⚡ electrical engineering

Near-Field NLOS Localization via Position-Unknown HRIS:From Self-Localization to Target Positioning

This paper proposes a two-stage gridless localization framework that enables near-field non-line-of-sight target positioning using a hybrid reconfigurable intelligent surface (HRIS) at an unknown location, first achieving HRIS self-localization via a virtual far-field conversion and decoupled atomic norm minimization, and then refining target positions through geometric triangulation and semidefinite relaxation-based phase optimization.

Original authors: Hua Chen, Linke Yu, Tuo Wu, Maged Elkashlan, Naofal Al-Dhahir, Merouane Debbah, K. C. Ho

Published 2026-03-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hua Chen, Linke Yu, Tuo Wu, Maged Elkashlan, Naofal Al-Dhahir, Merouane Debbah, K. C. Ho

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are in a large, pitch-black room filled with obstacles. You need to find the exact location of a friend (the Target) who is hiding behind a wall, but you can't see them directly.

Usually, to find someone in the dark, you might use a mirror (RIS - Reconfigurable Intelligent Surface) to bounce sound or light off the wall so you can hear or see your friend. However, there's a catch: You don't know where the mirror is placed. If you don't know where the mirror is, you can't calculate where your friend is, because your math depends on the mirror's position.

This paper solves that exact problem using a "Super Mirror" called an HRIS (Hybrid RIS). Here is how they did it, broken down into simple concepts:

1. The "Super Mirror" (HRIS)

Traditional mirrors only reflect light. This new "Super Mirror" is special because it can do two things at once:

Reflect: It bounces the signal to the main receiver (the Base Station) so the receiver can talk to the hidden friend.
Listen: It also listens to the signal coming from the main receiver.

The Analogy: Imagine a two-way street. A normal mirror is like a one-way glass; you can see out, but you can't see in. The HRIS is like a window with a camera on both sides. It lets the signal pass through to the receiver and records the signal coming from the receiver. This "listening" ability is the key to solving the mystery of where the mirror itself is standing.

2. The Problem: The "Curved" Signal

In the old days, signals were treated like flat sheets of paper (Far-Field). But because the friend is close to the mirror (Near-Field), the signal waves are actually curved, like ripples in a pond.

The Challenge: Trying to measure the angle and distance of a ripple is hard because the angle and distance are "glued" together. If you guess the angle wrong, your distance guess is wrong, and vice versa.
The Paper's Trick: They use a mathematical "magic trick" (Cross-Correlation) to flatten those ripples back into a flat sheet. This turns a messy, curved problem into a clean, flat one that computers can solve easily.

3. The Two-Stage Solution

The authors propose a two-step game plan:

Stage 1: The "Relative" Game
First, they ignore the fact that they don't know where the mirror is. They calculate where the friend is relative to the mirror.

Analogy: Imagine you are standing on a boat. You don't know where the boat is in the ocean, but you can measure exactly how far the lighthouse is from your boat. You know the lighthouse is "50 meters North" of you.
They use a clever math tool (called DANM) to find the angle and a correction tool (called TLS) to fix small errors caused by the "ripples" mentioned earlier.

Stage 2: The "Global" Game
Now that they know where the friend is relative to the mirror, they need to find the mirror's location in the real world.

They use the "listening" feature of the Super Mirror. The mirror listens to signals from two different towers (Base Stations).
By comparing the angles from these two towers, they can use simple geometry (triangulation) to figure out exactly where the mirror is standing.
Analogy: If you know the lighthouse is 50 meters North of you, and you suddenly figure out your boat is at "Dock 5," you instantly know the lighthouse is at "Dock 5 + 50 meters North."

4. The "Smart Mirror" Tuning (Phase Optimization)

Once they have a rough idea of where everything is, they tweak the mirror's surface.

The Analogy: Imagine the mirror is made of thousands of tiny, adjustable tiles. Initially, they are just guessing how to tilt them. Once they know roughly where the friend and the towers are, they can "tune" the tiles to focus the signal perfectly, like a satellite dish locking onto a satellite.
This makes the signal stronger and the location calculation even more precise.

Why Does This Matter?

No More "Calibration": In the past, you had to hire a surveyor to measure the exact spot of every mirror before you could use it. This paper says, "We don't need that! We can figure it out on the fly."
Emergency Use: This is perfect for disaster zones or drone networks where you can't stop to measure everything. You just drop the mirror, and the system figures out where it is and finds the targets automatically.
6G Ready: As our future internet (6G) gets faster and uses higher frequencies, signals will act more like these "ripples." This paper provides the rulebook for how to navigate that new world.

Summary

The paper introduces a smart system that uses a special mirror to find hidden objects. Even if the mirror is dropped in a random spot, the system listens to the mirror to find its location, then uses that to find the hidden object. It's like finding a lost friend in the dark by first figuring out where your own flashlight is, without ever needing to look at a map.

1. Problem Statement

The paper addresses a critical limitation in current Reconfigurable Intelligent Surface (RIS)-aided localization systems: the assumption that the RIS position is known a priori. In practical 6G scenarios, especially for Non-Line-of-Sight (NLOS) Near-Field (NF) targets, the RIS position is often unknown (e.g., in UAV-mounted or emergency deployment scenarios).

Key Challenges:

Parameter Coupling: In the NF region, spherical wavefronts cause strong coupling between angle (azimuth/elevation) and range parameters, making them difficult to decouple.
Model Mismatch: Standard Fresnel approximations simplify the model but introduce systematic biases that degrade accuracy, particularly at high Signal-to-Noise Ratios (SNR).
Observability: Without knowing the RIS position, the Base Station (BS) cannot establish the geometric relationship to the target. The channel is a cascade of two unknown links (BS-RIS and RIS-Target), making separation impossible without additional observability.
Circular Dependency: Optimizing the RIS phase to improve localization requires knowing the channel (which depends on the RIS position), but the position is what needs to be estimated.

2. Methodology

The authors propose a two-stage gridless localization framework utilizing a Hybrid RIS (HRIS). Unlike passive RISs, an HRIS can simultaneously reflect signals to the BS and receive signals from targets, breaking the coupling between target location and RIS location.

Stage 1: HRIS Self-Localization and Relative Target Estimation

Virtual Far-Field (FF) Construction:
- The authors use the NF Fresnel approximation and perform delay-based cross-correlation on centrally symmetric HRIS elements.
- This converts the NF signal model into a virtual Far-Field model, effectively extending the array aperture and decoupling the angle and range parameters.
Angle Estimation (DANM):
- A Single-Snapshot Decoupled Atomic Norm Minimization (DANM) algorithm is proposed. It estimates 2-D angles (elevation and azimuth) without grid discretization errors.
- A specific pairing algorithm is used to associate the estimated elevation and azimuth angles correctly.
Range Estimation & Correction (MUSIC + TLS):
- Once angles are estimated, the MUSIC algorithm is used for range estimation.
- To correct the systematic bias introduced by the Fresnel approximation, a Total Least Squares (TLS) method is applied. This refines the parameters using the exact NF model, eliminating the "error floor" seen in high-SNR scenarios.
HRIS Position Estimation:
- Using the HRIS's receiving capability, the system estimates the direction vectors from the HRIS to two Base Stations (BSs) using Atomic Norm Minimization (ANM).
- A Least Squares (LS) geometric triangulation method combines these angles with the known BS positions to determine the 3-D coordinates of the HRIS ( $p_R$ ).

Stage 2: Phase Optimization and Absolute Target Positioning

Phase Optimization (SDR):
- To enhance the signal power received at the BSs (improving HRIS self-localization), the HRIS phase matrix is optimized.
- The non-convex unit-modulus constraint is handled via Semidefinite Relaxation (SDR) followed by Gaussian Randomization to find a near-optimal phase configuration.
Absolute Positioning:
- With the HRIS position now known, the relative target parameters (estimated in Stage 1) are transformed into absolute global coordinates.

3. Key Contributions

Novel Paradigm: First framework to achieve NLOS NF localization without prior knowledge of the RIS position, leveraging the dual sensing/reflecting capability of HRIS.
Gridless Decoupling: Introduction of a single-snapshot DANM algorithm that transforms the coupled NF model into a virtual FF model, enabling efficient 2-D angle estimation.
Bias Mitigation: Development of a TLS-based correction mechanism that eliminates Fresnel approximation errors, allowing the system to approach the Cramér-Rao Bound (CRB) at high SNR.
Joint Optimization: A closed-loop approach where phase optimization (via SDR) improves HRIS self-localization, which in turn enhances the accuracy of the final target positioning.
Theoretical Bounds: Derivation of the CRB for NF target parameters and the Position Error Bound (PEB) for the HRIS, providing theoretical benchmarks for performance analysis.

4. Simulation Results

Extensive Monte Carlo simulations validate the proposed framework:

Accuracy: The DANM + TLS algorithm significantly outperforms standard DANM, particularly in high SNR regimes where it avoids the error floor caused by model mismatch.
Robustness: The method successfully localizes multiple targets and correctly pairs angles and ranges in complex multi-target scenarios.
Phase Optimization Impact: SDR-based phase optimization improves HRIS angle estimation accuracy, which directly reduces the HRIS position error (PEB) and subsequently improves the absolute positioning accuracy of the targets.
Convergence: The algorithms converge to the theoretical CRB/PEB limits as SNR and the number of snapshots increase, provided the systematic bias is corrected.

5. Significance

This work fundamentally expands the applicability of RIS-aided sensing from controlled indoor environments to dynamic outdoor scenarios where RIS deployment is flexible and position data is unavailable. By solving the "chicken-and-egg" problem of needing a known RIS position to locate targets, this framework enables:

Rapid, infrastructure-free deployment of RIS for emergency communications.
Cost reduction by eliminating the need for precise positioning hardware and calibration for RIS units.
Robustness against environmental displacement (e.g., wind, UAV movement).
High-precision 6G localization in the Near-Field, a critical requirement for future ultra-dense networks and sensing-integrated communications.