Md Tarek Hassan | PhD Researcher in 6G Wireless, RIS and ISAC

Why Localization Needs RIS

Localization: map radio observations to position.
Useful observations: time delay, angle, phase, Doppler, and received power.
Problem: blockage removes direct paths; uncontrolled reflections are harder to interpret geometrically.

RIS changes this situation because it creates a known controllable path.

References for this section3

K. Li, J. He, M. El-Hajjar, and L.-L. Yang, "Localization in Reconfigurable Intelligent Surface Aided mmWave Systems: A Multiple Measurement Vector Based Channel Estimation Method", IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 13326-13339, Sept. 2024.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G", IEEE Vehicular Technology Magazine, 2024.
M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.

Virtual Anchors

A physical anchor is a transmitter or receiver with known position. An RIS can behave like a virtual anchor because its location is known and its reflection pattern is controlled.

If the receiver estimates the delay and angle of the RIS-reflected path, it can infer geometric constraints. With multiple RIS states, multiple RIS panels, or a direct path plus reflected path, the position becomes easier to solve.

The receiver does not directly observe a floor-plan position:

Pilots: reveal channel observations at known signal locations.
Channel estimate: extracts path gain, delay, angle, and possibly Doppler.
Position estimate: maps those parameters to geometry.
RIS role: known surface location and state can make one reflected path easier to identify.

The RIS as a virtual anchor: how precisely can we place the user?

1. Formula and symbols

\sigma_d=\frac{c}{2\pi\beta\sqrt{2\gamma}},\quad\beta=B/\sqrt{12}

\sigma_\theta=\sqrt{\frac6{\pi^2\cos^2\theta\,\gamma(M^2-1)}}

\sigma_p\approx\sqrt{\sigma_d^2+(r\sigma_\theta)^2}

$B$ : bandwidth
$\beta$ : RMS bandwidth for the stated flat spectrum
$\gamma$ : linear SNR
$M$ : elements per side
$\theta$ : departure angle
$r$ : range from anchor
$\sigma_d$ : Local range-error standard deviation
$\sigma_\theta$ : Local angle-error standard deviation
$\sigma_p$ : Approximate local position uncertainty

Angle error uses radians.

Bandwidth

RIS elements per side

Carrier

User position (east)58 m

User position (south)28 m

2. Work with the current inputs

\sigma_d = \frac{c}{2\pi\beta\sqrt{2\,\mathrm{SNR}}},\ \ \beta = \tfrac{B}{\sqrt{12}} \;\Rightarrow\; \sigma_d = \frac{3\times10^{8}\cdot\sqrt{12}}{2\pi\cdot 400\times10^{6}\cdot\sqrt{2\cdot 12.5}} = 8.3\ \text{cm}

\sigma_\theta = \sqrt{\frac{6}{\pi^{2}\cos^{2}\theta\;\mathrm{SNR}\,(M^{2}-1)}} = \sqrt{\frac{6}{\pi^{2}\cdot 0.737^{2}\cdot 12.5\cdot(32^{2}-1)}} = 0.5368^\circ

\sigma_p \approx \sqrt{\sigma_d^{2} + (r\,\sigma_\theta)^{2}} = \sqrt{(8.3\ \text{cm})^{2} + (32.6\ \text{m}\times 9.37\times10^{-3})^{2}} = 31.6\ \text{cm}

3. Result

SNR via the RIS11.0 dBdirect path blocked

Range error σ_d8.3 cmrange 32.6 m

Angle error σ_θ0.537°AoD 42.5°

Position error31.6 cmCRB, one snapshot

The BS knows where the RIS is. From the reflected path it measures two things: total delay (giving range from the RIS, once the known BS–RIS leg is removed) and the departure angle across the surface. Range and angle cross at one point. Their accuracy follows the Cramér–Rao bound, the best any unbiased estimator can do: wider bandwidth sharpens range, a larger surface sharpens angle, and both improve with SNR. SNR comes from the same plate link model (50 dBm EIRP, 30 dB per building crossing). Assumes synchronised nodes and a known BS–RIS geometry. Drag the user.

References for this section3

K. Li, J. He, M. El-Hajjar, and L.-L. Yang, "Localization in Reconfigurable Intelligent Surface Aided mmWave Systems: A Multiple Measurement Vector Based Channel Estimation Method", IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 13326-13339, Sept. 2024.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G", IEEE Vehicular Technology Magazine, 2024.
M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.

Measurements Used for RIS Localization

ToA: Time of arrival gives path length.
TDoA: Time difference of arrival gives relative path length.
AoA: Angle of arrival gives direction at the receiver.
AoD: Angle of departure gives direction from the transmitter or RIS.
RSS: Received signal strength can help but is less reliable.
Doppler: Motion-induced frequency shift supports tracking.

References for this section3

K. Li, J. He, M. El-Hajjar, and L.-L. Yang, "Localization in Reconfigurable Intelligent Surface Aided mmWave Systems: A Multiple Measurement Vector Based Channel Estimation Method", IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 13326-13339, Sept. 2024.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G", IEEE Vehicular Technology Magazine, 2024.
M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.

Near-Field Localization

Large RIS panels and high carrier frequencies create near-field behavior. In the near field, wavefronts are spherical rather than planar.

This is not just a complication. It is also an opportunity. Spherical wavefront curvature contains range information. That means a large RIS may help estimate both angle and distance, not only direction.

Near or far field? Watch the wavefront bend

1. Formula and symbols

\Delta\phi_{\rm edge}=\frac{2\pi}{\lambda}(\sqrt{r^2+(D/2)^2}-r)

r_{\rm FF}\approx2D^2/\lambda

$D$ : aperture size
$\lambda$ : wavelength
$r$ : range
$\Delta\phi_{\rm edge}$ : edge-to-centre spherical phase difference in radians

The far-field distance is the stated approximate phase-error convention.

Carrier

Elements across the aperture

User distance17.78 m

2. Work with the current inputs

\begin{gathered}\Delta\phi_{\text{edge}} = \frac{2\pi}{\lambda}\left(\sqrt{r^{2}+\left(\tfrac{D}{2}\right)^{2}} - r\right) \approx \frac{\pi D^{2}}{4\lambda r} \\[4pt] \Delta\phi_{\text{edge}} = \frac{\pi}{8} \iff r = \frac{2D^{2}}{\lambda} = \frac{2\cdot(34.3\ \text{cm})^{2}}{1.1\ \text{cm}} = 21.93\ \text{m}\end{gathered}

3. Result

Aperture D34.3 cm

Rayleigh distance21.93 m

Edge phase error27.74°limit 22.5°

RegimeNear fieldrange is observable

A user straight in front of the surface sends a spherical wave. The curve shows how much extra phase the edge elements see compared with a flat wave, as the user moves away. Close in, that curvature is large and carries range information; far away the wave looks flat and the surface only learns direction. The usual rule draws the line at π/8 (22.5°), which happens at the Rayleigh distance 2D²/λ (shaded: near field).

References for this section3

K. Li, J. He, M. El-Hajjar, and L.-L. Yang, "Localization in Reconfigurable Intelligent Surface Aided mmWave Systems: A Multiple Measurement Vector Based Channel Estimation Method", IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 13326-13339, Sept. 2024.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G", IEEE Vehicular Technology Magazine, 2024.
M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.

Channel Estimation Link

RIS localization usually begins with channel estimation. In mmWave systems, the channel is sparse: only a few dominant paths exist. Estimating those path parameters gives the geometry needed for localization.

Recent IEEE TVT work has studied multiple-measurement-vector channel estimation for RIS-aided mmWave localization, highlighting the link between sparse channel recovery and position estimation.

References for this section3

K. Li, J. He, M. El-Hajjar, and L.-L. Yang, "Localization in Reconfigurable Intelligent Surface Aided mmWave Systems: A Multiple Measurement Vector Based Channel Estimation Method", IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 13326-13339, Sept. 2024.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G", IEEE Vehicular Technology Magazine, 2024.
M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.

Key Challenges

RIS phase pattern design for localization, not only data rate.
Synchronization between transmitter, receiver, and RIS controller.
Hardware impairments and phase quantization.
Multipath association: deciding which estimated path corresponds to which reflector.
Mobility and real-time tracking.
Near-field channel modeling.

References for this section3

K. Li, J. He, M. El-Hajjar, and L.-L. Yang, "Localization in Reconfigurable Intelligent Surface Aided mmWave Systems: A Multiple Measurement Vector Based Channel Estimation Method", IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 13326-13339, Sept. 2024.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G", IEEE Vehicular Technology Magazine, 2024.
M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.

Takeaway

Why RIS helps: a controlled path can act as a known geometric reference.
Where strongest: blocked direct links or large near-field apertures with range-sensitive phases.

References for this section3

K. Li, J. He, M. El-Hajjar, and L.-L. Yang, "Localization in Reconfigurable Intelligent Surface Aided mmWave Systems: A Multiple Measurement Vector Based Channel Estimation Method", IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 13326-13339, Sept. 2024.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G", IEEE Vehicular Technology Magazine, 2024.
M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.

Check your understanding

0 of 4 answered

Which two measurements of the RIS path locate the user in the virtual-anchor demo?
At the same SNR, doubling the bandwidth changes the range error how?
Far from the RIS, why does the angle term often dominate the position error?
Inside the Rayleigh distance, what extra information does the surface observe?

Complete references and further reading

K. Li, J. He, M. El-Hajjar, and L.-L. Yang, "Localization in Reconfigurable Intelligent Surface Aided mmWave Systems: A Multiple Measurement Vector Based Channel Estimation Method", IEEE Transactions on Vehicular Technology, vol. 73, no. 9, pp. 13326-13339, Sept. 2024.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G", IEEE Vehicular Technology Magazine, 2024.
M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.