Manifold Optimization Empowered Two-Timescale Channel Estimation for RIS-Assisted Systems

In reconfigurable intelligent surfaces (RISs) aided millimeter wave communication systems, accurate channel state information (CSI) is particularly crucial to achieve high passive beamforming gain. However, the complexity of channel estimation increases significantly due to the high-dimensional channel matrix and the additional RISs' assisted channels. To tackle this challenge, an alternating direction method of multipliers (ADMM) based channel estimation method is proposed to improve the CSI estimation accuracy and reduce the training overhead. By converting the cascaded channel matrix into a sparse matrix recovery problem, both low rank and sparsity properties are exploited by the ADMM algorithm to solve the sparse matrix recovery problem. The simulation results verify that the proposed ADMM algorithm can significantly increase the accuracy of channel estimation and reduce the training overhead, compared with the well-known competing channel estimation algorithms.

Channel estimation (CE) plays a key role in reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) communication systems, while it poses a challenging task due to the passive nature of RIS and the cascaded channel structures. In this paper, a partially decoupled atomic norm minimization (PDANM) framework is proposed for CE of RIS-aided MIMO systems, which exploits the three-dimensional angular sparsity of the channel. In particular, PDANM partially decouples the differential angles at the RIS from other angles at the base station and user equipment, reducing the computational complexity compared with existing methods. A reweighted PDANM (RPDANM) algorithm is proposed to further improve CE accuracy, which iteratively refines CE through a specifically designed reweighting strategy. Building upon RPDANM, we propose an iterative approach named RPDANM with adaptive phase control (RPDANM-APC), which adaptively adjusts the RIS phases based on previously estimated channel parameters to facilitate CE, achieving superior CE accuracy while reducing training overhead. Numerical simulations demonstrate the superiority of our proposed approaches in terms of running time, CE accuracy, and training overhead. In particular, the RPDANM-APC approach can achieve higher CE accuracy than existing methods within less than 30 percent training overhead while reducing the running time by tens of times.

In this paper, we adopt a three-stage based uplink channel estimation protocol with reduced pilot overhead for an reconfigurable intelligent surface (RIS)-aided multi-user (MU) millimeter wave (mmWave) communication system, in which both the base station (BS) and the RIS are equipped with a uniform planar array (UPA). Specifically, in Stage I, the channel state information (CSI) of a typical user is estimated. To address the power leakage issue for the common angles-of-arrival (AoAs) estimation in this stage, we develop a low-complexity one-dimensional search method. In Stage II, a re-parameterized common BS-RIS channel is constructed with the estimated information from Stage I to estimate other users’ CSI. In Stage III, only the rapidly varying channel gains need to re-estimated. Furthermore, the proposed method can be extended to multi-antenna UPA-type users, by decomposing the estimation of a multi-antenna channel with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$J$ </tex-math></inline-formula> scatterers into estimating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$J$ </tex-math></inline-formula> single-scatterer channels for a virtual single-antenna user. An orthogonal matching pursuit (OMP)-based method is proposed to estimate the angles-of-departure (AoDs) at the users. Simulation results demonstrate that the proposed algorithm significantly achieves high channel estimation accuracy, which approaches the genie-aided upper bound in the high signal-to-noise ratio (SNR) regime.

Reconfigurable intelligent surface (RIS) is thought to be a potential key technique for future wireless communications due to its ability for manipulating the electromagnetic environment smartly. This paper focuses on the rank and capacity analysis when a RIS is introduced into a multiple-input multiple-output (MIMO) system. By establishing a system model for this communication system, various simulations are conducted for identifying the characteristics of the channel. The simulations of different distance between the access point (AP) and user equipment (UE) show that the condition number of the channel is worsen when the distance increases and the role of the RIS in rank improvement is weaken. The spatial distributions of the reciprocal condition number of the channel which corresponds to the RIS locations are obtained and rank-deficient zones are found in different AP, UE and RIS configurations, which depicts the spatial characteristics of the RIS-assisted MIMO channel. The simulations also indicate that the condition number of the channel not only varies with the RIS location, but is also affected by the antenna array size and orientation of AP and UE. In addition, when the AP has a larger amount of antennas than UE, it is advantageous to place the RIS near the UE rather than the AP to achieve better channel condition. Modulation and coding schemes are applied in the simulations for comparison and capacity improvement is witnessed. Beneficial suggestions for RIS deployment in the MIMO system are concluded according to the simulation results.

In this paper, we propose a location-aware channel estimation based on the atomic norm minimization (ANM) for the reconfigurable intelligent surface (RIS)-aided millimeter-wave multiple-input-multiple-output (MIMO) systems. The beam training overhead at the base station (BS) is reduced by the direct beam steering towards the RIS with the location of the BS and the RIS. The RIS beamwidth adaptation is proposed to reduce the beam training overhead at the RIS, and also it enables accurate channel estimation by ensuring the user equipment receives all the multipath components from the RIS. After the beam training, the cascaded effective channel of the RIS-aided MIMO systems is estimated by ANM. Depending on whether the beam training overhead at the BS or at the RIS is reduced or not, the channel is represented as a linear combination of either 1D atoms, 2D atoms, or 3D atoms, and the ANM is applied to estimate the channel. Simulation results show that the proposed location-aware channel estimation via 2D ANM and 3D ANM achieves superior estimation accuracy to benchmarks.

In this paper, we propose a novel computer vision-based approach to aid reconfigurable intelligent surface (RIS) for dynamic beam tracking and implement the corresponding prototype verification system. A camera is attached at the RIS to obtain the visual information about the surroundings, with which RIS identifies the incident beam direction and the desired reflected beam direction, and then adjusts the reflection coefficients according to the pre-designed codebooks. We build a 20-by-20 RIS running at 5.4 GHz and develop a high-speed control board to ensure the real-time refresh of the reflection coefficients. Meanwhile we implement an independent peer-to-peer communications system to simulate the physical link between the base station and the user equipment. The vision-aided RIS prototype system is tested in two mobile scenarios: RIS works in near-field conditions as a passive array antenna of the base station; RIS works in far-field conditions to assist the communication between the base station and the user equipment. The experimental results show that RIS can quickly adjust the reflection coefficients for dynamic beam tracking with the help of visual information.

Recently, using a Reconfigurable Intelligent Surface (RIS) to aid wireless communication systems has received much attention from academia and industry. RIS is a uniform planar array composed of a large number of low-cost, passive, and tunable reflecting elements, in which the reflector elements steer the incident signal in fully customizable ways by passive beamforming. However, due to a large number of passive RIS elements without signal processing capability, which will result in a sharp increase of the pilot overhead for Channel Estimation (CE). To tackle this challenge, we propose a holographic version of RIS based on the holographic principle and Hall effect to accomplish communication without CE, which can simplify the complicated CE in RIS to the invisible CE containing holographic principle, avoiding the complicated CE. The scheme accomplished communication by interference patterns to restore the communication information required by the user. We loaded the Hall sensor on the RIS to fulfill the electromagnetic recording about the pattern. Finally, simulation results illustrate the effectiveness of the proposed scheme.

The reconfigurable intelligent surfaces (RISs) have garnered a lot of interest in the development of smart radios. The acquisition of channel state information in RIS aided systems are extremely challenging as pilot overhead is considerably large. Previous works have shown an improvement in reducing pilot over head by exploiting the structured sparsity. In this contribution, we consider a sparse RIS under the environment of multiuser MIMO communication system by randomly selecting the elements of RIS in uniform planar arrays to eliminate unnecessary elements and to reduce the large pilot overhead. The random distribution models i.e Gaussian, Poisson and Geometric are adopted and analyzed for selection of sparse RIS. The numerical results show a significant improvement in NMSE performance with reduced pilot overhead.

This study presents a novel approach to enhance the power level at millimeter waves (mm-waves) with very low cost. Considering an mm-wave base station (BS) in a fixed location and the user equipment (UE) in the far-field (FF) region, a plane wave with a known direction of propagation reaches a specific region. A very large, predesigned fixed focal spot passive surface (S1) is designed and installed within the viewing angle of the plane wave to reflect and focus it in the near-field (NF) region on another wall. A small reconfigurable intelligent surface (RIS) device is installed on the other wall to be illuminated by the focused beam, and the RIS steers the beam dynamically inside the desired region toward the UE. By using this scheme, a large amount of power can be focused on the UEs to enhance the signal level. The components are modeled with full-wave electromagnetic simulation, and the best approach to design the mm-wave system is discussed. A prototype was fabricated and measured at 26 GHz to demonstrate the 2-D beam steering. The large passive fixed-beam surface is a single-layer printed circuit board (PCB) with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$20\times 20$</tex-math> </inline-formula> cm, and the RIS is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7\times 7$</tex-math> </inline-formula> cm (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$14\times 14$</tex-math> </inline-formula> elements). For demonstration, 1-bit mechanical tuning elements are used for simplicity. Measurement results show <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx \pm 50^{\circ }$</tex-math> </inline-formula> of 2-D beam steering with around 10% gain bandwidth. The radiation characteristics of both surfaces are analyzed, and an expression for received power under the general condition is obtained. The entire system can be implemented at a very low cost due to its simple PCB design and small-scale RIS. Moreover, due to the large passive surface and small RIS, the power consumption can be significantly reduced compared to conventional RIS.

Reconfigurable intelligent surface (RIS) partitioning offers a strategic solution for serving multiple users equipment (UEs) simultaneously in blockage-prone wireless environments, leveraging multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA) technologies within the millimeter-wave (mmWave) spectrum. However, deploying RIS partitioning (RISP) in MIMONOMA is hindered by the exacerbated computational complexity involved in acquiring accurate channel state information (CSI). This paper proposes a novel learning framework based on multi-agent deep reinforcement learning (MA-DRL) that maximizes the sum rate of the RISP-aided MIMO-NOMA system without requiring UEs’ CSI. The proposed framework jointly optimizes RIS phase shifts, number of RIS partitions, UEs beamformers, and NOMA power allocation (PA), transforming the challenge into a high-dimensional combinatorial optimization problem. The MA-DRL algorithm integrates double deep Q networks (DDQN) and deep deterministic policy gradient (DDPG) agents, where each UE acts as a DDQN agent optimizing its beamformer, while the RIS serves as a DDPG agent handling partitioning and power control. An experimental testbed is developed to gather real-world data for training and evaluation. Results show that the MA-DRL algorithm closely approaches optimal performance, trailing the exhaustive search by only 8%, while reducing complexity by 95% and improving the sum rate by an average of 18% compared to traditional full RIS setups.

Channel estimation is essential for reconfigurable intelligent surface (RIS)-aided wireless communications. Irregular RIS structures can provide more design degrees of freedom to enhance system performance. In this paper, we investigate the channel estimation problem for an irregular subarrayed RIS-aided millimeter wave (mmWave) system. Specifically, we formulate the channel estimation problem as a sparse recovery problem by exploiting the sparsity of the mmWave channel, which can be effectively solved by the proposed two-stage algorithm. In the first stage, the common angles of arrival (AoAs) at the base station (BS) are estimated using the discrete Fourier transform (DFT) method. In the second stage, the estimated AoA information is used to decouple signals from different paths, thus leading to the user-specific subchannel estimation problem. Moreover, effective sparse angles are sampled within the sine and cosine domains to reduce the number of channel parameters. Then, we apply the expectation-maximization-based variational Bayesian inference (EM-VBI) method to estimate these parameters. Furthermore, taking into account practical calibration errors among sub-RISs, we propose to estimate channel parameters and auxiliary error parameters simultaneously, along with an effective method to extract the original error information from these auxiliary parameters. Simulation results demonstrate the superiority of the proposed algorithms over existing benchmark schemes in terms of the channel estimation accuracy and the calibration accuracy of intersubarray errors.

Reconfigurable intelligent surface (RIS)-aided mmWave communication offers a promising approach to overcome the issue of severe signal blockage that limits the data rate of mmWave networks. However, joint base station beamforming and RIS phase shift (BF-PS) design presents great challenges not only because of the intricate relationship between the beamforming and phase shift matrices in determining the network sum-rate, but also due to the lack of accurate channel estimation when the number of RIS elements gets large. In this work, we study learning-based BF-PS design for RIS-aided mmWave networks under sparse channel estimation. Our main finding is that, under the practical constraint of pilot overhead for RIS channel estimation, learning-based BF-PS design can yield superior performance to that achieved by the conventional block-coordinate-descent (BCD) algorithm. This work provides an initial study of learning-based BF-PS design under the compressed-sensing framework for mmWave channel estimation. The proposed BF-PS design adopts an enhanced four-stage neural-network architecture that improves upon the existing two-stage design by utilizing outputs from earlier stages to form new features for later stages. The new four-stage design using hybrid beamforming (HBF) outperforms those of the two-stage design using either HBF or fully digital beamforming (DBF).

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.

Active reconfigurable intelligent surface (RIS) emerges as an effective technique to resist the double-fading attenuation of passive RIS. By embedding with power harvesting function, it further evolves to zero-power active RIS, which can effectively enhance the flexibility of RIS deployment without external power demand. Nevertheless, existing works neglected the inherent difficulty of channel estimation (CE) for RIS-assisted systems, and the discrete phase shift constraint in practical deployment. In this paper we design a new element-wise RIS architecture and propose a distributed location-aided transmission scheme with low complexity to enhance the reflected gain for channel state information (CSI)-limited RIS-assisted near-field communications. Specifically, the new element-wise RIS provides dynamic element selection capability with low hardware resources. Based on Fresnel diffraction theory, we construct the mapping from locations in space-domain to phase distributions of waves in phase-domain and reveal the priority of elements for harvesting and reflecting. Then, the distributed beamforming design with the phase of determine-then-align is proposed, where the estimation overhead reduction stems from exempted requirements of RIS-associated CE at base station (BS). The asymptotic analysis indicates that the proposed scheme can achieve the optimal gain with a fixed proportion of reflective elements when RIS is large, followed by simulations to verify its superiority to other protocols.

In this study, to address the problems of high feedback latency and redundant codebook traversal in traditional Reconfigurable Intelligent Surface (RIS) beam tracking systems, two novel experimental schemes are proposed: the Edge-Integrated RIS Control Mechanism (EIR-CM) and the Visually Steered RIS Control Mechanism (VSR-CM). The EIR-CM eliminates the feedback latency of the remote server and optimizes the local computation by integrating the RIS control system and the User Equipment (UE) into the same edge server to reduce the beam tuning time by 50%. The VSR-CM realizes beam tracking based on visual perception, and directly maps the UE position to the optimal RIS codebook with a response speed as low as milliseconds. Experimental results show that the EIR-CM reduces the RIS feedback latency to 1–2 s, and the VSR-CM can be further optimized to less than 0.5 s. The two mechanisms are applicable to 6G communications, smart transport, and drone networks, providing feasibility verification for low-latency and efficient RIS deployment.