4. Geometry and Phase Design for RIS-Assisted Sensing

NLoS Sensing Needs an Open Route

A blocked BS–target line does not prohibit every indirect path. Check both BS–RIS and RIS–target visibility, then evaluate the complete return budget. The RIS cannot repair a segment blocked by the same building.

Correct the interpretation: a conventional radar can sometimes exploit natural multipath too. The attraction of a RIS is a configurable response at a known location, rather than a claim that NLoS sensing is otherwise impossible.

References for this section3

• M. Rihan et al., "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication", IEEE Network, 2023.
• M. Rihan et al., "Active RIS-Aided ISAC Systems", IEEE Transactions on Communications, 2024.
• A. Tishchenko et al., "Multi-Functional and Hybrid RIS for ISAC: A Survey", IEEE Communications Surveys & Tutorials, 2025.

Better Sensing Geometry

One range restricts a 2-D target to a circle. A second known anchor adds another range, but the resulting position information depends on the angle between the two viewing directions.

Let $u_A$ and $u_B$ be unit vectors from anchors A and B toward the target. For independent, unbiased range errors with common standard deviation $\sigma_r$, the local Fisher information matrix and position error bound are:

$$J=\sigma_r^{-2}(u_Au_A^T+u_Bu_B^T),\qquad \mathrm{PEB}=\sqrt{\mathrm{tr}(J^{-1})}=\frac{\sqrt2\sigma_r}{|\sin\theta|}.$$

The trace adds the two coordinate error bounds; $\theta$ is the angle between the viewing directions. Parallel or opposite directions make $J$ singular. At right angles, $\sigma_r=0.5$ m gives a bound of approximately 0.71 m.

The lab uses an independent direct BS range and a RIS–target range recovered after subtracting a calibrated BS–RIS leg. If only one RIS echo exists and the direct range is blocked, this two-range model does not apply. You need another path, angle measurement or motion information. Even two ranges can leave a global mirror ambiguity; the local bound does not resolve it.

Does a second viewpoint actually help?

1. Formula and symbols

$$J=\sigma^{-2}(u_Au_A^T+u_Bu_B^T)$$

$$\mathrm{PEB}=\sqrt{\operatorname{tr}(J^{-1})}=\frac{\sqrt2\sigma}{|\sin\theta|}$$

• $\sigma$: independent range-error standard deviation
• $u_A$: Unit direction toward anchor A
• $u_B$: Unit direction toward anchor B
• $\theta$: angle between directions
• $J$: position information
• $\mathrm{PEB}$: local position-error bound

Parallel directions make the bound singular.

Anchor separation

20 m

Target horizontal position

15 m

Target height above baseline

20 m

Range standard deviation

0.5 m

2. Work with the current inputs

$$J=\sigma^{-2}(u_Au_A^T+u_Bu_B^T),\quad \mathrm{PEB}=\sqrt{\mathrm{tr}(J^{-1})}$$

$$\mathrm{PEB}=\frac{\sqrt{2}\sigma}{|\sin\theta|}=\frac{\sqrt{2}\times0.5}{0.776}\ \approx 0.91\ \mathrm{m}$$

3. Result

Position error bound0.91 m

Range from A / B25.0 / 20.6 m

Viewpoint diversity |sin θ|0.776

References for this section3

• M. Rihan et al., "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication", IEEE Network, 2023.
• M. Rihan et al., "Active RIS-Aided ISAC Systems", IEEE Transactions on Communications, 2024.
• A. Tishchenko et al., "Multi-Functional and Hybrid RIS for ISAC: A Survey", IEEE Communications Surveys & Tutorials, 2025.

Phase Design for a Hidden Target

To focus on point F, compensate the total path through each element. With element index $n$, source-to-element distance $r_{Bn}$ and element-to-focus distance $r_{nF}$:

$$\phi_n=Q_b\!\left[\frac{2\pi}{\lambda}(r_{Bn}+r_{nF})\right].$$

• $\phi_n$: programmed phase of cell $n$.
• $\lambda$: wavelength.
• $Q_b$: rounding to the selected quantized phase state.
• $b$: number of phase-control bits, giving $2^b$ equally spaced states modulo $2\pi$.

Continuous phase means no rounding. The positive sign compensates the negative propagation phase used in this model.

At an observation point $(x,y)$, with element-to-observation distance $r_n(x,y)$ and $N_e$ elements, normalized coherent power is:

$$g(x,y)=\frac{1}{N_e^2}\left|\sum_{n=1}^{N_e}e^{j[\phi_n-2\pi(r_{Bn}+r_n(x,y))/\lambda]}\right|^2.$$

The lab uses 16 half-wavelength-spaced cells along $y=0$ at 3 GHz and a source at $(−2,−4)$ m. It assumes equal element amplitudes to isolate phase alignment. Try continuous versus one-bit control and move F. The spherical distances model focusing; the colour map omits path attenuation and obstructions, so it is not an absolute coverage map.

Can the phases illuminate a chosen point?

1. Formula and symbols

$$\phi_n=Q_b[2\pi(r_{Bn}+r_{nF})/\lambda]$$

$$g(P)=\frac1{N^2}\left|\sum_ne^{j[\phi_n-2\pi(r_{Bn}+r_{nP})/\lambda]}\right|^2$$

• $r_{Bn}$: Distance from the source to cell n
• $r_{nF}$: Distance from cell n to the focus
• $r_{nP}$: Distance from cell n to the observation point
• $Q_b$: b-bit phase quantizer
• $\lambda$: wavelength
• $N$: cells
• $g$: power relative to full coherence

The diagram includes the complete source and destination paths.

Focus horizontal position

1 m

Focus distance

4 m

Phase resolution

Continuous1 bit2 bits3 bits

2. Work with the current inputs

$$\phi_n=Q_b\!\left[\frac{2\pi}{\lambda}(r_{Bn}+r_{nF})\right],\quad F=(1.0,4.0)\ \mathrm{m}$$

$$g(x,y)=\frac{1}{16^2}\left|\sum_{n=1}^{16}e^{j[\phi_n-2\pi(r_{Bn}+r_n(x,y))/\lambda]}\right|^2,\quad g(F)=0.818$$

3. Result

Power at intended focus81.8% of coherent ideal

One-way coherence loss-0.87 dB

References for this section3

• M. Rihan et al., "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication", IEEE Network, 2023.
• M. Rihan et al., "Active RIS-Aided ISAC Systems", IEEE Transactions on Communications, 2024.
• A. Tishchenko et al., "Multi-Functional and Hybrid RIS for ISAC: A Survey", IEEE Communications Surveys & Tutorials, 2025.

Feedback, Active and Hybrid Assistance

• Sensing to communication: a position estimate can narrow a beam search, but stale estimates can misdirect it.
• Active surface: amplification may help weak returns, while adding noise and power demand.
• Hybrid surface: receiving elements can supply local observations, with calibration and hardware cost.

A known surface is an anchor only when its measurements can be identified and calibrated. Merely knowing a panel’s location supplies no target measurement.

References for this section3

• M. Rihan et al., "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication", IEEE Network, 2023.
• M. Rihan et al., "Active RIS-Aided ISAC Systems", IEEE Transactions on Communications, 2024.
• A. Tishchenko et al., "Multi-Functional and Hybrid RIS for ISAC: A Survey", IEEE Communications Surveys & Tutorials, 2025.

Takeaway

Good placement supplies useful directions; good phase control supplies coherent illumination. Next, compare surface architectures under explicit energy and noise constraints.

References for this section3

• M. Rihan et al., "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication", IEEE Network, 2023.
• M. Rihan et al., "Active RIS-Aided ISAC Systems", IEEE Transactions on Communications, 2024.
• A. Tishchenko et al., "Multi-Functional and Hybrid RIS for ISAC: A Survey", IEEE Communications Surveys & Tutorials, 2025.