LTE Cell Range & Coverage Estimator
LTE cell range and site count from a maximum allowable path loss, under 3GPP TR 38.901 and Okumura-Hata side by side, with the spread between them.
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Worked example: a 135 dB MAPL at 900 MHz, rural macro
Sites for 500 km² at the lower bound: 28
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How it works
LTE cell range from the MAPL
The cell range is the distance at which a propagation model's median path loss reaches the maximum allowable path loss (MAPL) from the link budget, less any building entry loss for indoor users. Models that are equally defensible give different distances for the same budget, so the range is solved under each model, and the planning bounds are the shortest and the longest of the comparable ones.
The models are the 3GPP TR 38.901 rural macro (RMa), urban macro (UMa) and street canyon (UMi) path losses, each in line of sight and non line of sight, a blend of the two weighted by the TR 38.901 line of sight probability, and Okumura-Hata with its COST 231 extension above 1500 MHz. The bounds come from the chosen deployment's non line of sight and blended curves and Okumura-Hata, each only inside its stated range; line of sight results and the other deployments are listed but never set a bound. Site counts use hexagonal cells.
PL(d) = MAPL − BEL, solved for d
RMa NLOS: PL = 161.04 − 7.1 log₁₀(W) + 7.5 log₁₀(h) − (24.37 − 3.7(h/hBS)²) log₁₀(hBS) + (43.42 − 3.1 log₁₀(hBS))(log₁₀(d₃D) − 3) + 20 log₁₀(fc) − (3.2(log₁₀(11.75 hUT))² − 4.97), not less than RMa LOS
d₃D = √(d₂D² + (hBS − hUT)²)
Okumura-Hata, urban: PL = 69.55 + 26.16 log₁₀(f) − 13.82 log₁₀(hb) − a(hm) + (44.9 − 6.55 log₁₀(hb)) log₁₀(d)
a(hm) = (1.1 log₁₀(f) − 0.7) hm − (1.56 log₁₀(f) − 0.8)
Okumura-Hata, open area: PL = PL(urban) − 4.78 (log₁₀(f))² + 18.33 log₁₀(f) − 40.94
Sites = ⌈A / (2.598 r²)⌉
- MAPL, BEL
- maximum allowable path loss from the link budget, and ITU-R P.2109 building entry loss for indoor users (zero outdoors), in dB
- PL
- the model's median path loss, in dB
- d₂D, d₃D
- ground distance, and the straight line distance between the antennas, in metres (TR 38.901)
- d
- distance, in kilometres (Okumura-Hata)
- fc, f
- frequency, in GHz for TR 38.901 and in MHz for Okumura-Hata
- hBS, hUT, hb, hm
- base station and terminal antenna heights, in metres
- h, W
- average building height and street width for RMa, in metres: TR 38.901 defaults of 5 m and 20 m
- a(hm)
- Hata's terminal height correction, in dB: the medium and small city form shown, and the large city form for dense urban clutter
- A, r
- service area in km² and cell range in km; 2.598 r² is the area of a hexagon of radius r
Standards
- 3GPP TR 38.901 Table 7.4.1-1: RMa, UMa and UMi path loss models
- 3GPP TR 38.901 Table 7.4.2-1: line of sight probability
- ITU-R P.2109: building entry loss
Worked example
Worked example: a 135 dB MAPL at 900 MHz, rural macro
An uplink limited budget gives a MAPL of 135 dB at 900 MHz for outdoor handsets at 1.5 m, served from rural macro sites at 35 m across a 500 km² service area, with Okumura-Hata for open areas. The rural clutter takes the TR 38.901 defaults of 5 m buildings and 20 m streets.
| Step | Working | Result |
|---|---|---|
| RMa NLOS loss at 1 km | 161.04 − 7.1 log₁₀(20) + 7.5 log₁₀(5) − (24.37 − 3.7(5/35)²) log₁₀(35) + 20 log₁₀(0.9) − (3.2(log₁₀(11.75 × 1.5))² − 4.97) | 118.62 dB |
| Lower bound: RMa NLOS range | √((1000 × 10^((135 − 118.62) / (43.42 − 3.1 log₁₀(35))))² − 33.5²) | 2.65 km |
| Okumura-Hata open area loss at 1 km | 69.55 + 26.16 log₁₀(900) − 13.82 log₁₀(35) − a(1.5) − 4.78 (log₁₀(900))² + 18.33 log₁₀(900) − 40.94 | 96.97 dB |
| Upper bound: Okumura-Hata range | 10^((135 − 96.97) / (44.9 − 6.55 log₁₀(35))) | 12.39 km |
| Sites for 500 km² at the lower bound | ⌈500 / (2.598 × 2.65²)⌉ | 28 |
Planned at the upper bound, the same 500 km² would take 2 sites, so the choice between two defensible models is worth 26 sites here. The RMa blended curve gives 2.88 km, between the bounds. The RMa line of sight loss is still below the MAPL at 10 km, the furthest RMa line of sight is stated for, so it gives no range and never sets a bound.
How do you calculate LTE cell range from the MAPL?
Find the distance at which a propagation model's median path loss equals the MAPL. Path loss rises steadily with distance in every model here, so the estimator solves each one by bisection between 10 m and 100 km, after taking off any building entry loss for indoor users. The MAPL comes from a link budget: the LTE Link Budget calculator works out the limiting one and can pass it straight in with the frequency and antenna heights, or you can enter it directly.
What are the validity ranges of TR 38.901 and Okumura-Hata?
TR 38.901 path loss applies from 0.5 to 100 GHz, and to 30 GHz for RMa. UMa and UMi apply from 10 m to 5 km of ground distance with terminals at 1.5 to 22.5 m. RMa applies from 10 m to 10 km in line of sight and to 5 km out of it, with base stations at 10 to 150 m and terminals at 1 to 10 m. TR 38.901 states UMa and UMi at one base height each, 25 m and 10 m, rather than a range, so at any other base height the estimator flags their results and leaves them out of the bounds. Okumura-Hata covers 150 to 1500 MHz and its COST 231 extension 1500 to 2000 MHz, with base stations at 30 to 200 m, terminals at 1 to 10 m and distances of 1 to 20 km, or to 100 km up to 1500 MHz with the distance term of ITU-R P.529-3.
What happens when a model is outside its validity range?
The result is flagged with the reason and excluded from the planning bounds. If a model cannot reach the required path loss at all, it reports no range rather than extrapolating. When fewer than two comparable models are in range, the tool says so instead of reporting a spread. When the ones in range all come from one model family, as above 2000 MHz where Okumura-Hata stops, it reports the spread with a warning that it understates the model uncertainty.
How is building entry loss handled?
For indoor terminals the tool applies ITU-R P.2109 building entry loss for the chosen building class and percentile, and subtracts it from the MAPL before solving the range. When a budget handed over from the LTE Link Budget calculator already includes building entry loss, the hand off turns the indoor option off so the loss is not counted twice.
Why hexagons rather than circles for the site count?
Cells tile a service area as hexagons. A hexagon of radius r covers about 2.6 r², while a circle covers about 3.14 r², so using the circle overstates the area each site serves by about a fifth and undercounts the sites needed.
Does this account for terrain?
No. These are scenario based and measurement fitted models, and none of them sees hills or buildings at specific locations. Use this tool for scoping, and use the Coverage Predictor for terrain aware prediction once site positions are known.
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