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Near-field Localization with a Reconfigurable Intelligent Surface Acting as Lens
Zohair Abu-Shaban, Kamran Keykhosravi, Musa Furkan Keskin, George C. Alexandropoulos, Gonzalo Seco-Granados, Henk Wymeersch
TL;DR
The paper addresses 3D transmitter localization with limited infrastructure by using a RIS-based lens near a single receive antenna and exploiting near-field wavefront curvature. It analyzes Fisher information, evaluates RIS phase configurations, and develops a low-complexity localization algorithm. Simulations report sub-meter or decimeter-scale accuracy near the lens, with positional beamforming favored when prior location information is available and randomized configurations favored for low-complexity estimation.
Problem
The paper investigates 3D transmitter localization using a RIS lens and a single receive antenna, where wavefront curvature provides positional information.
Method
The paper combines near-field channel modeling, Fisher information analysis, RIS phase-profile evaluation, and a low-complexity 3D localization algorithm.
Results
Sub-meter localization RMSE is achieved within 10 meters using randomized RIS configurations, while positional phase profiles yield lower PEB when prior location information is available.
Takeaways & Limitations
Random RIS phase configurations are recommended when low-complexity estimation is targeted, whereas positional beamforming can perform better with a priori location information.
Takeaways & Limitations
The channel model assumes excitation only along the RIS plane’s Y-axis, so it does not cover arbitrary user orientations.
Abstract
from arXiv · showhide
Exploiting wavefront curvature enables localization with limited infrastructure and hardware complexity. With the introduction of reconfigurable intelligent surfaces (RISs), new opportunities arise, in particular when the RIS is functioning as a lens receiver. We investigate the localization of a transmitter using a RIS-based lens in close proximity to a single receive antenna element attached to reception radio frequency chain. We perform a Fisher information analysis, evaluate the impact of different lens configurations, and propose a two-stage localization algorithm. Our results indicate that positional beamforming can lead to better performance when a priori location information is available, while random beamforming is preferred when a priori information is lacking. Our simulation results for a moderate size lens operating at 28 GHz showcased that decimeter-level accuracy can be attained within 3 meters to the lens.
I. INTRODUCTION
The paper studies 3D transmitter localization using a low-complexity RIS lens and a single receive antenna, exploiting near-field wavefront curvature. It develops Fisher-information analysis and a location estimator while examining RIS phase-profile effects.
- Motivation: RIS lenses offer a hardware and signal-processing complexity trade-off compared with RIS reflector operation.RIS reflectors typically require channel estimation and beamforming optimization, whereas lens operation uses a nearly continuous phase profile.
- Contribution: The study targets 3D localization with reconfigurable discrete RIS lenses and one antenna connected to a receive RF chain.The user location is estimated from scalar baseband observations collected over time.
- Contribution: The Fisher information analysis shows that position-error bounds depend on the RIS phase profiles.The paper evaluates this dependence under a near-field channel model.
- Contribution: The paper designs a low-complexity location estimator and evaluates it using a realistic 28 GHz channel model.The estimator is developed for the single-antenna RIS-lens architecture.
A. Geometry Model
The system models a transmitter and planar RIS lens geometrically, then distinguishes far-field and near-field channel models by how amplitude and phase vary across RIS elements. The improved near-field model captures both wavefront curvature and location-dependent amplitudes.
- A. Geometry Model: The geometry comprises a 3D transmitter, an M-element RIS lens in the XY plane, and a nearby single receive antenna with an RF chain.The transmitter position is p = [x y z]^T with z > 0, while each RIS element has a defined planar location.
- A. Geometry Model: The user position is parameterized by distance d and AoAs ϑ and ϕ through the wavevector.The model also represents prior location information with a Gaussian distribution having mean m_p and covariance Σ_p.
- B. Signal Model: The transmitter sends pilot signals through time-varying unit-modulus RIS phase profiles to the single-antenna receiver.The phase profile at time t is represented by Ω_t, and the observations are collected across T time instants.
- C. Channel Model: CM1 uses constant RIS-element amplitude and AoA-dependent phase, whereas CM2 uses constant amplitude and distance-dependent phase capturing wavefront curvature.When d is much larger than the RIS dimensions, CM2 reverts to CM1.
- C. Channel Model: CM3 additionally makes RIS-element amplitudes depend on each element’s location relative to the user.The paper uses CM3 for the actual channel and performance evaluation, but CM1 and CM2 for analysis and algorithm derivation.
- C. Channel Model: The channel treatment ignores electromagnetic near-field effects within the Fraunhofer distance.The cited polarization model assumes excitation only along the RIS plane’s Y-axis and is not valid for arbitrary user orientations.
A. Introduction
The paper formulates the received pilot observations under a near-field channel and uses the Fisher information matrix to derive position-error bounds. These bounds provide a benchmark for evaluating localization estimators.
- Signal and Information Model: Under CM2, the receiver’s baseband observations are modeled for the T transmitted pilots.The model describes the signal used for location estimation at the single-antenna receiver.
- Signal and Information Model: The Fisher information matrix is formed for five unknowns: channel amplitude, phase offset, and the three position coordinates.The noise-free observation vector is introduced before defining the FIM.
- Signal and Information Model: The position error bound is expressed in meters and related to the RMSE of any unbiased position estimator.The resulting inequality provides a performance benchmark for localization accuracy.
B. PEB Derivation
The equivalent Fisher information analysis expresses the position error bound through the projected steering-vector derivative, showing how RIS phase profiles determine positional information and distance-dependent accuracy.
- B. PEB Derivation: The FIM is derived from partial derivatives of the noise-free observation with respect to channel gain, phase, and user position.The position derivative uses D(p) = ∂a(p).
- B. PEB Derivation: The equivalent Fisher information matrix is formed from the projected derivative E = W^⊤D(p) relative to the steering vector c = W^⊤a(p).The projection removes the component of the derivative lying along c.
- B. PEB Derivation: The PEB depends on the component of W^⊤D(p) orthogonal to W^⊤a(p), up to an SNR scaling.Greater orthogonality provides more positional information and lowers the PEB.
- B. PEB Derivation: When d ≫ r_i, the position information tends to zero under the plane-wave model, so the PEB increases farther from the RIS lens regardless of path loss.This follows from the limiting behavior J(p) → 0.
IV. RIS PHASE PROFILE DESIGN
The RIS phase-profile design compares random, directional, and positional configurations, relating each to prior location information and resulting spatial SNR patterns.
- IV. RIS PHASE PROFILE DESIGN: The phase design removes known transmitter-to-antenna phases before selecting the remaining RIS phases.The fixed profile accounts for the known channel, while the designed profile controls localization behavior.
- IV. RIS PHASE PROFILE DESIGN: Random profiles draw each RIS-element phase independently and uniformly over [0, 2π] at every time instant.This design does not target a specific direction or position.
- IV. RIS PHASE PROFILE DESIGN: Directional profiles focus phase configurations on angle samples obtained from the prior location distribution.The sampled angles determine the steering direction used for each configuration.
- IV. RIS PHASE PROFILE DESIGN: Random profiles produce relatively uniform SNR subject to path loss, whereas directional profiles concentrate higher SNR along the selected direction.Directional profiles have reduced SNR elsewhere compared with random profiles; positional beams tend to be slightly broader.
A. Maximum Likelihood Estimator
The estimator decomposes near-field localization into angular and distance searches, using a truncated Jacobi–Anger representation to make the steering vector separable in the two angles.
- A. Maximum Likelihood Estimator: The maximum-likelihood procedure estimates the channel gain as a function of the candidate position and then optimizes the resulting location estimate.The gain estimate is obtained by solving for α before estimating p.
- A. Maximum Likelihood Estimator: The three-stage estimator first searches for ϑ, then ϕ, and finally distance d.The first two stages use angular structure; the final stage evaluates positions parameterized by the estimated angles.
- A. Maximum Likelihood Estimator: The steering vector is approximated using a truncated Jacobi–Anger expansion whose omitted Bessel terms decay as their order increases.The truncation retains terms with |n| ≤ N.
- A. Maximum Likelihood Estimator: The expansion yields an approximately separable steering vector, a(ϑ, ϕ) ≈ G^⊤(ϑ)h(ϕ), in elevation and azimuth angles.This separability supports separate angular searches.
- A. Maximum Likelihood Estimator: Each estimator stage is implemented through a line search, with the distance stage requiring the third and final search.The distance estimate uses the previously estimated angles and an unstructured gain estimate.
A. Simulation Setup
The simulation uses a 2500-element RIS lens at 28 GHz with one nearby receive antenna and a 0.2 ms observation for localization evaluation.
- A. Simulation Setup: The simulated RIS has M = 2500 elements arranged as 50 × 50 at 28 GHz with λ/2 spacing.Its element area is A = λ^2/4, and the receive antenna is placed behind the lens at [0 0 −λ]^⊤.
- A. Simulation Setup: Localization uses T = 200 time instants over 1 MHz bandwidth, corresponding to a 0.2 ms observation.The transmit power is 1 mW, with −174 dBm/Hz noise spectral density and an 8 dB reception noise figure.
- A. Simulation Setup: The user wavevector is set along [1 1 1]^⊤, and the generated channels follow the CM3 model.CM3 generates both the antenna channel and the RIS-assisted channel used in evaluation.
B. PEB Evaluation
PEB and RMSE evaluate RIS-lens localization across distance and phase-profile choices. Randomized profiles provide robust sub-meter performance, while optimized profiles can offer stronger bounds but require sufficiently high-resolution estimation.
- Directional and positional phase profiles substantially reduce PEB, with positional profiles performing only negligibly better.
- Smaller prior-location uncertainty σ improves PEB, while RIS measurements outperform the σ = 0.1 m prior only below 10 m.
- Sub-meter localization RMSE is achieved within 10 m using the randomized codebook, with performance close to the PEB.
- Directional profiles can produce much worse RMSE than predicted because finite-resolution searches miss their narrow objective-function peaks.
- The study’s simulations evaluate RIS-lens localization using Fisher information and a low-complexity algorithm under multiple phase configurations.