Article

# Reconfigurable Intelligent Surfaces-Assisted Communications With Discrete Phase Shifts: How Many Quantization Levels Are Required to Achieve Full Diversity?

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## Abstract

Due to hardware limitations, the phase shifts of the reflecting elements of reconfigurable intelligent surfaces (RISs) need to be quantized into discrete values. This letter aims to unveil the minimum required number of phase quantization levels L in order to achieve the full diversity order in RIS-assisted wireless communication systems. With the aid of an upper bound of the outage probability, we first prove that the full diversity order is achievable provided that L is not less than three. If L=2, on the other hand, we prove that the achievable diversity order cannot exceed (N+1)/2, where N is the number of reflecting elements. This is obtained with the aid of a lower bound of the outage probability. Therefore, we prove that the minimum required value of L for achieving the full diversity order is L=3. Simulation results verify the theoretical analysis and the impact of phase quantization levels on RIS-assisted communication systems.

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... In particular, dirty paper coding is known to suffer from extremely high complexity, and thus is unsuitable for mMIMO systems, where linear precoders are applied such as the zero-forcing (ZF) and CB. Furthermore, in practical scenarios, the IRS is expected to be implemented with only a few quantization levels [25], and as a result, it is more convenient to take discrete phase-shifts into account when designing such algorithms. In [26], the authors studied the problem of AS in an IRS-assisted network for the case of a single-antenna user and continuous phase-shifts. ...
... Note that we only need to evaluate {Z 1 , Z 2 , ..., Z K } once for the optimization of all M reflecting elements. In particular, and considering the mth reflecting element, it is not difficult to see that the optimal phase can now be obtained as shown in (29), which does not involve any vector or matrix multiplications, resulting in a significant complexity reduction compared to the conventional successive refinement scheme given in (25), and without any compromise in the performance. After optimizing the phase of each reflecting element, H should be updated according to (18), while Π can be updated as follows (27) and the optimal phase for the mth reflecting element can be obtained as [ϕ ⋆ ] m = [α] lm . ...
... Evaluating the objective function of (25) for each of the L values of [ϕ] m in α at any given iteration t requires M K 2 (8N − 8tv) + K 2 (8N − 8tv + 4) + (3K − 1) FLOPs. As a result, the total number of FLOPs required for optimizing all M phase-shifts with an arbitrary number of iterations T , utilizing the conventional ISM (cISM)-PSD approach in (25), is ...
Article
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We propose two novel antenna selection (AS) and discrete phase-shifts design (PSD) schemes for use in intelligent reflecting surface (IRS) assisted multiuser massive multiple-input multiple-output (mMIMO) networks. The first AS and PSD method aims at maximizing the gain of the channels; while the second method is an iterative sum-rate maximization (ISM) scheme that aims at maximizing the total achievable rate. For the AS part, we demonstrate that the ISM method achieves near optimal performance with much lower complexity compared to benchmark AS schemes, and can be utilized with any precoder at the mMIMO base station. For the PSD, our proposed successive-refinement optimization methods are not only efficient, but their complexities scale linearly with the number of elements at the IRS, making them highly attractive when dealing with large surfaces. A thorough complexity analysis for the proposed methods is carried out in terms of the number of floating point operations required for their implementations. Finally, extensive numerical results are provided and some key points are highlighted on the performance of the proposed schemes with both conjugate beamforming and zero-forcing precoders.
... Under the assumption of Rayleigh fading, it was shown in [18], [20], [21] that the distribution of a single RIS equivalent channel follows a modified Bessel function. In [22] and [23], an RIS-aided transmission system in the presence of phase errors was considered, and the composite channel was shown to be equivalent to a point-to-point Nakagami-m fading channel by using the central limit theorem (CLT). It is known, however, that the CLT is inaccurate when the number of reconfigurable elements of the RIS is small. ...
... However, this approach is accurate only for a large number of reconfigurable elements [3], and, in general, it is not sufficiently accurate for high-SNR analysis, which is the regime of interest for analyzing the diversity order [23]. In [19], for example, the diversity order was shown to be N 2 π 2 16−π 2 in Rayleigh fading, which implies that the full diversity order cannot be obtained even in the absence of phase errors. ...
... In [19], for example, the diversity order was shown to be N 2 π 2 16−π 2 in Rayleigh fading, which implies that the full diversity order cannot be obtained even in the absence of phase errors. By resorting to some bounds, however, the authors of [23] recently showed that the full diversity order equal to N is achievable in Rayleigh fading (even in the presence of phase errors). A detailed summary of the current methods and results on the diversity order of RIS-aided systems is available in Table I. ...
Preprint
In this paper, we develop a comprehensive theoretical framework for analyzing the performance of reconfigurable intelligent surfaces (RISs)-assisted communication systems over generalized fading channels and in the presence of phase noise. To this end, we propose the Fox's H model as a unified fading distribution for a large number of widely used generalized fading channels. In particular, we derive a unified analytical framework for computing the outage probability and for estimating the achievable diversity order of RIS-aided systems in the presence of phase shifts that either are optimally configured or are impaired by phase noise. The resulting expressions are general, as they hold for an arbitrary number of reflecting elements, and various channel fading and phase noise distributions. As far as the diversity order is concerned, notably, we introduce an asymptotic analytical framework for determining the diversity order in the absence of phase noise, as well as sufficient conditions based on upper bounds and lower bounds for ensuring that RIS-assisted systems achieve the full diversity order in the presence of phase noise. More specifically, if the absolute difference between pairs of phase errors is less than $\pi/2$, RIS-assisted communications achieve the full diversity order over independent fading channels, even in the presence of phase noise. The theoretical frameworks and findings are validated with the aid of Monte Carlo simulations.
... Motivated by these considerations, recent attempts for studying RIS-aided systems in the presence of phase errors include the use of approximate distributions and asymptotic analysis [7]- [11]. By using the central limit theorem (CLT), the authors of [7] and [8] obtained approximate BER expressions considering a large number of reconfigurable elements at the RIS. ...
... The Gamma-based framework appears, however, unsuitable for diversity analysis since it fails to extract the full diversity order even in the absence of phase errors. Recently, the authors of [9] and [11] identified sufficient conditions based on upper and lower bounds for ensuring that RIS-assisted systems achieve the full diversity order in the presence of phase noise. More specifically, it was shown in [9] that if the absolute difference between pairs of phase errors is less than π/2, RIS-assisted communications achieve full diversity. ...
... Although the results from [7]- [11] are insightful, these works have been successfully tractable due to approximate SNR distributions and bounds yielding a diversity analysis in the presence of phase errors which is, so far, steadily inaccurate [9], [11]. Moreover, to the best of our knowledge, no exact error analysis for RIS with quantized phase shifts and arbitrary number of reconfigurable elements has been reported in the literature. ...
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In this paper, we analyze the error probability of reconfigurable intelligent surfaces (RIS)-enabled communication systems with quantized channel phase compensation over Rayleigh fading channels. The probability density and characteristic functions of the received signal amplitude are derive dand used to compute exact expressions for the bit error rate(BER). The resulting expressions are general, as they hold for an arbitrary number of reflecting elements N, and quantization levels, L. We introduce an exact asymptotic analysis in the high signal-to-noise ratio (SNR) regime, from which we demonstrate, in particular, that the diversity order is N/2 when L=2 and N when L >2. The theoretical frameworks and findings are validated with the aid of Monte Carlo simulation.
... Moreover, to address the difficulty in addressing the constraints of both discrete phase-shifts and amplitudes, a penalty-based method was proposed in [180] that introduces auxiliary continuous variables for their discrete versions and imposes a penalty term for controlling their difference in optimization. In addition, the effects of low-resolution phase shifters on the passive beamforming performance were studied in [181], [182]. It was shown that a 3-bit phase-shifter is able to achieve the full diversity order [181], while a 2-bit phase-shifter is enough for achieving close rate performance to the continuous-value baseline when the IRS size becomes large [182]. ...
... In addition, the effects of low-resolution phase shifters on the passive beamforming performance were studied in [181], [182]. It was shown that a 3-bit phase-shifter is able to achieve the full diversity order [181], while a 2-bit phase-shifter is enough for achieving close rate performance to the continuous-value baseline when the IRS size becomes large [182]. ...
... • Relax-and-quantize technique [103], [176] • Element-wise BCD method [178], [179] • Penalty-based optimization method [180] • The effects of low-resolution phase shifters on the passive beamforming performance [181], [182] Phase-dependent amplitude ...
Preprint
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Intelligent reflecting surface (IRS) has emerged as a key enabling technology to realize smart and reconfigurable radio environment for wireless communications, by digitally controlling the signal reflection via a large number of passive reflecting elements in real time. Different from conventional wireless communication techniques that only adapt to but have no or limited control over dynamic wireless channels, IRS provides a new and cost-effective means to combat the wireless channel impair-ments in a proactive manner. However, despite its great potential, IRS faces new and unique challenges in its efficient integration into wireless communication systems, especially its channel estimation and passive beamforming design under various practical hardware constraints. In this paper, we provide a comprehensive survey on the up-to-date research in IRS-aided wireless communications, with an emphasis on the promising solutions to tackle practical design issues. Furthermore, we discuss new and emerging IRS architectures and applications as well as their practical design problems to motivate future research.
... Moreover, to address the difficulty in addressing the constraints of both discrete phase-shifts and amplitudes, a penalty-based method was proposed in [186] that introduces auxiliary continuous variables for their discrete versions and imposes a penalty term for controlling their difference in optimization. In addition, the effects of low-resolution phase shifters on the passive beamforming performance were studied in [187], [188]. It was shown that a 3-bit phase-shifter is able to achieve the full diversity order [187], while a 2-bit phase-shifter is enough for achieving close rate performance to the continuous-value baseline when the IRS size becomes large [188]. ...
... In addition, the effects of low-resolution phase shifters on the passive beamforming performance were studied in [187], [188]. It was shown that a 3-bit phase-shifter is able to achieve the full diversity order [187], while a 2-bit phase-shifter is enough for achieving close rate performance to the continuous-value baseline when the IRS size becomes large [188]. ...
... • Relax-and-quantize technique [107], [182] • Element-wise BCD method [184], [185] • Penalty-based optimization method [186] • The effects of low-resolution phase shifters on the passive beamforming performance [187], [188] Phase-dependent amplitude ...
Article
Full-text available
Intelligent reflecting surface (IRS) has emerged as a key enabling technology to realize smart and reconfigurable radio environment for wireless communications, by digitally controlling the signal reflection via a large number of passive reflecting elements in real time. Different from conventional wireless communication techniques that only adapt to but have no or limited control over dynamic wireless channels, IRS provides a new and cost-effective means to combat the wireless channel impairments in a proactive manner. However, despite its great potential, IRS faces new and unique challenges in its efficient integration into wireless communication systems, especially its channel estimation and passive beamforming design under various practical hardware constraints. In this paper, we provide a comprehensive survey on the up-to-date research in IRS-aided wireless communications, with an emphasis on the promising solutions to tackle practical design issues. Furthermore, we discuss new and emerging IRS architectures and applications as well as their practical design problems to motivate future research.
... Recent research works have shown that RISs whose geometric size is sufficiently large can outperform other technologies, e.g., relays, at a reduced hardware and signal processing complexity [2], and can enhance the reliability of wireless links by reducing the fading severity [3]. In addition, the achievable performance of RIS-assisted systems has been proved to be robust to various hardware impairments, e.g., the phase noise, which may further reduce the implementation cost [4]. ...
... The proposed approach is applicable to single-antenna transmitters and receivers that operate in the far-field of the RIS. Possible generalizations of the proposed approach includes the optimization of RIS-assisted systems with multiantenna transmitters and receivers in both the far-field and near-field regimes, as well as the optimization in the presence of discrete-valued impedances and the analysis of the impact of the associated discretization noise [3], [4], [11]. ...
Preprint
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Reconfigurable intelligent surfaces (RISs) are an emerging technology for enhancing the performance of wireless networks at a low and affordable cost, complexity, and power consumption. We introduce an algorithm for optimizing a single-input single-output RIS-assisted system in which the RIS is modeled by using an electromagnetic-compliant framework based on mutual impedances. More precisely, we provide the following new contributions: (i) in the absence of mutual coupling among the scattering elements of the RIS, we derive a closed-form expression for the optimal tunable impedances, which inherently accounts for the interplay between the amplitude and phase of the lumped loads of the RIS; and (ii) in the presence of mutual coupling, we introduce an iterative algorithm for optimizing the tunable impedances of the RIS. The algorithm is proved to be convergent by showing that the objective function is non-decreasing and upper bounded. Numerical results reveal that the mutual coupling among the scattering elements of the RIS significantly affects the end-to-end signal-to-noise ratio (SNR) if the inter-distance is less than half of the wavelength. If the RIS is optimized by explicitly taking into account the impact of mutual coupling, a better end-to-end SNR is obtained.
... The effect of RIS quantization levels on the channel distribution and diversity gain has been analyzed. In [2], Xu et al. claimed that full diversity order can be achieved by RIS with a quantization level of L = 3. In [3], Wang et al. showed the diversity order of the one-bit discrete phase shift RIS system is (M + 3)/2, where M is the number of elements of the RIS. ...
... Proof. For the 1-D phase scanning, the RIS phase shift is configured according to (2). Suppose the beamwidth is θ d , according to Theorem 2, the maximum phase difference between the diversity branches should satisfy: ...
Preprint
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The reconfigurable intelligent surface (RIS) is one of the promising technology contributing to the next generation smart radio environment. The application scenarios include massive connectivity support, signal enhancement, and security protection. One crucial difficulty of analyzing the RIS-assisted networks is that the channel performance is sensitive to the change of user receiving direction. This paper tackles the problem by categorizing the RIS illuminated space into four categories: perfect alignment, coherent alignment, random alignment, and destructive alignment. These four categories cover all the possible phase alignment conditions that a user could experience within the overall $2$ pi solid angle of RIS-illuminated space. We perform analysis for each of these categories, deriving analytical expressions for the outage probability and diversity order. Simulation results are presented to confirm the effectiveness of the proposed analytical results.
... Therefore, in this paper we apply the practical model to obtain the amplitude and phase shift based on the reflection coefficient as in Fig. 3(b) of [11] with the effective resistance R = 2 Ω. Moreover, we assume that the phase shifts are discrete variables for implementing the IRS in practice as in [19], and the range of the phase shift for each IRS element can be given as ...
... Unless otherwise stated, we set the parameters for the system as follows: the number of relays K = 5, the transmit power to noise ratio P/σ 2 n = P S /σ 2 n = P R /σ 2 n = 35 dB, the number of IRS elements M = 16, the path loss exponentα = 2,ᾱ = 2.5, the Rician factor K = 10 dB for links with Rician fading, the target rate ϑ = 0.5 bps/Hz, the discount coefficients δ = 0.9, the number of time slots for updating the prediction network T = 500, the training sample number W = 32, and the iteration number of updating the target network V = 100. Moreover, the suggested quantization for the IRS log 2 (L) is two bits based on [5], [19]. Thus, we consider the number of phase quantization level L = 4 in this paper. ...
Article
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This paper proposes a deep reinforcement learning (DRL) based relay selection scheme for cooperative networks with the intelligent reflecting surface (IRS). We consider a practical phase-dependent amplitude model in which the IRS reflection amplitudes vary with the discrete phase-shifts. Furthermore, we apply the relay selection to reduce the signal loss over distance in IRS-assisted networks. To solve the complicated problem of joint relay selection and IRS reflection coefficient optimization, we introduce DRL to learn from the environment to obtain the solution and reduce the computational complexity. Simulation results show that the throughput is significantly improved with the proposed DRL-based algorithm compared to random relay selection and random reflection coefficients methods.
... Recent research works have shown that RISs whose geometric size is sufficiently large can outperform other technologies, e.g., relays, at a reduced hardware and signal processing complexity [2], and can enhance the reliability of wireless links by reducing the fading severity [3]. In addition, the achievable performance of RIS-assisted systems has been proved to be robust to various hardware impairments, e.g., the phase noise, which may further reduce the implementation cost [4]. ...
... The proposed approach is applicable to single-antenna transmitters and receivers that operate in the far-field of the RIS. Possible generalizations of the proposed approach includes the optimization of RIS-assisted systems with multiantenna transmitters and receivers in both the far-field and near-field regimes, as well as the optimization in the presence of discrete-valued impedances and the analysis of the impact of the associated discretization noise [3], [4], [11]. ...
Article
Full-text available
We introduce algorithms for optimizing a single-input single-output reconfigurable intelligent surface (RIS) assisted system. The RIS is modeled by using an electromagnetic-compliant framework based on mutual impedances and its reconfigurability is realized through tunable lumped impedances. In the absence of mutual coupling among the scattering elements of the RIS, we derive a closed-form expression for the optimal tunable impedances, which accounts for the interplay between the amplitude and phase of the lumped loads of the RIS. In the presence of mutual coupling, we introduce an iterative algorithm for optimizing the tunable impedances of the RIS. The algorithm is proved to be convergent by showing that the objective function is non-decreasing and upper bounded. Numerical results reveal that the mutual coupling significantly affects the end-to-end received power. If the RIS is optimized by taking the mutual coupling into account, the received power can be increased.
... The authors in [29] approximated an arbitrary fading model with Nakagami-m distributed to develop performance analysis of the RIS-assisted transmission with phase noise. The reference [26] studied the effect of quantization level of the phase noise on the diversity order of the system. The authors in [27] derived approximate performance bounds for Rician fading model with phase errors. ...
Preprint
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Recent research provides an approximation on the performance for reconfigurable intelligent surface (RIS) assisted systems over generalized fading channels with phase noise resulting from imperfect phase compensation at the RIS. In this paper, we developed exact analysis and upper bounds on the performance of RIS-assisted vehicular communication system considering phase noise with mobility over asymmetric fading channels by coherently combining received signals reflected by RIS elements and direct transmissions from the source terminal. We employ a novel approach to represent the PDF and CDF of the product of four channel coefficients in terms of a single univariate Fox-H function. We use the derived PDF to develop an exact statistical analysis of the end-to-end SNR for the RIS-assisted system using multi-variate Fox-H function.
... where the effective resistance R is 2 Ω. Moreover, in order to support the practical implementation [47], we assume discrete phase shifts for IRS reflecting elements. The range of discrete phase shifts is ...
Article
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This paper proposes a multi-agent deep reinforcement learning-based buffer-aided relay selection scheme for an intelligent reflecting surface (IRS)-assisted secure cooperative network in the presence of an eavesdropper. We consider a practical phase model where both phase shift and reflection amplitude are discrete variables to vary the reflection coefficients of the IRS. Furthermore, we introduce the buffer-aided relay to enhance the secrecy performance, but the use of the buffer leads to the cost of delay. Thus, we aim to maximize either the average secrecy rate with a delay constraint or the throughput with both delay and secrecy constraints, by jointly optimizing the buffer-aided relay selection and the IRS reflection coefficients. To obtain the solution of these two optimization problems, we divide each of the problems into two sub-tasks and then develop a distributed multi-agent reinforcement learning scheme for the two cooperative sub-tasks, each relay node represents an agent in the distributed learning. We apply the distributed reinforcement learning scheme to optimize the IRS reflection coefficients, and then utilize an agent on the source to learn the optimal relay selection based on the optimal IRS reflection coefficients in each iteration. Simulation results show that the proposed learning-based scheme uses an iterative approach to learn from the environment for approximating an optimal solution via the exploration of multiple agents, which outperforms the benchmark schemes.
... Hence, a good balance between modeling accuracy and mathematical tractability is key for performance analysis purposes. A deep inspection of the RIS-related research in channel modeling reveals that the common assumption of independent and identically distributed (i.i.d.) fading to model the RIS channels is only justified for the sake of mathematical tractability; several relevant examples include somehow idealistic set-ups [7][8][9] as well as more realistic scenarios that consider hardware impairments and imperfect phase estimation [10][11][12]. Very recently, based upon the formulation in [13], a Gamma approximation for the equivalent composite model in RIS-assisted set-ups that explicitly considers the impact of spatial channel correlation in Rayleigh fading was given using the moment-matching (MoM) technique [14]. ...
Article
Full-text available
Channel modeling is a critical issue when designing or evaluating the performance of reconfigurable intelligent surface (RIS)-assisted communications. Inspired by the promising potential of learning-based methods for characterizing the radio environment, we present a general approach to model the RIS end-to-end equivalent channel using the unsupervised expectation-maximization (EM) learning algorithm. We show that an EM-based approximation through a simple mixture of two Nakagami-m distributions suffices to accurately approximate the equivalent channel, while allowing for the incorporation of crucial aspects into RIS’s channel modeling such as beamforming, spatial channel correlation, phase-shift errors, arbitrary fading conditions, and coexistence of direct and RIS channels. Based on the proposed analytical framework, we evaluate the outage probability under different settings of RIS’s channel features and confirm the superiority of this approach compared to recent results in the literature.
... In [7], the authors introduced a finite number of phase-shift elements of RIS where the power is minimized while maintaining certain signal-to-interferenceplus-noise ratio threshold. [13] proved how discrete phaseshift RIS is able to achieve high performance with minimum required number of phase quantization levels. This work shows that 3 levels are enough to attain the full diversity order. ...
Preprint
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Given its ability to control and manipulate wireless environments, reconfigurable intelligent surface (RIS), also known as intelligent reflecting surface (IRS), has emerged as a key enabler technology for the six-generation (6G) cellular networks. In the meantime, vehicular environment radio propagation is negatively influenced by a large set of objects that cause transmission distortion such as high buildings. Therefore, this work is devoted to explore the area of RIS technology integration with vehicular communications while considering the dynamic nature of such communication environment. Specifically, we provide a system model where RoadSide Unit (RSU) leverages RIS to provide indirect wireless transmissions to disconnected areas, known as dark zones. Dark zones are spots within RSU coverage where the communication links are blocked due to the existence of blockages. In details, a discrete RIS is utilized to provide communication links between the RSU and the vehicles passing through out-of-service zones. Therefore, the joint problem of RSU resource scheduling and RIS passive beamforming or phase-shift matrix is formulated as an optimization problem with the objective of maximizing the minimum average bit rate. The formulated problem is mixed integer non-convex program which is difficult to be solved and does not account for the uncertain dynamic environment in vehicular networks. Thereby, we resort to alternative methods based on Deep Reinforcement Learning to determine RSU wireless scheduling and Block Coordinate Descent (BCD) to solve for the phase-shift matrix, \textit{i.e.,} passive beamforming, of the RIS. The Markov Decision Process (MDP) is defined and the complexity of the solution approach is discussed. Our numerical results demonstrate the superiority of our proposed approach over baseline techniques.
... The work of J. D. Vega Sánchez was funded by the Escuela Politécnica Nacional, for the development of the project PIGR-19-06 and through a teaching assistant fellowship for doctoral studies. The work of F.J. Lopez-Martinez was funded by the Spanish Government and the European Fund for Regional Development FEDER (project TEC2017-87913-R) and by Junta de Andalucia (project P18-RT-3175, TETRA5G RIS channels is only justified for the sake of mathematical tractability; several relevant examples include somehow idealistic set-ups [5][6][7] as well as more realistic scenarios that consider hardware impairments and imperfect phase estimation [8][9][10][11]. Very recently, based upon the formulation in [12], a Gamma approximation for the equivalent composite model in RIS-assisted set-ups that explicitly considers the impact of spatial channel correlation in Rayleigh fading was given using the moment-matching technique [13]. ...
... Once more, this shows that to achieve satisfactory accuracy, a few numbers of available bits will be sufficient instead of high precision and high complexity quantizers. Moreover, it is proved that to reach full diversity in RIS-aided communications the number of quantization levels must be Q ≥ 3 [42] that holds when b ≥ 2. Furthermore, the Shannon capacity and the gap with FBL regime is illustrated in Fig. 3. We observe that the gap is increased until some saturation value. ...
Preprint
In this paper, the average achievable rate and error probability of a reconfigurable intelligent surface (RIS) aided systems is investigated for the finite blocklength (FBL) regime. The performance loss due to the presence of phase errors arising from limited quantization levels as well as hardware impairments at the RIS elements is also discussed. First, the composite channel containing the direct path plus the product of reflected channels through the RIS is characterized. Then, the distribution of the received signal-to-noise ratio (SNR) is matched to a Gamma random variable whose parameters depend on the total number of RIS elements, phase errors and the channels' path loss. Next, by considering the FBL regime, the achievable rate expression and error probability are identified and the corresponding average rate and average error probability are elaborated based on the proposed SNR distribution. Furthermore, the impact of the presence of phase error due to either limited quantization levels or hardware impairments on the average rate and error probability is discussed. The numerical results show that Monte Carlo simulations conform to matched Gamma distribution to received SNR for sufficiently large number of RIS elements. In addition, the system reliability indicated by the tightness of the SNR distribution increases when RIS is leveraged particularly when only the reflected channel exists. This highlights the advantages of RIS-aided communications for ultra-reliable and low-latency systems. The difference between Shannon capacity and achievable rate in FBL regime is also discussed. Additionally, the required number of RIS elements to achieve a desired error probability in the FBL regime will be significantly reduced when the phase shifts are performed without error.
... Therefore, the phase quantization error is [15], [17]. According to (1) and (2), the received SNRs at D and E k can be formulated, respectively, as follows ...
Article
This letter investigates the ergodic secrecy rate (ESR) of a reconfigurable intelligent surface (RIS)-assisted communication system in the presence multiple eavesdroppers (Eves), and by assuming discrete phase shifts at the RIS. In particular, a closed-form approximation of the ESR is derived for both non-colluding and colluding Eves. The analytical results are shown to be accurate when the number of reflecting elements of the RIS ${N}$ is large. Asymptotic analysis is provided to investigate the impact of ${N}$ on the ESR, and it is proved that the ESR scales with $\log \,_{2} N$ for both non-colluding and colluding Eves. Numerical results are provided to verify the analytical results and the obtained scaling laws.
... In Fig. 1 the RIS consists of 4 × 5 elements for illustration purposes only. Due to hardware limitations, the complex values (amplitude and phase-shifts) applied by the N load impedances of the RIS reflecting elements are usually quantized into D discrete phase values between 0 and 2π [28]. Thus, the RIS can be electronically controlled into any one of Q = D N possible configurations. ...
Article
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Reconfigurable Intelligent Surfaces (RISs) promise improved, secure, and more efficient wireless communications. One less understood aspect relates to the benefits of RIS towards wireless localization and positioning of mobile users and devices. In this paper we propose and demonstrate two practical solutions that exploit the diversity offered by RIS-enhanced indoor environments and to select RIS state configurations that generate easily differentiable radio maps for use with wireless fingerprinting localization estimators. Specifically, we first investigate supervised learning feature selection methods to prune the large state space of the RIS, thus reducing complexity and enhancing localization accuracy and device position acquisition time. We then analytically derive noise correlated heuristics that can further reduce the computational complexity of our proposed solution. Finally, we validate and benchmark our proposed solutions through accurate end-to-end models and computer simulations while demonstrating an average localization accuracy improvement of about 33%. Our explorations thus demonstrate how and why accuracy improvements are achieved and also hint towards how these can be further enhanced in practical localization settings while utilizing more than one RIS.
... ] , similar to [15], [17]. According to (1) and (2), the received SNRs at D and E k can be formulated, respectively, as follows ...
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This letter investigates the ergodic secrecy capacity (ESC) of a reconfigurable intelligent surface (RIS)-assisted communication system in the presence of discrete phase shifts and multiple eavesdroppers (Eves). In particular, a closed-form approximation of the ESC is derived for both non-colluding and colluding Eves. The analytical results are shown to be accurate when the number of reflecting elements of the RIS $N$ is large. Asymptotic analysis is provided to investigate the impact of $N$ on the ESC, and it is proved that the ESC scales with $\log_2 N$ for both non-colluding and colluding Eves. Numerical results are provided to verify the analytical results and the obtained scaling laws.
... To enable the practical development of RISs, research on RISs with discrete amplitude and phase shifts is crucial. Considering a single-user RIS-aided Single-Input Single-Output (SISO) system, the effects of discrete phase shifts on the diversity order [5], [6] and on the ergodic capacity [7] have been investigated. In addition, several discrete optimization strategies have been recently presented with different objectives. ...
Preprint
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Reconfigurable Intelligent Surfaces (RISs) allow to control the propagation environment in wireless networks by properly tuning multiple reflecting elements. Traditionally, RISs have been realized through single connected reconfigurable impedance networks, in which each RIS element is independently controlled by an impedance connected to ground. In a recent work, this architecture has been extended by realizing more efficient RISs with group and fully connected reconfigurable impedance networks. However, impedance networks tunable with arbitrary precision are hard to realize in practice. In this paper, we propose a practical RIS design strategy based on reconfigurable impedance networks with discrete values. Besides, we address the problem of how to group the RIS elements in group connected architectures. We optimize single, group, and fully connected architectures considering finite-resolution elements, and we compare them in terms of received signal power. Through Monte Carlo simulations, supported by theoretical justifications, we show that only a few resolution bits per reconfigurable impedance are sufficient to achieve the performance upper bound. In particular, while four resolution bits are needed to reach the upper bound in single connected architectures, only a single resolution bit is sufficient in fully connected ones, simplifying significantly the future development of these promising RIS architectures.
... In this context, many works have addressed this task intending to find a suitable equilibrium between channel characterization exactness and analytical tractability. For instance, to approximate the RIS end-to-end channel, several traditional approaches based on the Moment-Matching Method (MoM) or the Central Limit Theorem were extensively investigated in [15], [18]- [20]. However, these contributions are limited to idealistic set-ups since they do not contemplate critical aspects in the RIS channel characterization, including channel correlation, phase noise, or the presence of the direct path between the communication sides. ...
... The RIS is also used for location awareness communication in the beyond 5G network [10,11]. Due to hardware limitations, the phase shifts of RIS cannot be controlled continually, so the discretized effect is analyzed in [12]. In [13,14], the target detection problem in the radar system using RIS is considered. ...
Preprint
The reconfigurable intelligent surface (RIS) has been a potential technology for future radar and wireless communication applications. In this letter, the passive sensing problem using wireless communications signal and RIS is addressed in the scenario with the interference from the wireless access point (AP). An atomic norm minimization (ANM) method is formulated to exploit the target sparsity in the spatial domain and estimate the direction of arrival (DOA), but the conventional semidefinite programming (SDP)-based method to solve the ANM problem is complex and cannot be realized efficiently. Therefore, we proposed a RIS-ADMM method as an alternating direction method of multipliers (ADMM)-based iterative method. The closed-form expressions are derived, and the interference signal is also suppressed. Simulation results show that the proposed RIS-ADMM method outperforms the compared methods in the DOA estimation performance with low computational complexity. The code about the proposed method is avaliable online \url{https://github.com/chenpengseu/RIS-ADMM.git}.
... Continuous or analog phase changes can be challenging to accomplish in practice. Recently, as stated in [56], quantized phase shift configurable RISs have been built. When the input or output signal is a plane, the basic features of RIS can be summarized in the following steps: ...
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With possible new use cases and demanding requirements of future 5th generation (5G) and beyond cellular networks, the future of mobile communications sounds promising. However, the propagation medium has been considered a randomly acting agent between the transmitter and the receiver. With the advent of the digital age of wireless communications, the received signal quality is degrading due to the uncontrollable interactions of the transmitted radio waves with the surrounding artifacts. This paper presents a comprehensive literature review on reconfigurable intelligent surfaces (RISs) and assisted application areas. With the RIS, the network operators can control radio waves’ scattering, reflection, and refraction characteristics by resolving the harmful properties of environmental wireless propagation. Further, the RIS can effectively control the wavefront, such as amplitude, phase, frequency, and even polarization, without requiring complex encoding, decoding, or radio wave processing techniques. Motivated by technological advances, the metasurfaces, reflectarrays, phase shift, and liquid crystals are potential candidates for implementing RIS. Thus, they can be considered the front runner for realizing the 5G and beyond network. Furthermore, the current research activities in the evolving field of wireless networks operated by RIS are reviewed and discussed thoroughly. Finally, to fully explore the potential of RISs in wireless networks, the fundamental research issues to be addressed have been discussed.
... Hence, the ability to control in a precise and known manner is essential for ISLAC applications, which necessitates the availability of accurate and simple RIS phase control models. Such models should ideally account for the per-element response [22], the finite quantization of the control [13], [23], mutual coupling [24], calibration effects, as well as power losses. Most studies on RIS localization have considered ideal phase shifters (e.g. ...
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We investigate a reconfigurable intelligent surface (RIS)-aided near-field localization system with single-antenna user equipment (UE) and base station (BS) under hardware impairments by considering a practical phase-dependent RIS amplitude variations model. To analyze the localization performance under the mismatch between the practical model and the ideal model with unit-amplitude RIS elements, we employ the misspecified Cram\'{e}r-Rao bound (MCRB). Based on the MCRB derivation, the lower bound (LB) on the mean-squared error for estimation of UE position is evaluated and shown to converge to the MCRB at low signal-to-noise ratios (SNRs). Simulation results indicate more severe performance degradation due to the model misspecification with increasing SNR. In addition, the mismatched maximum likelihood (MML) estimator is derived and found to be tight to the LB in the high SNR regime. Finally, we observe that the model mismatch can lead to an order-of-magnitude localization performance loss at high SNRs.
... It is noted that the binary code is not necessarily restricted to reflection phase responses, but also can represent the phase or amplitude of the EM transmission, two distinct EM boundaries, etc. Similar to the results in the community of microwave antennas, the phase quantization of meta-atom will give rise to quantization noise [135][136][137][138], i.e., quantization energy leakage of main lobes into side lobes. In order to overcome this drawback, the reprogrammable coding metasurfaces with two-bit quantization and beyond have also been investigated [139,182]. ...
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... Hence, the ability to control the RIS in a precise and known manner is essential for ISLAC applications, which necessitates the availability of accurate and simple RIS phase control models. Such models should ideally account for the per-element response [36], the finite quantization of the control [14], [37], mutual coupling [38], calibration effects, and power losses. Most studies on RIS localization have considered ideal phase shifters (e.g. ...
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We investigate the problem of reconfigurable intelligent surface (RIS)-aided near-field localization of a user equipment (UE) served by a base station (BS) under phase-dependent amplitude variations at each RIS element. Through a misspecified Cram\'{e}r-Rao bound (MCRB) analysis and a resulting lower bound (LB) on localization, we show that when the UE is unaware of amplitude variations (i.e., assumes unit-amplitude responses), severe performance penalties can arise, especially at high signal-to-noise ratios (SNRs). Leveraging Jacobi-Anger expansion to decouple range-azimuth-elevation dimensions, we develop a low-complexity approximated mismatched maximum likelihood (AMML) estimator, which is asymptotically tight to the LB. To mitigate performance loss due to model mismatch, we propose to jointly estimate the UE location and the RIS amplitude model parameters. The corresponding Cram\'{e}r-Rao bound (CRB) is derived, as well as an iterative refinement algorithm, which employs the AMML method as a subroutine and alternatingly updates individual parameters of the RIS amplitude model. Simulation results indicate fast convergence and performance close to the CRB. The proposed method can successfully recover the performance loss of the AMML under a wide range of RIS parameters and effectively calibrate the RIS amplitude model online with the help of a user that has an a-priori unknown location.
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In this paper, we investigate the performance of an RIS-aided wireless communication system subject to outdated channel state information that may operate in both the near- and far-field regions. In particular, we take two RIS deployment strategies into consideration: (i) the centralized deployment, where all the reflecting elements are installed on a single RIS and (ii) the distributed deployment, where the same number of reflecting elements are placed on multiple RISs. For both deployment strategies, we derive accurate closed-form approximations for the ergodic capacity, and we introduce tight upper and lower bounds for the ergodic capacity to obtain useful design insights. From this analysis, we unveil that an increase of the transmit power, the Rician-K factor, the accuracy of the channel state information and the number of reflecting elements help improve the system performance. Moreover, we prove that the centralized RIS-aided deployment may achieve a higher ergodic capacity as compared with the distributed RIS-aided deployment when the RIS is located near the base station or near the user. In different setups, on the other hand, we prove that the distributed deployment outperforms the centralized deployment. Finally, the analytical results are verified by using Monte Carlo simulations.
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This letter investigates the error probability of reconfigurable intelligent surfaces (RIS)-enabled communication systems with quantized channel phase compensation. Exact and asymptotic bit error rate (BER) expressions are derived assuming different practical channel environments and the presence of the direct link. The theoretical frameworks and findings are validated with the aid of Monte Carlo simulations.
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Future wireless networks are expected to evolve toward an intelligent and software reconfigurable paradigm enabling ubiquitous communications between humans and mobile devices. They will also be capable of sensing, controlling, and optimizing the wireless environment to fulfill the visions of low-power, high-throughput, massively-connected, and low-latency communications. A key conceptual enabler that is recently gaining increasing popularity is the HMIMOS that refers to a low-cost transformative wireless planar structure comprised of sub-wavelength metallic or dielectric scattering particles, which is capable of shaping electromagnetic waves according to desired objectives. In this article, we provide an overview of HMIMOS communications including the available hardware architectures for reconfiguring such surfaces, and highlight the opportunities and key challenges in designing HMIMOS-enabled wireless communications.
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This letter proposes a novel hybrid relay and Intelligent Reflecting Surface (IRS) assisted system for future wireless networks. We demonstrate that for practical scenarios where the amount of radiated power and/or the number of reflecting elements are/is limited, the performance of an IRS-supported system can be significantly enhanced by utilizing a simple Decode-and-Forward (DF) relay. Tight upper bounds for the ergodic capacity are derived for the proposed scheme under different channel environments, and shown to closely match Monte-Carlo simulations.
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One of the key enablers of future wireless communications is constituted by massive multiple-input multiple-output (MIMO) systems, which can improve the spectral efficiency by orders of magnitude. In existing massive MIMO systems, however, conventional phased arrays are used for beamforming. This method results in excessive power consumption and high hardware costs. Recently, reconfigurable intelligent surface (RIS) has been considered as one of the revolutionary technologies to enable energy-efficient and smart wireless communications, which is a two-dimensional structure with a large number of passive elements. In this paper, we develop a new type of high-gain yet low-cost RIS that bears 256 elements. The proposed RIS combines the functions of phase shift and radiation together on an electromagnetic surface, where positive intrinsic-negative (PIN) diodes are used to realize 2-bit phase shifting for beamforming. This radical design forms the basis for the world’s first wireless communication prototype using RIS having 256 two-bit elements. The prototype consists of modular hardware and flexible software that encompass the following: the hosts for parameter setting and data exchange, the universal software radio peripherals (USRPs) for baseband and radio frequency (RF) signal processing, as well as the RIS for signal transmission and reception. Our performance evaluation confirms the feasibility and efficiency of RISs in wireless communications. We show that, at 2.3 GHz, the proposed RIS can achieve a 21.7 dBi antenna gain. At the millimeter wave (mmWave) frequency, that is, 28.5 GHz, it attains a 19.1 dBi antenna gain. Furthermore, it has been shown that the RIS-based wireless communication prototype developed is capable of significantly reducing the power consumption.<br/
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In this paper, we propose intelligent reflecting surface (IRS) aided multi-antenna physical layer security. We present a power efficient scheme to design the secure transmit power allocation and the surface reflecting phase shift. It aims to minimize the transmit power subject to the secrecy rate constraint at the legitimate user. Due to the non-convex nature of the formulated problem, we propose an alternative optimization algorithm and the semidefinite programming (SDP) relaxation to deal with this issue. Also, the closed-form expression of the optimal secure beamformer is derived. Finally, simulation results are presented to validate the proposed algorithm, which highlights the performance gains of the IRS to improve the secure transmission.
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Large intelligent surface (LIS)-assisted wireless communications have drawn attention worldwide. With the use of low-cost LIS on building walls, signals can be reflected by the LIS and sent out along desired directions by controlling its phases, thereby providing supplementary links for wireless communication systems. In this study, we evaluate the performance of an LIS-assisted large-scale antenna system by formulating a tight approximation of the ergodic capacity and investigate the effect of the phase shifts on the ergodic capacity in different propagation scenarios. In particular, we propose an optimal phase shift design based on the ergodic capacity approximation and statistical channel state information. Furthermore, we derive the requirement on the quantization bits of the LIS to promise an acceptable capacity degradation. Numerical results show that using the proposed phase shift design can achieve the maximum ergodic capacity, and a 2-bit quantizer is sufficient to ensure capacity degradation of no more than 1 bit/s/Hz.
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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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In this letter, we investigate the ergodic capacity of the intelligent reflecting surface (IRS)-assisted communication system with quantization phase errors, which is different from existing works assuming ideal continuous or discrete phases. The ergodic capacity, however, does not admit an exact closed-form expression if not impossible. In order to gain insight into the capacity performance, the impact of phase errors on the capacity degradation is quantified, and the minimum number of the reflectors to achieve a given rate threshold is obtained. Simulation results verify the effectiveness of the IRS-assisted system and the capacity scaling law.
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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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The integration of intelligent reflecting surface (IRS) to multiple access networks is a cost-effective solution for boosting spectrum/energy efficiency and enlarging network coverage/connections. However, due to the new capability of IRS in reconfiguring the wireless propagation channels, it is fundamentally unknown which multiple access scheme is superior in the IRS-assisted wireless network. In this letter, we pursue a theoretical performance comparison between non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) in the IRS-assisted downlink communication, for which the transmit power minimization problems are formulated under the discrete unit-modulus reflection constraint on each IRS element. We analyze the minimum transmit powers required by different multiple access schemes and compare them numerically, which turn out to not fully comply with the stereotyped superiority of NOMA over OMA in conventional systems without IRS. Moreover, to avoid the exponential complexity of the brute-force search for the optimal discrete IRS phase shifts, we propose a low-complexity solution to achieve near-optimal performance.
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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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Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. In this paper, we propose the point of view that both types of gains can be simultaneously obtained for a given multiple antenna channel, but there is a fundamental tradeoff between how much of each any coding scheme can get. We give a simple characterization of the optimal tradeoff curve and use it to evaluate the performance of existing multiple antenna schemes.