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What rain, air and walls really cost above 10 GHz

Above 10 GHz, the street costs far more than the sky. On a 1 km link at 28 GHz, free space takes 121.4 dB. A heavy shower of 25 mm/h adds 4.6 dB and the air another 0.1 dB. The buildings around the receiver add 32.7 dB, and one outside wall adds 20.2 dB more. Those last two are medians, and half of all locations do worse.

Each of those numbers comes from a free calculator that implements one ITU-R recommendation and shows its formula. These are the seven used in this post:

• Free-space path loss calculator the 121.4 dB baseline every other term is added to
• Rain attenuation calculator (ITU-R P.838) specific attenuation of rain from rain rate, frequency and polarisation
• Atmospheric gas attenuation calculator (ITU-R P.676) oxygen and water vapour, line by line from 1 to 1000 GHz
• Cloud and fog attenuation calculator (ITU-R P.840) fog in dB/km and the slant path through a cloud layer
• Clutter loss calculator (ITU-R P.2108) the statistical loss from buildings and trees around one terminal
• Building entry loss calculator (ITU-R P.2109) outdoor to indoor, for traditional and thermally efficient buildings
• Vegetation attenuation calculator (ITU-R P.833) loss through woodland, with a measured ceiling

What does a 28 GHz link lose on its way into a house?

Take a fixed wireless link at 28 GHz from a rooftop antenna to a house 1 km away. The chart stacks every loss the calculators know about, in the order the signal meets them. Each bar starts where the previous one ended, so the right end of the last bar is the total.

Free space is the biggest single term, and no calculator can make it smaller. Of the 57.6 dB on top of it, 52.9 dB come from the buildings around the house and the wall the signal has to cross. Rain and air together add 4.7 dB. On this link, planning starts at the receiver, not in the sky.

The rain bar is pessimistic on purpose. It assumes the same 25 mm/h along the whole kilometre, while ITU-R P.530 shortens the path to an effective length because heavy rain cells are small. The clutter bar counts one end only, the house, because the rooftop antenna stands above its surroundings.

Why does the loss climb so steeply above 10 GHz?

Because the wavelength shrinks towards the size of what floats in the air. It is 3 cm at 10 GHz and about 1 cm at 28 GHz, only a few times the size of a large raindrop. Drops that a 3 GHz wave hardly notices start to absorb and scatter it. Gas molecules add their own resonances on top. The chart shows each effect per kilometre, on one scale.

Rain dominates almost everywhere a link would sensibly run. At 25 mm/h it costs 0.70 dB/km at 10 GHz, 4.62 dB/km at 28 GHz and 10.1 dB/km at 60 GHz. Above 100 GHz the curve levels off just under 13 dB/km. The gases stay below 0.2 dB/km from 1 to 45 GHz, even at the water-vapour line near 22 GHz. Then the oxygen band takes them to 14.7 dB/km at 60 GHz, and water vapour to 28.3 dB/km at 183 GHz.

When does rain decide whether a link closes?

When the margin is thin and the frequency is high. At 28 GHz a cloudburst of 100 mm/h costs 17.7 dB/km, almost four times as much as the 25 mm/h shower. Link planners therefore size the fade margin for the rain rate exceeded during 0.01 % of an average year. That is about 53 minutes, read from the ITU-R P.837 maps for the site.

Polarisation helps a little. Falling drops are flattened, so they attenuate horizontal waves more than vertical ones. At 28 GHz and 25 mm/h that is 4.62 dB/km against 3.89 dB/km. The calculator gives the specific attenuation and the loss over uniform rain. The step to a real fade statistic, with an effective path length, is ITU-R P.530 for terrestrial links and P.618 for satellites. The calculator’s rain-zone presets come from the superseded P.837-1 table and are labelled as historical.

Do oxygen and water vapour matter outside the 60 GHz band?

Rarely, on terrestrial links. At 28 GHz the air at sea level costs 0.10 dB/km, a tenth of a decibel over our kilometre. Near 60 GHz the picture changes. At 14.7 dB/km the band suits short links where it helps that the signal dies off quickly. The calculator takes pressure, temperature and humidity and applies ITU-R P.676-13 line by line. It covers terrestrial paths only. Slant paths to satellites are out of scope.

How much do clouds and fog add?

Less than rain, but not nothing at millimetre waves. Thick fog holding 0.5 g/m³ of liquid water costs 0.26 dB/km at 28 GHz and 2.31 dB/km at 100 GHz, at 10 °C. Medium fog holds a tenth of that water and costs a tenth as much. On a satellite link at 28 GHz, a cloud layer with 0.6 kg/m² of water costs 0.37 dB straight up and 0.75 dB at 30° elevation, because the slant path crosses twice as much cloud.

One detail surprises people. On the slant path, ITU-R P.840-9 evaluates the water at a fixed 273.75 K and corrects the result empirically. The slant result therefore does not depend on the temperature you enter. Temperature only matters in the fog mode.

Why do clutter and walls cost more than the whole kilometre of air?

Because they belong to the place, not to the air. ITU-R P.2108 treats the buildings and trees around a terminal as a statistical loss, since nobody knows the layout of every street. At 28 GHz and 1 km it is 32.7 dB at 50 % of locations and 38.1 dB at 90 %. At 3.5 GHz the median is 30.1 dB, barely less. The clutter term hardly depends on frequency.

Walls depend on it much more. ITU-R P.2109 gives building entry loss as a distribution, for two classes of building. At 28 GHz and horizontal incidence, a traditional building costs 20.2 dB at the median. A thermally efficient one, with metallised glass and foil-backed panels, costs 41.7 dB. At 3.5 GHz the same medians are 15.7 dB and 30.9 dB. At 90 % probability the thermally efficient building reaches 66.0 dB at 28 GHz, more than any rain fade over a kilometre.

What do trees cost at millimetre waves?

A lot per metre. ITU-R P.833-10 gives woodland a typical specific attenuation of about 5.6 dB per metre of trees at 28 GHz, against 0.48 dB/m at 2.4 GHz. The curve is a typical one, and the calculator shows it with a ±20 % band, roughly trees in leaf and without. Five metres of crown would cost 28 dB at that rate.

The loss does not grow forever. It saturates at a measured maximum attenuation, and the three campaigns P.833 fits that maximum to ran between about 100 MHz and 2.2 GHz. At 2 GHz, 20 m of woodland costs 7.1 dB with the St Petersburg fit, whose ceiling there is 33.4 dB. At 28 GHz any ceiling is an extrapolation. Plan around the trees rather than through them.

Where do the formulas stop and the map take over?

Every term above assumes there is a path to attenuate. Whether a ridge or a block of houses cuts the line of sight first is a question of terrain, and that is what the coverage simulator answers, with line of sight and ITM over real elevation data. Start there, then add the losses from the atmosphere and environment calculators on top.