio (SNR) if the inter-distance is less than half of the wavelength. If the RIS is optimized by explicitly taking into account the impact of mutual coupling, a better end-to-end SNR is obtained.
... As outlined in a recent survey and tutorial paper [7], several authors have investigated the joint optimization of the beamforming vector at the transmitter, the matrix of phase shifts at the RIS, and the combining vector at the receiver. However, very few papers have tackled the evaluation of the performance of multiple-input multiple-output (MIMO) RIS-aided systems in fading channels [126]. In [126], the authors have recently characterized the distribution of the signal-to-noise-ratio (SNR) by using tools from random matrix theory and by capitalizing on the optimization framework introduced in [93]. ...
... However, very few papers have tackled the evaluation of the performance of multiple-input multiple-output (MIMO) RIS-aided systems in fading channels [126]. In [126], the authors have recently characterized the distribution of the signal-to-noise-ratio (SNR) by using tools from random matrix theory and by capitalizing on the optimization framework introduced in [93]. The existing works, however, consider a single transmitter, a single RIS, and a single receiver. ...
... The distribution of SNR i in (4.2) is characterized in [126]. In this chapter, on the other hand, we focus our attention on the INR at UE 1 that is obtained by considering the optimized triplet (q 2 , Φ 2 , w 1 ) in (4.3). ...
Thesis
Recently, the emergence of reconfigurable intelligent surface (RIS) has attracted heated attention from both industry and academia. A RIS is a planar surface that consists of a large number of low-cost passive reflecting elements. By carefully adjusting the phase shifts of the reflecting elements, an RIS can reshape the wireless environment for better communication. In this thesis, we focus on two subjects: (i) To study the modeling and optimization of RIS-aided communication systems. (ii) To study RIS-aided spatial modulation, especially the detection using deep learning techniques. Chapter 1 introduces the concept of smart radio environments and RIS. In 5G and future communications, RIS is a key technique to achieve seamless connectivity and less energy consumption at the same time. Chapter 2 introduces RIS-aided communication systems. The reflection principle, channel estimation problem and system design problem are introduced in detail. State-of-the-art research on the problems of channel estimation and system design are overviewed. Chapter 3 investigates the distribution of the signal-to-noise ratio (SNR) as a random variable in an RIS-aided multiple-input multiple-output (MIMO) system. Rayleigh fading and line-of-sight propagation are considered separately. The theoretical derivation and numerical simulation prove that the SNR is equivalent in distribution to the product of three (Rayleigh fading) or two (line-of-sight propagation) independent random variables. Chapter 4 studies the behavior of interference in an RIS-aided MIMO system, where each base station serves a user equipment (UE) through an RIS. The interference at a UE is caused by its non-serving RIS. It is proven that the interference-to-noise ratio is equivalent in distribution to the product of a Chi-squared random variable and a random variable which can be approximated with a Gamma distribution. Chapter 5 focuses on RIS-aided spatial modulation. First, we introduce deep learning aided detection for MIMO systems. Then, by generalizing RIS-aided spatial modulation systems as a special case of traditional spatial modulation systems, we investigate deep learning based detection for RIS-aided spatial modulation systems. Numerical results validate the proposed data-based and model-based deep learning detection schemes for RIS-aided spatial modulation systems. Finally, Chapter 6 concludes the thesis and discusses possible future research directions.
... In [20], only single-antennas nodes were considered, and the phase errors were assumed known (deterministic). In addition, the phase noise, induced by an IRS and, henceforth called IRS-HWIs, has been studied in [21], [22] in the case of perfect CSI, but no expectation was taken over the phase noise. Note that this phase noise, coming from the finite precision configuration of the phase drifts, is irrelevant with the phase noise coming from imperfect signal generation in local oscillators in standard antenna systems Moreover, in [23], despite its randomness, again, no averaging of the phase noise was applied. ...
... For the sake of further convenience, we denote by σ 2 Generally, MRC and conventional MMSE decoders are the most common linear receivers for the uplink of next-generation systems such as mMIMO [38], [41]. However, the expectations in (22) and (23) cannot be derived in closed-form in the case of the optimal MMSE receiver expect if the deterministic equivalent analysis is applied [17], [41]. Also, the next step that includes the optimization with respect to reflection coefficients would be quite intractable. ...
... Generally, we are going to apply a useful property suggesting that x H y = tr(yx H ) for any vectors x, y. First, we obtain the S k given by (22). Specifically, the desired signal part DS k (without ρ k ) is written as ...
Preprint
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Most works in IRS-assisted systems have ignored the impact of the inevitable residual hardware impairments (HWIs) at both the transceiver hardware and the IRS while any relevant works have addressed only simple scenarios, e.g., with single-antenna network nodes and/or without taking the randomness of phase noise at the IRS into account. In this work, we aim at filling up this gap by considering a general IRS-assisted multi-user (MU) multiple-input single-output (MISO) system with imperfect CSI and correlated Rayleigh fading. In parallel, we present a general computationally efficient methodology for IRS reflect beamforming (RB) optimization. Specifically, we introduce an advantageous channel estimation (CE) method for such systems accounting for the HWIs. Moreover, we derive the uplink achievable spectral efficiency (SE) with maximal-ratio combining (MRC) receiver, displaying three significant advantages being: 1) its closed-form expression, 2) its dependence only on large-scale statistics, and 3) its low training overhead. Notably, by exploiting the first two benefits, we achieve to perform optimization with respect to the reflect beamforming matrix (RBM) that can take place only at every several coherence intervals, and thus, reduces significantly the computational cost compared to other methods which require frequent phase optimization. Among the insightful observations, we highlight that uncorrelated Rayleigh fading does not allow optimization of the SE, which makes the application of an IRS ineffective. Also, in the case that the phase drifts, describing the distortion of the phases in the RBM, are uniformly distributed, the presence of an IRS provides no advantage. The analytical results outperform previous works and are verified by Monte-Carlo (MC) simulations.
... For two-way communications, the outage probability and spectral efficiency of the system are explored in [5]. Apart from the previous works considering ideal operational conditions, a few research studies examined the performance of RIS-assisted systems in the presence of several practical considerations, such as RF transceiver hardware impairments [6] and phase noise [7]. ...
... Although the results from [2]- [7] are insightful, the performance of the considered systems is studied under the additive white Gaussian noise (AWGN) assumption. While this assumption accurately models the distribution of thermal noise, which is due to the random motion of free electrons at the receiver, it ignores the impulsive nature of electromagnetic interference, atmospheric noise and/or man-made noise, which might be dominant in numerous applications and lead to severe performance degradation. ...
... The assumption of Rayleigh fading channels presents the scenario in which a line-of-sight (LOS) propagation cannot be established due to random RIS deployments, e.g., if the RISs are deployed on spatial blockages. In such a case, the system designer has no control over optimizing the locations of the RISs [7]. 1 If the source node transmits the symbol x with power P s , then the baseband equivalent received signal at D through RIS is expressed as ...
Preprint
In this letter, we investigate the performance of reconfigurable intelligent surface (RIS)-assisted communications, under the assumption of generalized Gaussian noise (GGN), over Rayleigh fading channels. Specifically, we consider an RIS, equipped with $N$ reflecting elements, and derive a novel closed-form expression for the symbol error rate (SER) of arbitrary modulation schemes. The usefulness of the derived new expression is that it can be used to capture the SER performance in the presence of special additive noise distributions such as Gamma, Laplacian, and Gaussian noise. These special cases are also considered and their associated asymptotic SER expressions are derived, and then employed to quantify the achievable diversity order of the system. The theoretical framework is corroborated by numerical results, which reveal that the shaping parameter of the GGN ($\alpha$) has a negligible effect on the diversity order of RIS-assisted systems, particularly for large $\alpha$ values. Accordingly, the maximum achievable diversity order is determined by $N$.
... By appropriately configuring the electronic circuits, different wave transformations can be realized. Recent research works have shown that RISs whose geometric size is sufficiently large can outperform other technologies, e.g., relays, at a reduced hardware and signal processing complexity [2], and can enhance the reliability of wireless links by reducing the fading severity [3]. In addition, the achievable performance of RIS-assisted systems has been proved to be robust to various hardware impairments, e.g., the phase noise, which may further reduce the implementation cost [4]. ...
... This completes the proof. Remark 2: The optimization of RIS-assisted systems based on (1) is different from, e.g., [3] and [8]. From (10), we observe that: (i) the amplitude and the phase of the tunable load impedances are not independent of each other; and (ii) the internal losses (through R 0 ) of the tunable circuits are explicitly taken into account along with the self impedance of the radiating elements (through Z SS ) of the RIS. ...
... Remark 3: From (15), we evince that, in the far-field region, the received power after optimizing the RIS scales with the square of the number of elements, i.e., |H E2E | 2 ∝ |F (θ)| 2 ∝ N 2 RIS . This is in agreement with conventional communication models for RISs, e.g., [3] and [8]. In addition, the power of the signal scattered by an RIS scales with the reciprocal of the product of the square of the transmission distances between the transmitter and the mid-point of the RIS, and the mid-point of the RIS and the receiver. ...
Article
Full-text available
We introduce algorithms for optimizing a single-input single-output reconfigurable intelligent surface (RIS) assisted system. The RIS is modeled by using an electromagnetic-compliant framework based on mutual impedances and its reconfigurability is realized through tunable lumped impedances. In the absence of mutual coupling among the scattering elements of the RIS, we derive a closed-form expression for the optimal tunable impedances, which accounts for the interplay between the amplitude and phase of the lumped loads of the RIS. In the presence of mutual coupling, we introduce an iterative algorithm for optimizing the tunable impedances of the RIS. The algorithm is proved to be convergent by showing that the objective function is non-decreasing and upper bounded. Numerical results reveal that the mutual coupling significantly affects the end-to-end received power. If the RIS is optimized by taking the mutual coupling into account, the received power can be increased.
... It has already been shown that in RIS-aided single-user systems with N reflecting elements, the achievable rate could scale as O (log 2 (N 2 )) [10], [24], or even O (log 2 (N 4 )) [25] if two RISs cooperate. Similar scaling orders were also reported for some other RISaided communication scenarios, such as the RIS-aided relay [26], RIS with scattering parameter analysis [27], and RISs with hardware impairments [28], [29]. However, these works focused on the simple single-user case, and cannot be easily generalized to multi-user systems. ...
... Next, we focus on the Max-Min problem (28), which is more challenging since the objective function min k f k (v) is non-differential. Therefore, we first adopt the log-sum-exp approximation in [32] to obtain a lower-bounded smooth objective function, as follows ...
... Based on the MM algorithm, the Max-Min problem (28) can be solved by maximizing the lower bound f (v | v n ) in each iteration. Given the solution v n in the n-th iteration, the closedform optimal solution at the (n + 1)-th iteration is ...
Preprint
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This paper provides a theoretical framework for understanding the performance of reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) with zero-forcing (ZF) detectors under imperfect channel state information (CSI). We first propose a low-overhead minimum mean square error (MMSE) channel estimator, and then derive and analyze closed-form expressions for the uplink achievable rate. Our analytical results demonstrate that: $1)$ regardless of the RIS phase shift design, the rate of all users scales at least on the order of $\mathcal{O}\left(\log_2\left(MN\right)\right)$, where $M$ and $N$ are the numbers of antennas and reflecting elements, respectively; $2)$ by aligning the RIS phase shifts to one user, the rate of this user can at most scale on the order of $\mathcal{O}\left(\log_2\left(MN^2\right)\right)$; $3)$ either $M$ or the transmit power can be reduced inversely proportional to $N$, while maintaining a given rate. Furthermore, we propose two low-complexity majorization-minimization (MM)-based algorithms to optimize the sum user rate and the minimum user rate, respectively, where closed-form solutions are obtained in each iteration. Finally, simulation results validate all derived analytical results. Our simulation results also show that the maximum sum rate can be closely approached by simply aligning the RIS phase shifts to an arbitrary user.
... RIS with machine learning and deep learning algorithms have been suggested in [18,19]. RIS has been studied for multiple input multiple output (MIMO) systems [20][21][22]. When there are multiple antennas at the receiver, the best receive antenna can be used. ...
... where p R (x T ) is the PDF of T given in (22) and L opt (x T ) is provided in (36). The optimal packet length (36) depends on the instantaneous SNR x T = T . ...
... where p T (x) is the PDF of SNR when there is a single antenna given in (22). The optimal packet length maximizing the average throughput is obtained using the Gradient algorithm as shown in (28). ...
Article
Full-text available
Reconfigurable intelligent surfaces (RIS) allow significant throughput enhancement as all reflections have the same phase at the receiver. In this paper, we suggest to optimize packet length for wireless communications using RIS. Two techniques are suggested in order to maximize average or instantaneous throughput. Average throughput maximization requires only the average signal to noise ratio to determine the optimal packet length. The Gradient algorithm is used to maximize the average throughput. Instantaneous throughput maximization requires the instantaneous SNR in order to adapt packet length to channel conditions. We derive in closed form the expression of optimal packet length, maximizing the instantaneous throughput. Our results are valid for any number of reflecting meta-surfaces N of the RIS.
... The effects of hardware impairments and environmental imperfections have been rarely studied in the literature. For instance, [9]- [11] consider RIS operating under finite resolution of the phase shifts or phase estimation errors from imperfect channel estimation. More completely, [12] and [13] consider different environmental effects on the RIS and propose methods to jointly estimate the channel and array blockage parameters in millimeter wave (mmWave) RISassisted systems. ...
... From (11), we can define the new column-wise collection [Y] (1) = [Y 1 , . . . , Y P ] ∈ C L×M KP as the 1-mode matrix unfolding of the received signal tensor Y ∈ C L×M ×K×P in (9), which is given by ...
Preprint
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Reconfigurable intelligent surface (RIS) is a candidate technology for future wireless networks. It enables to shape the wireless environment to reach massive connectivity and enhanced data rate. The promising gains of RIS-assisted networks are, however, strongly depends on the accuracy of the channel state information. Due to the passive nature of the RIS elements, channel estimation may become challenging. This becomes most evident when physical imperfections or electronic impairments affect the RIS due to its exposition to different environmental effects or caused by hardware limitations from the circuitry. In this paper, we propose an efficient and low-complexity tensor-based channel estimation approach in RIS-assisted networks taking different imperfections into account. By assuming a short-term model in which the RIS imperfections behavior, modeled as unknown amplitude and phase shifts deviations, is non-static with respect to the channel coherence time, we formulate a closed-form higher order singular value decomposition based algorithm for the joint estimation of the involved channels and the unknown impairments. Furthermore, the identifiability and computational complexity of the proposed algorithm are analyzed, and we study the effect of different imperfections on the channel estimation quality. Simulation results demonstrate the effectiveness of our proposed tensor-based algorithm in terms of the estimation accuracy and computational complexity compared to competing tensor-based iterative alternating solutions.
... In practice, the phase shifts of the reconfigurable elements of an RIS cannot be optimized with an arbitrary precision, e.g., because of the finite number of quantization bits used or because of errors when estimating the phases of the fading channels [22], [24]. In these cases, the phase of the ith element of the RIS can be written as φ i = −∠h i − ∠g i + θ i , where θ i denotes a random phase noise, which is assumed to be i.i.d. in this paper. ...
... where L ≥ 1 is a positive integer that denotes the number of quantization bits used [22], [24]. ...
Preprint
In this paper, we develop a comprehensive theoretical framework for analyzing the performance of reconfigurable intelligent surfaces (RISs)-assisted communication systems over generalized fading channels and in the presence of phase noise. To this end, we propose the Fox's H model as a unified fading distribution for a large number of widely used generalized fading channels. In particular, we derive a unified analytical framework for computing the outage probability and for estimating the achievable diversity order of RIS-aided systems in the presence of phase shifts that either are optimally configured or are impaired by phase noise. The resulting expressions are general, as they hold for an arbitrary number of reflecting elements, and various channel fading and phase noise distributions. As far as the diversity order is concerned, notably, we introduce an asymptotic analytical framework for determining the diversity order in the absence of phase noise, as well as sufficient conditions based on upper bounds and lower bounds for ensuring that RIS-assisted systems achieve the full diversity order in the presence of phase noise. More specifically, if the absolute difference between pairs of phase errors is less than $\pi/2$, RIS-assisted communications achieve the full diversity order over independent fading channels, even in the presence of phase noise. The theoretical frameworks and findings are validated with the aid of Monte Carlo simulations.
... For a large number of elements at the RIS, the authors of [12] investigate an RIS-assisted multiple-input and multiple-output (MIMO) network. Exact analytical characterization of finite dimensional RIS-assisted systems, on the other hand, is not available in the current literature. ...
... The channel matrices are referred to the equivalent channel from the transmitter to the tiles of the RIS and to the tiles of the RIS to the receiver. Rayleigh fading is assumed for analytical tractability and under the assumption that the location of the RIS cannot be optimized in order to ensure line-of-sight propagation [12]. Moreover, we make the common assumption that perfect channel state information (CSI) ...
Article
We consider a two–tile reconfigurable intelligent surface (RIS) assisted wireless network with a two-antenna transmitter and receiver over Rayleigh fading. We show that the average received signal-to-noise-ratio (SNR) optimal combining and transmission vectors are given by the left and right singular spaces of the RIS-receiver and transmit-RIS channel matrices, respectively. Moreover, the optimal phases at the two tiles of the RIS are determined by the phases of the elements of the latter spaces. To further study the effect of phase compensation, we statistically characterize the average SNR of all possible combinations of transmission and combining directions pertaining to the latter singular spaces by deriving novel expressions for the outage probability and throughput of each of those modes. Furthermore, for comparison, we derive the corresponding expressions in the absence of RIS. Our results show an approximate SNR improvement of 2 dB due to the phase compensation at the RIS.
... 2 Since the elements of the RIS are spaced half of the wavelength apart and we assume that the location of the RIS cannot be optimized to ensure strong line-of-sight links, we have, as a first approximation similar to [14]- [16], that the channels can be modeled as independent and identically distributed, and follow a Rayleigh distribution. ...
... An interesting future direction is to analyze the ESR of RIS-assisted systems in the presence of multi-antenna transmitters. For example, the recent research works in [16], [25] could be generalized in order to take into account security constraints. ...
Article
This letter investigates the ergodic secrecy rate (ESR) of a reconfigurable intelligent surface (RIS)-assisted communication system in the presence multiple eavesdroppers (Eves), and by assuming discrete phase shifts at the RIS. In particular, a closed-form approximation of the ESR is derived for both non-colluding and colluding Eves. The analytical results are shown to be accurate when the number of reflecting elements of the RIS ${N}$ is large. Asymptotic analysis is provided to investigate the impact of ${N}$ on the ESR, and it is proved that the ESR scales with $\log \,_{2} N$ for both non-colluding and colluding Eves. Numerical results are provided to verify the analytical results and the obtained scaling laws.
... Regarding the fading model, Rayleigh fading model is commonly chosen for performance analysis [5], [10]- [12] which may not be a legit choice for a practical RIS-assisted communication scenario due to the fact that RISs are carefully deployed to leverage line-of-sight (LoS) links between the terminals. In order to achieve perfect phase estimation, the RIS requires channel state information (CSI). ...
... We set m 1 = 3, m 2 = 1, Ω 1 = 1 and Ω 2 = 1, which corresponds to a scenario where there is a LoS link between the BS and the RRS and a NLoS link between the RRS and the user. This scenario is motivated by the mobility of the user and, thus, the difficulty of establishing a LoS link [12]. Moreover, we also examine the setup where m 1 = 1 and m 2 = 1 in order to illustrate a performance lower bound which represents a scenario where the RRS is randomly deployed, since there is no LoS link. ...
Preprint
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Meta-surfaces intend to improve significantly the performance of future wireless networks by controlling the wireless propagation and shaping the radio waves according to the generalized Snell’s laws of reflection and refraction. A recent application of meta-surfaces is reconfigurable intelligent surfaces which are practically limited by the requirement for perfect channel state information (CSI). To avoid this practical limitation and reduce the complexity, we introduce randomly reconfigurable surfaces (RRSs), being defined as reconfigurable meta-surfaces that each of their elements induces a randomly selected time-variant phase shift on the reflected signal without requiring CSI, and investigate the performance of a RRS-assisted wireless communication network. To facilitate the performance analysis of the considered RRS-assisted system, first, we present novel closed-form expressions for the probability density function, the cumulative distribution function, the moments, and the characteristic function of the distribution of the sum of double-Nakagami-m random vectors, whose amplitudes follow the double-Nakagami-m distribution, i.e., the distribution of the product of two random variables following the Nakagami-m distribution, and phases follow the circular uniform distribution. We also consider a special case of this distribution, namely the distribution of the sum of Rayleigh-Nakagami-m random vectors. Then, we exploit these expressions to investigate the performance of the RRS-assisted composite channel, assuming that the two links undergo Nakagami-m fading and the equivalent phase follows the circular uniform distribution. Closed-form expressions for the outage probability, the average received signal-to-noise ratio, the ergodic capacity, the bit error probability, the amount of fading, and the channel quality estimation index are provided to evaluate the performance of the considered system. These metrics are also derived for the practical special case where one of the two links undergoes Rayleigh fading.
... A. Related Work 1) RIS Related Studies on Channel Characterization: A number of studies investigate either the ergodic capacity or outage probability analysis of RIS-aided systems by identifying the characteristics of the channel response and received SNR [15]- [26]. In [15] the distribution of the absolute value of the composite channel containing direct link is considered to be a Gaussian random variable (RV) for large RIS elements according to the central limit theorem (CLT) and then the ergodic capacity is studied. ...
... Note that the analysis is performed over infinite blocklength regime without the presence of the direct channel. Finally, the authors in [26] considered the optimal SNR derived in [27] and then, they proposed that the SNR distribution is composed of the product of three independent Gamma RVs and sum of two scaled non-central chi-square RVs based on the eigenvalues of the channel matrices of RIS-AP and RIS-user. The authors compare the proposed analytical distributions with the case that the SNR is only approximated with one Gamma RV. ...
Preprint
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.
... A number of studies have investigated the ergodic capacity or outage probability analysis of RIS-aided systems by identifying the characteristics of the channel response and received SNR [12]- [15]. In [12], [13] the SNR distribution is approximated as a Gamma random variable (RV), and the ergodic capacity is studied in an infinite blocklength channel [13] in which the composite channel contains the direct link plus the reflected signal from RIS with arbitrary phase shifts and as a result only statistical properties of the phase shifts was taken into account. ...
... The best case and worst case channel responses are formulated as a Gamma RV with separate scale and shape parameters for each case in [14]. The authors in [15] considered the optimal SNR derived in [16] and then, they proposed that the SNR distribution is composed of the product of three independent Gamma RVs and sum of two scaled non-central chi-square RVs based on the eigenvalues of the channel matrices of RIS-access point (AP) and RIS-user. The authors compare the proposed analytical distributions with the case that the SNR is only approximated with one gamma RV. ...
Preprint
In this paper, the average achievable rate of a re-configurable intelligent surface (RIS) aided factory automation is investigated in finite blocklength (FBL) regime. First, the composite channel containing the direct path plus the product of reflected paths 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 as well as the channel pathloss. Next, by assuming FBL model, the achievable rate expression is identified and the corresponding average rate is elaborated based on the proposed SNR distribution. The phase error due to quantizing the phase shifts is considered in the simulation. The numerical results show that Monte Carlo simulations conform to the matched Gamma distribution for the received SNR for 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 low-latency communications (URLLC) systems. The reduction of average achievable rate due to working in FBL regime with respect to Shannon capacity is also investigated as a function of total RIS elements.
... Hence, a good balance between modeling accuracy and mathematical tractability is key for performance analysis purposes. A deep inspection of the RIS-related research in channel modeling reveals that the common assumption of independent and identically distributed (i.i.d.) fading to model the RIS channels is only justified for the sake of mathematical tractability; several relevant examples include somehow idealistic set-ups [7][8][9] as well as more realistic scenarios that consider hardware impairments and imperfect phase estimation [10][11][12]. Very recently, based upon the formulation in [13], a Gamma approximation for the equivalent composite model in RIS-assisted set-ups that explicitly considers the impact of spatial channel correlation in Rayleigh fading was given using the moment-matching (MoM) technique [14]. ...
... From (13), the OP in (12) can be obtained directly from the cumulative distribution function (CDF) of (9). ...
Article
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Channel modeling is a critical issue when designing or evaluating the performance of reconfigurable intelligent surface (RIS)-assisted communications. Inspired by the promising potential of learning-based methods for characterizing the radio environment, we present a general approach to model the RIS end-to-end equivalent channel using the unsupervised expectation-maximization (EM) learning algorithm. We show that an EM-based approximation through a simple mixture of two Nakagami-m distributions suffices to accurately approximate the equivalent channel, while allowing for the incorporation of crucial aspects into RIS’s channel modeling such as beamforming, spatial channel correlation, phase-shift errors, arbitrary fading conditions, and coexistence of direct and RIS channels. Based on the proposed analytical framework, we evaluate the outage probability under different settings of RIS’s channel features and confirm the superiority of this approach compared to recent results in the literature.
... The concept of RISs as a controllable device enhance aforementioned function as of its controllability on propagation environments. Many works focus on link transmission metric [16][17][18][19][20], channel estimation [21][22][23][24], PHY security [25][26][27], and practical applications [28][29][30] to analyze performance of RISs-assisted systems. Specifically, [16] optimizes transmission power and reflection coefficient to achieve sum-rate maximization when each mobile user has QoS guarantee. ...
... Considering link budget guarantee of a user in downlink communication, [17] proposes an energyefficient scheme by joint optimization transmission power allocation and RIS phase shift. Combined with transmitter and receiver, [18] optimizes beamforming vector, combining vector, and phase shifts at transmitter to maximize SNR at the receiver. When interference is introduced to user, the transmit power is allocated in [19] by joint active and passive beamforming to improve the performance of RISsassisted wireless networks. ...
Article
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The multipath fading and Doppler effect are well-known phenomena affecting channel quality in mobile wireless communication systems. Within this context, the emergence of reconfigurable intelligence surfaces (RISs) brings a chance to achieve this goal. RISs as a potential solution are considered to be proposed in sixth generation (6G). The core idea of RISs is to change the channel characteristic from uncontrollable to controllable. This is reflected by some novel functionalities with wave absorption and abnormal reflection. In this paper, the multipath fading and Doppler effect are characterized by establishing a mathematical model from the perspective of reflectors and RISs in different mobile wireless communication processes. In addition, the solutions that improve the multipath fading and Doppler effect stemming from the movement of mobile transmitter are discussed by utilizing multiple RISs. A large number of experimental results demonstrate that the received signal strength abnormal fluctuations due to Doppler effect can be eliminated effectively by real-time control of RISs. Meanwhile, the multipath fading is also mitigated when all reflectors deployed are coated with RISs.
... satisfying a target data transmission rate R (in bps/Hz). 2 Note that the large-scale RIS-to-receiver channel gains ξ 2 H are identical for all the involved channel links since the interelement distance at RIS (or the inter-antenna distance at the receiver) is considered negligible compared to the corresponding RIS-to-receiver distance. ...
... Consider the reasonable scenario when the receiver knows the channel status of the direct link and knows nothing about the (instantaneous) RIS-enabled small-scale channel fading. The received signal here is identical to (2). Yet, it is convenient for performance analysis reasons to follow an alternative approach by adopting the QR decomposition of the given channel fading matrix. ...
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A multiuser multiple-input multiple-output wireless communication system is analytically studied, which operates with the aid of a reconfigurable intelligent surface (RIS). The intermediate RIS is equipped with multiple elements and operates via random phase rotations to simultaneously serve multiple users. Independent Rayleigh fading conditions are assumed among the included channels. The system performance is analytically studied when the linear yet efficient zero-forcing detection is implemented at the receiver. In particular, the outage performance is derived in closed-form expression for different system configuration setups with regards to the available channel state information at the receiver. Further, a joint coherent/noncoherent linear detection is analytically presented. Finally, some new engineering insights are provided, such as how the channel state information and/or the volume of antenna/RIS arrays impact on the overall system performance as well as the arising efficiency on the performance/complexity tradeoff by utilizing the joint coherent/noncoherent scheme.
... However, to describe the performance of the considered network, integral expressions are provided for small number of reflecting elements and CLT approximation is used for large number of reflecting elements. Regarding the fading model, Rayleigh fading is frequently considered for both communication links [5], [17], [18] which is not a legit choice for a practical RIS-assisted communication scenario since RISs are carefully deployed to leverage line-of-sight (LoS) links between the terminals. ...
... We set m 1 = 3, m 2 = 1, Ω 1 = 1 and Ω 2 = 1, which corresponds to a scenario where there is a LoS link between the BS and the RRS and a non-LoS link between the RRS and the user. This scenario is motivated by the mobility of the user and, thus, the difficulty of establishing a LoS link [18]. Moreover, we also examine the setup where m 1 = 1 and m 2 = 1 to illustrate a performance lower bound representing a scenario where the RRS is randomly deployed since there is no LoS link. ...
... 3) Convergence and Complexity Analysis: As the objective value of (P1-NoIUs) is nondecreasing over the iterations and also upper-bounded by a finite value, the proposed algorithm is guaranteed to converge. Besides, the main computational burden stems from solving the SDP in (9) and the QCQP in (12). Simply speaking, given a solution accuracy ε, problem (9) can be solved with a computational complexity 3 of O M 3.5 log( 1 ε ) , while the arithmetic cost 4 of solving problem (12) is less than O N 1.5 ln 2(N +1)V ε , where V is a constant defined in [41]. ...
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In this paper, we study an active IRS-aided simultaneous wireless information and power transfer (SWIPT) system. Specifically, an active IRS is deployed to assist a multi-antenna access point (AP) to convey information and energy simultaneously to multiple single-antenna information users (IUs) and energy users (EUs). Two joint transmit and reflect beamforming optimization problems are investigated with different practical objectives. The first problem maximizes the weighted sum-power harvested by the EUs subject to individual signal-to-interference-plus-noise ratio (SINR) constraints at the IUs, while the second problem maximizes the weighted sum-rate of the IUs subject to individual energy harvesting (EH) constraints at the EUs. The optimization problems are non-convex and difficult to solve optimally. To tackle these two problems, we first rigorously prove that dedicated energy beams are not required for their corresponding semidefinite relaxation (SDR) reformulations and the SDR is tight for the first problem, thus greatly simplifying the AP precoding design. Then, by capitalizing on the techniques of alternating optimization (AO), SDR, and successive convex approximation (SCA), computationally efficient algorithms are developed to obtain suboptimal solutions of the resulting optimization problems. Simulation results demonstrate that, given the same total system power budget, significant performance gains in terms of operating range of wireless power transfer (WPT), total harvested energy, as well as achievable rate can be obtained by our proposed designs over benchmark schemes (especially the one adopting a passive IRS). Moreover, it is advisable to deploy an active IRS in the proximity of the users for the effective operation of WPT/SWIPT.
... Data throughput and coverage enhancements are of paramount importance in fifth-generation (5G) and beyond networks [1]. In this context, reconfigurable intelligent surfaces (RISs) have received significant attention from academic and industrial researchers because of their ability to control the wireless propagation environment through passive reflecting elements integrated with low-cost electronics [2][3][4]. ...
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Reconfigurable intelligent surfaces (RISs) have recently gained significant interest as an emerging technology for future wireless networks. This paper studies an RIS-assisted propagation environment, where a single-antenna source transmits data to a single-antenna destination in the presence of a weak direct link. We analyze and compare RIS designs based on long-term and short-term channel statistics in terms of coverage probability and ergodic rate. For the considered optimization designs, closed-form expressions for the coverage probability and ergodic rate are derived. We use numerical simulations to analyze and compare against analytic results in finite samples. Also, we show that the considered optimal phase shift designs outperform several heuristic benchmarks.
... We observe that the virtual LoS link provided by an RIS in THz massive MIMO systems significantly increases the ASE. In addition, we investigate the impact of quantization error, i.e., only a finite number of phase shifts can be realized in practice, on the performance of the proposed schemes, similar to [18], [32]. Note that some state-of-the-art architectures of reflecting element, such as semiconductor diodes in [24], are not suited to much higher frequencies (e.g., THz) [46]. ...
Article
We propose a holographic version of a reconfigurable intelligent surface (RIS) and investigate its application to terahertz (THz) massive multiple-input multiple-output systems. Capitalizing on the miniaturization of THz electronic components, RISs can be implemented by densely packing sub-wavelength unit cells, so as to realize continuous or quasi-continuous apertures and to enable holographic communications . In this paper, in particular, we derive the beam pattern of a holographic RIS. Our analysis reveals that the beam pattern of an ideal holographic RIS can be well approximated by that of an ultra-dense RIS, which has a more practical hardware architecture. In addition, we propose a closed-loop channel estimation (CE) scheme to effectively estimate the broadband channels that characterize THz massive MIMO systems aided by holographic RISs. The proposed CE scheme includes a downlink coarse CE stage and an uplink finer-grained CE stage. The uplink pilot signals are judiciously designed for obtaining good CE performance. Moreover, to reduce the pilot overhead, we introduce a compressive sensing-based CE algorithm, which exploits the dual sparsity of THz MIMO channels in both the angular domain and delay domain. Simulation results demonstrate the superiority of holographic RISs over the non-holographic ones, and the effectiveness of the proposed CE scheme.
... It is worth noting that the intertwinement between the amplitude and phase response of the individual passive scatterers of the RIS is inherently accounted for in H E2E through Z RIS [6], and it depends on the circuital model of the tuning circuit. resembles communication-theoretic models that are formulated in terms of the received signal-to-noise ratio (SNR) and that are typically used in wireless communications [10,Eq. (1)]. ...
Article
Reconfigurable intelligent surfaces (RISs) are an emerging technology for application to wireless networks. We introduce a physics and electromagnetic (EM) compliant communication model for analyzing and optimizing RIS-assisted wireless systems. The proposed model has four main notable attributes: (i) it is end-to-end , i.e., it is formulated in terms of an equivalent channel that yields a one-to-one mapping between the voltages fed into the ports of a transmitter and the voltages measured at the ports of a receiver; (ii) it is EM-compliant , i.e., it accounts for the generation and propagation of the EM fields; (iii) it is mutual coupling aware , i.e., it accounts for the mutual coupling among the sub-wavelength unit cells of the RIS; and (iv) it is unit cell aware , i.e., it accounts for the intertwinement between the amplitude and phase response of the unit cells of the RIS.
... The work of J. D. Vega Sánchez was funded by the Escuela Politécnica Nacional, for the development of the project PIGR-19-06 and through a teaching assistant fellowship for doctoral studies. The work of F.J. Lopez-Martinez was funded by the Spanish Government and the European Fund for Regional Development FEDER (project TEC2017-87913-R) and by Junta de Andalucia (project P18-RT-3175, TETRA5G RIS channels is only justified for the sake of mathematical tractability; several relevant examples include somehow idealistic set-ups [5][6][7] as well as more realistic scenarios that consider hardware impairments and imperfect phase estimation [8][9][10][11]. Very recently, based upon the formulation in [12], a Gamma approximation for the equivalent composite model in RIS-assisted set-ups that explicitly considers the impact of spatial channel correlation in Rayleigh fading was given using the moment-matching technique [13]. ...
... We consider to analyze the capacity gain achievable by active RIS by studying the user's achievable SNR in a simple SISO scenario. To focus on the capacity gain provided by the active RIS aided reflection link, we ignore the direct link by setting h k 0 [28]. For simplicity, we assume that every active RIS element has the same amplification factor (p n p, ∀n ∈ {1, · · · , N }), and redefine G g = ...
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From 1G to 5G, wireless channels have been traditionally considered to be uncontrollable. Thanks to the recent advances in meta-materials, reconfigurable intelligent surfaces (RISs) have emerged as a new paradigm for controlling wireless channels intelligently, thus making it a revolutionary technique for future 6G wireless communications. However, due to the "double fading" effect, RIS only achieves a negligible capacity gain in typical communication scenarios, which however has been widely ignored in many existing works. In this paper, the concept of active RIS is proposed to break this fundamental physical limit. Different from the existing passive RIS that reflects signals passively without amplification, active RIS can actively amplify the reflected signals. We then develop a signal model for active RIS, which is validated through experimental measurements. Based on this new signal model, we analyze the capacity gain achievable by active RIS and formulate the capacity maximization problem in an active RIS aided system. Next, a joint transmit and reflect precoding algorithm is proposed to solve this problem. Finally, extensive results show that, compared with the baseline without RIS, the existing passive RIS can realize a negligible capacity gain of only 3% in typical application scenarios, while the proposed active RIS can achieve a noticeable capacity gain of 129%, thus overcoming the fundamental limit of "double fading" effect.
... The assumption of Rayleigh fading channels is representative of scenarios in which line-of-sight (LOS) propagation cannot be established due to random RIS deployments, e.g., if the RISs are deployed on spatial blockages. In this case, the system designer has no control over optimizing RISs locations [52]. ...
Article
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In this paper, we develop an analytical framework for the statistical analysis of the battery recharging time (BRT) in reconfigurable intelligent surfaces (RISs)-aided wireless power transfer (WPT) systems. Specifically, we derive novel closed-form expressions for the probability density function (PDF), cumulative distribution function, and moments of the BRT of the radio frequency energy harvesting wireless nodes. Moreover, a closed-form expression of the PDF of the BRT is obtained for the special case when the RIS consists of a large number of elements. Capitalizing on the derived expressions, we offer a comprehensive treatment for the statistical characterization of the BRT and study the impact of the system and battery parameters on its performance. Our results reveal that the proposed statistical models are analytically tractable, accurate, and efficient in assessing the sustainability of RIS-assisted WPT networks and in providing key design insights for large-scale future wireless applications. For example, we demonstrate that a 4-fold reduction in the mean time of the BRT can be achieved by doubling the number of RIS elements. Monte Carlo simulation results corroborate the accuracy of the proposed theoretical framework.
... RISs with discrete reflection coefficients have been proposed to enhance the performance of Multiple-Input Multiple-Output (MIMO) communications by solving rate maximization problems in single-user systems [8], [9], [10], [11] and sum-rate maximization problems in multi-user systems [12], [13], [14], [15], [16]. In [10], besides the discrete reflection coefficients assumption, a practical model capturing the phase-dependent amplitude variation in the reflection coefficients is considered while maximizing the user rate. ...
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Reconfigurable Intelligent Surfaces (RISs) allow to control the propagation environment in wireless networks by properly tuning multiple reflecting elements. Traditionally, RISs have been realized through single connected reconfigurable impedance networks, in which each RIS element is independently controlled by an impedance connected to ground. In a recent work, this architecture has been extended by realizing more efficient RISs with group and fully connected reconfigurable impedance networks. However, impedance networks tunable with arbitrary precision are hard to realize in practice. In this paper, we propose a practical RIS design strategy based on reconfigurable impedance networks with discrete values. Besides, we address the problem of how to group the RIS elements in group connected architectures. We optimize single, group, and fully connected architectures considering finite-resolution elements, and we compare them in terms of received signal power. Through Monte Carlo simulations, supported by theoretical justifications, we show that only a few resolution bits per reconfigurable impedance are sufficient to achieve the performance upper bound. In particular, while four resolution bits are needed to reach the upper bound in single connected architectures, only a single resolution bit is sufficient in fully connected ones, simplifying significantly the future development of these promising RIS architectures.
... The computation of the total FSPL of the indirect link is an intractable problem in a MIMO system, since the optimal RIS element phase shifts are a priori unknown and can only be obtained by implementing an iterative optimization method. This problem was approximately tackled only for the singlestream scenario in [33], and the obtained results were then used in [35] to quantify the performance of RISs in the far field regime (which is also the case considered in this paper), but only for Rayleigh and deterministic LOS channels. To overcome this issue, we consider the total FSPL of the indirect link in a SISO system, which is given by ...
Article
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Reconfigurable intelligent surfaces (RISs) represent a new technology that can shape the radio wave propagation in wireless networks and offers a great variety of possible performance and implementation gains. Motivated by this, we study the achievable rate optimization for multi-stream multiple-input multiple-output (MIMO) systems equipped with an RIS, and formulate a joint optimization problem of the covariance matrix of the transmitted signal and the RIS elements. To solve this problem, we propose an iterative optimization algorithm that is based on the projected gradient method (PGM). We derive the step size that guarantees the convergence of the proposed algorithm and we define a backtracking line search to improve its convergence rate. Furthermore, we introduce the total free space path loss (FSPL) ratio of the indirect and direct links as a first-order measure of the applicability of RISs in the considered communication system. Simulation results show that the proposed PGM achieves the same achievable rate as a state-of-the-art benchmark scheme, but with a significantly lower computational complexity. In addition, we demonstrate that the RIS application is particularly suitable to increase the achievable rate in indoor environments, as even a small number of RIS elements can provide a substantial achievable rate gain.
... An RIS is a planar structure made of several individually tunable elements, called meta-atoms or passive scatterers, that can be programmed and appropriately reconfigured to control the phase of the incoming electromagnetic signal, by reflecting or refracting it towards specified locations [1]. In [7] and [8] the signal-to-noise ratio (SNR) scaling law of RIS-aided transmission is characterized, and the impact of hardware impairments is analyzed, respectively. Experimental testbeds have confirmed the potential gains of RISs [9], [10], [11], [12]. ...
Article
This work considers a point-to-point link where a reconfigurable intelligent surface assists the communication between a transmitter and a receiver. The system rate, energy efficiency, and their trade-off are optimized by tuning the number of reflecting elements to be activated and the phase shifts that they apply. Unlike most previous works, the considered resource allocation problem explicitly accounts, at the design stage, for the time and energy that are necessary for channel estimation and for reporting the optimal configuration of the phase shifts to the reconfigurable intelligent surface. Numerical results confirm the optimality of the proposed methods and show the potential gains of reconfigurable intelligent surfaces.
... Among related problems left open by this study, we mention the design of low-complexity joint encoding and decoding strategies that approach capacity, the derivation of the capacity for noisy RIS [32] and for RIS with mutual coupling [23], and extensions to RIS systems with multiple users/surfaces [33] or with security constraints [34]. Another related problem is finding the optimal input distribution for a slowly fading channel with CSI only at the receiver [35]. ...
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A communication link aided by a reconfigurable intelligent surface (RIS) is studied in which the transmitter can control the state of the RIS via a finite-rate control link. Channel state information (CSI) is acquired at the receiver based on pilot-assisted channel estimation, and it may or may not be shared with the transmitter. Considering quasi-static fading channels with imperfect CSI, capacity-achieving signalling is shown to implement joint encoding of the transmitted signal and of the response of the RIS. This demonstrates the information-theoretic optimality of RIS-based modulation, or "single-RF MIMO" systems. In addition, a novel signalling strategy based on separate layered encoding that enables practical successive cancellation-type decoding at the receiver is proposed. Numerical experiments show that the conventional scheme that fixes the reflection pattern of the RIS, irrespective of the transmitted information, as to maximize the achievable rate is strictly suboptimal, and is outperformed by the proposed adaptive coding strategies at all practical signal-to-noise ratio (SNR) levels.
... In particular, RISs do not require any costly radio frequency (RF) chains for signal reception and retransmission, nor complex signal processing techniques for self-interference cancellation; thereby greatly reducing hardware cost and energy consumption [7], [8]. These appealing advantages have driven a variety of wireless communications empowered by RISs, such as RIS-aided MIMO systems [9]- [11], RIS-aided energy transfer [12], RISaided orthogonal frequency division multiplexing (OFDM) systems over frequency-selective channels [13], and so on. The authors of [14] realized an RIS-based 8-phase shift-keying transmitter that uses an RIS with 256 reconfigurable elements instead of an RF chain. ...
... Moreover, some authors investigated the OP and ergodic capacity (EC) of an RIS-assisted system by considering the impact of hardware imperfection [11] . The secrecy OP of an RIS-assisted communication system was also studied [12,13] . In particular, the impact of discrete phase shifts was analyzed [12] . ...
Article
Reconfigurable intelligent surfaces (RISs) have attracted significant attention due to their capability in customizing wireless communication environments to improve system performance. In this study, we investigate the performance of an RIS-assisted multi-user multiple-input single-output wireless communication system, considering the impact of channel aging caused by users’ relative movements. In particular, first, we propose a model incorporating the joint effects of channel aging and channel estimation errors to investigate the performance of the RIS-assisted system. Then, we derive novel closed-form expressions for characterizing the sum spectral efficiency with zero-forcing precoding. From our analysis, we unveil that an increase in the temporal channel correlation coefficient, the number of base station antennas, and the received power at the users could help improve system performance. Furthermore, increasing the number of reflecting elements M of the RIS generally yields a good system performance, but with a diminishing return when M is sufficiently large. Finally, simulation results are presented to validate the accuracy of the analytical results.
... In particular, RISs do not require any costly radio frequency (RF) chain for signal reception and retransmission, nor complex signal processing technique for self-interference cancellation; therefore greatly reducing hardware cost and energy consumption [7], [8]. These appealing advantages have driven a variety of wireless communications empowered by RISs, such as RIS-aided single-user MIMO systems [9], RIS-aided multi-user MIMO systems [10], [11], RIS-aided energy transfer [12], RIS-aided orthogonal frequency division multiplexing (OFDM) systems over frequency-selective channels [13], and so on. The authors of [14] realized an RISbased 8-phase shift-keying transmitter that uses an RIS with 256 reconfigurable elements instead of an RF chain. ...
Article
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Reflection modulation based on reconfigurable intelligent surface (RIS) is considered to be a promising information transfer mechanism without requiring any additional radio frequency chains. However, existing reflection modulation schemes consider manipulating the ON/OFF states of RIS elements, which suffers from power loss. In this paper, we propose a new scheme, called RIS-aided quadrature reflection modulation (RIS-QRM), for harvesting the reflection power based on an RIS-aided downlink multiple-input single-output (MISO) wireless system. To this end, RIS-QRM partitions RIS elements into two subsets for reflecting impinging signals into two orthogonal directions as well as passive beamforming and encodes its local data onto the element partition options. A closed-form expression for the unconditional pairwise error probability of RIS-QRM in Rician fading is derived assuming the maximum-likelihood detection. Moreover, we propose a low-complexity detection method with compromised performance for decoupling the joint search of the constellation symbol and the RIS element partition. Computer simulation results corroborate the effectiveness of RIS-QRM and validate the analytical results. It is shown that RIS-QRM is able to improve the error performance of the additional bits delivered by the RIS without deteriorating that of the bits carried on the constellation symbol, as compared to ON/OFF-based schemes.). 2 Reconfigurable intelligent surface (RIS), simultaneous passive beamforming and information transfer , metasurface, error performance, reflection modulation.
... Moreover, in [25] the authors explore the optimization of the RIS-AP distance and the orientation of the RIS in order to maximize the received SNR with the help of a coverage maximization algorithm. In [26] the authors present an analytical approach for the characterization of the SNR distribution and its scaling laws as a function of the number of scattering elements. In [27], the improvement of coverage with the help of RIS in the form of an intelligent wall is explored. ...
Article
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Future wireless networks designed to operate in the millimeter-wave and terahertz bands are expected to be highly assisted by Reconfigurable Intelligent Surfaces (RIS). The role of the RIS will be to mediate possible non-line-of-sight link by redirecting the incident beam from the transmitter to the receiver and possibly modifying its characteristics, in order to optimize the beamforming efficiency and to maximize the signal power at the receiver. Therefore, it is crucial to understand what are the bounds imposed on the received power and how these bounds depend on the system design parameters. In this paper we show that, contrary to typical line-of-sight links, the increase of the transmitter gain does not always guarantee power increase at the receiver, even for an infinitely large RIS, and we explain how the RIS size can further affect the received power. We present an analytical model that captures the performance of the RIS-aided link in the limit of very large RIS, and we demonstrate numerical examples that provide insight on the interplay between the RIS size and the properties of the transmitter beam.
... Similarly, lots of research work [97][98][99][100][101] are available where passive beamformation and its optimization issues are addressed. In [98], authors have demonstrated a deep learning-based LIS reflection design is proposed to enhance the energy efficiency and to reduce the training overhead. ...
Article
This paper presents a comprehensive literature review on the intelligent reflecting surface (IRS) assisted multiple input multiple output(MIMO) system. IRS is a new and key enabling technology that significantly improves the system performance and in combination with MIMO, it is considered to be the front runner for realizing the 6G networks. In this survey, we first discussed the basic concepts of the IRS and the following which we have discussed its advantages and possible applications. we have also provided an overview of the different applications of IRS assisted wireless networks and related issues in a very comprehensive way. The channel estimation protocols and the deployment strategies are reviewed and discussed thoroughly. It also highlights different applications, developed algorithms, and design considerations related to IRS assisted MIMO (IRS-MIMO) systems. And in the final section, we have discussed the research challenges and future research direction related to the IRS-MIMO system for realizing beyond 5G/6G networks.
Article
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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.
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Statistical characterization of the signal-to-noise ratio (SNR) of reconfigurable intelligent surface (RIS)-assistedcommunications in the presence of phase noise is an important open issue. In this letter, we exploit the concept of copula modeling to capture the non-standard dependence features that appear due to the presence of discrete phase noise. In particular,we consider the outage probability of RIS systems in Rayleighfading channels and provide joint distributions to characterize the dependencies due to the use of finite resolution phase shifters at the RIS. Numerical assessments confirm the validity of closed-form expressions of the outage probability and motivate the use of bivariate copula for further RIS studies.
Preprint
This paper derives the asymptotic k-th maximum order statistics of a sequence of independent and non-identically distributed (i.n.i.d.) non-central chi-square random variables with two degrees of freedom. We demonstrate the utility of these results in characterising the signal to noise ratio of a k-th best selection combining receiver with access to a large number of i.n.i.d. signal links each experiencing Rician fading. Furthermore, we derive simple expressions for the corresponding outage probability,average throughput, achievable throughput, and the average bit error probability. The proposed results are validated via extensive Monte Carlo simulations.
Preprint
In this paper, we investigate the performance of an RIS-aided wireless communication system subject to outdated channel state information that may operate in both the near- and far-field regions. In particular, we take two RIS deployment strategies into consideration: (i) the centralized deployment, where all the reflecting elements are installed on a single RIS and (ii) the distributed deployment, where the same number of reflecting elements are placed on multiple RISs. For both deployment strategies, we derive accurate closed-form approximations for the ergodic capacity, and we introduce tight upper and lower bounds for the ergodic capacity to obtain useful design insights. From this analysis, we unveil that an increase of the transmit power, the Rician-K factor, the accuracy of the channel state information and the number of reflecting elements help improve the system performance. Moreover, we prove that the centralized RIS-aided deployment may achieve a higher ergodic capacity as compared with the distributed RIS-aided deployment when the RIS is located near the base station or near the user. In different setups, on the other hand, we prove that the distributed deployment outperforms the centralized deployment. Finally, the analytical results are verified by using Monte Carlo simulations.
Chapter
The diverse and stringent requirements of 6G networks, detailed in the present book, give rise to fully flexible, end-to-end, software-defined network paradigm, where every part of the network can be configured and controlled via software. However, the wireless environment per se – i.e. the wireless medium or channel – is generally assumed uncontrollable, thus, imposing inherent limitations to 6G networks, that arise by the very nature of wireless operation. To this end, the emergence of the newly introduced concept of reconfigurable intelligent surfaces (RISs) challenges the fundamental status quo that the wireless environment is fixed by nature, paving the way for the realization of end-to-end fully reconfigurable 6G networks. RISs are network devices that can control and manipulate the radio waves traversing through the wireless channel. Since RISs reside within the wireless channel and not at the communication endpoints, they can control the wireless channels from within. In this context, the present chapter introduces the concept of RISs within the 6G framework, elaborating on their advantages and limitations. RISs are then compared with other transmission technologies, e.g. phased arrays, multi-antenna transmitters, and relays, while demonstrating the trade-offs governing their operation and applicability. Subsequently, the different types of RIS implementations are presented from a theoretical standpoint, along the available prototypes in the literature; thus, demonstrating how the RIS technology is already a reality, ushering wireless networks into the 6G era.
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Reconfigurable intelligent surfaces (RISs), also known as intelligent reflecting surfaces (IRSs), or large intelligent surfaces (LISs), <sup>1</sup> have received significant attention for their potential to enhance the capacity and coverage of wireless networks by smartly reconfiguring the wireless propagation environment. Therefore, RISs are considered a promising technology for the sixth-generation (6G) of communication networks. In this context, we provide a comprehensive overview of the state-of-the-art on RISs, with focus on their operating principles, performance evaluation, beamforming design and resource management, applications of machine learning to RIS-enhanced wireless networks, as well as the integration of RISs with other emerging technologies. We describe the basic principles of RISs both from physics and communications perspectives, based on which we present performance evaluation of multiantenna assisted RIS systems. In addition, we systematically survey existing designs for RIS-enhanced wireless networks encompassing performance analysis, information theory, and performance optimization perspectives. Furthermore, we survey existing research contributions that apply machine learning for tackling challenges in dynamic scenarios, such as random fluctuations of wireless channels and user mobility in RIS-enhanced wireless networks. Last but not least, we identify major issues and research opportunities associated with the integration of RISs and other emerging technologies for applications to next-generation networks. <sup>1</sup> Without loss of generality, we use the name of RIS in the remainder of this paper. </fn
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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 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.
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Hybrid analog/digital beamforming architecture compromises cost and power consumption of the massive multiple-input multiple-output (massive MIMO) system. On the other hand, the mismatches among different radio frequency (RF) chains, particularly the mismatches of analog phase shifters, can destroy the beamforming accuracy and significantly degrade the system performance. In this paper, we study the system performance of hybrid beamforming systems in the presence of analog mismatches. An upper bound of the system performance is derived. Simulation results show that in typical hybrid beamforming settings, the performance loss can be as large as 64% with 5° analog mismatches. The results also suggest that the advantage of increasing the number of transmit antennas or increasing the signal-to-noise ratio (SNR) is diminishing even with limited analog mismatches. To deal with the mismatch, we propose a new two-phase beamforming algorithm that compensates for the analog mismatches with digital precoder simulation shows, the proposed beamforming algorithm provides satisfactory performance.
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Due to hardware limitations, the phase shifts of the reflecting elements of reconfigurable intelligent surfaces (RISs) need to be quantized into discrete values. This letter aims to unveil the minimum required number of phase quantization levels L in order to achieve the full diversity order in RIS-assisted wireless communication systems. With the aid of an upper bound of the outage probability, we first prove that the full diversity order is achievable provided that L is not less than three. If L=2, on the other hand, we prove that the achievable diversity order cannot exceed (N+1)/2, where N is the number of reflecting elements. This is obtained with the aid of a lower bound of the outage probability. Therefore, we prove that the minimum required value of L for achieving the full diversity order is L=3. Simulation results verify the theoretical analysis and the impact of phase quantization levels on RIS-assisted communication systems.
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Reconfigurable intelligent surfaces (RISs) comprised of tunable unit cells have recently drawn significant attention due to their superior capability in manipulating electromagnetic waves. In particular, RIS-assisted wireless communications have the great potential to achieve significant performance improvement and coverage enhancement in a cost-effective and energy-efficient manner, by properly programming the reflection coefficients of the unit cells of RISs. In this paper, free-space path loss models for RIS-assisted wireless communications are developed for different scenarios by studying the physics and electromagnetic nature of RISs. The proposed models, which are first validated through extensive simulation results, reveal the relationships between the free-space path loss of RIS-assisted wireless communications and the distances from the transmitter/receiver to the RIS, the size of the RIS, the near-field/far-field effects of the RIS, and the radiation patterns of antennas and unit cells. In addition, three fabricated RISs (metasurfaces) are utilized to further corroborate the theoretical findings through experimental measurements conducted in a microwave anechoic chamber. The measurement results match well with the modeling results, thus validating the proposed free-space path loss models for RIS, which may pave the way for further theoretical studies and practical applications in this field.
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In this letter, we analyze the spectral and energy efficiency of an intelligent reflecting surface (IRS)-assisted multiple-input single-output (MISO) downlink system with hardware impairments. An extended error vector magnitude (EEVM) model is utilized to characterize the impact of radio-frequency (RF) impairments at the access point (AP) and phase noise is considered for the imperfect IRS. We show that the spectral efficiency is limited due to the hardware impairments even when the numbers of AP antennas and IRS elements grow infinitely large, which is in contrast with the conventional case with ideal hardware. Moreover, the performance degradation at high SNR is shown to be mainly affected by the AP hardware impairments rather than the phase noise of IRS. We further obtain in closed form the optimal transmit power for energy efficiency maximization. Simulation results are provided to verify the obtained results.
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The future of mobile communications looks exciting with the potential new use cases and challenging requirements of future 6th generation (6G) and beyond wireless networks. Since the beginning of the modern era of wireless communications, the propagation medium has been perceived as a randomly behaving entity between the transmitter and the receiver, which degrades the quality of the received signal due to the uncontrollable interactions of the transmitted radio waves with the surrounding objects. The recent advent of reconfigurable intelligent surfaces in wireless communications enables, on the other hand, network operators to control the scattering, reflection, and refraction characteristics of the radio waves, by overcoming the negative effects of natural wireless propagation. Recent results have revealed that reconfigurable intelligent surfaces can effectively control the wavefront, e.g., the phase, amplitude, frequency, and even polarization, of the impinging signals without the need of complex decoding, encoding, and radio frequency processing operations. Motivated by the potential of this emerging technology, the present article is aimed to provide the readers with a detailed overview and historical perspective on state-of-the-art solutions, and to elaborate on the fundamental differences with other technologies, the most important open research issues to tackle, and the reasons why the use of reconfigurable intelligent surfaces necessitates to rethink the communication-theoretic models currently employed in wireless networks. This article also explores theoretical performance limits of reconfigurable intelligent surface-assisted communication systems using mathematical techniques and elaborates on the potential use cases of intelligent surfaces in 6G and beyond wireless networks.
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Abstract An emerging and promising vision of wireless networks consists of coating the environmental objects with reconfigurable metasurfaces that are capable of modifying the radio waves impinging upon them according to the generalized law of reflection. By relying on tools from point processes, stochastic geometry, and random spatial processes, we model the environmental objects with a modified random line process of fixed length and with random orientations and locations. Based on the proposed modeling approach, we develop the first analytical framework that provides one with the probability that a randomly distributed object that is coated with a reconfigurable metasurface acts as a reflector for a given pair of transmitter and receiver. In contrast to the conventional network setup where the environmental objects are not coated with reconfigurable metasurfaces, we prove that the probability that the typical random object acts as a reflector is independent of the length of the object itself. The proposed analytical approach is validated against Monte Carlo simulations, and numerical illustrations are given and discussed.
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We derive Laguerre expansions for the density and distribution functions of a sum of positive weighted noncentral chi-square variables. The procedure that we use is based on the inversion of Laplace transforms. The formulas so obtained depend on certain parameters, which adequately chosen will give some expansions already known in the literature and some new ones. We also derive precise bounds for the truncation error.
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Reconfigurable intelligent surface~(RIS) has drawn a great attention worldwide as it can create favorable propagation conditions by controlling the phase shifts of the reflected signals at the surface to enhance the communication quality. However, the practical RIS only has limited phase shifts, which will lead to the performance degradation. In this letter, we evaluate the performance of an uplink RIS assisted communication system by giving an approximation of the achievable data rate, and investigate the effect of limited phase shifts on the data rate. In particular, we derive the required number of phase shifts under a data rate degradation constraint. Numerical results verify our analysis.
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Intelligent reflecting surface (IRS) is a cost-effective solution for achieving high spectrum and energy efficiency in future wireless networks by leveraging massive low-cost passive elements that are able to reflect the signals with adjustable phase shifts. Prior works on IRS mainly consider continuous phase shifts at reflecting elements, which are practically difficult to implement due to the hardware limitation. In contrast, we study in this paper an IRS-aided wireless network, where an IRS with only a finite number of phase shifts at each element is deployed to assist in the communication from a multi-antenna access point (AP) to multiple single-antenna users. We aim to minimize the transmit power at the AP by jointly optimizing the continuous transmit precoding at the AP and the discrete reflect phase shifts at the IRS, subject to a given set of minimum signal-to-interference-plus-noise ratio (SINR) constraints at the user receivers. The considered problem is shown to be a mixed-integer non-linear program (MINLP) and thus is difficult to solve in general. To tackle this problem, we first study the single-user case with one user assisted by the IRS and propose both optimal and suboptimal algorithms for solving it. Besides, we analytically show that as compared to the ideal case with continuous phase shifts, the IRS with discrete phase shifts achieves the same squared power gain in terms of asymptotically large number of reflecting elements, while a constant proportional power loss is incurred that depends only on the number of phase-shift levels. The proposed designs for the single-user case are also extended to the general setup with multiple users among which some are aided by the IRS. Simulation results verify our performance analysis as well as the effectiveness of our proposed designs as compared to various benchmark schemes.
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Assume the communication between a source and a destination is supported by a large reflecting surface (LRS), which consists of an array of reflector elements with adjustable reflection phases. By knowing the phase shifts induced by the composite propagation channels through the LRS, the phases of the reflectors can be configured such that the signals combine coherently at the destination, which improves the communication performance. However, perfect phase estimation or high-precision configuration of the reflection phases is unfeasible. We study the transmission through an LRS with phase errors that have a generic distribution. We show that the LRS-based composite channel is equivalent to a direct channel with Nakagami scalar fading. This equivalent representation allows for theoretical analysis of the performance and can help the system designer study the interplay between performance, the distribution of phase errors, and the number of reflectors. Numerical evaluation of the error probability for a limited number of reflectors confirms the theoretical prediction and shows that the performance is remarkably robust against the phase errors.
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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.
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In this paper, we analyze the non-asymptotic performance of scaled largest eigenvalue based detection, which is an optimal detector in the presence of a single primary user. Exact distributions of the test statistics have been derived, which lead to finite-dimensional characterizations of the false alarm probability. These results are obtained by taking advantage of the properties of the Mellin transform for products of independent random variables. Simulations are provided to verify the derived results, and to compare with the asymptotic result in literature.
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This paper introduces a new probability distribution based on the H-function of Fox. The distribution is shown to be a generalization of most common “nonnegative” (Pr $\Pr ([X < 0] = 0)$ distributions. Furthermore, it is proved that products, quotients and powers of H-function variates are H-function variates. Several examples are given.
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We derive efficient recursive formulas giving the exact distribution of the largest eigen- value for finite dimensions real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the limiting distribution of large random matrices, we also show that the Tracy-Widom laws can be approximated by a properly scaled and shifted Gamma distribution, with great accuracy for the values of common interest in statistical applications. Thus, the largest eigenvalue distribution for Wishart and Gaussian matrices can be approximated simply by a shifted Gamma distribution with known parameters.
RFocus: Beamforming using thousands of passive antennas
  • V Arun
  • H Balakrishnan
V. Arun and H. Balakrishnan, "RFocus: Beamforming using thousands of passive antennas", USENIX NSDI, pp. 1047-1061, Feb. 2020.
  • Di Renzo
M. Di Renzo et al., "Reconfigurable intelligent surfaces vs. relaying: Differences, similarities, and performance comparison", arXiv, Aug. 2019. [Online]. Available: arXiv:1908.08747.
Analytical modeling of the path-loss for reconfigurable intelligent surfaces -Anomalous mirror or scatterer?
  • Di Renzo
M. Di Renzo et al., "Analytical modeling of the path-loss for reconfigurable intelligent surfaces -Anomalous mirror or scatterer?", IEEE SPAWC, Jan. 2020. [Online]. Available: arXiv:2001.10862.