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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... RIS using deep learning was considered in Huang et al. (2019a). RIS using multiple antennas was proposed in Dai et al. (2020), Zhang et al. (2020b), Khaleel and Basar (2020) and Qian et al. (2020). RIS has been used with fixed MCS which is not the optimal configuration (Basar et al., 2019;Zhang et al., 2020aZhang et al., , 2020bDi Renzo, 2019;Basar, 2020;Wu and Zhang, 2020;Huang et al., 2019aHuang et al., , 2019bAlexandropoulos and Vlachos, 2020;Guo et al., 2020;Thirumavalavan and Jayaraman, 2020;Pradhan et al., 2020;Ying et al., 2020;Yang et al., 2020;Di et al., 2020;Nadeem et al., 2020;Zhao et al., 2020;Li et al., 2020;Hua and Shi, 2019;Dai et al., 2020;Khaleel and Basar, 2020;Qian et al., 2020. ...
... RIS using multiple antennas was proposed in Dai et al. (2020), Zhang et al. (2020b), Khaleel and Basar (2020) and Qian et al. (2020). RIS has been used with fixed MCS which is not the optimal configuration (Basar et al., 2019;Zhang et al., 2020aZhang et al., , 2020bDi Renzo, 2019;Basar, 2020;Wu and Zhang, 2020;Huang et al., 2019aHuang et al., , 2019bAlexandropoulos and Vlachos, 2020;Guo et al., 2020;Thirumavalavan and Jayaraman, 2020;Pradhan et al., 2020;Ying et al., 2020;Yang et al., 2020;Di et al., 2020;Nadeem et al., 2020;Zhao et al., 2020;Li et al., 2020;Hua and Shi, 2019;Dai et al., 2020;Khaleel and Basar, 2020;Qian et al., 2020. In this paper, the signal to noise ratio (SNR) at the receiver is sent to the transmitter on the feedback channel so that the transmitter can choose the best MCS to maximise the data rate. ...
... The used parameters for RIS with AMC are: L = 200, ple = 3, D T,RIS = 1.5, D RIS,D = 2. Figures 5-10 show the throughput of RIS with AMC and with fixed MCS for N = 8, 16,32,64,128,256. The suggested RIS with AMC offers the largest throughput and better than RIS with fixed MCS (Basar et al., 2019;Zhang et al., 2020aZhang et al., , 2020bDi Renzo, 2019;Basar, 2020;Wu and Zhang, 2020;Huang et al., 2019aHuang et al., , 2019bAlexandropoulos and Vlachos, 2020;Guo et al., 2020;Thirumavalavan and Jayaraman, 2020;Pradhan et al., 2020;Ying et al., 2020;Yang et al., 2020;Di et al., 2020;Nadeem et al., 2020;Zhao et al., 2020;Li et al., 2020;Hua and Shi, 2019;Dai et al., 2020;Khaleel and Basar, 2020;Qian et al., 2020. The suggested RIS using AMC offers a larger throughput than Basar et al. (2019), Dai et al. (2020), Khaleel and Basar (2020) and Qian et al. (2020) as the best MCS maximising the throughput is selected. ...
Article
In this article, the throughput of reconfigurable intelligent surfaces (RIS) is improved using adaptive modulation and coding (AMC). The best modulation and coding scheme (MCS) is selected at the transmitter using the instantaneous signal to noise ratio (SNR) measured at the receiver and sent back on the feedback channel. RIS is placed between the transmitter and the receiver so that the SNR is maximized at the receiver side as RIS reflections are combined coherently at the receiver and results in significant spatial diversity. All reflections on RIS have a zero phase at the receiver. We show that RIS using AMC offers a larger throughput than conventional RIS with fixed MCS for all SNR range. RIS with AMC offers 48, 42, 36, 30, 24, 18 dB gain for N = 256, 128, 64, 32, 16, 8 reflectors. We obtained 10 dB gain when RIS uses AMC versus 256-QAM. We also improve the throughput of Simultaneously Transmitting And Reflecting RIS (STARRIS) using AMC. We obtained 13 dB gain when STARRIS uses AMC versus 256-QAM.
... RIS using deep learning was considered in Huang et al. (2019a). RIS using multiple antennas was proposed in Dai et al. (2020), Zhang et al. (2020b), Khaleel and Basar (2020) and Qian et al. (2020). RIS has been used with fixed MCS which is not the optimal configuration (Basar et al., 2019;Zhang et al., 2020aZhang et al., , 2020bDi Renzo, 2019;Basar, 2020;Wu and Zhang, 2020;Huang et al., 2019aHuang et al., , 2019bAlexandropoulos and Vlachos, 2020;Guo et al., 2020;Thirumavalavan and Jayaraman, 2020;Pradhan et al., 2020;Ying et al., 2020;Yang et al., 2020;Di et al., 2020;Nadeem et al., 2020;Zhao et al., 2020;Li et al., 2020;Hua and Shi, 2019;Dai et al., 2020;Khaleel and Basar, 2020;Qian et al., 2020. ...
... RIS using multiple antennas was proposed in Dai et al. (2020), Zhang et al. (2020b), Khaleel and Basar (2020) and Qian et al. (2020). RIS has been used with fixed MCS which is not the optimal configuration (Basar et al., 2019;Zhang et al., 2020aZhang et al., , 2020bDi Renzo, 2019;Basar, 2020;Wu and Zhang, 2020;Huang et al., 2019aHuang et al., , 2019bAlexandropoulos and Vlachos, 2020;Guo et al., 2020;Thirumavalavan and Jayaraman, 2020;Pradhan et al., 2020;Ying et al., 2020;Yang et al., 2020;Di et al., 2020;Nadeem et al., 2020;Zhao et al., 2020;Li et al., 2020;Hua and Shi, 2019;Dai et al., 2020;Khaleel and Basar, 2020;Qian et al., 2020. In this paper, the signal to noise ratio (SNR) at the receiver is sent to the transmitter on the feedback channel so that the transmitter can choose the best MCS to maximise the data rate. ...
... The used parameters for RIS with AMC are: L = 200, ple = 3, D T,RIS = 1.5, D RIS,D = 2. Figures 5-10 show the throughput of RIS with AMC and with fixed MCS for N = 8, 16,32,64,128,256. The suggested RIS with AMC offers the largest throughput and better than RIS with fixed MCS (Basar et al., 2019;Zhang et al., 2020aZhang et al., , 2020bDi Renzo, 2019;Basar, 2020;Wu and Zhang, 2020;Huang et al., 2019aHuang et al., , 2019bAlexandropoulos and Vlachos, 2020;Guo et al., 2020;Thirumavalavan and Jayaraman, 2020;Pradhan et al., 2020;Ying et al., 2020;Yang et al., 2020;Di et al., 2020;Nadeem et al., 2020;Zhao et al., 2020;Li et al., 2020;Hua and Shi, 2019;Dai et al., 2020;Khaleel and Basar, 2020;Qian et al., 2020. The suggested RIS using AMC offers a larger throughput than Basar et al. (2019), Dai et al. (2020), Khaleel and Basar (2020) and Qian et al. (2020) as the best MCS maximising the throughput is selected. ...
Article
In this article, the throughput of reconfigurable intelligent surfaces (RIS) is improved using adaptive modulation and coding (AMC). The best modulation and coding scheme (MCS) is selected at the transmitter using the instantaneous signal to noise ratio (SNR) measured at the receiver and sent back on the feedback channel. RIS is placed between the transmitter and the receiver so that the SNR is maximised at the receiver side as RIS reflections are combined coherently at the receiver and results in significant spatial diversity. All reflections on RIS have a zero phase at the receiver. We show that RIS using AMC offers a larger throughput than conventional RIS with fixed MCS for all SNR range. RIS with AMC offers 48, 42, 36, 30, 24, 18 dB gain for N = 256,128,64,32,16,8 reflectors. We obtained 10 dB gain when RIS uses AMC versus 256-QAM. We also improve the throughput of Simultaneously Transmitting And Reflecting RIS (STARRIS) using AMC. We obtained 13 dB gain when STARRIS uses AMC versus 256-QAM.
... The integration of RIS in wireless networks holds great potential for maximizing spectral efficiency and addressing the increasing demands for data transmission in a more intelligent and sustainable manner [4]. RIS has demonstrated its effectiveness in synergy with other enabling technologies, such as non-orthogonal multiple access (NOMA) and multipleinput multiple-output (MIMO) systems [5]- [7]. RIS has also found extensive application in different communication scenarios, including unmanned aerial vehicle (UAV), device-todevice (D2D), and terahertz (THz) communications [8]- [20]. ...
... and Bounds [25] Rayleigh Rayleigh No No Multivar. Fox H-function Exact (Numerical) [5], [26], [27] Rayleigh Rayleigh No No Gamma Approximated [6], [28], [29] Rayleigh Rayleigh No Yes Gamma Approximated [30] Rayleigh [10], [15], [47] Nakagami-m Nakagami-m No No Gamma Approximated [48], [49] Nakagami-m Nakagami-m No No CLT Approximated [16] Nakagami-m Nakagami-m No Yes LT Approximated [17] Nakagami-m Nakagami-m No Yes LT and CLT Approximated [50] Nakagami-m Nakagami-m No No HT Exact [11], [51] Nakagami-m Nakagami-m No Yes Gamma Approximated [52] Nakagami-m Nakagami-m No Yes CLT Approximated [53] Nakagami-m Nakagami-m No Yes Laguerre Expansion Approximated [54] Nakagami-m Nakagami-m Rayleigh Yes CLT Approximated [14] Nakagami-m Nakagami-m Nakagami-m Yes Laguerre Expansion Approximated [55] Nakagami-m Nakagami-m Nakagami-m Yes Gamma Approximated [12] Nakagami-m Nakagami-m Nakagami-m Both CLT and Gamma Approximated [9], [56] Nakagami-m Nakagami-m Nakagami-m Yes Gamma Approximated [13], [57] Nakagami-m Nakagami-m Nakagami-m Yes CLT Approximated [58] Nakagami-m Nakagami-m Nakagami-m No Hankel Transform Exact [59] Nakagami-m Nakagami-m Nakagami-m Yes Gamma and Log-Normal Approximated [60] Nakagami-m Nakagami-m Nakagami-m Yes CLT and Gil-Pelaez's Integral Approximated [61] Nakagami-m Nakagami-m Nakagami-m Both CLT, HT, and Gil-Pelaez's Integral Approx. and Exact (Numerical) [62] Rician/Nakagami-m Rician/Nakagami-m No Yes CLT and Gamma Approximated [63] Nakagami-m/α-µ /Rician/K G /FS-F [19] α-µ α-µ No Both CLT and Gamma Approximated [66], [67] κ-µ κ-µ κ-µ Yes Gamma Approximated [68] κ-µ κ-µ κ-µ No Gamma and KL Diverg. ...
... Interchanging the order of integration in (33) by invoking Fubini's theorem then evaluating the inner integral, 5 ...
Preprint
Full-text available
This study focuses on characterizing the channel of a reconfigurable intelligent surface (RIS)-assisted wireless system operating over Nakagami-m fading channels. Although numerous works have proposed approximate or asymptotic solutions for the RIS channel statistics (namely, the probability density function (PDF) and the cumulative distribution function (CDF)), only a limited number of studies have tackled this problem by resorting to exact approaches. Regrettably, as the number of RIS elements increases, these approaches lead to solutions that are computa-tionally expensive or entail a high mathematical intricacy. This has prompted the analytical development undertaken in this work. Herein, our emphasis is on an exact approach. Specifically, we furnish handy and tractable formulas for the PDF and the CDF of the investigated RIS channel. The expressions introduced in this study stand out as new contributions to the literature and are arguably the most efficient exact solutions available to date. Numerical simulations revealed the heightened efficiency of our proposed PDF and CDF expressions against the state-of-the-art solutions. Furthermore, we conducted a performance assessment analysis for the considered RIS-assisted wireless communication system by deriving exact and asymptotic expressions for key performance indicators, namely the outage probability (OP) and the average bit-error rate (ABER). Comprehensive numerical simulations validated the accuracy of our analytical results. Index Terms-Average bit-error rate, channel characterization, cumulative distribution function, Nakagami-m fading channels, outage probability, probability density function, reconfigurable intelligent surface.
... For complex communication scenarios, algorithms are developed with the assumption of continuous phase shifts at the RIS, for ease of optimization [6], [7], [8], [9]. In [6], to achieve a globally optimal solution, the authors developed an algorithm which is based on the branchand-bound method. ...
... Assuming perfect knowledge of the channels in [8], the authors jointly designed the active and passive beamforming to minimize the transmit power, subject to individual signal-to-interference-ratio constraints of the users. In [9], the authors consider an RIS-aided multiantenna transmission with the effect of channel fading and phase noise impairments at the RIS, to maximize the signalto-noise-ratio (SNR) at the receiver. ...
... is the arriving signal direction from BS antenna m. Here, a(ϑ, φ) is the array response vector defined in (9) in the next section. Similar to the analysis in the Appendix of the fifth version of [14], equation (7) can be rewritten as ...
Article
Full-text available
The problem of optimizing discrete phases in a reconfigurable intelligent surface (RIS) to maximize the received power at a user equipment is addressed. Necessary and sufficient conditions to achieve this maximization are given. These conditions are employed in an algorithm to achieve the maximization. New versions of the algorithm are given that are proven to achieve convergence in N or fewer steps whether the direct link is completely blocked or not, where N is the number of the RIS elements, whereas previously published results achieve this in KN or 2N number of steps where K is the number of discrete phases. Thus, for a discrete-phase RIS, the techniques presented in this paper achieve the optimum received power in the smallest number of steps published in the literature. In addition, in each of those N steps, the techniques presented in this paper determine only one or a small number of phase shifts with a simple elementwise update rule, which result in a substantial reduction of computation time, as compared to the algorithms in the literature. As a secondary result, we define the uniform polar quantization (UPQ) algorithm which is an intuitive quantization algorithm that can approximate the continuous solution with an approximation ratio of 2(1/K) and achieve low time-complexity, given perfect knowledge of the channel.
... Then the CPU fuses the signals gleaned from all distributed BSs via the fronthaul and designs the digital beamformer based on the overall CSI received from all BSs to detect the UEs' desired information. Furthermore, due to the hardware imperfections of practical systems, having HWIs at the RF chains [32], [33] and PSE at the RHS elements [28], [34] are inevitable. In this paper, we consider both of these non-ideal characteristics and analyse their effects on the system performance. ...
... n being the expected phase shift value of the nth RHS element, while θ (l) n represents the phase error due to the realistic RHS hardware imperfection. The phase error θ (l) n obeys identically and independently distributed (i.i.d.) random variables having the mean of 0, and it may also be modelled by the von-Mises distribution or the uniform distribution [28], [34]. These may be represented as θ n cannot be obtained, we can exploit the statistical information for beamforming designs. ...
... Theorem 2. In the case of an infinitely large physical size, i.e. N x → ∞ and N y → ∞, the ergodic achievable rate upper bound is given in (34), where ζ = 1 ...
Article
Full-text available
We propose a hybrid beamforming architecture for near-field reconfigurable holographic surfaces (RHS) harnessed in cell-free networks. Specifically, the holographic beamformer of each base station (BS) is designed for maximizing the channel gain based on the local channel state information (CSI). By contrast, the digital beamformer at the central processing unit is designed based on the minimum mean squared error criterion. Furthermore, the near-field spectral efficiency of the RHS in cell-free networks is derived theoretically by harnessing the popular stochastic geometry approach. We consider both the phase shift error (PSE) at the RHS elements and the hardware impairment (HWI) at the radio frequency (RF) chains of the transceivers. Furthermore, we theoretically derive the asymptotic capacity bound, when considering an infinite physical size for the RHS in the near-field channel model. The theoretical analysis and simulation results show that the PSE at the RHS elements and the HWI at the RF chains of transceivers limit the spectral efficiency in the high signal-to-noise ratio region. Moreover, we show that the PSE at the RHS elements and the HWI at the RF chains of BSs can be compensated by increasing the number of BSs. Finally, we also demonstrate that the ergodic spectral efficiency based on the near-field channel model is higher than that based on the far-field channel model assumption. Index Terms-Reconfigurable holographic surfaces (RHS), near-field, cell-free network, stochastic geometry, phase shift error (PSE), hardware impairment (HWI).
... 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. ...
Preprint
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.
... This results in changing the direction of an impingent electromagnetic wave [2]- [4]. Assuming the phase shifts at the RIS elements are continuous, optimization algorithms are developed, for example, [5]- [8]. ...
... Because |g| is real-valued, the second and fourth terms in (8) sum to zero, and ...
Article
Full-text available
To maximize the received power at a user equipment, the problem of optimizing a reconfigurable intelligent surface (RIS) with a limited phase range and nonuniform discrete phase shifts with adjustable gains is addressed. Necessary and sufficient conditions to achieve this maximization are given. These conditions are employed in two algorithms to achieve the global optimum in linear time. Depending on the phase range limitation, it is shown that the global optimality is achieved in NK or fewer and N(K+1) or fewer steps, where N is the number of RIS elements and K is the number of discrete phase shifts which may be placed nonuniformly over the limited phase range. In addition, we define two quantization algorithms that we call nonuniform polar quantization (NPQ) algorithm and extended nonuniform polar quantization (ENPQ) algorithm, where the latter is a novel quantization algorithm for RISs with a significant phase range restriction. With NPQ, we provide a closed-form solution for the approximation ratio with which an arbitrary set of nonuniform discrete phase shifts can approximate the continuous solution. We also show that with a phase range limitation, equal separation among the nonuniform discrete phase shifts maximizes the normalized performance. Furthermore, for a larger RIS phase range limitation, we show that the gain of increasing K is only marginal, whereas, ON/OFF selection for the RIS elements can bring significant performance compared to the case when the RIS elements are strictly ON.
... Therefore, the phase error is denoted as θ n = θ opt n − θ n . Based on the above, we provide two key assumptions as follows 1) When the phase information of the cascade channel is unknown completely, the phase error θ n is modeled as random variables distributing on [−π, π) and E θn [e jt θn ] = sinc(t) [8], [17], [27]; sinc(t) = sin(tπ) tπ and t > 0 is a positive integer. ...
... 2) When the phase information of the cascade channel is known partially, the phase error θ n is modeled as random variables following the Von Mises distribution with a zeromean and concentration parameter κ θ [8], [17], [27], which captures the accuracy of the estimation; E θn [e jt θ ] = I |t| (κ θ ) I0(κ θ ) ; I p (κ θ ) is the modified Bessel function of the first kind and order p. ...
Article
Full-text available
Reconfigurable intelligent surfaces (RIS) can dynamically reconstruct wireless environments to enhance spectral efficiency. However, most existing studies have ignored the impact of the phase error and imperfect amplitude gain of the RIS. In this paper, we investigate the practical RIS-aided multiuser communication systems by maximizing the sum of users’ average achievable rate, filling the current research gap. Specifically, a novel RIS phase shift design approach, namely amplitude feedback (AF), is proposed by utilizing the coupling relationship between the amplitude and phase to derive the optimal phase shift under the worst phase error. The feasibility of AF is demonstrated by proving the measurability of amplitude response through the electromagnetic theory. We propose a channel estimation design with low pilot overhead and provide an effective closed-form achievable rate to approximate the average achievable rate. Moreover, an efficient optimization algorithm is proposed to achieve the optimal closed-form precoding at the base station and the optimal trade-off design between the amplitude and phase of RIS, and the algorithm is extended to active RIS systems. Numerical results demonstrate that our proposed AF method and optimization algorithm can efficiently improve the performance in terms of achievable sum rate compared to existing methods.
... Recent investigations have employed approximation methods to assess the performance of RIS systems under various channel fading models in the presence of phase errors [13], [14], [21]- [27]. In [14], [21], [22], and [23], the authors applied the central limit theorem (CLT) to analyze RIS system performance over Rayleigh fading channels with phase errors. ...
... Recent investigations have employed approximation methods to assess the performance of RIS systems under various channel fading models in the presence of phase errors [13], [14], [21]- [27]. In [14], [21], [22], and [23], the authors applied the central limit theorem (CLT) to analyze RIS system performance over Rayleigh fading channels with phase errors. In [28], an arbitrary fading model was approximated using the Nakagami-m distribution to develop a performance analysis of RIS-assisted transmissions with phase errors. ...
Article
Full-text available
Existing performance analysis of wireless systems based on reconfigurable intelligent surfaces (RIS) over fading channels has primarily focused on providing statistical insights into the sum and product of random variables, typically represented as a single-variate Fox-H function. A research gap exists for an exact performance analysis when the statistical characterization of wireless systems, including RIS-assisted systems, requires more than a single-variate Fox-H function. In such cases, incorporating a multivariate representation becomes imperative, particularly when addressing generalized fading models and channel estimation errors, even with simpler one-parameter fading models. This paper introduces a novel approach to derive the distribution of the sum and product of independent and nonidentical distributed (i.ni.d) random variables characterized by the multivariate Fox-H function. We also establish a general framework for an exact analysis of ergodic capacity and average signal-to-noise ratio (SNR) when the multivariate Fox-H function describes the statistics of the channel. Applying the derived results, we conduct an exact performance analysis of outage probability and ergodic capacity, exemplified by RIS-assisted communication over Rician fading channels with imperfect phase compensation and channel estimation errors. Computer simulations validate the exact analysis and illustrate the performance of the RIS-assisted system under various practically relevant scenarios, enhancing the overall performance assessment.
... Multiantenna beamforming for the receivers and transmitters operating in a Rayleigh fading environment with impaired phase noise uses the reconfigurable intelligent surface. The SNR distribution is approximated as either gamma random variables or as the chi-squared non-central random variables with two or three independent random variables associated with it; thus the amount of fading experienced by the channel decreases linearly with N ≫ 1 [15]. ...
... The previous and current signal transmit direction values along with the autocorrelation and cross correlation matrix aid in computation of the gradient pathway, which is represented in Eq. (15). ...
... 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. ...
Preprint
Full-text available
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.
... Estimating the individual channels is important since, for optimizing the IRS phase shifts, the precoder, and the combiner jointly in a MIMO scenario, the knowledge of the individual channel matrices and is required (see, e.g., [62,198,199]). On the other hand, in the SISO and MISO cases, the knowledge of the cascaded channel is enough (see, e.g, [200], [201]). ...
Thesis
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The fifth-generation (5G) is in its business version, and researchers have started to look at the potential technologies to be employed in the next generation. In this context, intelligent reflecting surface (IRS) is a promising technology for the sixth-generation (6G) of wireless systems by introducing the smart radio environment concept. The promised gains of IRS-assisted communications depend on the accuracy of the channel state information. Using a tensor framework, particularly tensor decomposition, we propose different solutions to solve the channel estimation problem for different scenarios. We firstly address the receiver design for an IRS-assisted multiple-input multiple-output (MIMO) communication system via a tensor modeling approach to solve the channel estimation problem using supervised (pilot-assisted) methods. Considering a structured time-domain pattern of pilots and IRS phase shifts, we present two channel estimation methods that rely on a parallel factors (PARAFAC) tensor modeling of the received signals. The first method has a closed-form solution based on a Khatri-Rao factorization of the cascaded MIMO channel by solving rank-1 matrix approximation problems, while the second is an iterative alternating estimation scheme. The common feature of both methods is the decoupling of the estimates of the involved MIMO channel matrices (base station (BS)-IRS and IRS-user terminal (UT)), which provides performance enhancements in comparison to competing methods that are based on unstructured least squares (LS) estimates of the cascaded channel. In this scenario, the numerical results show the effectiveness of the proposed receivers, highlight the involved trade-offs, and corroborate their superior performance compared to competing LS-based solutions. Second, we develop algorithms to jointly estimate the involved channel matrices and the transmitted symbols in a semi-blind fashion. This is achieved by introducing a simple space-time coding scheme at the transmitter, such that the received signal model can be advantageously built using the PARATUCK tensor model. As a result, a semi-blind receiver is derived by exploiting the algebraic structure of the PARATUCK tensor model. In this context, we first formulate a semi-blind receiver based on a trilinear alternating least squares method that iteratively estimates the two involved communication channels – IRS-BS and UT-IRS – and the transmitted symbol matrix. Second, we formulate an enhanced two-stage semi-blind receiver that efficiently exploits the direct link to refine the channel and symbol estimates iteratively. In addition, we discuss the impact of an imperfect IRS absorption (residual reflection) on the performance of the proposed receiver. Finally, we formulate a tensor-based semi-blind receiver for an IRS-assisted uplink multi-user MIMO system where the proposed approach relies on a generalized PARATUCK tensor model of the signals reflected by the IRS, based on a two-stage closed-form semi-blind receiver using Khatri-Rao and Kronecker factorizations.
... For instance, planar arrays of programmable and passive reflecting elements, i.e., elements whose just reflect impinging radio frequency signals on their surfaces in controllable ways, have been proposed for 6G wireless networks as an effective approach to enhance the wireless propagation environments, hence improving the wireless networks' performances. Such programmable arrays are know as intelligent reflective surfaces (IRS) or reconfigurable intelligent surfaces (RIS), see e.g., [65,18,17,3,53,21,55,75,1,80,77,62,67,58,8]. Particularly, an RIS is placed between a conventional transmitter and its mobile receivers to assist the communication. ...
Chapter
This chapter uses a swarm-intelligence-based approach to solve transmit beamforming problems in wireless communications. An extensive review has been carried out about transmit beamforming designs and the generalized Firefly Algorithm (FA) introduced by Le and Yang in 2023 as an optimization framework for solving transmit beamforming problems. Such design problems are subject to multiple, nonlinear multivariate constraints with matrix inputs. The proposed approaches are described in detail and two transmit beamforming problems are then used to illustrate the effectiveness of the generalized Firefly Algorithm to find optimal solutions. Semidefinite relaxation (SDR) technique is also utilized to solve the same problems for comparison with the results obtained by the FA approaches. Comparison and analyses reveal the fact that when the number of antennas is large, the proposed FA approaches have less computational complexities, compared with those of their SDR counterparts. Numerical results also indicate that the FA approach can obtain the same global optimal design solution as the SDR does for a hidden-convex problem in transmit beamforming. Furthermore, the FA approach can outperform its SDR counterpart in terms of attaining better optimal solutions for non-convex, multivariate optimization problems in wireless communications.
... However, additive noise does not affect IRSs that exhibit aberrant reflector behavior. Nevertheless, phase noises might interfere with them [26]. Furthermore, they are unable to amplify or renew the impulses if they are almost inactive [27]. ...
Article
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By adjusting the propagation environment using reconfigurable reflecting elements, intelligent reflecting surfaces (IRSs) have become potential techniques used to improve the efficiency of wireless communication networks. In IRS-assisted communication systems, accurate channel estimation is crucial for optimizing signal transmission and achieving high spectral efficiency. As mobile data traffic continues to surge and the demand for high-capacity and low-latency wireless connectivity grows, IRSs are becoming pivotal technologies in the development of next-generation communication networks. IRSs offer the potential to revolutionize wireless propagation environments, improving network capacity and coverage, particularly in high-frequency wave scenarios where traditional signals encounter obstacles. Amidst this evolving landscape, machine learning (ML) emerges as a powerful tool to harness the full potential of IRS-assisted communication systems, particularly given the escalating computational complexity associated with deploying and operating IRSs in dynamic environments. This paper presents an overview of preliminary results for IRS-assisted communication using recurrent neural networks (RNNs). We first implement single- and double-layer LSTM, BiLSTM, and GRU techniques for an IRS-based communication system. In the next phase, we explore a hybrid approach, combining different RNN techniques, including LSTM-BiLSTM, LSTM-GRU, and BiLSTM-GRU, as well as their reverse configurations. These RNN algorithms were evaluated with respect to bit error rate (BER) and symbol error rate (SER) for IRS-enhanced communication. According to the experimental results, the BiLSTM double-layer model and the BiLSTM-GRU combination demonstrated the highest BER and SER accuracy compared to other approaches.
... , where K is the Rician factor that describes the LOS component. Similar to [24], [44], 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 the ESC of the network by setting m 2 = 1, which emulates the Rayleigh channel for the RIS-Bob/Eves links. ...
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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 (CF) expressions for 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 CF 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, the proposed deployment approaches converge in less than a second using CF optimal RIS portions, making it suitable for dynamic A-RIS deployment. Index Terms-Artificial noise (AN), ergodic secrecy capacity (ESC), physical layer security (PLS), optimization, partitioning, power control, unmanned aerial vehicle (UAV), reconfigurable intelligent surface (RIS).
... Other research work has been investigated in the RIS system. It includes the deployment of the RIS system in the WCN, joint beamforming [31], and resilient transmission schemes in the RIS system [32], [33]. Radar-based RIS system deployment has also been investigated. ...
Article
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The Sixth Generation (6G) Wireless Communication Network (WCN) is the successive provision to ameliorate the gain with ultra-low latency, and e xtremely high energy efficiency. The 6G WCN enables the specifications of artificial intelligence to optimize the services and capabilities. The vision of the 6G era is expected to address a seamless fusion of communication between the human, physical world, and digital world. The latest 6G WCN standard is a fundamental foundation and requires immense attention in the field of research. This paper presents the framework of 6G WCN with an illustration of its key technologies. The different technologies involved in 6G are well explained with the demonstration of the communication scenario such that the key performance indicators are improved with major differences. The primary contribution of this paper is the explanation of the 6G with the technologies that have a drastic impact on the characteristic aspects of a wireless communication network such as data rate, spectrum efficiency, energy efficiency, connection density, and reliability. All these technologies have the capability to revolutionize the subsequent WCN.
... In fact the Gaussian copula fails to model the SNR distribution under both positive and negative dependencies, and this behavior becomes more noticeable when M increases. As a conclusion, applying Gaussian copula with positive 8 VOLUME , ...
Article
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Reconfigurable intelligent surfaces have received remarkable attention as promising solutions to enhance the capacity and coverage of wireless cellular networks. In this paper, we evaluate the performance of reconfigurable intelligent surfaces-assisted communication systems in the presence of phase noise, and consider a direct link in conjunction with cascade link between the transmitter and receiver by exploring different copulas. In particular, we first analyze the cumulative distribution function and the probability density function of the signal-to-noise-ratio distribution under phase noise in the presence of both direct and cascaded channel links. Moreover, we propose a copula-based solution to effectively model the non-linear dependencies among signal components induced by phase noise, and derive several exact closed-form expressions for outage probability in reconfigurable intelligent surfaces-assisted networks. In our method of analysis, we employ various copula families, including Archimedean copulas such as Farlie-Gumbel-Morgenstern, Frank, and Clayton, along with Elliptical copulas such as Gaussian and Student-T. Finally, numerical results are shown to confirm the validity of the closed-form expressions.
... which is known as the angular spectrum representation [35], [36]. The result of (9) states that the field at any z > 0 is determined entirely by its Fourier spectrum at z = 0. Hence, to calculate the reflected field, only knowledge of E RIS (x, y) is required, which is given by (2), using (1) and (4). Then, the reflected field at any observation point (x, y, z) is calculated using (5), the Fourier transform of E RIS (x, y), and inserting the result into (9). ...
Article
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Reconfigurable intelligent surfaces (RISs) are typically utilized in the far-field as an effective means of creating virtual line-of-sight (LOS) links to mediate non-LOS propagation in wireless communications via beamforming. Owing to their large surface and the multitude of scatterers, the use of RISs can be extended in the near-field, to transform the incident beam into a focused beam that is able to address the challenges of high frequencies more efficiently than conventional beamforming. In this paper we explain from a physics’ standpoint how the RIS can engineer wavefronts to transform the incident beam into a focused beam targeted at the user, and we employ the angular spectrum representation approach to describe analytically the dynamics of beamfocusing. We derive analytical expressions that provide the necessary insight into the dependencies and trade-offs between crucial parameters, such as the incident beam’s footprint on the RIS, the intended focal distance of the reflected beam, and the link topology. To assess the beamfocusing efficiency we provide metrics that are crucial for future applications, including energy efficient communications, wireless power transfer, tracking and localization.
... 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. ...
Article
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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 ...
Preprint
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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 ...
Article
Full-text available
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. ...
Preprint
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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]. ...
Preprint
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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. ...
Preprint
Full-text available
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.
Article
Future wireless connectivity is envisioned to accommodate functionalities far beyond broadband data transmission over point-to-point direct links, enabling novel scenarios, such as communication behind blockers and around corners, and innovative concepts, such as situational awareness, localization and joint communications and sensing. In this landscape, beams that are able to propagate on bent paths are ideal candidates for dynamic blockage avoidance, interference management in selected regions, and user connectivity on curved trajectories. In this work, we study beam shaping for applications in near-field wireless connectivity. We explain the underlying mechanism of beam bending and we present the design principles for tailoring the curvature of the propagation trajectory. We discuss design aspects for generation of such beams with large arrays and analyze the impact of several parameters on their performance, including the beam’s footprint shape, the aperture size, the inter-element spacing, the sub-array selection of active elements, the available phase levels of the array elements and the operating frequency. We introduce the concept of near-field virtual routing (NFVR) and we demonstrate that such beams are able to address challenges of high frequency communications, such as dynamic routing, blockage avoidance and energy-efficiency, more efficiently than conventional beamforming.
Preprint
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Future wireless connectivity is envisioned to accommodate functionalities far beyond broadband data transmission over point-to-point direct links, enabling novel scenarios, such as communication behind blockers and around corners, and innovative concepts, such as situational awareness, localization and joint communications and sensing. In this landscape, beams that are able to propagate on bent paths are ideal candidates for dynamic blockage avoidance, interference management in selected regions, and user connectivity on curved trajectories. In this work, we study beam shaping for applications in near-field wireless connectivity. We explain the underlying mechanism of beam bending and we present the design principles for tailoring the curvature of the propagation trajectory. We discuss design aspects for generation of such beams with large arrays and analyze the impact of several parameters on their performance, including the beam's footprint shape, the aperture size, the inter-element spacing, the sub-array selection of active elements, the available phase levels of the array elements and the operating frequency. We introduce the concept of near-field virtual routing (NFVR) and we demonstrate that such beams are able to address challenges of high frequency communications, such as dynamic routing, blockage avoidance and energy-efficiency, more efficiently than conventional beamforming.
Preprint
Due to circuit failures, defective elements that cannot adaptively adjust the phase shifts of their impinging signals in a desired manner may exist on an intelligent reflecting surface (IRS). Traditional way to find these defective IRS elements requires a thorough diagnosis of all the circuits belonging to a huge number of IRS elements, which is practically challenging. In this paper, we will devise a novel approach under which a transmitter sends known pilot signals and a receiver localizes all the defective IRS elements just based on its over-the-air measurements reflected from the IRS. The key lies in the fact that the over-the-air measurements at the receiver side are functions of the set of defective IRS elements. Based on this observation, we propose a bisection based method to localize all the defective IRS elements. Specifically, at each time slot, we properly control the desired phase shifts of all the IRS elements such that half of the considered regime that is not useful to localize the defective elements can be found based on the received signals and removed. Via numerical results, it is shown that our proposed bisection method can exploit the over-the-air measurements to localize all the defective IRS elements quickly and accurately.
Article
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Various applications, including reconfigurable intelligent surfaces, radio frequency identification, and ambient backscatter devices, are based on scattering. Predicting the scattering properties of these systems accurately and universally in a computationally efficient manner is crucial. In this paper, we propose a model for predicting the scattering properties of an electromagnetic structure controlled by loads terminated to multiple ports. This model is based on 1) S-parameters describing the coupling between the ports, 2) embedded element radiation patterns associated with each port, and 3) structural scattering under multiple incident wave directions. To construct the model, one set of electromagnetic descriptions (e.g., simulations or measurements) needs to be done for a structure before computing the scattering properties of the structure for arbitrary tunable load values. Unlike many other methods, the proposed method fully takes into account structural scattering in different directions simultaneously and requires no simplifications or approximations to the scattering structure, such as the assumption of local periodicity or element identity. This method facilitates characterizing the scattering ability of the structure in terms of bistatic cross section, also known as bistatic radar cross section (bRCS), and can be beneficial, for instance, in designing reconfigurable intelligent surfaces and backscatter systems. Simulations and experiments at different frequencies verified the proposed model.
Article
Recently, a promising technique of aggregating massive data from distributed Internet-of-Things Nodes (IoTNs) has been proposed, which is referred to as over-the-air computation (AirComp). Since the computational accuracy degrades as the number of IoTNs increases, reconfigurable intelligent surfaces (RISs) may be considered for improving the computation performance by improving the degrees of freedom. However, the passive beamforming performance of RISs degrades in the face of environmental factors, e.g., snow, dirt, and precipitation. To address this impediment, we investigate the robust design of RIS-assisted AirComp systems under realistic imperfections. We first characterize two models of imperfections in terms of their statistical features, namely by the long-term and the short-term model. To deal with the long-term imperfections, a minimum-mean-squared-error (MMSE) estimator is harnessed first for estimating the imperfections. Then we propose an optimization algorithm to optimize the computational accuracy by alternatively updating the transmit coefficients of the IoTNs, the active receive beamforming of the fusion center (FC), and the passive beamforming of the RIS. In particular, the penalty dual decomposition (PDD) technique is invoked for updating the passive beamforming vector. As for the short-term imperfections, we resort to optimize the computational accuracy in the worst-case scenario owing to imperfect passive beamforming at the RIS. Another alternating optimization algorithm is developed for solving the associated Min-max problem. Our numerical results verify that our developed beamforming designs substantially outperform their non-robust counterparts. Specifically, our algorithm conceived for mitigating the long-term imperfections approaches the performance of idealized perfect beamforming designs relying on unimpaired RISs.
Article
Reconfigurable intelligent surfaces (RISs) have emerged as a candidate technology in future wireless communications for their appealing advantages in controlling the direction of the beam. In addition, as a new paradigm to realize large-scale antenna arrays with reduced cost and power consumption, dynamic metasurface antennas (DMAs) have great potential to be deployed at the base station (BS) as a low-cost alternative for conventional array antennas. For the best mutual benefit of RIS and DMA technologies, we amalgamate them to investigate the hybrid RIS and DMA assisted MIMO interfering broadcast channel with high communication sum-rate at low implementation cost, wherein a DMA-based BS communicates with multiple multi-antenna users via the assistance of RIS. Due to the physical implementation of RIS and DMA, conventional MIMO interfering broadcast channel models are no longer valid. Focusing on the weighted sum-rate performance of the system with additional interference-plus-noise among users, we propose an efficient mechanism to jointly design the transmit precoding matrices at the BS, the phase shift matrix at the RIS, and the weight matrix at the DMA. By transforming the original weighted sum-rate maximization problem to a solvable one, we propose an alternating algorithm where the three optimization variables are all obtained in closed-form expressions. Simulation results verify the superior weighted sum-rate performance of the proposed algorithms. We also find that under the considered framework the performance loss brought by the mutual coupling in the DMA is negligible compared to the conventional array antennas.
Article
Reconfigurable intelligent surface (RIS) is a promising solution to support a large volume of data traffic and massive connectivity for future wireless mobile networks. Especially, RIS can mitigate the drawbacks in massive multiple-input multiple-output (MIMO) systems, such as the blockage caused by obstacles and the signal processing overhead by constructively and passively reflecting the incident wave toward the destination. In this paper, we provide an asymptotic analysis of the distribution of sum rate (SR) in RIS-aided massive MIMO systems. Using the asymptotic distribution of SR, the achievable scheduling gain and the optimal number of users are determined. In addition, we examined the channel hardening effect and outage probability through the achievable scheduling gain, and the optimal number of users is utilized to develop a low-complexity scheduling algorithm. Simulation results reveal that the SR obtained from our analysis closely aligns with the actual SR. The results also show that the channel hardening effect can vanish with many users thereby achieving the multiuser diversity gain, and an RIS-aided system is more reliable than a conventional massive MIMO system in terms of the outage probability. Furthermore, the proposed scheduling algorithm is shown to reduce computational complexity compared to the conventional scheduling algorithm.
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Integrated sensing and communications (ISAC) is an emerging critical technique for the next generation of communication systems. However, due to multiple performance metrics used for communication and sensing, the limited degrees-of-freedom (DoF) in optimizing ISAC systems poses a challenge. Reconfigurable intelligent surfaces (RIS) can introduce new DoF for beamforming in ISAC systems, thereby enhancing the performance of communication and sensing simultaneously. In this paper, we propose two optimization techniques for beamforming in RIS-assisted ISAC systems. The first technique is an alternating optimization (AO) algorithm based on the semidefinite relaxation (SDR) method and a one-dimension iterative (ODI) algorithm, which can maximize the radar mutual information (MI) while imposing constraints on the communication rates. The second technique is an AO algorithm based on the Riemannian gradient (RG) method, which can maximize the weighted ISAC performance metrics. Simulation results verify the effectiveness of the proposed schemes. The AO-SDR-ODI method is shown to achieve better communication and sensing performance, than the AO-RG method, at a higher complexity. It is also shown that the mean-squared-error (MSE) of the estimates of the sensing parameters decreases as the radar MI increases.
Article
Deploying reconfigurable intelligent surfaces (RIS) is promising for enhancing the transmission reliability of wireless communications by controlling the wireless environment, in which the active beamforming at the base station and the passive beamforming at the RIS are jointly designed based on the acquisition of channel state information. Hence, channel estimation is crucial for RIS-aided systems. Due to the lack of active radio frequency chains at the RIS to process and transmit pilot sequences, only the cascaded twin-hop transmitter-RIS-receiver channel can be estimated, which results in extremely high pilot overhead, when a large number of RIS reflecting elements is used. As a remedy, we propose a channel estimation method relying on low pilot overhead, namely the Karhunen-Loève transformation based linear minimal mean square error (KL-LMMSE) estimator. This exploits the spatial correlation of the RIS-cascaded channels, for our multi-cell multiple-input and multiple-output RIS-aided systems. Furthermore, we extend our investigations to the effects of realistic phase quantization errors. Additionally, we derive the theoretical mean square error (MSE) of our proposed channel estimators verified by numerical simulations, and compare the results to various benchmark schemes. We show that the MSE performance of our proposed KL-LMMSE estimator is better than that of the state-of-the-art low-overhead channel estimators. Index Terms-Reconfigurable intelligent surfaces (RIS), channel estimation, linear minimal mean square error (LMMSE), Karhunen-Loève (KL) transformation, phase quantization error.
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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.
Article
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 communication system, 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 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 the system performance.
Article
Reconfigurable intelligent surface (RIS) has emerged as a cost-effective solution to improve wireless communication performance through just passive reflection. Recently, the concept of simultaneously transmitting and reflecting RIS (STAR-RIS) has appeared but the study of minimum signal-to-interference-plus-noise ratio (SINR) and the impact of hardware impairments (HWIs) remain open. In addition to previous works on STAR-RIS, we consider a massive multiple-input multiple-output (mMIMO) base station (BS) serving multiple user equipments (UEs) at both sides of the RIS. Specifically, in this work, focusing on the downlink of a single cell, we derive the minimum SINR obtained by the optimal linear precoder (OLP) with HWIs in closed form. The OLP maximises the minimum SINR subject to a given power constraint for any given passive beamforming matrix (PBM). Next, we obtain deterministic equivalents (DEs) for the OLP and the minimum SINR, which are then used to optimise the PBM. Notably, based on the DEs and statistical channel state information (CSI), we optimise simultaneously the amplitude and phase shift by using a projected gradient ascent algorithm (PGAM) for both energy splitting (ES) and mode switching (MS) STAR-RIS operation protocols with reduced feedback, which is quite crucial for STAR-RIS systems that include the double number or variables compared to reflecting only RIS. Simulations verify the analytical results, shed light on the impact of HWIs, and demonstrate the better performance of STAR-RIS compared to conventional RIS. Also, a benchmark full instantaneous CSI (I-CSI) based design is provided and shown to result in higher SINR but lower net achievable sum-rate than the statistical CSI based design because of large overhead associated with the acquisition of full I-CSI acquisition. Thus, not only do we evaluate the impact of HWIs but we also propose a statistical CSI based design that provides higher net sum-rate with low overhead and complexity.
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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, the proposed OBOA design can be applied in the scenario with dramatic wind changes, and allows the UAV to adjust its velocity dynamically to achieve better performance in terms of EE.
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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 κ\kappa - μ\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.
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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.
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Intelligent reflecting surface (IRS) is a promising technology for the 6th6^\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.
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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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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.
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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 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.
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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 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.
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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.
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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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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.
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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)\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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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.