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Beamforming Through Reconfigurable Intelligent Surfaces in Single-User MIMO Systems: SNR Distribution and Scaling Laws in the Presence of Channel Fading and Phase Noise
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.
... Within the third generation partnership program (3GPP), for example, different new network nodes are currently being discussed, including the integrated access and backhaul (IAB) node, the network-controlled repeater node, the reconfigurable intelligent surface (RIS) node, and the smart skin node [6]. Recently, RISs have gained considerable attention from academia and industry due to their ability of controlling the propagation characteristics of wireless environments via passive scattering elements integrated with lowcost and low-power electronics [7]- [11]. For example, the authors of [7] studied the statistics of the signal-to-noise ratio (SNR) when the number of RIS elements grows large. ...
... Recently, RISs have gained considerable attention from academia and industry due to their ability of controlling the propagation characteristics of wireless environments via passive scattering elements integrated with lowcost and low-power electronics [7]- [11]. For example, the authors of [7] studied the statistics of the signal-to-noise ratio (SNR) when the number of RIS elements grows large. The minimization of the total transmit power at a multiple antenna access point (AP) in multiple-input single-output (MISO) RISassisted wireless systems was investigated in [8], by jointly optimizing the transmit beamforming at the AP and the phase profile at the RIS. ...
... The deployment of an RIS in cognitive radio systems was studied in [10], where the spectrum is shared between the primary and secondary users. With the exception of [7], which relies on large-scale analysis, these research works are focused on optimization algorithms and do not provide any closed-form expressions for the distribution of the signal-to-noise ratio (SNR) and ergodic rate of RIS-aided networks. ...
Reconfigurable intelligent surface (RIS) has recently gained significant interest as an emerging technology for future wireless networks thanks to its potential for improving the coverage probability in challenging propagation environments. This paper studies an RIS-assisted propagation environment, where a source transmits data to a 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, we derive closed-form expressions for the coverage probability and ergodic rate, which explicitly unveil the impact of both the propagation environment and the RIS on the system performance. Besides the optimization of the RIS phase profile, we formulate an RIS placement optimization problem with the aim of maximizing the coverage probability by relying only on partial channel state information. An efficient algorithm is proposed based on the gradient ascent method. Simulation results are illustrated in order to corroborate the analytical framework and findings. The proposed RIS phase profile is shown to outperform several heuristic benchmarks in terms of outage probability and ergodic rate. In addition, the proposed RIS placement strategy provides an extra degree of freedom that remarkably improves system performance.
... Generally, the phase noise is statistically distributed as Gaussian or generalized uniform [22]. Under the statistical phase noise, performance [23] No No Symmetric (Rayleigh, Rayleigh) CLT [29] No No Symmetric (General, General) Approximation [24] Yes No Symmetric (Rayleigh, Rayleigh) CLT [25] Yes No Symmetric (Rayleigh, Rayleigh) CLT [27] No No Symmetric (Rician, Rician) Approximation [22] No No Symmetric (Fox-H, Fox-H) CLT, lower and upper bounds [28] No No Symmetric (Nakagami-m, Nakagami-m) Exact for integer m This Paper Yes Yes Asymmetric (κ-µ, dGG) Exact and Bounds of RIS-assisted wireless system requires the analysis for the sum of the product of three fading coefficients. As is for perfect phase compensations, existing works approximate the performance of RIS system for various fading channels in the presence of phase noise [5], [23]- [28]. ...
... Under the statistical phase noise, performance [23] No No Symmetric (Rayleigh, Rayleigh) CLT [29] No No Symmetric (General, General) Approximation [24] Yes No Symmetric (Rayleigh, Rayleigh) CLT [25] Yes No Symmetric (Rayleigh, Rayleigh) CLT [27] No No Symmetric (Rician, Rician) Approximation [22] No No Symmetric (Fox-H, Fox-H) CLT, lower and upper bounds [28] No No Symmetric (Nakagami-m, Nakagami-m) Exact for integer m This Paper Yes Yes Asymmetric (κ-µ, dGG) Exact and Bounds of RIS-assisted wireless system requires the analysis for the sum of the product of three fading coefficients. As is for perfect phase compensations, existing works approximate the performance of RIS system for various fading channels in the presence of phase noise [5], [23]- [28]. In [5], [23], [24], [25], authors applied the CLT to analyze the performance of RIS system over Rayleigh fading channel with phase errors. ...
... As is for perfect phase compensations, existing works approximate the performance of RIS system for various fading channels in the presence of phase noise [5], [23]- [28]. In [5], [23], [24], [25], authors applied the CLT to analyze the performance of RIS system over Rayleigh fading channel with phase errors. The authors in [29] approximated an arbitrary fading model with Nakagami-m distributed to develop performance analysis of the RIS-assisted transmission with phase noise. ...
Recent research provides an approximation on the performance for reconfigurable intelligent surface (RIS) assisted systems over generalized fading channels with phase noise resulting from imperfect phase compensation at the RIS. In this paper, we developed exact analysis and upper bounds on the performance of RIS-assisted vehicular communication system considering phase noise with mobility over asymmetric fading channels by coherently combining received signals reflected by RIS elements and direct transmissions from the source terminal. We employ a novel approach to represent the PDF and CDF of the product of four channel coefficients in terms of a single univariate Fox-H function. We use the derived PDF to develop an exact statistical analysis of the end-to-end SNR for the RIS-assisted system using multi-variate Fox-H function.
... 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). ...
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.
... 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 ...
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 optimizing the reflection coefficients of the RIS elements, it is possible to overcome the adverse effects of uncontrolled wireless propagation, resulting in a variety of performance and implementation gains. The RIS technology can be used to improve the received power [3], achievable rate [4], [5], mutual information [6], [7], interference management [8] and coverage [9]. In the aforementioned papers, it is assumed that each RIS element can reflect any impinging radio wave with unitary power efficiency and an arbitrary phase shift, and that the electromagnetic (EM) coupling between adjacent RIS elements is negligible. ...
... It is worth noting that the mutual impedances depend on the system geometry, i.e., the relative position and orientation of the transmitter, receiver and RIS, which are assumed to be fixed in this work. Also, finding the optimal position and orientation of the RIS in this context is an interesting open issue.3 The optimization of z RIS,Re implies that the RIS may also consist of active reflecting elements. ...
The electromagnetic (EM) features of reconfigurable intelligent surfaces (RISs) fundamentally determine their operating principles and performance. Motivated by these considerations, we study a single-input single-output (SISO) system in the presence of an RIS, which is characterized by a circuit-based EM-compliant model. Specifically, we model the RIS as a collection of thin wire dipoles controlled by tunable load impedances, and we propose a gradient-based algorithm for calculating the optimal impedances of the scattering elements of the RIS in the presence of mutual coupling. Furthermore, we prove the convergence of the proposed algorithm and derive its computational complexity in terms of number of complex multiplications. Numerical results show that the proposed algorithm provides better performance than a benchmark algorithm and that it converges in a shorter amount of time.
... 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 [18], [20]. In these cases, the phase of the ith element of the RIS can be written as ...
... Likewise, due to hardware limitations, only a finite number of phase shifts can be realized, which leads to quantization errors. In this case, the generalized uniform distribution constitutes a versatile model to account for the quantization noise by setting q = 2 −L , where L ≥ 1 is a positive integer that denotes the number of quantization bits used [18], [20]. ...
In this paper, we develop a unified theoretical framework for analyzing the outage performance of reconfigurable intelligent surfaces (RISs)-assisted communication systems over generalized fading channels and in the presence of phase noise. Fox’s H function theory is then utilized to derive the outage probability for various channel fading and phase noise distributions in closed-form. We further conduct an asymptotic outage analysis to obtain insightful findings. In particular, we present the maximum diversity order achievable over such channels and demonstrate the performance variation in comparison to conventional Rayleigh channels. Then, based on upper bounds and lower bounds, we propose a design criteria for RISs to achieve the maximum diversity order in the presence of phase noise. More specifically, we show that 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.
... However, the effects of hardware impairments and environmental imperfections have been rarely studied in the literature. For instance, [32]- [35], consider RISs operating under finite resolution of the phase shifts or phase estimation errors from imperfect channel estimation. Then, [36] and [37] consider different environmental effects on the RIS and propose methods to jointly estimate the channel and array blockage parameters in mmWave RIS-assisted systems. ...
... 2) α n,p = 1 and θ n,p = 0 represent the phase noise perturbations from low-resolution phase shifts or phase errors from imperfect channel estimation [32]- [35]. ...
Reconfigurable intelligent surface is a potential technology component of future wireless networks due to its capability of shaping the wireless environment. The promising MIMO systems in terms of extended coverage and enhanced capacity are, however, critically dependent on the accuracy of the channel state information. However, traditional channel estimation schemes are not applicable in RIS-assisted MIMO networks, since passive RISs typically lack the signal processing capabilities that are assumed by channel estimation algorithms. This becomes most problematic 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. While these real-world effects are typically ignored in the literature, in this paper we propose efficient channel estimation schemes for RIS-assisted MIMO systems taking different imperfections into account. Specifically, we propose two sets of tensor-based algorithms, based on the parallel factor analysis decomposition schemes. First, by assuming a long-term model in which the RIS imperfections, modeled as unknown phase shifts, are static within the channel coherence time we formulate an iterative alternating least squares (ALS)-based algorithm for the joint estimation of the communication channels and the unknown phase deviations. Next, we develop the short-term imperfection model, which allows both amplitude and phase RIS imperfections to be non-static with respect to the channel coherence time. We propose two iterative ALS-based and closed-form higher order singular value decomposition-based algorithms for the joint estimation of the channels and the unknown impairments. Moreover, we analyze the identifiability and computational complexity of the proposed algorithms and study the effects of various imperfections on the channel estimation quality.
... 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 ...
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.
... 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. ...
Meta-surfaces intend to improve the performance of future wireless networks significantly by controlling the wireless propagation and shaping the radio waves according to the generalized Snell's law. A recent application of meta-surfaces are reconfigurable intelligent surfaces that are mainly proposed for the reflection and steering of the impinging signal. In this article, we introduce randomly reconfigurable surfaces (RRSs) aiming to diffuse the incoming wave and characterize the performance of an RRS-assisted communication network. To facilitate the performance analysis of an RRS-assisted network, first, we present novel closed-form expressions for the probability density function, the cumulative distribution function, the moments, and the characteristic function of the amplitude of the distribution of the sum of double-Nakagami-
$m$
random vectors, whose amplitudes follow the double-Nakagami-
$m$
distribution, and phases following 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 the obtained expressions to investigate the RRS-assisted composite channel, assuming that the two links undergo Nakagami-
$m$
fading. Specifically, 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. Finally, these metrics are also derived for the practical special case where one of the two links undergoes Rayleigh fading, implying that this link is non-line-of-sight.
... 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. ...
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.
... In [13], a codebook-based framework is studied to strike flexible trade-offs between communication performance and signaling overhead. Discrete reflection coefficients have been optimized to enhance the performance of multiple-input multiple-output (MIMO) communications by solving rate maximization problems in single-user systems [14], [15], [16], [17] and sum-rate maximization problems in multi-user systems [18], [19], [20], [21], [22], [23]. In [24], [25], the transmit power is minimized by jointly optimizing the continuous transmit precoding and the discrete phase shifts in the RIS. ...
Reconfigurable intelligent surfaces (RISs) allow controlling the propagation environment in wireless networks through reconfigurable elements. Recently, beyond diagonal RISs (BD-RISs) have been proposed as novel RIS architectures whose scattering matrix is not limited to being diagonal. However, BD-RISs have been studied assuming continuous-value scattering matrices, which are hard to implement in practice. In this paper, we address this problem by proposing two solutions to realize discrete-value group and fully connected RISs. First, we propose scalar-discrete RISs, in which each entry of the RIS impedance matrix is independently discretized. Second, we propose vector-discrete RISs, where the entries in each group of the RIS impedance matrix are jointly discretized. In both solutions, the codebook is designed offline such as to minimize the distortion caused in the RIS impedance matrix by the discretization operation. Numerical results show that vector-discrete RISs achieve higher performance than scalar-discrete RISs at the cost of increased optimization complexity. Furthermore, fewer resolution bits per impedance are necessary to achieve the performance upper bound as the group size of the group connected architecture increases. In particular, only a single resolution bit is sufficient in fully connected RISs to approximately achieve the performance upper bound.
... According to (30), (31), (33), (34), (35) and (36), the instantaneous sum-rate of the STAR-RIS aided NOMA uplink is given by ...
Reconfigurable intelligent surfaces (RIS) are capable of beneficially ameliorating the propagation environment by appropriately controlling the passive reflecting elements. To extend the coverage area, the concept of simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) has been proposed, yielding supporting 360^circ coverage user equipment (UE) located on both sides of the RIS. In this paper, we theoretically formulate the ergodic sum-rate of the STAR-RIS assisted non-orthogonal multiple access (NOMA) uplink in the face of channel estimation errors and hardware impairments (HWI). Specifically, the STAR-RIS phase shift is configured based on the statistical channel state information (CSI), followed by linear minimum mean square error (LMMSE) channel estimation of the equivalent channel spanning from the UEs to the access point (AP). Afterwards, successive interference cancellation (SIC) is employed at the AP using the estimated instantaneous CSI, and we derive the theoretical ergodic sum-rate upper bound for both perfect and imperfect SIC decoding algorithm. The theoretical analysis and the simulation results show that both the channel estimation and the ergodic sum-rate have performance floor at high transmit power region caused by transceiver hardware impairments.
... According to (30), (31), (33), (34), (35) and (36), the instantaneous sum-rate of the STAR-RIS aided NOMA uplink is given by ...
Reconfigurable intelligent surfaces (RIS) are capable of beneficially ameliorating the propagation environment by appropriately controlling the passive reflecting elements. To extend the coverage area, the concept of simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) has been proposed, yielding supporting 360^\circ coverage user equipment (UE) located on both sides of the RIS. In this paper, we theoretically formulate the ergodic sum-rate of the STAR-RIS assisted non-orthogonal multiple access (NOMA) uplink in the face of channel estimation errors and hardware impairments (HWI). Specifically, the STAR-RIS phase shift is configured based on the statistical channel state information (CSI), followed by linear minimum mean square error (LMMSE) channel estimation of the equivalent channel spanning from the UEs to the access point (AP). Afterwards, successive interference cancellation (SIC) is employed at the AP using the estimated instantaneous CSI, and we derive the theoretical ergodic sum-rate upper bound for both perfect and imperfect SIC decoding algorithm. The theoretical analysis and the simulation results show that both the channel estimation and the ergodic sum-rate have performance floor at high transmit power region caused by transceiver hardware impairments. Index Terms-Reconfigurable intelligent surfaces (RIS), simultaneous transmitting and reflecting (STAR), non-orthogonal multiple access (NOMA), imperfect channel state information (CSI), hardware impairments (HWI).
... where ρ 0 denotes the channel power gain at the unit reference distance in LoS state, µ 0 is the additional signal attenuation factor due to the more complex electromagnetic propagation environment in NLoS state [40]. α L and α N denote the path loss exponents for LoS and NLoS states, respectively. ...
The rapid development of unmanned aerial vehicle (UAV) technology provides flexible communication services to terrestrial nodes. Energy efficiency is crucial to the deployment of UAVs, especially rotary-wing UAVs whose propulsion power is sensitive to the wind effect. In this paper, we first derive a three-dimensional (3D) generalised propulsion energy consumption model (GPECM) for rotary-wing UAVs under the consideration of stochastic wind modeling and 3D force analysis. Based on the GPECM, we study a UAV-enabled downlink communication system, where a rotary-wing UAV flies subject to stochastic wind disturbance and provides communication services for ground users (GUs). We aim to maximize the energy efficiency (EE) of the UAV by jointly optimizing the 3D trajectory and user scheduling among the GUs based on the GPECM. We formulate the problem as stochastic optimization, which is difficult to solve due to the lack of real-time wind information. To address this issue, we propose an offline-based online adaptive (OBOA) design with two phases, namely, an offline phase and an online phase. In the offline phase, we average the wind effect on the UAV by leveraging stochastic programming (SP) based on wind statistics; then, in the online phase, we further optimize the instantaneous velocity to adapt the real-time wind. Simulation results show that the optimized trajectories of the UAV in both two phases can better adapt to the wind in changing speed and direction, and achieves a higher EE compared with the windless scheme. In particular, our proposed OBOA design can be applied in the scenario with dramatic wind changes, and makes the UAV adjust its velocity dynamically to achieve a better performance in terms of EE.
... ISAC systems is enhanced. Many papers have investigated how to deploy RISs in communication systems, with contributions on joint beamforming [16]- [18] and robust transmission design [19], [20]. In general, the knowledge of CSI of the base station (BS)-RIS and RIS-user equipment (UE) links is needed for RIS optimization [21]. ...
Integrated sensing and communications (ISAC) is emerging as a critical technique for next-generation communication systems. Reconfigurable intelligent surface (RIS) can simultaneously enhance the performance of communication and sensing by introducing new degrees-of-freedom for beamforming in ISAC systems. This paper proposes two optimization techniques for joint beamforming in RIS-assisted ISAC systems. We first aim to maximize the radar mutual information (MI) by imposing constraints on communication rate, transmit power, and unit modulus reflection coefficients at the RIS. An alternating optimization (AO) algorithm based on the semidefinite relaxation (SDR) method is proposed to solve the optimization problem by introducing a convergence-accelerating method. To achieve lower computational complexity and better reliability, we then formulate a new optimization problem for maximizing the weighted ISAC performance metrics under fewer constraints. An AO algorithm based on the Riemannian gradient (RG) method is proposed to solve this problem. This is achieved by reformulating the transmit and RIS beamforming on the complex hypersphere manifold and complex circle manifold, respectively. Numerical results show that the proposed algorithms can enhance the radar MI and the weighted communication rate simultaneously. The AO algorithm based on RG exhibits better performance than the SDR-based method.
... All channels are modeled with Nakagami-m distribution, which can be used in LOS and NLOS propagation since m = (K+1) 2 2K+1 [40], where K is the Rician factor that describes the LOS component. Similar to [25], [41], we assume the LoS link between Alice and RIS, while the RIS and Bob/Eves links are assumed to be NLoS due to the mobility of ground users. Therefore, we calculate ESC of the network by setting m 2 = 1, which emulates the Rayleigh channel for the RIS-Bob/Alice link. ...
We propose a novel approach for enhancing physical layer security (PLS) in wireless networks by utilizing a combination of reconfigurable intelligent surfaces (RIS) and artificial noise (AN). The proposed aerial RIS (A-RIS) concept utilizes a RIS-attached unmanned aerial vehicle (UAV) that hovers over the network area to improve the signal quality for legitimate users and jam that of illegitimate ones. We propose a method of virtually partitioning the RIS, such that the partition phase shifts are configured to improve the intended signal at a legitimate user while simultaneously increasing the impact of AN on illegitimate users. Closed-form expressions for both legitimate and illegitimate users' ergodic secrecy capacity (ESC) are derived and validated. Then, optimization problems are formulated to maximize network ESC by optimizing the 3D deployment of the A-RIS and RIS portions for users subject to predefined quality-of-service constraints. Simulation results validate closed-form solutions and demonstrate that the proposed joint A-RIS deployment and partitioning framework can significantly improve network security compared to benchmarks where RIS and AN are separately used without deployment optimization. Additionally, thanks to the availability of closed-form optimal RIS portions, the proposed deployment approaches converge in less than a second, making it suitable for dynamic A-RIS deployment.
... Upon substituting (15), (16), (17) and (18) into (14), we can express the power of the equivalent noise as ...
The linear minimal mean square error (LMMSE) estimator for active reconfigurable intelligent surface (RIS)-aided wireless systems is formulated. Furthermore, based on the moment-matching method, we employ the Gamma distribution to approximate the distribution of the instantaneous received signal-to-interference-plus-noise ratio (SINR), and then derive the closed-form outage probability and ergodic channel capacity in the presence of realistic channel estimation errors, the thermal noise of RIS amplifiers and the RIS phase shift noise. Our theoretical analysis and simulation results show that the introduction of RIS amplifiers is equivalent to increasing of the transmit power, and also present the performance degradation resulting from the channel estimation error and the RIS phase noise.
... Upon substituting (15), (16), (17) and (18) into (14), we can express the power of the equivalent noise as ...
The linear minimal mean square error (LMMSE) estimator for active reconfigurable intelligent surface (RIS)-aided wireless systems is formulated. Furthermore, based on the moment-matching method, we employ the Gamma distribution to approximate the distribution of the instantaneous received signal-to-interference-plus-noise ratio (SINR), and then derive the closed-form outage probability and ergodic channel capacity in the presence of realistic channel estimation errors, the thermal noise of RIS amplifiers and the RIS phase shift noise. Our theoretical analysis and simulation results show that the introduction of RIS amplifiers is equivalent to increasing of the transmit power, and also present the performance degradation resulting from the channel estimation error and the RIS phase noise. Index Terms-Active reconfigurable intelligent surfaces (RIS), channel estimation, outage probability, ergodic channel capacity.
... It should be mentioned that the combined effect of fading and phase noise has been extensively studied in the context of RIS-RF [16]- [21]. In [16], [17], [18], [19], authors have applied the central limit theorem (CLT) to derive an achievable diversity order, maximize SNR and quantifying capacity degradation of the RIS system. Although in [22] , more accurate methods than CLT are used, authors approximated an arbitrary fading model with Nakagami-m distributed to develop performance analysis of the RIS-assisted transmission with phase noise. ...
Existing research works on reconfigurable intelligent surfaces (RIS) based terahertz (THz) system ignores the effect of phase noise and employ the zero-boresight pointing errors model of the free-space optics channel in performance analysis. In this paper, we analyze the performance of RIS-THz transmission under the combined effect of channel fading, THz pointing error (TPE), and statistical phase noise due to imperfect phase compensation at each RIS element. First, we derive statistical results of the double $\alpha$-$\mu$ fading combined with the TPE and phase noise at individual RIS elements using single-variate Fox's function. Next, we use the multi-variate Fox's H-function representation to develop exact analytical expressions for the density and distribution functions of the resultant signal-to-noise ratio (SNR) of the RIS-THz link considering the accumulating propagation effect from all RIS elements. Using the derived statistical results, we analyze the exact and asymptotic expressions for the considered system's outage probability and average bit-error rate (BER). The analytical results show that the diversity order of the system is independent of phase noise, depends on the channel fading parameters $\alpha$ and $\mu$, and depends on the $\beta$ parameter of the TPE.
... This is especially the case in scenarios where the power along the scattered components are negligible. links between the transmitter and the receiver, and the receiver makes use of the signal along only one of these links for information processing 6 . Here, we study the case where the receiver selects the k-th best (out of M) link in terms of the SNR at the receiver for information processing. ...
This paper derives the asymptotic distribution of the normalized
k
-th maximum order statistics of a sequence of non-central chi-square random variables with non-identical non-centrality parameters. We demonstrate the utility of these results in characterizing the signal-to-noise ratio in three different applications in wireless communication systems where the statistics of the
k
-th maximum channel power over Rician fading links are of interest. Furthermore, we derive simple expressions for the asymptotic outage probability, average throughput, achievable throughput, and average bit error probability. The proposed results are validated via extensive Monte Carlo simulations.
... 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] . ...
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.
... 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]. ...
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.
Reconfigurable intelligent surfaces (RISs) are programmable metasurface structures that can control the propagation of electromagnetic waves by changing the electrical and magnetic properties of the surface. They can be used to intelligently reconfigure the wireless environment to improve the capacity and coverage of wireless networks. In recent years, numerous theoretical innovations and prototype tests have demonstrated that the RIS has the advantages of low cost, low power consumption, and easy deployment, and creates many potential opportunities and broad application prospects in 5G and future 6G networks. In this paper, starting from the technological development of RISs, we discussed the technical issues of RISs. The standardization of RISs, types of RISs according to operation modes, channel modeling, considerations for hardware implementation, differences from existing communication modules and the need for active RIS implementation, noise and power characteristics to ensure the efficiency of RISs, and performance parameters of RISs and field test results of RISs in indoor and outdoor environments were reviewed. By resolving the current technical issues of RISs, it is expected that RISs will be successfully used for B5G/6G communication through commercialization.
The current research offers only approximations for evaluating the performance of wireless systems that use reconfigurable intelligent surfaces (RIS) over generalized fading channels with phase error caused by imperfect phase compensation at the RIS. This paper presents an exact analysis of RIS-assisted vehicular communication considering uniformly distributed phase error and generalized fading channels with a coherent combining of received signals reflected by RIS elements and direct transmissions from the source terminal. We use a generalized-
$K$
shadowed distribution for the direct link and asymmetrical channels for the RIS-assisted transmission with
$\kappa$
-
$\mu$
distribution for the first link and double generalized Gamma (dGG) distribution for the second link, combined with a statistical random waypoint (RWP) model for the moving vehicle. We employ a novel approach to represent the probability density function (PDF) and cumulative distribution function (CDF) of the resultant channel in terms of a single univariate Fox-H function and use the multivariate Fox-H approach to develop an exact statistical analysis of the end-to-end signal-to-noise ratio (SNR) for the RIS-assisted system. We also use the inequality between the arithmetic and geometric means to simplify the statistical results of the considered system in terms of the univariate Fox-H function. Our analysis also provides exact, upper bound, and asymptotic expressions of the outage probability and average bit-error-rate (BER) performance using the derived density and distribution functions. We conduct computer simulations in various practically relevant scenarios to assert that mitigating phase errors is achievable by augmenting the number of elements in the RIS module and employing a higher quantization level.
The promising gains of reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) systems, in terms of extended coverage and enhanced capacity, are critically dependent on the accuracy of the channel state information. However, traditional channel estimation (CE) schemes are not applicable in RIS-assisted MIMO networks, since passive RISs typically lack the signal processing capabilities that are assumed by CE algorithms. This becomes problematic 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. While these real-world effects are typically ignored in the literature, in this paper we propose efficient CE schemes for RIS-assisted MIMO systems taking different imperfections into account. Specifically, we propose two sets of tensor-based algorithms, based on the parallel factor analysis decomposition schemes. First, assuming a long-term model-where the RIS imperfections, modeled as unknown phase shifts, are static within the channel coherence time-we formulate an iterative alternating least squares (ALS)- based algorithm for the joint estimation of the unknown phase deviations and the communication channels. Then, we develop the short-term imperfection model, which allows both amplitude and phase RIS imperfections to be non-static with respect to the channel coherence time. We propose two iterative ALS-based and closed-form higher-order singular value decomposition-based algorithms for jointly estimating the channels and the unknown impairments. We also investigate the computational complexity and the identifiability of the proposed algorithms and study the effect of various imperfections on the CE quality. Simulation results show the effectiveness of our proposed tensor-based algorithms in terms of estimation accuracy and computational complexity.
Intelligent reflecting surface (IRS) is a promising technology for the
$6^\mathrm{th}$
generation of wireless systems, realizing the smart radio environment concept. This paper presents a novel tensor-based receiver for IRS-assisted multiple-input multipleoutput communications capable of jointly estimating the channels and the transmitted data streams in a semi-blind fashion. Assuming a fully passive IRS architecture and introducing a simple space-time coding scheme at the transmitter, the received signal model can be advantageously built using the PARATUCK tensor model, which can be seen as a hybrid of parallel factor analysis and Tucker models. A semi-blind receiver is derived by exploiting the algebraic structure of the PARATUCK tensor model. We first formulate a semi-blind receiver based on a trilinear alternating least squares method that iteratively estimates the two involved-IRS-base station and user terminal-IRS-communication channels and the transmitted symbol matrix. We discuss identifiability conditions that ensure the joint semi-blind recovery of the involved channel and symbol matrices and propose a joint design of the coding and IRS reflection matrices to optimize the receiver performance. We also formulate an enhanced two-stage semiblind receiver that efficiently exploits the direct link to refine the channel and symbol estimates iteratively. In particular, we discuss the impact of an imperfect IRS absorption (residual reflection) on the performance of the proposed receiver. Numerical results are proposed for performance evaluation in several system settings in terms of the normalized mean squared error of the estimated channels and the achieved symbol error rate, corroborating the merits of the proposed semi-blind receiver in comparison to competing methods.
In this paper, we study surface-based communication systems based on different levels of channel state information for system optimization. We analyze the system performance in terms of rate and degrees of freedom (DoF). We show that the deployment of a reconfigurable intelligent surface (RIS) results in increasing the number of DoF, by extending the near-field region. Over Rician fading channels, we show that an RIS can be efficiently optimized only based on the positions of the transmitting and receiving surfaces, while providing good performance if the Rician fading factor is not too small.
Recent studies have shown that intelligent reflecting surfaces (IRS) can significantly improve the spectral and energy efficiency of wireless communication links. However, most works assume perfect transceivers and IRS, which is impractical in real communication systems. In this work, we study the effect of the hardware impairments in IRS-assisted MISO systems with single user, where we consider both phase noise caused by the imperfect transceivers and IRS. To this end, we propose a linear minimum mean square error (LMMSE) channel estimation algorithm that takes the phase noise into account. Furthermore, we study the impact of phase noise on the downlink performance of an IRS-assisted system. Both analytical and numerical results are presented, where we prove that the transceiver phase noise can be compensated with the optimized IRS, while the IRS phase noise remains but is not exacerbated. As the number of reflective elements
N
approaches infinity, the IRS phase noise results in a constant loss in terms of the ergodic rate. Moreover, we find that the phase noise has no impact on the scaling laws. If the direct channel is blocked and as
N
→ ∞, the transmit power can be scaled down by 1/
N
and 1/
N
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>
, respectively, for random and optimized IRS, without compromising the received signal to noise ratio (SNR).
i>Active intelligent reflecting surface (IRS) has been recently proposed to alleviate the product path loss attenuation inherent in the IRS-aided cascaded channel. 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.
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 introduce 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 the accuracy of 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.
New technologies, applications, and services demand high throughput, robustness, reliability, massive connections support, and low latency. This quality of service (QoS) requirements imply the redefinition of networks and wireless communication systems. However, the mobile network does not exploit the maximum channel capacity due to the effects of signal propagation in free space. Therefore, it is necessary to improve wireless communication through the evolution of the current systems by adding new technologies such as reconfigurable intelligent surfaces (RIS). RIS comprises surface arranged elements used to control impinging signal's phase and amplitude towards a predefined direction, allowing mitigating propagation effects such as attenuation and multipath propagation phenomena. This article presents a study about RIS-related aspects such as operation principles, propagation models, and potential application scenarios. First, it highlights the metasurface basic concepts and their limitations related to implementation. Second, the propagation models are discussed and compared concerning their parameters. Finally, some RIS application scenarios are described.
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.
In this letter, we employ quadrature spatial modulation (QSM) in both transmitter and receiver with the assistance of an intelligent reflecting surface (IRS), which we refer to as IRS-transceiver QSM (IRS-TQSM). In the compressive sensing (CS) framework, we cast the receiver processing as a sparsity recovery problem and propose a low-complexity algorithm by coupling the energy detector (ED) with convex programming (CP), referred to as ED-CP. The out-performance of the proposed IRS-TQSM with ED-CP compared to closely related works is demonstrated with numerical results.
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.
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.
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.
Statistical characterization of the signal-to-noise ratio (SNR) of reconfigurable intelligent surface (RIS)-assisted communications 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 Rayleigh fading 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.
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
$N$
.
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.
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.
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.
Future wireless networks are expected to constitute a distributed intelligent wireless communications, sensing, and computing platform, which will have the challenging requirement of interconnecting the physical and digital worlds in a seamless and sustainable manner. Currently, two main factors prevent wireless network operators from building such networks: (1) the lack of control of the wireless environment, whose impact on the radio waves cannot be customized, and (2) the current operation of wireless radios, which consume a lot of power because new signals are generated whenever data has to be transmitted. In this paper, we challenge the usual “more data needs more power and emission of radio waves” status quo, and motivate that future wireless networks necessitate a smart radio environment: a transformative wireless concept, where the environmental objects are coated with artificial thin films of electromagnetic and reconfigurable material (that are referred to as reconfigurable intelligent meta-surfaces), which are capable of sensing the environment and of applying customized transformations to the radio waves. Smart radio environments have the potential to provide future wireless networks with uninterrupted wireless connectivity, and with the capability of transmitting data without generating new signals but recycling existing radio waves. We will discuss, in particular, two major types of reconfigurable intelligent meta-surfaces applied to wireless networks. The first type of meta-surfaces will be embedded into, e.g., walls, and will be directly controlled by the wireless network operators via a software controller in order to shape the radio waves for, e.g., improving the network coverage. The second type of meta-surfaces will be embedded into objects, e.g., smart t-shirts with sensors for health monitoring, and will backscatter the radio waves generated by cellular base stations in order to report their sensed data to mobile phones. These functionalities will enable wireless network operators to offer new services without the emission of additional radio waves, but by recycling those already existing for other purposes. This paper overviews the current research efforts on smart radio environments, the enabling technologies to realize them in practice, the need of new communication-theoretic models for their analysis and design, and the long-term and open research issues to be solved towards their massive deployment. In a nutshell, this paper is focused on discussing how the availability of reconfigurable intelligent meta-surfaces will allow wireless network operators to redesign common and well-known network communication paradigms.
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.
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.
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.
Reconfigurable intelligent surfaces have emerged as a promising technology for future wireless networks. Given that a large number of reflecting elements is typically used and that the surface has no signal processing capabilities, a major challenge is to cope with the overhead that is required to estimate the channel state information and to report the optimized phase shifts to the surface. This issue has not been addressed by previous works, which do not explicitly consider the overhead during the resource allocation phase. This work aims at filling this gap, by developing an overhead-aware resource allocation framework for wireless networks where reconfigurable intelligent surfaces are used to improve the communication performance. An overhead model is proposed and incorporated in the expressions of the system rate and energy efficiency, which are then optimized with respect to the phase shifts of the reconfigurable intelligent surface, the transmit and receive filters, the power and bandwidth used for the communication and feedback phases. The bi-objective maximization of the rate and energy efficiency is investigated, too. The proposed framework characterizes the trade-off between optimized radio resource allocation policies and the related overhead in networks with reconfigurable intelligent surfaces.
Reconfigurable intelligent surfaces (RISs) are an emerging transmission technology for application to wireless communications. RISs can be realized in different ways, which include (i) large arrays of inexpensive antennas that are usually spaced half of the wavelength apart; and (ii) metamaterial-based planar or conformal large surfaces whose scattering elements have sizes and inter-distances much smaller than the wavelength. Compared with other transmission technologies, e.g., phased arrays, multi-antenna transmitters, and relays, RISs require the largest number of scattering elements, but each of them needs to be backed by the fewest and least costly components. Also, no power amplifiers are usually needed. For these reasons, RISs constitute a promising software-defined architecture that can be realized at reduced cost, size, weight, and power (C-SWaP design), and are regarded as an enabling technology for realizing the emerging concept of smart radio environments (SREs). In this paper, we (i) introduce the emerging research field of RIS-empowered SREs; (ii) overview the most suitable applications of RISs in wireless networks; (iii) present an electromagnetic-based communication-theoretic framework for analyzing and optimizing metamaterial-based RISs; (iv) provide a comprehensive overview of the current state of research; and (v) discuss the most important research issues to tackle. Owing to the interdisciplinary essence of RIS-empowered SREs, finally, we put forth the need of reconciling and reuniting C. E. Shannon’s mathematical theory of communication with G. Green’s and J. C. Maxwell’s mathematical theories of electromagnetism for appropriately modeling, analyzing, optimizing, and deploying future wireless networks empowered by RISs.
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.
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.
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.
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.
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.
Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.
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.
Scaled largest eigenvalue based detection is an ideal solution to spectrum sensing problem in cognitive radio networks. However, results on the sensing performance are very limited. In this paper, we analytically investigate the detection performance by deriving simple and accurate test statistics distributions. These results are obtained by taking advantage of properties of the Mellin transform for products of independent random variables. The derived results yield a useful analytical tool in realistic sensing scenarios.
RFocus: Beamforming using thousands of passive antennas
- arun
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.