1) Wavelength: λ = c / f where c is the speed of light and f is carrier frequency.
2) Free-space path loss (Friis): PL(dB)=20·log10(4πd/λ).
3) Log-distance option: PL(d)=PL(d₀)+10·n·log10(d/d₀).
4) Direct received power: Pr=Pt+Gt+Gr−PL−L.
5) RIS coherent gain: coherent combining approximates GRIS(dB)=20·log10(N·ρ·η), reflecting an N² power scaling when phases align.
6) RIS received power: Pr,RIS=Pt+Gt+Gr−(PL1+PL2)+GRIS−(L+LRIS).
7) Surface gain: Gain(dB)=Pr,RIS−Pr,direct. Noise floor is N(dBm)=−174+10·log10(BHz)+NF and SNR=Pr−N.
- Enter frequency and transmit power used on the site.
- Provide direct distance and the two RIS hop distances.
- Set RIS element count, reflection amplitude ρ, and alignment η.
- Add antenna gains and realistic system and RIS losses.
- Choose a model: free-space for open paths, log-distance for clutter.
- Click Calculate to view gain, power, SNR, and margins.
| Scenario | Pt (dBm) | f (GHz) | d0 (m) | d1 (m) | d2 (m) | N | ρ | η | Typical Gain (dB) |
|---|---|---|---|---|---|---|---|---|---|
| Warehouse aisle link | 20 | 3.5 | 120 | 60 | 70 | 256 | 0.85 | 0.90 | 5–15 |
| Concrete corridor turn | 23 | 5.8 | 80 | 35 | 55 | 400 | 0.80 | 0.85 | 8–18 |
| Outdoor yard edge | 18 | 2.6 | 200 | 90 | 120 | 196 | 0.90 | 0.90 | 3–12 |
These are indicative ranges. Real gain depends on geometry, blockage, and tuning quality.
Project Intent and Design Checks
This calculator estimates how a reconfigurable intelligent surface can lift received signal strength on construction sites where steel framing, temporary partitions, and equipment create dead zones. It compares a direct link budget to a two-hop reflected path and reports the surface gain as the difference in received power.
Inputs That Matter on Construction Sites
Distance dominates. If the direct path is 120 m and the RIS path splits into 60 m and 70 m, the reflected route may outperform only when coherent gain offsets the extra path loss. Frequency also shifts loss: moving from 2.6 GHz to 5.8 GHz increases free-space loss, so higher element counts or lower losses become more important. When using the log-distance option, exponents of 2.7–3.5 often fit cluttered interiors, while open yards sit nearer 2.0–2.3.
Understanding Coherent Element Gain
The model uses a coherent gain term of 20·log10(N·ρ·η). Doubling the number of elements N increases this term by about 6 dB when reflection amplitude ρ and alignment efficiency η stay constant. If ρ=0.85 and η=0.90, then N=256 yields roughly 20·log10(195.8) ≈ 45.8 dB before applying RIS implementation loss.
Noise Floor, SNR, and Margin Planning
Power alone is not enough; you also need SNR headroom. The noise floor is computed as −174 dBm/Hz + 10·log10(B) + NF. For 20 MHz bandwidth and 7 dB noise figure, the noise floor is about −94 dBm. The calculator then reports SNR and a sensitivity-based link margin, helping you verify whether the design can carry stable data under site variability.
Practical Placement and Reporting
Place the surface where it can “see” both endpoints with minimal blockage, often near corridor turns, stair cores, or façade openings. Keep cable and connector losses realistic, and include an RIS loss budget for control and quantization. Use the CSV and PDF exports to document assumptions, compare scenarios, and support commissioning checks during phased construction. Validate with a quick walk test after installation on site, then tune ρ and η expectations.
Frequently Asked Questions
1) What does “surface gain” mean here?
It is the difference in received power between the RIS-assisted path and the direct path, in dB. Positive gain indicates the reflected path delivers stronger received power under the same transmit and system assumptions.
2) Why are two distances needed for the RIS path?
The RIS link is modeled as two hops: transmitter to surface, and surface to receiver. Each hop has its own path loss, so long or obstructed segments can erase the coherent gain from the surface.
3) How should I choose ρ and η?
Use ρ for reflection efficiency and η for phase alignment quality. Early planning can assume ρ=0.75–0.90 and η=0.80–0.95. Commissioning data can refine them based on measured RSSI or SNR.
4) When should I use the log-distance model?
Select it for corridors, dense rebar, heavy equipment yards, or partial blockages. Set the exponent n from site experience: around 2.0–2.3 for open areas, and 2.7–3.5 for cluttered interiors.
5) Why include RIS implementation loss?
Real surfaces have control overhead, phase quantization, element coupling, and scattering that reduce ideal coherent gain. RIS loss lets you represent these effects as a single dB budget, improving realism in early design.
6) What result indicates a workable installation?
Look for positive surface gain, adequate SNR for your modulation, and a positive link margin against receiver sensitivity. If margin is near zero, shorten distances, increase N, or reduce losses before deployment.