apsis-book/content/concepts/rf/link-budget.md

title	tags	summary
Link budget	link-budget, eirp, g-t, fspl, margin, rain	The arithmetic of whether a signal arrives strong enough to be used, and every term that turns a comfortable design into an impossible one.

Link budget

A link budget is the addition of every gain and loss between two antennas, compared with the power needed to be heard. It is arithmetic, but it is arithmetic on quantities that are all uncertain, and the margin left over is the only thing standing between a design and an outage.

Definition

The received power at the far end is

P_r = EIRP * G_t / L

with L the total propagation and implementation loss. The link closes when P_r exceeds the sensitivity of the receiver, and the link margin is the difference in decibels.

Every term is a ratio, so the budget is written in decibels throughout:

EIRP = P_t + G_t - L_feeder
P_r  = EIRP + G_r - L_space - L_polarisation - L_pointing
margin = P_r - sensitivity

The two that decide the result are free space loss, which is fixed by geometry, and the losses that are not: rain, pointing, polarisation mismatch.

Mathematics

Free space loss

The loss grows with the fourth power of distance and with the square of frequency:

L_fs = (4 pi d f / c)^2

in linear units, or in decibels,

L_fs(dB) = 92.45 + 20 log10 d_km + 20 log10 f_GHz

The fourth power is why doubling the frequency costs six decibels and doubling the distance costs six. A constellation at 550 km versus one at 1100 km has twelve decibels less margin for the same equipment, which is more than a doubling of the transmit power recovers, because doubling power is only three decibels.

Polarisation loss

An antenna receives a polarisation close to its own. A mismatch of an angle psi costs

L_pol = -log10( cos^2 psi )   dB

which is small below a few degrees and large beyond thirty. A tilted heliostat or a rotating spacecraft body can put a link over this threshold during a pass, and this is a common cause of an outage that appears only in part of the orbit.

Rain attenuation

Attenuation from rain at frequencies above 10 GHz is significant. It scales roughly with f^0.75 up to about 30 GHz and is then given by the specific attenuation gamma times the path length through the rain cell. The design figure is not the average attenuation but the value exceeded for a stated fraction of the worst hour in a year, because the budget is closed against the rain, not against the median.

Pointing and pointing loss

Pointing loss is the amount of beam that misses. It is small when the ground station tracks a narrow beam well and large when a wide beam is used to reach a mobile user, where the beam is pointed at the user rather than at a fixed station.

Margin

Margin is what is left after every term. What it is spent on depends on what was left out: a modest margin covers pointing jitter and small fades; it does not cover a rain cell that was sized from an average.

Unit conventions

• Power in decibels relative to one milliwatt, abbreviated dBm.
• Gains and losses in decibels.
• Distances in kilometres, frequencies in gigahertz, which is the form the free space formula is usually written in.
• EIRP in dBW when the figure is compared with a spacecraft power, dBm when with a receiver.

Applicability

A budget computed with average losses over a terrain and an average rain rate does not close a link. The two terms that have to be exceeded rather than averaged are rain and pointing, and they are the two that cause outages in systems whose budget was signed off.

Above roughly 30 GHz the rain attenuation keeps rising and the fade margin required becomes large enough to dominate the hardware. This is the reason the geostationary bands fill the sky below about 10 GHz and the higher bands are used where rain is rare or where the link can afford a large antenna.

A budget does not account for interference, which is not a loss but a corruption; it needs interference treated separately.

Standards

• Free space loss and the link budget convention: ITU-R recommendations on radiowave propagation and on the satellite broadcasting and telecommunications services
• Rain attenuation: ITU-R P.838 and P.618
• Regional rain rate data: ITU-R P.837

See also

• doppler-and-rate for what is measured once the link closes
• atmospheric-propagation for the medium the budget travels through
• constellations for how the budget sets the orbital shell