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Clutter loss calculator (ITU-R P.2108)

Clutter loss is the extra loss that buildings, trees and other objects around a terminal add to a radio path. This calculator implements Recommendation ITU-R P.2108-1: the statistical loss for terrestrial links from 0.5 to 67 GHz, the loss towards satellites and aircraft from 10 to 100 GHz, and the median height-gain correction below 3 GHz.

§3.2 and §3.3 are statistical, §3.1 gives a median. §3.2 is what most link budgets mean by clutter loss.

§3.2 covers 0.5–67 GHz.

The correction applies at one end from 0.25 km and at both ends from 1 km. Beyond 2 km the loss no longer grows.

%

The loss is not exceeded at this share of locations. 50 % is the median, 90 % a pessimistic spot.

Clutter loss at one end
30.1 dB
not exceeded at 50 % of locations, for one cluttered terminal only
Median (50 % of locations)
30.1 dB
frequency term 30.4 dB and distance term 34.6 dB combined
Location spread
4.30 dB
Q⁻¹ = 0.000, so the percentage term adds 0.0 dB
Two-kilometre ceiling (eq. 6)
Not reached
L(d) 30.1 dB stays below L(2 km) 30.4 dB
Both ends in clutter, medians added
60.2 dB
each end is its own random draw. Medians add, values at other percentages do not.
101520253035400.512510path length (km)loss at one end, dB · log distance axis2 km ceiling90 %50 %10 %30.1 dB

Clutter loss at one end against total path length, on a logarithmic distance axis, at your frequency. The curves are 10, 50 and 90 % of locations, and the green one is your percentage. The dot is your path. Every curve flattens at the dashed line, because eq. (6) caps the loss at its 2 km value.

P.2108-1 is a statistical end correction for urban and suburban clutter, fitted to measurements with terminals up to about 6 m above ground. It does not replace a path model, and it must not be added to one that already models clutter along the whole path, such as ITU-R P.1411. §3.1 gives a median only. Results outside each method’s frequency range are left blank.

How it works

  1. 01

    Pick the method

    §3.2 is for a terrestrial link with one terminal in urban or suburban clutter, 0.5–67 GHz. §3.3 is for a ground terminal working a satellite or an aircraft, 10–100 GHz. §3.1 is the older median correction for an antenna below the local clutter height, 30 MHz to 3 GHz.

  2. 02

    Blend a frequency term and a distance term

    In §3.2 the median combines Ll, which depends only on frequency, and Ls, which grows with path length: L50 = −5·log(10−0.2·Ll + 10−0.2·Ls). The smaller term dominates. At 3.5 GHz over 1 km the median is 30.1 dB.

  3. 03

    Choose a percentage of locations

    Clutter changes from street to street, so the method returns a distribution. The term σcb·Q−1(p/100) moves the median up or down. At 3.5 GHz over 1 km, 10 % of locations see less than 24.6 dB and 90 % less than 35.5 dB.

  4. 04

    Stop at two kilometres

    Eq. (6) caps the loss at its value for a 2 km path. The same link at 99.9 % gives 43.4 dB at 1 km but 42.8 dB at 2 km, because the spread σcb shrinks as the distance term takes over. The answer is therefore 42.8 dB.

  5. 05

    Add it once per cluttered end

    The result is the extra loss at one terminal. Add it to a path loss that ignores clutter, such as free-space or terrain loss. With clutter at both ends, add a second value for the other end and keep the path at least 1 km long.

Formulas

Terrestrial, §3.2, one cluttered end
L = L50 − σcb·Q−1(p/100)
  • L50 = −5·log(a + b) — median, dB, with a = 10−0.2·Ll, b = 10−0.2·Ls
  • Ll = −2·log(10−5·log f − 12.5 + 10−16.5) — frequency term, dB
  • Ls = 32.98 + 23.9·log d + 3·log f — distance term, dB
  • σcb = (16·a + 36·b) / (a + b) — spread, dB
  • Lctt = min(L(d), L(2 km)) — eq. (6), the result
  • f — frequency, GHz · d — total path length, km · p — percentage of locations, %
  • Q−1 — inverse complementary normal: Q−1(0.5) = 0, Q−1(0.9) = −1.28
Satellite or aircraft path, §3.3
Lces = Be − 1 − 0.6·Q−1(p/100)
  • B = −K1·ln(1 − p/100)·cot(A1·(1 − θ/90) + π·θ/180) — natural log, cot argument in radians
  • e = 0.5·(90 − θ)/90
  • K1 = 93·f0.175, A1 = 0.05 — f in GHz
  • θ — elevation angle of the satellite or aircraft seen from the terminal, degrees
  • Lces — loss at the ground terminal, dB, negative at low p near the zenith
Antenna below clutter height, §3.1
Ah = J(ν) − 6.03
  • J(ν) = 6.9 + 20·log((ν − 0.1)2 + 1 + ν − 0.1) — eq. (1), diffraction form (2a)
  • Ah = −Kh2·log(h/R) — form (2b) instead, for water, sea and open or rural ground
  • ν = 0.342·f·hdif·θclut — θclut in degrees, as published
  • hdif = R − h, θclut = atan(hdif/ws) — m and degrees
  • Kh2 = 21.8 + 6.2·log f — height-gain form (2b), f in GHz
  • h — antenna height, R — clutter height, ws — street width, m
  • Ah = 0 for h ≥ R, otherwise added to a basic loss computed to height R

Worked example

A 3.5 GHz link of 1 km, one end in clutter, 50 % of locations
  1. Ll = −2·log(10−5·log 3.5 − 12.5 + 10−16.5) = 30.40 dB
  2. Ls = 32.98 + 23.9·log 1 + 3·log 3.5 = 34.61 dB
  3. σcb = 4.30 dB, and Q−1(0.5) = 0 at the median
  4. L(1 km) = −5·log(10−6.079 + 10−6.922) = 30.1 dB
  5. L(2 km) = 30.4 dB is higher, so the loss at one end stays 30.1 dB
  6. at 99.9 %: 30.1 + 4.30·3.09 = 43.4 dB exceeds L(2 km) = 42.8 dB, so 42.8 dB (the NTIA test value)

FAQ

What is clutter loss?
Clutter loss is the extra loss from buildings, trees and other objects close to a terminal, on top of the path loss over open terrain. P.2108 defines it as the difference in loss with and without that local clutter, with all other path details unchanged. It is a correction for the ends of a path, not a path model.
Why is the result statistical?
Because nobody knows the street layout around every terminal. Two phones a few metres apart can see losses 10 dB apart. P.2108 therefore gives the loss not exceeded at p % of locations. Use 50 % for a typical spot and 90 % or more when most locations must work. In §3.3 a low percentage can even give a slightly negative loss, which the fitted model allows and this calculator keeps.
Which terminal does the loss apply to?
Each method returns the loss at one end. In §3.2, add one value per cluttered terminal, as two independent draws, and use it at both ends only on paths of 1 km or more. In §3.3 only the ground terminal sits in clutter. In §3.1, add the correction at each end whose antenna is below the clutter height, and compute the basic loss to height R.
Why does 99.9 % at 1 km give the 2 km value?
Because eq. (6) caps the loss at its value for a 2 km path. At 3.5 GHz and 99.9 % the formula gives 43.4 dB at 1 km but only 42.8 dB at 2 km, since the spread σcb shrinks from 4.30 to 4.01 dB as the distance term takes over. The cap wins, so the answer is 42.8 dB, which is also NTIA’s reference value.
Clutter loss, building entry loss or the simulator’s buildings?
Use clutter loss for an outdoor terminal whose surroundings you do not know. Add building entry loss (ITU-R P.2109) on top when the terminal is indoors. Waveshed’s simulator takes the deterministic route instead. It rasterises real building footprints into the terrain, so each building blocks the path where it stands. Do not add P.2108 to a run that already includes buildings, or the same buildings count twice.

Clutter loss is a statistical guess about the buildings you cannot see. Waveshed draws the terrain and the real building footprints between your antennas, so you can see which streets the signal reaches.

Simulate with real buildings →

Related guides

  • Including buildings — how the simulator turns real building footprints into obstructions
  • LOS vs RF — what a coverage run already models before you add any end correction

Sources & further reading

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