Link budgets and noise

Overview

A link budget is an accounting exercise in decibels. It starts with the power leaving the transmitter, adds gains, subtracts losses and compares what arrives with what the receiver needs. If the received signal clears the requirement with enough margin for fading and interference, the link closes. If not, something must change: power, antennas, bandwidth, modulation, coding or distance.

Noise sets the requirement. Every receiver has a floor set by thermal noise and by the noise its own circuits add. This hub explains where that floor comes from, how to build a budget on top of it, and how the Shannon bound connects SNR to the data rate a link can carry. It suits anyone sizing a link, choosing a radio module, or checking a vendor’s range claim.

Key ideas

Thermal noise and noise figure

Any resistor at a temperature above absolute zero produces random voltage, first described by Johnson and Nyquist in 1928. The available noise power is kTB, where k is Boltzmann’s constant, T the temperature and B the bandwidth. At the reference temperature of 290 K this is about −174 dBm/Hz, so a 1 MHz channel has a floor near −114 dBm and a 20 MHz channel near −101 dBm. Thermal noise grows in proportion to bandwidth. That is why wideband links need more received power.

Real receivers add noise. The noise figure NF is the factor, in dB, by which a stage degrades SNR. For a chain of stages, Friis’s 1944 cascade formula divides each later stage’s excess noise by the total gain ahead of it. The first stage therefore dominates. An LNA with 1 dB NF and 15 dB gain, followed by a mixer with 10 dB NF, gives a cascade NF of about 1.9 dB. Put a filter or cable with 2 dB loss in front of the LNA and the cascade rises to about 3.9 dB, because loss before the first gain adds directly. At lower frequencies, external noise from electrical equipment, lightning and, below about 100 MHz, the galaxy can exceed the receiver’s own noise. ITU-R Recommendation P.372 gives typical levels by environment.

Sensitivity and the budget

Receiver sensitivity is the weakest signal that still meets a stated error-rate target. In dBm it is −174 + 10 log10(B) + NF + SNRreq, where SNRreq is the SNR the demodulator and decoder need. For a 20 MHz channel, 7 dB NF and 10 dB required SNR, sensitivity is about −84 dBm. Halving the bandwidth or the required SNR improves it by 3 dB. A sensitivity figure means little without the bandwidth, data rate and error-rate target it was measured at.

The budget runs from transmitter to receiver. Transmit power plus antenna gain minus feeder loss is the EIRP. Subtract path loss, add receive antenna gain, subtract receive feeder and body losses, and you have the received power. The margin is received power minus sensitivity.

Margin, fading and interference

The margin pays for what the median budget leaves out. Shadowing by buildings and terrain varies slowly and is usually modelled as log-normal, with a standard deviation of several dB. Multipath fading varies quickly and can take the signal 20 dB or more below its mean for short periods. Bodies, vehicles, foliage and rain add more. How much margin you need depends on the availability target: a link that must work 99.9 % of the time needs far more than one that may drop for a few seconds and retry.

Interference behaves like extra noise when it is wideband and uncorrelated with the signal. The quantity that matters is then the signal to interference plus noise ratio (SINR). In a busy cellular or Wi-Fi network, interference from other cells or other networks often exceeds thermal noise. The receiver’s noise figure then matters less and frequency reuse, power control and scheduling matter more.

Shannon capacity

The Shannon capacity C = B log2(1 + SNR) is the most a channel with Gaussian noise can carry with arbitrarily low error rate. It sets a ceiling, not a design. Two regimes follow from it. At low SNR, capacity grows almost linearly with power and adding bandwidth helps little, because the noise grows with it. At high SNR, capacity grows linearly with bandwidth but only logarithmically with power: each extra 3 dB adds about one bit per second per hertz. Written in terms of energy per bit, reliable communication needs Eb/N0 above ln 2, about −1.6 dB, however much bandwidth is available. Modern LDPC and polar codes operate within a few dB of the bound, so most gains now come from more bandwidth, more antennas or less interference.

Where to start

Work through /learn/beginner/03-decibels-and-link-budgets/ and then /learn/beginner/04-noise-snr-and-capacity/. The project /projects/lorawan-link-budget-coverage/ builds a complete budget and coverage estimate. Keep /reference/decibels-and-link-budgets/ and /reference/capacity-and-spectral-efficiency/ open. Intermediate lessons on interference and system-level budgets are in preparation.

Tools and platforms

Common mistakes

• Mixing dB and dBm, or adding two powers in dBm.
• Using a sensitivity figure measured at a narrower bandwidth or a looser error-rate target than your link uses.
• Leaving out cable, connector, body and penetration losses.
• Budgeting for the median path loss and calling the result the cell edge.
• Ignoring man-made noise at low frequencies, or interference in licence-exempt bands.
• Quoting the Shannon bound as an achievable rate.

Going deeper

• J. B. Johnson, Thermal agitation of electricity in conductors, and H. Nyquist, Thermal agitation of electric charge in conductors, Physical Review 32(1), 1928.
• H. T. Friis, Noise figures of radio receivers, Proceedings of the IRE 32(7), 1944.
• H. T. Friis, A note on a simple transmission formula, Proceedings of the IRE 34(5), 1946.
• C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal 27(3), 1948.
• ITU-R Recommendations P.372 (radio noise) and P.525 (free-space attenuation).
• D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005, chapter 5 on capacity.