Channel Estimation for RIS-Empowered Multi-User MISO Wireless Communications
TL;DR: A channel estimation framework based on the parallel factor decomposition to unfold the resulting cascaded channel model is proposed and it is demonstrated that the sum rate using the estimated channels always reach that of perfect channels under various settings, thus, verifying the effectiveness and robustness of the proposed estimation algorithms.
Abstract: Reconfigurable Intelligent Surfaces (RISs) have been recently considered as an energy-efficient solution for future wireless networks due to their fast and low-power configuration, which has increased potential in enabling massive connectivity and low-latency communications. Accurate and low-overhead channel estimation in RIS-based systems is one of the most critical challenges due to the usually large number of RIS unit elements and their distinctive hardware constraints. In this paper, we focus on the uplink of a RIS-empowered multi-user Multiple Input Single Output (MISO) uplink communication systems and propose a channel estimation framework based on the parallel factor decomposition to unfold the resulting cascaded channel model. We present two iterative estimation algorithms for the channels between the base station and RIS, as well as the channels between RIS and users. One is based on alternating least squares (ALS), while the other uses vector approximate message passing to iteratively reconstruct two unknown channels from the estimated vectors. To theoretically assess the performance of the ALS-based algorithm, we derived its estimation Cramer-Rao Bound (CRB). We also discuss the downlink achievable sum rate computation with estimated channels and different precoding schemes for the base station. Our extensive simulation results show that our algorithms outperform benchmark schemes and that the ALS technique achieves the CRB. It is also demonstrated that the sum rate using the estimated channels always reach that of perfect channels under various settings, thus, verifying the effectiveness and robustness of the proposed estimation algorithms.
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TL;DR: This paper provides a tutorial overview of IRS-aided wireless communications, and elaborate its reflection and channel models, hardware architecture and practical constraints, as well as various appealing applications in wireless networks.
Abstract: Intelligent reflecting surface (IRS) is an enabling technology to engineer the radio signal propagation in wireless networks. By smartly tuning the signal reflection via a large number of low-cost passive reflecting elements, IRS is capable of dynamically altering wireless channels to enhance the communication performance. It is thus expected that the new IRS-aided hybrid wireless network comprising both active and passive components will be highly promising to achieve a sustainable capacity growth cost-effectively in the future. Despite its great potential, IRS faces new challenges to be efficiently integrated into wireless networks, such as reflection optimization, channel estimation, and deployment from communication design perspectives. In this paper, we provide a tutorial overview of IRS-aided wireless communications to address the above issues, and elaborate its reflection and channel models, hardware architecture and practical constraints, as well as various appealing applications in wireless networks. Moreover, we highlight important directions worthy of further investigation in future work.
1,325 citations
TL;DR: In this paper, the authors proposed a hybrid beamforming scheme for the multi-hop RIS-assisted communication networks to improve the coverage range at the TeraHertz-band frequencies.
Abstract: Wireless communication in the TeraHertz band (0.1–10 THz) is envisioned as one of the key enabling technologies for the future sixth generation (6G) wireless communication systems scaled up beyond massive multiple input multiple output (Massive-MIMO) technology. However, very high propagation attenuations and molecular absorptions of THz frequencies often limit the signal transmission distance and coverage range. Benefited from the recent breakthrough on the reconfigurable intelligent surfaces (RIS) for realizing smart radio propagation environment, we propose a novel hybrid beamforming scheme for the multi-hop RIS-assisted communication networks to improve the coverage range at THz-band frequencies. Particularly, multiple passive and controllable RISs are deployed to assist the transmissions between the base station (BS) and multiple single-antenna users. We investigate the joint design of digital beamforming matrix at the BS and analog beamforming matrices at the RISs, by leveraging the recent advances in deep reinforcement learning (DRL) to combat the propagation loss. To improve the convergence of the proposed DRL-based algorithm, two algorithms are then designed to initialize the digital beamforming and the analog beamforming matrices utilizing the alternating optimization technique. Simulation results show that our proposed scheme is able to improve 50% more coverage range of THz communications compared with the benchmarks. Furthermore, it is also shown that our proposed DRL-based method is a state-of-the-art method to solve the NP-hard beamforming problem, especially when the signals at RIS-assisted THz communication networks experience multiple hops.
206 citations
TL;DR: This article proposes a new three-dimensional (3D) wireless system architecture enabled by aerial IRS (AIRS), based on a novel 3D beam broadening and flattening technique, where the passive array of the AIRS is divided into sub-arrays of appropriate size, and their phase shifts are designed to form a flattened beam pattern with adjustable beamwidth catering to the size of the coverage area.
Abstract: Intelligent reflecting surface (IRS) is a promising technology to reconfigure wireless channels, which brings a new degree of freedom for the design of future wireless networks. This article proposes a new three-dimensional (3D) wireless system architecture enabled by aerial IRS (AIRS). Compared to the conventional terrestrial IRS, AIRS enjoys more deployment flexibility as well as wider-view signal reflection, thanks to its high altitude and thus more likelihood of establishing line-of-sight (LoS) links with ground source/destination nodes. We aim to maximize the worst-case signal-to-noise ratio (SNR) over all locations in a target area by jointly optimizing the transmit beamforming for the source node, as well as the placement and 3D passive beamforming for the AIRS. The formulated problem is non-convex and difficult to solve. To gain useful insights, we first consider the special case of maximizing the SNR at a given target location, for which the optimal solution is obtained in closed-form. The result shows that the optimal horizontal AIRS placement only depends on the ratio between the source-destination distance and the AIRS altitude. Then for the general case of AIRS-enabled area coverage, we propose an efficient solution by decoupling the AIRS passive beamforming design to maximize the worst-case array gain , from its placement optimization by balancing the resulting angular span and the cascaded channel path loss. Our proposed solution is based on a novel 3D beam broadening and flattening technique, where the passive array of the AIRS is divided into sub-arrays of appropriate size, and their phase shifts are designed to form a flattened beam pattern with adjustable beamwidth catering to the size of the coverage area. Both uniform linear array (ULA)-based and uniform planar array (UPA)-based AIRSs are considered in our design, which enable two-dimensional (2D) and 3D passive beamforming, respectively. Numerical results show that the proposed designs achieve significant performance gains over the benchmark schemes.
186 citations
TL;DR: In this paper, a physics-based model and a scalable optimization framework for large RISs were developed to optimize a large number of sub-wavelength RIS elements for online transmission.
Abstract: Intelligent reflecting surfaces (IRSs) have the potential to transform wireless communication channels into smart reconfigurable propagation environments. To realize this new paradigm, the passive IRSs have to be large, especially for communication in far-field scenarios, so that they can compensate for the large end-to-end path-loss, which is caused by the multiplication of the individual path-losses of the transmitter-to-IRS and IRS-to-receiver channels. However, optimizing a large number of sub-wavelength IRS elements imposes a significant challenge for online transmission. To address this issue, in this article, we develop a physics-based model and a scalable optimization framework for large IRSs. The basic idea is to partition the IRS unit cells into several subsets, referred to as tiles, model the impact of each tile on the wireless channel, and then optimize each tile in two stages, namely an offline design stage and an online optimization stage. For physics-based modeling, we borrow concepts from the radar literature, model each tile as an anomalous reflector, and derive its impact on the wireless channel for a given phase shift by solving the corresponding integral equations for the electric and magnetic vector fields. In the offline design stage, the IRS unit cells of each tile are jointly designed for the support of different transmission modes, where each transmission mode effectively corresponds to a given configuration of the phase shifts that the unit cells of the tile apply to an impinging electromagnetic wave. In the online optimization stage, the best transmission mode of each tile is selected such that a desired quality-of-service (QoS) criterion is maximized. We consider an exemplary downlink system and study the minimization of the base station (BS) transmit power subject to QoS constraints for the users. Since the resulting mixed-integer programming problem for joint optimization of the BS beamforming vectors and the tile transmission modes is non-convex, we derive two efficient suboptimal solutions, which are based on alternating optimization and a greedy approach, respectively. We show that the proposed modeling and optimization framework can be used to efficiently optimize large IRSs comprising thousands of unit cells.
166 citations
TL;DR: A framework for the joint optimization of UTs’ transmit precoding and RIS reflective beamforming to maximize a performance metric called resource efficiency (RE) is developed and results illustrate the effectiveness and rapid convergence rate of this proposed optimization framework.
Abstract: The emergence of reconfigurable intelligent surfaces (RISs) enables us to establish programmable radio wave propagation that caters for wireless communications, via employing low-cost passive reflecting units. This work studies the non-trivial tradeoff between energy efficiency (EE) and spectral efficiency (SE) in multiuser multiple-input multiple-output (MIMO) uplink communications aided by a RIS equipped with discrete phase shifters. For reducing the required signaling overhead and energy consumption, our transmission strategy design is based on the partial channel state information (CSI), including the statistical CSI between the RIS and user terminals (UTs) and the instantaneous CSI between the RIS and the base station. To investigate the EE-SE tradeoff, we develop a framework for the joint optimization of UTs’ transmit precoding and RIS reflective beamforming to maximize a performance metric called resource efficiency (RE). For the design of UT's precoding, it is simplified into that of UTs’ transmit powers with the aid of the closed-form solutions of UTs’ optimal transmit directions. To avoid the high complexity in computing the nested integrals involved in the expectations, we derive an asymptotic deterministic objective expression. For the design of the RIS phases, an iterative mean-square error minimization approach is proposed via capitalizing on the homotopy, accelerated projected gradient, and majorization-minimization methods. Numerical results illustrate the effectiveness and rapid convergence rate of our proposed optimization framework.
145 citations
Cites methods from "Channel Estimation for RIS-Empowere..."
...As stated previously, we consider a scenario with partial CSI, in which the instantaneous knowledge of the RIS-to-BS channel H1 can be perfectly known by adopting some existing methods such as [42]....
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References
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TL;DR: This survey provides an overview of higher-order tensor decompositions, their applications, and available software.
Abstract: This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.
9,227 citations
"Channel Estimation for RIS-Empowere..." refers background in this paper
...The presented algorithms capitalize on the unfolded forms [46], [47] of the involved matrices to yield efficient CE....
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...Then, the unfolded forms [46], [47] of the mode-1, mode-2, and mode-3 of Z can be expressed as...
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TL;DR: In this article, the authors developed energy-efficient designs for both the transmit power allocation and the phase shifts of the surface reflecting elements subject to individual link budget guarantees for the mobile users.
Abstract: The adoption of a reconfigurable intelligent surface (RIS) for downlink multi-user communication from a multi-antenna base station is investigated in this paper. We develop energy-efficient designs for both the transmit power allocation and the phase shifts of the surface reflecting elements subject to individual link budget guarantees for the mobile users. This leads to non-convex design optimization problems for which to tackle we propose two computationally affordable approaches, capitalizing on alternating maximization, gradient descent search, and sequential fractional programming. Specifically, one algorithm employs gradient descent for obtaining the RIS phase coefficients, and fractional programming for optimal transmit power allocation. Instead, the second algorithm employs sequential fractional programming for the optimization of the RIS phase shifts. In addition, a realistic power consumption model for RIS-based systems is presented, and the performance of the proposed methods is analyzed in a realistic outdoor environment. In particular, our results show that the proposed RIS-based resource allocation methods are able to provide up to 300% higher energy efficiency in comparison with the use of regular multi-antenna amplify-and-forward relaying.
1,967 citations
TL;DR: In this paper, the authors 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.
Abstract: 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.
1,897 citations
TL;DR: This paper overviews the current research efforts on smart radio environments, the enabling technologies to realize them in practice, the need of new communication-theoretic models for their analysis and design, and the long-term and open research issues to be solved towards their massive deployment.
Abstract: Future wireless networks are expected to constitute a distributed intelligent wireless communications, sensing, and computing platform, which will have the challenging requirement of interconnecting the physical and digital worlds in a seamless and sustainable manner. Currently, two main factors prevent wireless network operators from building such networks: (1) the lack of control of the wireless environment, whose impact on the radio waves cannot be customized, and (2) the current operation of wireless radios, which consume a lot of power because new signals are generated whenever data has to be transmitted. In this paper, we challenge the usual “more data needs more power and emission of radio waves” status quo, and motivate that future wireless networks necessitate a smart radio environment: a transformative wireless concept, where the environmental objects are coated with artificial thin films of electromagnetic and reconfigurable material (that are referred to as reconfigurable intelligent meta-surfaces), which are capable of sensing the environment and of applying customized transformations to the radio waves. Smart radio environments have the potential to provide future wireless networks with uninterrupted wireless connectivity, and with the capability of transmitting data without generating new signals but recycling existing radio waves. We will discuss, in particular, two major types of reconfigurable intelligent meta-surfaces applied to wireless networks. The first type of meta-surfaces will be embedded into, e.g., walls, and will be directly controlled by the wireless network operators via a software controller in order to shape the radio waves for, e.g., improving the network coverage. The second type of meta-surfaces will be embedded into objects, e.g., smart t-shirts with sensors for health monitoring, and will backscatter the radio waves generated by cellular base stations in order to report their sensed data to mobile phones. These functionalities will enable wireless network operators to offer new services without the emission of additional radio waves, but by recycling those already existing for other purposes. This paper overviews the current research efforts on smart radio environments, the enabling technologies to realize them in practice, the need of new communication-theoretic models for their analysis and design, and the long-term and open research issues to be solved towards their massive deployment. In a nutshell, this paper is focused on discussing how the availability of reconfigurable intelligent meta-surfaces will allow wireless network operators to redesign common and well-known network communication paradigms.
1,504 citations
TL;DR: The core consistency diagnostic (CORCONDIA) as discussed by the authors is a diagnostic for determining the appropriate number of components for multiway models, which is based on scrutinizing the appropriateness of the structural model based on the data and the estimated parameters.
Abstract: A new diagnostic called the core consistency diagnostic (CORCONDIA) is suggested for determining the proper number of components for multiway models. It applies especially to the parallel factor analysis (PARAFAC) model, but also to other models that can be considered as restricted Tucker3 models. It is based on scrutinizing the ‘appropriateness’ of the structural model based on the data and the estimated parameters of gradually augmented models. A PARAFAC model (employing dimension-wise combinations of components for all modes) is called appropriate if adding other combinations of the same components does not improve the fit considerably. It is proposed to choose the largest model that is still sufficiently appropriate. Using examples from a range of different types of data, it is shown that the core consistency diagnostic is an effective tool for determining the appropriate number of components in e.g. PARAFAC models. However, it is also shown, using simulated data, that the theoretical understanding of CORCONDIA is not yet complete. Copyright © 2003 John Wiley & Sons, Ltd.
1,110 citations