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Scalable Beamforming Design for Multi-RIS-Aided MU-MIMO Systems with Imperfect CSIT
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Abstract
A reconfigurable intelligent surface (RIS) has emerged as a promising solution for enhancing the capabilities of wireless communications. This paper presents a scalable beamforming design for maximizing the spectral efficiency (SE) of multi-RIS-aided communications through joint optimization of the precoder and RIS phase shifts in multi-user multiple-input multiple-output (MU-MIMO) systems under imperfect channel state information at the transmitter (CSIT). To address key challenges of the joint optimization problem, we first decompose it into two subproblems with deriving a proper lower bound. We then leverage a generalized power iteration (GPI) approach to identify a superior local optimal precoding solution. We further extend this approach to the RIS design using regularization; we set a RIS regularization function to efficiently handle the unitmodulus constraints, and also find the superior local optimal solution for RIS phase shifts under the GPI-based optimization framework. Subsequently, we propose an alternating optimization method. In particular, utilizing the block-diagonal structure of the matrices the GPI method, the proposed algorithm offers multi-RIS scalable beamforming as well as superior SE performance. Simulations validate the proposed method in terms of both the sum SE performance and the scalability.
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This paper analyzes the performance of multiple reconfigurable intelligent surfaces (RISs)-aided networks with opportunistic RIS scheduling. The paper also provides some optimization results on the number of reflecting elements on RISs and the optimal placement of RISs. We first derive accurate closed-form approximations for RIS channels' distributions assuming independent non-identically distributed (i.ni.d.) Nakagami-
m
fading environment. Then, the approximate expressions for outage probability (OP) and average symbol error probability (ASEP) are derived in closed-form. Furthermore, to get more insights into the system performance, we derive the asymptotic OP at the high signal-to-noise ratio (SNR) regime and provide closed-form expressions for the system diversity order and coding gain. Finally, the accuracy of our theoretical analysis is validated through Monte-Carlo simulations. The obtained results show that the considered RIS scenario can provide a diversity order of
, where
a
is a function of the Nakagami fading parameter
m
and the number of meta-surface elements
N
, and
K
is the number of RISs.
Next-generation communication systems aim for providing pervasive services, including the high-mobility scenarios routinely encountered in mission-critical applications. Hence we harness the recently-developed reconfigurable intelligent surfaces (RIS) to assist the high-mobility cell-edge users. More explicitly, the passive elements of RISs generate beneficial phase rotations for the reflected signals, so that the signal power received by the high-mobility users is enhanced. However, in the face of high Doppler frequencies, the existing RIS channel estimation techniques that assume block fading generally result in irreducible error floors. In order to mitigate this problem, we propose a new RIS channel estimation technique, which is the first one that performs minimum mean square error (MMSE) based interpolation for the sake of taking into account the time-varying nature of fading even within the coherence time. The RIS modelling invokes only passive elements without relying on RF chains, where both the direct link and RIS-reflected links as well as both the line-of-sight (LoS) and non-LoS (NLoS) paths are taken into account. As a result, the cascaded base station (BS)-RIS-user links involve the multiplicative concatenation of the channel coefficients in the LoS and NLoS paths across the two segments of the BS-RIS and RIS-user links. Against this background, we model the multiplicative RIS fading correlation functions for the first time in the literature, which facilitates MMSE interpolation for estimating the high-dimensional and high-Doppler RIS-reflected fading channels. Our simulation results demonstrate that for a vehicle travelling at a speed as high as 90 mph, employing a low-complexity RIS at the cell-edge using as few as 16 RIS elements is sufficient for achieving substantial power-effieincy gains, where the Doppler-induced error floor is mitigated by the proposed channel estimation technique.
Intelligent reflecting surface (IRS) has emerged as a promising technique for wireless communication networks. By dynamically tuning the reflection amplitudes/phase shifts of a large number of passive elements, IRS enables flexible wireless channel control and configuration and thereby enhances the wireless signal transmission rate and reliability significantly. Despite the vast literature on designing and optimizing assorted IRS-aided wireless systems, prior works have mainly focused on enhancing wireless links with single signal reflection only by one or multiple IRSs, which may be insufficient to boost the wireless link capacity under some harsh propagation conditions (e.g., indoor environment with dense blockages/obstructions). This issue can be tackled by employing two or more IRSs to assist each wireless link and jointly exploiting their single as well as multiple signal reflections over them. However, the resultant double-/multi-IRS-aided wireless systems face more complex design issues as well as new practical challenges for implementation compared to the conventional single-IRS counterpart, in terms of IRS reflection optimization, channel acquisition, as well as IRS deployment and association/selection. As such, a new paradigm for designing multi-IRS cooperative passive beamforming and joint active/passive beam routing arises, which calls for innovative design approaches and optimization methods. In this article, we give a tutorial overview of multi-IRS-aided wireless networks, with an emphasis on addressing the new challenges due to multi-IRS signal reflection and routing. Moreover, we point out important directions worthy of research and investigation in the future.
As the standardization of 5G solidifies, researchers are speculating what 6G will be. The integration of sensing functionality is emerging as a key feature of the 6G Radio Access Network (RAN), allowing for the exploitation of dense cell infrastructures to construct a perceptive network. In this IEEE Journal on Selected Areas in Commmunications (JSAC) Special Issue overview, we provide a comprehensive review on the background, range of key applications and state-of-the-art approaches of Integrated Sensing and Communications (ISAC). We commence by discussing the interplay between sensing and communications (S&C) from a historical point of view, and then consider the multiple facets of ISAC and the resulting performance gains. By introducing both ongoing and potential use cases, we shed light on the industrial progress and standardization activities related to ISAC. We analyze a number of performance tradeoffs between S&C, spanning from information theoretical limits to physical layer performance tradeoffs, and the cross-layer design tradeoffs. Next, we discuss the signal processing aspects of ISAC, namely ISAC waveform design and receive signal processing. As a step further, we provide our vision on the deeper integration between S&C within the framework of perceptive networks, where the two functionalities are expected to mutually assist each other, i.e., via communication-assisted sensing and sensing-assisted communications. Finally, we identify the potential integration of ISAC with other emerging communication technologies, and their positive impacts on the future of wireless networks.
We consider the channel estimation problem and the channel-based wireless applications in multiple-input multiple-output orthogonal frequency division multiplexing systems assisted by intelligent reconfigurable surfaces (IRSs). To obtain the necessary channel parameters, i.e., angles, delays and gains, for environment mapping and user localization, we propose a novel twin-IRS structure consisting of two IRS planes with a relative spatial rotation. We model the training signal from the user equipment to the base station via IRSs as a third-order canonical polyadic tensor with a maximal tensor rank equal to the number of IRS unit cells. We present four designs of IRS training coefficients, i.e., random, structured, grouping and sparse patterns, and analyze the corresponding uniqueness conditions of channel estimation. We extract the cascaded channel parameters by leveraging array signal processing and atomic norm denoising techniques. Based on the characteristics of the twin-IRS structures, we formulate a nonlinear equation system to exactly recover the multipath parameters by two efficient decoupling modes. We realize environment mapping and user localization based on the estimated channel parameters. Simulation results indicate that the proposed twin-IRS structure and estimation schemes can recover the channel state information with remarkable accuracy, thereby offering a centimeter-level resolution of user positioning.
We consider multi-antenna wireless systems aided by reconfigurable intelligent surfaces (RIS). RIS presents a new physical layer technology for improving coverage and energy efficiency by intelligently controlling the propagation environment. In practice however, achieving the anticipated gains of RIS requires accurate channel estimation. Recent attempts to solve this problem have considered the least-squares (LS) approach, which is simple but also sub-optimal. The optimal channel estimator, based on the minimum mean-squared-error (MMSE) criterion, is challenging to obtain and is non-linear due to the non-Gaussianity of the effective channel seen at the receiver. Here we present approaches to approximate the optimal MMSE channel estimator. As a first approach, we analytically develop the best linear estimator, the LMMSE, together with a corresponding majorization-minimization based algorithm designed to optimize the RIS phase shift matrix during the training phase. This estimator is shown to yield improved accuracy over the LS approach by exploiting second-order statistical properties of the wireless channel and the noise. To further improve performance and better approximate the globally-optimal MMSE channel estimator, we propose data-driven non-linear solutions based on deep learning. Specifically, by posing the MMSE channel estimation problem as an image denoising problem, we propose two convolutional neural network (CNN) based methods to perform the denoising and approximate the optimal MMSE channel estimation solution. Our numerical results show that these CNN-based estimators give superior performance compared with linear estimation approaches. They also have low computational complexity requirements, thereby motivating their potential use in future RIS-aided wireless communication systems.
In this paper, large-scale intelligent reflecting surface (IRS)-assisted multiple-input single-output (MISO) system is considered in the presence of channel uncertainty. To maximize the average sum rate of the system by jointly optimizing the active beamforming at the BS and the passive phase shifts at the IRS, while satisfying the power constraints, a novel robust beamforming design is proposed by using the penalty dual decomposition (PDD) algorithm. By applying the upper bound maximization/minimization (BSUM) method, in each iteration of the algorithm, the optimal solution for each variable can be obtained with closed-form expression. Simulation results show that the proposed scheme achieves high performance with very low computational complexity.
This letter studies a multiuser multiple-input single-output (MISO) intelligent reflecting surface (IRS)-aided simultaneous wireless information and power transfer (SWIPT) system. Specifically, a multi-antenna base station (BS) transmits data along with energy to a set of users to decode data and harvest energy by adopting the power splitting (PS) simultaneously. The energy efficiency indicator (EEI) is introduced to trade off between data rate and harvested energy, which is maximized by jointly optimizing beamforming vectors at the BS, PS ratio at each user, and phase shifts at the IRS. To solve this non-convex optimization problem, we first adopt the majorization-minimization (MM) approach to construct a concave-convex fractional function which can be handled via the Dinkelbach algorithm and then propose an efficient algorithm for solving two subproblems based on the alternating optimization (AO). For the first subproblem, semi-definite relaxation (SDR), MM approach, and Dinkelbach algorithm are adopted, while for the second sub-problem, a new manifold approach is proposed to handle the unit-modulus constraints due to IRS passive reflection. Simulation results demonstrate the superior performance of our proposed algorithm compared to other baseline schemes.
Intelligent reflecting surfaces (IRSs) constitute a disruptive wireless communication technique capable of creating a controllable propagation environment. In this paper, we propose to invoke an IRS at the cell boundary of multiple cells to assist the downlink transmission to cell-edge users, whilst mitigating the inter-cell interference, which is a crucial issue in multicell communication systems. We aim for maximizing the weighted sum rate (WSR) of all users through jointly optimizing the active precoding matrices at
the base stations (BSs) and the phase shifts at the IRS subject to each BS’s power constraint and unit modulus constraint. Both the BSs and the users are equipped with multiple antennas, which enhances the spectral efficiency by exploiting the spatial multiplexing gain. Due to the nonconvexity of the problem, we first reformulate it into an equivalent one, which is solved by using the block coordinate descent (BCD) algorithm, where the precoding matrices and phase shifts are alternately optimized. The optimal precoding matrices can be obtained in closed form, when fixing the phase shifts. A pair of efficient algorithms are proposed for solving the phase shift optimization problem, namely the Majorization-Minimization (MM) Algorithm and the Complex
Circle Manifold (CCM) Method. Both algorithms are guaranteed to converge to at least locally optimal solutions. We also extend the proposed algorithms to the more general multiple-IRS and network MIMO scenarios. Finally, our simulation results confirm the advantages of introducing IRSs in enhancing the cell-edge user performance.
Intelligent reflecting surface (IRS) has recently been envisioned to offer unprecedented massive multiple-input multiple-output (MIMO)-like gains by deploying large-scale and low-cost passive reflection elements. By adjusting the reflection coefficients, the IRS can change the phase shifts on the impinging electromagnetic waves so that it can smartly reconfigure the signal propagation environment and enhance the power of the desired received signal or suppress the interference signal. In this paper, we consider downlink multigroup multicast communication systems assisted by an IRS. We aim for maximizing the sum rate of all the multicasting groups by the joint optimization of the precoding matrix at the base station (BS) and the reflection coefficients at the IRS under both the power and unit-modulus constraint. To tackle this non-convex problem, we propose two efficient algorithms under the majorization-minimization (MM) algorithm framework. Specifically, a concave lower bound surro-gate objective function of each user's rate has been derived firstly, based on which two sets of variables can be updated alternately by solving two corresponding second-order cone programming (SOCP) problems. Then, in order to reduce the computational complexity, we derive another concave lower bound function of each group's rate for each set of variables at every iteration, and obtain the closed-form solutions under these loose surrogate objective functions. Finally, the simulation results demonstrate the benefits in terms of the spectral and energy efficiency of the introduced IRS and the effectiveness in terms of the convergence and complexity of our proposed algorithms.
Intelligent reflecting surface (IRS) is a promising technology to support high performance wireless communication. By adaptively configuring the reflection amplitude and/or phase of each passive reflecting element on it, the IRS can reshape the electromagnetic environment in favour of signal transmission. This letter advances the existing research by proposing and analyzing a double-IRS aided wireless communication system. Under the reasonable assumption that the reflection channel from IRS 1 to IRS 2 is of rank 1 (e.g., line-of-sight channel), we propose a joint passive beamforming design for the two IRSs. Based on this, we show that deploying two cooperative IRSs with in total K elements can yield a power gain of order O(K 4), which greatly outperforms the case of deploying one traditional IRS with a power gain of order O(K 2). Our simulation results validate that the performance of deploying two cooperative IRSs is significantly better than that of deploying one IRS given a sufficient total number of IRS elements. We also extend our line-of-sight channel model to show how different channel models affect the performance of the double-IRS aided wireless communication system.
This paper considers the Sum-Rate (SR) maximization problem in downlink MU-MISO systems under imperfect Channel State Information at the Transmitter (CSIT). Contrary to existing works, we consider a rather unorthodox transmission scheme. In particular, the message intended to one of the users is split into two parts: a common part which can be recovered by all users, and a private part recovered by the corresponding user. On the other hand, the rest of users receive their information through private messages. This Rate-Splitting (RS) approach was shown to boost the achievable Degrees of Freedom (DoF) when CSIT errors decay with increased SNR. In this work, the RS strategy is married with linear precoder design and optimization techniques to achieve a maximized Ergodic SR (ESR) performance over the entire range of SNRs. Precoders are designed based on partial CSIT knowledge by solving a stochastic rate optimization problem using means of Sample Average Approximation (SAA) coupled with the Weighted Minimum Mean Square Error (WMMSE) approach. Numerical results show that in addition to the ESR gains, the benefits of RS also include relaxed CSIT quality requirements and enhanced achievable rate regions compared to conventional transmission with NoRS.
Communication at millimeter wave (mmWave) frequencies is defining a new era
of wireless communication. The mmWave band offers higher bandwidth
communication channels versus those presently used in commercial wireless
systems. The applications of mmWave are immense: wireless local and personal
area networks in the unlicensed band, 5G cellular systems, not to mention
vehicular area networks, ad hoc networks, and wearables. Signal processing is
critical for enabling the next generation of mmWave communication. Due to the
use of large antenna arrays at the transmitter and receiver, combined with
radio frequency and mixed signal power constraints, new multiple-input
multiple-output (MIMO) communication signal processing techniques are needed.
Because of the wide bandwidths, low complexity transceiver algorithms become
important. There are opportunities to exploit techniques like compressed
sensing for channel estimation and beamforming. This article provides an
overview of signal processing challenges in mmWave wireless systems, with an
emphasis on those faced by using MIMO communication at higher carrier
frequencies.
With the severe spectrum shortage in conventional cellular bands, millimeter
wave (mmW) frequencies between 30 and 300 GHz have been attracting growing
attention as a possible candidate for next-generation micro- and picocellular
wireless networks. The mmW bands offer orders of magnitude greater spectrum
than current cellular allocations and enable very high-dimensional antenna
arrays for further gains via beamforming and spatial multiplexing. This paper
uses recent real-world measurements at 28 and 73 GHz in New York City to derive
detailed spatial statistical models of the channels and uses these models to
provide a realistic assessment of mmW micro- and picocellular networks in a
dense urban deployment. Statistical models are derived for key channel
parameters including the path loss, number of spatial clusters, angular
dispersion and blocking. It is found that, even in highly non-line-of-sight
environments, strong signals can be detected 100m to 200m from potential cell
sites, potentially with multiple clusters to support spatial multiplexing.
Moreover, a system simulation based on the models predicts that mmW systems
with cell radii of 100m can offer an order of magnitude increase in capacity
over current state-of-the-art 4G cellular networks with similar cell density.
We study boosting algorithms from a new perspective. We show that the Lagrange dual problems of l₁-norm-regularized AdaBoost, LogitBoost, and soft-margin LPBoost with generalized hinge loss are all entropy maximization problems. By looking at the dual problems of these boosting algorithms, we show that the success of boosting algorithms can be understood in terms of maintaining a better margin distribution by maximizing margins and at the same time controlling the margin variance. We also theoretically prove that approximately, l₁-norm-regularized AdaBoost maximizes the average margin, instead of the minimum margin. The duality formulation also enables us to develop column-generation-based optimization algorithms, which are totally corrective. We show that they exhibit almost identical classification results to that of standard stagewise additive boosting algorithms but with much faster convergence rates. Therefore, fewer weak classifiers are needed to build the ensemble using our proposed optimization technique.
Satellite communication (SatCom) is regarded as a key enabler for bridging connectivity and capacity gaps in sixth-generation (6G) networks. However, the proliferation of Low Earth Orbit (LEO) satellites raises significant intersystem interference risks with Geostationary Earth Orbit (GEO) systems. This paper introduces a cooperative multi-satellite multireconfigurable intelligent surface (RIS) transmission framework to mitigate such interference while enhancing LEO SatCom performance. Specifically, cooperative beamforming is designed under a non-coherent cell-free paradigm, considering both adaptive and max ratio (MR) precoding, as well as statistical and two-timescale channel state information (CSI), aiming to synthesize the advantages of cell-free and RIS into SatCom in a practical way. Firstly, an alternating optimization (AO)-based design leveraging statistical CSI with adaptive precoding is proposed. Then, we propose a power allocation algorithm under MR precoding with given RIS phase shifts obtained from the former, along with a direct two-stage design bypassing prior results. Additionally, we extend derived closed-form expressions and proposed algorithms to exploit two-timescale CSI. Numerical results demonstrate the impact of intersystem interference mitigation constraints, compare the performance of proposed algorithms, draw insights into the effects of transmit power, interference threshold, and Rician factors, validate SatCom performance enhancements achieved by RISs, and discuss the advantages of multi-satellite cooperation.
Sensing begins to rise as a fundamental functionality in integrated sensing and communication (ISAC), especially for sensing-aided communication enhancement (SACE), where base stations (BSs) are promising to perform ubiquitous sensing for communication enhancement. Resource allocation between sensing and communication is a crucial issue in SACE. Therefore, this paper investigates a RIS-assisted SACE (R-SACE) mechanism that jointly designs the time resource allocation between sensing and communication at the BS and the reflecting precoding at the RIS. The performance-guaranteed sensing result obtained at the BS serves as the basis for the proposed R-SACE mechanism, which aims to maximize the average achievable capacity of the RIS-assisted communication link and suppress caused interference. The closed-form expressions of sensing performance metrics are derived. Alternating algorithm (AO) is used to iteratively solve a proved convex optimization subproblem and a transformed quadratic constraint quadratic programming (QCQP) subproblem. Simulation results show priorities of the proposed R-SACE mechanism in enhancing communication capacity while suppressing interference with assists of sensing and RIS.
Cell free (CF) massive multiple-input multiple-output (mMIMO) is a promising technology in realizing beyond fifth generation (B5G) networks. Massive deployment of access points (APs) in a CF-mMIMO system increases the spectral efficiency, however it also increases the energy consumption and fronthaul requirements. Since recently reconfigurable intelligent surface (RIS) is shown to be a cost-effective solution to improve performance of wireless networks, RIS can be a promising technology to enhance the performance of CF-mMIMO systems. In this work, we study the downlink (DL) performance of CF-mMIMO system aided by multiple RISs, while considering correlated Rician fading channels, discrete RIS phase-shifts and low-complexity channel estimation (CE) protocol. Given the obtained imperfect channel state information (CSI), we derive lower bounds on the rates achieved using conjugate beamforming (CB) and zero-forcing (ZF) precoders. The obtained bounds depend on channel statistics, RIS phase-shifts and number of RIS elements. To optimize the performance with respect to RIS phase-shifts, we formulate a maximization problem and propose a sub-optimal genetic algorithm (GA)-based solution. Through simulations, we demonstrate that distributed RIS deployment outperforms centralized RIS deployment in terms of DL throughput. Interestingly, we demonstrate that the DL throughput improves as number of RISs increases until an optimal number of distributed RISs over which the DL performance of the system starts to drop. We discuss this effect under varying the number of APs and RISs. We extend the analysis by considering different precoders, CE and RIS optimization schemes, and verify the accuracy of our derived analytical results by Monte-Carlo simulations.
Different from previous literature assuming either single reconfigurable intelligent surface (RIS) or multiple RISs at given locations, this letter first studies a multi-user millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) system aided by multiple RISs following Poisson point processes. Then we derive an accurate closed-form expression for the spectral efficiency of an arbitrary user and an approximation for the ergodic spectral efficiency of the cell. Moreover, we consider the hardware impairment and model a practical phase-dependent amplitude for each reflecting element. Finally, the simulation results verify the derivations and demonstrate that RISs can provide greater performance gain than the active nodes and require different deployment strategy, which is related to the number of RISs.
Intelligent reflecting surface (IRS) has recently emerged as a promising technology for Internet-of-Things (IoT) networks to provide massive connectivity. In this paper, we propose IoT user selection methods and beamforming designs in a multi-IRS aided IoT network. Specifically, we aim to jointly optimize the base station (BS) beamforming, IRS reflection coefficients and user selection to maximize the weighted sum rate of selected users, which is a mixed integer non-linear (MINLP) problem. To solve this MINLP problem, we design a novel algorithm by absorbing user selection implicitly into BS beamforming design, and applying a fractional programming (FP) to alternate between BS beamforming design using a Lagrangian-based subgradient method and IRS coefficients optimization using a complex circle manifold (CCM) method. However, this algorithm has high complexity, thus we further propose two low complexity and non-alternating algorithms, one using a channel correlation based metric for user selection, and the other using zero-forcing (ZF) beamforming at the BS. Numerical results show that our proposed algorithms achieve significant performance gain over benchmark schemes, and the low complexity algorithms achieve a performance comparable with the joint optimization algorithm at a fraction of the run time. These algorithms demonstrate that multiple IRSs help improve the network sum rate, IRSs with more elements tend to select IoT users more close by, and the best locations for IRS placement are near IoT device clusters.
We propose secure max-min fairness (MMF) precoding for a downlink multi-antenna system with multiple users and eavesdroppers. Since the problem is non-convex and non-smooth and partial channel knowledge is assumed, it is highly challenging to solve. To resolve the difficulties, we first reformulate the problem with conditional average rates, allowing to exploit the partial channel knowledge. Then, we derive the original problem as an approximate smoothing problem using a LogSumExp approach. We identify the first-order optimality condition and cast it to a generalized eigenvalue problem. Solving the problem via a power iteration offers the best local optimal solution. Simulations validate the proposed secure-MMF precoding method.
Integrated sensing and communication (ISAC) is a key enabler for next-generation wireless communication systems to improve spectral efficiency. However, the coexistence of sensing and communication functionalities can cause harmful interference. In this paper, we propose to use a reconfigurable intelligent surface (RIS) in conjunction with ISAC to address this issue. The RIS is composed of a large number of low-cost elements that can adjust the amplitude and phase shift of impinging signals, thus providing a relatively high beamforming gain. To maximize the sum-rate of the communication system, we jointly optimize the beamformer at the base station (BS) and the phase shifts at the RIS, subject to a threshold on the interference power, the unit-norm constraint of the transmit power, and the unit modulus constraint of the RIS phase shifts. To efficiently tackle this NP-hard problem, we first reformulate the problem into a more tractable form using the fractional programming (FP) technique. Then, we exploit the geometrical properties of the constraints and adopt an alternating manifold-based optimization to compute the optimal active beamformer and the RIS phase shifts, respectively. Simulation results demonstrate that the proposed RIS-assisted design significantly reduces the mutual interference and improves the system sum-rate for the communication system.
In this paper, we consider the robust beamforming design in a reconfigurable intelligent surface (RIS)-aided cell-free (CF) system considering the channel state information (CSI) uncertainties of both the direct channels and cascaded channels at the transmitter with capacity-limited backhaul. We jointly optimize the precoding at the access points (APs) and the phase shifts at multiple RISs to maximize the worst-case sum rate of the CF system subject to the constraints of maximum transmit power of APs, unit-modulus phase shifts, limited backhaul capacity, and bounded CSI errors. By applying a series of transformations, the non-smoothness and semi-infinite constraints are tackled in a low-complexity manner that facilitates the design of an alternating optimization (AO)-based iterative algorithm. The proposed algorithm divides the considered problem into two subproblems. For the RIS phase shifts optimization subproblem, we exploit the penalty convex-concave procedure (P-CCP) to obtain a stationary solution and achieve effective initialization. For precoding optimization subproblem, successive convex approximation (SCA) is adopted with a convergence guarantee to a Karush-Kuhn-Tucker (KKT) solution. Numerical results demonstrate the effectiveness of the proposed robust beamforming design, which achieves superior performance with low complexity. Moreover, the importance of RIS phase shift optimization for robustness and the advantages of distributed RISs in the CF system are further highlighted.
Difficulties in controlling IRSs to form the optimized passive beamforming have rarely been considered in intelligent reflecting surface (IRS)-aided systems, which are summarized as follows: 1) sending the optimized passive precoding vectors to the IRS controller incurs significant control overheads; 2) implementing the optimized passive precoding needs to set massive modes in the IRS control circuit. To address these issues, we investigate codebook-based passive beamforming for multi-IRS-aided millimeter-wave (mmWave) multi-user multiple-input single-output (MU-MISO) systems, where the control overheads are reduced to several scalars and the number of modes set in the IRS control circuit is reduced to that of codewords. Moreover, we formulate a joint passive and active precoding problem in the multi-IRS-aided mmWave MU-MISO system as a mixed-integer nonlinear programming (MINLP) problem, and then develop a generalized Benders decomposition (GBD)-based joint passive and active precoding algorithm. The proposed algorithm offers near-optimal performance (
%) with significantly-reduced computational complexity. Simulation results show that the proposed algorithm achieves energy savings of up to 50% and 95%, compared to the benchmark by the maximum ratio transmission and that without IRSs, respectively. In addition, the energy savings increase with the number of reflecting elements packed on each IRS as well as that of codewords.
Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output (MIMO) system in the presence of transceiver hardware impairments, RIS phase noise and imperfect channel state information (CSI). Joint design of the MIMO transceiver and RIS reflection matrix to minimize the total average mean-square-error (MSE) of all data streams is particularly considered. This joint design problem is non-convex and challenging to solve due to the newly considered practical imperfections. To tackle the issue, we first analyze the total average MSE by incorporating the impacts of the above system imperfections. Then, in order to handle the tightly coupled optimization variables and non-convex NP-hard constraints, an efficient iterative algorithm based on alternating optimization (AO) framework is proposed with guaranteed convergence, where each subproblem admits a closed-form optimal solution by leveraging the majorization-minimization (MM) technique. Moreover, via exploiting the special structure of the unit-modulus constraints, we propose a modified Riemannian gradient ascent (RGA) algorithm for the discrete RIS phase shift optimization. Furthermore, the optimality of the proposed algorithm is validated under line-of-sight (LoS) channel conditions, and the irreducible MSE floor effect induced by imperfections of both hardware and CSI is also revealed in the high signal-to-noise ratio (SNR) regime. Numerical results show the superior MSE performance of our proposed algorithm over the adopted benchmark schemes, and demonstrate that increasing the number of RIS elements is not always beneficial under the above system imperfections.
In this paper, the robust design for the intelligent reflective surface (IRS) assisted wireless multi-group multicast system is considered, in which two optimization design problems under two different channel state information (CSI) error models are separately discussed, i.e., the fairness-based problems and the quality-of-service (QoS)-based problems for both the bounded CSI error model and the statistical CSI error model. In order to deal with the non-convex constraints of the considered problems, i.e., bounded CSI error based constraint and statistical CSI error based constraint, S-procedure is adopted to convert the non-convex SINR constraint with bounded CSI error into linear matrix inequalities (LMIs), and the Bernstein-type inequality is utilized to transform the outage probability constraint with statistical CSI error into a second-order cone (SOC) constraint and linear inequalities. Following that, two efficient algorithms based on alternate optimization (AO) are proposed to solve the fairness problems and QoS problems, wherein the semi-definite programming (SDP), penalty convex-concave procedure (CCP) and semi-definite relaxation (SDR) are utilized. Furthermore, we analyze the complexity of the proposed algorithms. Finally, some numerical simulation results are presented to verify the effectiveness of the proposed algorithms, and the impacts of the CSI error and the discrete precision of IRS reflection phase shift on the system performance are analyzed, which provides some insights for the IRS deployment and system robust design.
This paper deals with line-of-sight (LOS) MIMO communication via an intelligent reflecting surface (IRS). It is shown that the number of spatial degrees of freedom (DOF) afforded by this setting grows in proportion with the IRS aperture, as opposed to being dictated by the transmit and receive apertures; this buttresses the interest in IRS deployments at mmWave and terahertz frequencies, with wavelengths and transmission ranges small enough to enable LOS MIMO. Explicit and simple-to-implement IRS phase shifts are put forth that achieve, not only the maximum number of DOF, but the capacity, under a certain geometrical condition. The insights leading to the proposed phase shifts, and to the optimality condition itself, are asymptotic in nature, yet extensive simulations confirm that the performance is excellent for a broad range of settings and even if the optimality condition is not strictly met.
This paper investigates the joint beamforming design for the intelligent reflecting surface (IRS) aided multi-antenna multiuser (MU) multiple-input multiple-output (MIMO) downlink transmissions under imperfect channel state information (CSI), where the IRS can only take discrete PSs (PSs) at each element and the weighted sum rate (WSR) is adopted as the performance metric. By deriving the covariance matrix of the interference and noise at the users under the statistical channel estimation errors (CEEs) model, the joint WSR maximization problem is reformulated as an equivalent weighted minimum mean square error minimization problem and decoupled into two subproblems which are solved alternatively. In particular, two algorithms based on the majorization-minimization and gradient descent methods are proposed to obtain the optimal beamforming matrix at the IRS. Simulation results validate the accuracy of the proposed robust design and reveal that in case of imperfect CSI, the IRS can still achieve a significant improvement in WSR even with 2-bits PSs at the IRS. Moreover, it is also found that increasing the number of reflecting elements may not always be beneficial and that the optimal location of the IRS may be closer to the base station in the presence of CEEs.
The use of low-resolution digital-to-analog and analog-to-digital converters (DACs and ADCs) significantly benefits energy efficiency (EE) at the cost of high quantization noise for massive multiple-input multiple-output (MIMO) systems. This paper considers a precoding optimization problem for maximizing EE in quantized downlink massive MIMO systems. To this end, we jointly optimize an active antenna set, precoding vectors, and allocated power; yet acquiring such joint optimal solution is challenging. To resolve this challenge, we decompose the problem into precoding direction and power optimization problems. For precoding direction, we characterize the first-order optimality condition, which entails the effects of quantization distortion and antenna selection. We cast the derived condition as a functional eigenvalue problem, wherein finding the principal eigenvector attains the best local optimal point. To this end, we propose generalized power iteration based algorithm. To optimize precoding power for given precoding direction, we adopt a gradient descent algorithm for the EE maximization. Alternating these two methods, our algorithm identifies a joint solution of the active antenna set, the precoding direction, and allocated power. In simulations, the proposed methods provide considerable performance gains. Our results suggest that a few-bit DACs are sufficient for achieving high EE in massive MIMO systems.
In the past as well as present wireless communication systems, the wireless propagation environment is regarded as an uncontrollable black box that impairs the received signal quality, and its negative impacts are compensated for by relying on the design of various sophisticated transmission/reception schemes. However, the improvements through applying such schemes operating only at two endpoints (i.e., transmitter and receiver) are limited even after five generations of wireless systems. Reconfigurable intelligent surface (RIS) or intelligent reflecting surface (IRS) have emerged as a new and promising technology that can configure the wireless environment in a favorable manner by properly tuning the phase shifts of a large number of quasi passive and low-cost reflecting elements, thus standing out as a promising candidate technology for the next/sixth-generation (6G) wireless system. However, to reap the performance benefits promised by RIS/IRS, efficient signal processing techniques are crucial, for a variety of purposes such as channel estimation, transmission design, radio localization, and so on. In this paper, we provide a comprehensive overview of recent advances on RIS/IRS-aided wireless systems from the signal processing perspective.We also highlight promising research directions that are worthy of investigation in the future.
Reconfigurable intelligent surfaces (RISs), also known as intelligent reflecting surfaces (IRSs), or large intelligent surfaces (LISs),
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have received significant attention for their potential to enhance the capacity and coverage of wireless networks by smartly reconfiguring the wireless propagation environment. Therefore, RISs are considered a promising technology for the sixth-generation (6G) of communication networks. In this context, we provide a comprehensive overview of the state-of-the-art on RISs, with focus on their operating principles, performance evaluation, beamforming design and resource management, applications of machine learning to RIS-enhanced wireless networks, as well as the integration of RISs with other emerging technologies. We describe the basic principles of RISs both from physics and communications perspectives, based on which we present performance evaluation of multiantenna assisted RIS systems. In addition, we systematically survey existing designs for RIS-enhanced wireless networks encompassing performance analysis, information theory, and performance optimization perspectives. Furthermore, we survey existing research contributions that apply machine learning for tackling challenges in dynamic scenarios, such as random fluctuations of wireless channels and user mobility in RIS-enhanced wireless networks. Last but not least, we identify major issues and research opportunities associated with the integration of RISs and other emerging technologies for applications to next-generation networks.
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Without loss of generality, we use the name of RIS in the remainder of this paper.
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The reconfigurable intelligent surface (RIS) with low hardware cost and energy consumption has been recognized as a potential technique for future 6G communications to enhance coverage and capacity. To achieve this goal, accurate channel state information (CSI) in RIS assisted wireless communication system is essential for the joint beamforming at the base station (BS) and the RIS. However, channel estimation is challenging, since a large number of passive RIS elements cannot transmit, receive, or process signals. In the first part of this invited paper, we provide an overview of the fundamentals, solutions, and future opportunities of channel estimation in the RIS assisted wireless communication system. It is noted that a new channel estimation scheme with low pilot overhead will be provided in the second part of this letter.
Large intelligent surface (LIS) has recently emerged as a potential low-cost solution to reshape the wireless propagation environment for improving the spectral efficiency. In this paper, we consider a downlink millimeter-wave (mmWave) multiple-input-multiple-output (MIMO) system, where an LIS is deployed to assist the downlink data transmission from a base station (BS) to a user equipment (UE). Both the BS and the UE are equipped with a large number of antennas, and a hybrid analog/digital precoding/combining structure is used to reduce the hardware cost and energy consumption. We aim to maximize the spectral efficiency by jointly optimizing the LIS’s reflection coefficients and the hybrid precoder (combiner) at the BS (UE). To tackle this non-convex problem, we reformulate the complex optimization problem into a much more friendly optimization problem by exploiting the inherent structure of the effective (cascade) mmWave channel. A manifold optimization (MO)-based algorithm is then developed. Simulation results show that by carefully devising LIS’s reflection coefficients, our proposed method can help realize a favorable propagation environment with a small channel matrix condition number. Besides, it can achieve a performance comparable to those of state-of-the-art algorithms, while at a much lower computational complexity.
Intelligent reflection surface (IRS) has recently been recognized as a promising technique to enhance the performance of wireless systems due to its ability of reconfiguring the signal propagation environment. However, the perfect channel state information (CSI) is challenging to obtain at the base station (BS) due to the lack of radio frequency (RF) chains at the IRS. Since most of the existing channel estimation methods were developed to acquire the cascaded BS-IRS-user channels, this paper is the first work to study the robust beamforming based on the imperfect cascaded BSIRS- user channels at the transmitter (CBIUT). Specifically, the transmit power minimization problems are formulated subject to the worst-case rate constraints under the bounded CSI error model and the rate outage probability constraints under the statistical CSI error model, respectively. After approximating the worst-case rate constraints by using the S-procedure and the rate outage probability constraints by using the Bernsteintype inequality, the reformulated problems can be efficiently solved. Numerical results show that the negative impact of the CBIUT error on the system performance is greater than that of the direct CSI error.
This paper investigates multiple intelligent reflecting surfaces (IRSs) aided wireless network, where the IRSs are deployed to cooperatively assist communications between a multi-antenna base station (BS) and the multiple single-antenna cell-edge users. We aim at maximizing the weighted sum rate of all the cell-edge users by jointly optimizing the BS’s transmit beamforming and IRS’s phase shifts. Especially, the beamforming is optimally obtained based on the Lagrangian method, and the phase shifts are obtained based on the Riemannian manifold conjugate gradient (RMCG) method. Numerical results show that a significant gain is improved with the aid of IRSs.
IRS is a new and revolutionizing technology that is able to significantly improve the performance of wireless communication networks, by smartly reconfiguring the wireless propagation environment with the use of massive low-cost passive reflecting elements integrated on a planar surface. Specifically, different elements of an IRS can independently reflect the incident signal by controlling its amplitude and/or phase and thereby collaboratively achieve fine-grained 3D passive beamforming for directional signal enhancement or nulling. In this article, we first provide an overview of the IRS technology, including its main applications in wireless communication, competitive advantages over existing technologies, hardware architecture as well as the corresponding new signal model. We then address the key challenges in designing and implementing the new IRS-aided hybrid (with both active and passive components) wireless network, as compared to the traditional network comprising active components only. Finally, numerical results are provided to show the great performance enhancement with the use of IRS in typical wireless networks.
In this paper, a new optimization framework is presented for the joint design of user selection, power allocation, and precoding in multi-cell multi-user multiple-input multipleoutput (MU-MIMO) systems when imperfect channel state information at transmitter (CSIT) is available. By representing the joint optimization variables in a higher-dimensional space, the weighted sum-spectral efficiency maximization is formulated as the maximization of the product of Rayleigh quotients. Although this is still a non-convex problem, a computationally efficient algorithm, referred to as generalized power iteration precoding (GPIP), is proposed. The algorithm converges to a stationary point (local maximum) of the objective function and therefore it guarantees the first-order optimality of the solution. By adjusting the weights in the weighted sum-spectral efficiency, the GPIP yields a joint solution for user selection, power allocation, and downlink precoding. The GPIP can be extended to the multicell scenario where cooperative base stations perform joint usercell selection and design their precodes by taking into account the inter-cell interference by sharing global imperfect CSIT. System-level simulations show the gains of the proposed approach with respect to conventional user selection and linear downlink precoding.
The results of indoor multipath propagation measurements using 10 ns, 1.5 GHz, radarlike pulses are presented for a medium-size office building. The observed channel was very slowly time varying, with the delay spread extending over a range up to about 200 ns and rms values of up to about 50 ns. The attenuation varied over a 60 dB dynamic range. A simple statistical multipath model of the indoor radio channel is also presented, which fits our measurements well, and more importantly, appears to be extendable to other buildings. With this model, the received signal rays arrive in clusters. The rays have independent uniform phases, and independent Rayleigh amplitudes with variances that decay exponentially with cluster and ray delays. The clusters, and the rays within the cluster, form Poisson arrival processes with different, but fixed, rates. The clusters are formed by the building superstructure, while the individual rays are formed by objects in the vicinities of the transmitter and the receiver.
Robust beamforming design for an IRS-aided NOMA communication system with CSI uncertainty
- Y Omid
- S M Shahabi
- C Pan
- Y Deng
- A Nallanathan
Y. Omid, S. M. Shahabi, C. Pan, Y. Deng, and A. Nallanathan, "Robust
beamforming design for an IRS-aided NOMA communication system
with CSI uncertainty," IEEE Trans. Wireless Commun., vol. 23, no. 2,
pp. 874-889, 2023.
An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel
- Q Shi
- M Razaviyayn
- Z.-Q Luo
- C He
Q. Shi, M. Razaviyayn, Z.-Q. Luo, and C. He, "An iteratively weighted
MMSE approach to distributed sum-utility maximization for a MIMO
interfering broadcast channel," IEEE Trans. Signal Process., vol. 59,
no. 9, pp. 4331-4340, 2011.