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A Hardware Architecture for Reconfigurable Intelligent Surfaces with Minimal Active Elements for Explicit Channel Estimation
George C. Alexandropoulos, Evangelos Vlachos
TL;DR
RIS-involved channel estimation is difficult with nearly passive hardware and existing approaches can require lengthy training. The paper proposes a passive-element RIS with one RF chain and sparse beamspace-based estimation, achieving 7.6 bps/Hz with T = 200 training symbols versus 8.5 bps/Hz with perfect channel knowledge.
Problem
Nearly passive RIS hardware makes explicit RIS-side channel estimation challenging, while existing channel-estimation protocols require large training periods.
Method
The paper combines passive RIS elements and a single baseband reception RF chain with random analog combining and sparse beamspace channel modeling.
Results
7.6 bps/Hz is achieved with channel estimation using T = 200, around 10% below 8.5 bps/Hz with perfect channel knowledge.
Takeaways & Limitations
The architecture supports explicit RIS-involved channel estimation with one RF chain and preserves near-perfect-knowledge end-to-end rate in the reported setting.
Abstract
from arXiv · showhide
Intelligent surfaces comprising of cost effective, nearly passive, and reconfigurable unit elements are lately gaining increasing interest due to their potential in enabling fully programmable wireless environments. They are envisioned to offer environmental intelligence for diverse communication objectives, when coated on various objects of the deployment area of interest. To achieve this overarching goal, the channels where the Reconfigurable Intelligent Surfaces (RISs) are involved need to be in principle estimated. However, this is a challenging task with the currently available hardware RIS architectures requiring lengthy training periods among the network nodes utilizing RIS-assisted wireless communication. In this paper, we present a novel RIS architecture comprising of any number of passive reflecting elements, a simple controller for their adjustable configuration, and a single Radio Frequency (RF) chain for baseband measurements. Capitalizing on this architecture and assuming sparse wireless channels in the beamspace domain, we present an alternating optimization approach for explicit estimation of the channel gains at the RIS elements attached to the single RF chain. Representative simulation results demonstrate the channel estimation accuracy and achievable end-to-end performance for various training lengths and numbers of reflecting unit elements.
I. INTRODUCTION
RISs use programmable subwavelength unit cells to control electromagnetic behavior, but estimating RIS-involved channels remains difficult with nearly passive hardware and can require lengthy training. The paper addresses this gap with a passive-element architecture using one active RF chain for explicit channel estimation.
- RISs are artificial planar structures with integrated electronic circuits that can be programmed to manipulate incoming electromagnetic fields.
- Subwavelength unit cells provide overall control over a RIS metasurface’s electromagnetic behavior.
- Existing approaches estimate concatenated BS–RIS–UE channels at the BS or UE but require large training periods.
- The proposed architecture combines passive unit elements with a single active RF chain for baseband reception and explicit channel estimation at the RIS side.It is inspired by an extended analog combiner enabling matrix-completion-based estimation with relatively short training requirements.
II. SYSTEM AND CHANNEL MODELS
The system models a blocked single-antenna BS–UE link assisted by an N-element RIS, finite-resolution phase shifts, multipath channels, and sparse beamspace representations. The formulation also states extensions to multiantenna links, uplink communication, and cases with a direct link.
- The baseline system has single-antenna BS and UE terminals, no direct link because of blockages, and an RIS with N = N_vN_h unit elements.The stated solutions and results can be extended to multiantenna terminals, uplink communication, and an existing direct link.
- The received signal uses channel vectors h_1 and h_2, a diagonal RIS phase-shift matrix Φ, an information symbol s, and AWGN w.The channel vectors connect the BS to the RIS and the RIS to the UE; Φ contains the unit elements’ effective phase shifts.
- Each RIS phase shift has finite resolution, with b bits producing 2^b possible phase-shifting values per unit element.The feasible reflection set is denoted by F.
- Each channel is modeled with N_p propagation paths whose gains are zero-mean complex Gaussian variables scaled by the corresponding path losses.The path losses apply to the BS–RIS and RIS–UE links, and far-field path loss scales inversely with squared distance.
- In beamspace, h_1 and h_2 are represented using DFT-based unitary matrices and sparse virtual channel-gain vectors.The sparse representation is especially applicable for large RIS sizes and millimeter-wave channels.
III. PROPOSED RIS ARCHITECTURE
The proposed RIS replaces infeasible explicit estimation in nearly passive designs with one reception RF chain connected to passive unit elements. Random analog combining, control, and configuration tuning support baseband estimation with substantially fewer RF chains than a one-sensor-per-element design.
- Nearly passive RIS designs enable real-time reflection control but do not feasibly support explicit channel-gain estimation at the RIS side.
- The architecture connects RIS unit-element outputs to a single reception RF chain containing an amplifier, downconverting mixer, and analog-to-digital converter.Pilot signals provide the basis for baseband channel estimation.
- Random sampling selects among M ≤ S_F^N RIS configurations, where each configuration applies quantized unit-amplitude complex coefficients.The resulting matrix W contains the available configurations, and its columns represent analog receivers feeding the sole RF chain.
- A dedicated control unit runs channel estimation, calculates RIS tuning, and shares phase-shifting values with all N unit elements.
- The proposed hardware uses one RF chain instead of the N RF chains associated with N active channel sensors in the referenced architecture.
IV. RIS CHANNEL ESTIMATION AND TUNING
The paper formulates explicit RIS-side channel estimation as a multi-objective optimization problem built around the proposed hardware architecture.
- The estimation method uses a multi-objective optimization framework for explicit channel estimation at the RIS side.
A. Proposed Channel Estimation Formulation
The formulation collects randomly configured RIS training measurements through a single RF chain and exploits beamspace sparsity and low-rank structure to estimate the RIS-involved channels.
- Training measurements: During T dedicated training symbols, the BS sends known pilots, while RIS elements use randomly selected configurations and feed summed outputs to one RF chain.The received training signals are represented as y_t, and increasing T or using multiple configurations per symbol can increase baseband measurements.
- Training measurements: The random sampler selects one of M available RIS configurations for each training symbol, with the selected configuration represented by a one-hot vector ω_t.The sole nonzero entry identifies the configuration whose output is fed to the RF chain.
- Structured channel model: The noiseless training matrix has low rank in the beamspace domain because the BS–RIS channel is represented using a sparse beamspace vector.The beamspace representation is h_1 = D_R z_1, with z_1 containing only a few high-amplitude virtual channel gains.
- Optimization formulation: The h_1 estimation problem combines a nuclear-norm penalty for low rank, an ℓ1 penalty for beamspace sparsity, and measurement-consistency terms.The weighting factors τ_R and τ_Z generally depend on the number of propagation paths N_p.
- Optimization formulation: The h_2 channel is estimated similarly using training symbols sent from the UE, and orthogonal BS and UE pilots allow parallel estimation.This parallelization applies when the two training-symbol sets are orthogonal.
B. An ADMM-Based Algorithm
The coupled optimization is reformulated with auxiliary matrices and solved using an ADMM procedure whose main steps are summarized in Algorithm 1.
- Problem decomposition: The highly coupled optimization is decomposed into simpler subproblems by introducing auxiliary matrices X and C.Both auxiliary variables belong to C^(M×T) and re-express the original optimization constraints.
- ADMM formulation: The Lagrangian adds dual variables V^(1) and V^(2) for the reformulated constraints, with γ ∈ (0, 1) as the ADMM stepsize.The dual variables enforce the constraints introduced in the reformulated problem.
- Algorithm 1: The implementation uses the pseudo-inverse and Singular Value Thresholding operators within the ADMM updates.These operations appear in the algorithmic steps described after the initialization.
C. Online Tuning of the RIS Unit Elements
After estimating both channels, the RIS controller selects reflection coefficients to maximize achievable end-to-end rate, using exhaustive search or nearest feasible phase values.
- Online RIS tuning: Given estimated channels ĥ_1 and ĥ_2, the RIS controller optimizes the N reflection coefficients to maximize the achievable end-to-end rate.The optimization is posed separately for each RIS element index n = 1, 2, …, N.
- Online RIS tuning: For a reasonable number of available RIS configurations, the controller may solve the reflection-coefficient optimization by exhaustive search.The text identifies affordable M or S_F^N as the relevant configuration-count regime.
- Online RIS tuning: Alternatively, each phase coefficient [φ]_n is set to the feasible value in F closest to its continuous optimum e^{jθ_n}.This approach quantizes the phase shift while retaining the nearest available reflection coefficient.
- Channel-estimation implementation: Algorithm 1 takes the sampling matrix, beamspace transform, RIS configurations, training symbols, regularization weights, stepsize, and iteration limit as inputs, and outputs z_1.Its loop performs successive minimizations over Y~, X, z_1, and C, including a soft-thresholding step.
V. SIMULATION RESULTS
Simulations evaluate channel-estimation error for different RIS sizes and training lengths, then compare end-to-end rate under perfect channel knowledge and estimated channels.
- Channel-estimation accuracy: For N = 32 and 64, simulations use b = 4, M = N, N_p = 3 paths, and SNR = 5dB to evaluate beamspace NMSE.The normalized mean squared error compares z_1 with its estimate ẑ_1.
- Channel-estimation accuracy: As N increases, more training symbols T are required.Figure 2 plots NMSE against T for different numbers of RIS elements under b = 4 and SNR = 5dB.
- End-to-end rate: 8.5bps/Hz is achieved with perfect channel knowledge for N = 16, b = 1, and M = 216 RIS configurations.This is the reference rate for the indicative end-to-end evaluation.
- End-to-end rate: 7.6bps/Hz is achieved with channel estimation and T = 200, around 10% lower than the perfect-channel-knowledge rate.The exhaustive-search approach is used, with SNR = 5dB for channel estimation and data communication on both links.