How do I calculate the carrier to noise ratio at the receiver from the link budget parameters?
C/N Calculation Engineering
The carrier-to-noise ratio is the central figure of merit in any communication link budget, directly determining the achievable data rate, bit error rate, and link availability.
| Parameter | Free Space | Urban | Indoor |
|---|---|---|---|
| Path Loss Model | Friis (1/r²) | Okumura-Hata | IEEE 802.11 |
| Fading Margin | 0 dB | 10-30 dB | 5-15 dB |
| Multipath | None | Severe | Moderate-severe |
| Typical Range | Line of sight | 1-30 km | 10-100 m |
| Shadow Fading (σ) | 0 dB | 6-12 dB | 3-8 dB |
Margin Allocation
A professional link budget is organized as a spreadsheet with the following sections: Transmitter section: transmitter power (dBW), feed/cable loss (dB), antenna gain (dBi), EIRP (dBW). Path section: frequency (GHz), distance (km), FSPL (dB), atmospheric absorption (dB), rain attenuation (dB), scintillation (dB), pointing losses (dB), polarization mismatch (dB), total path loss (dB). Receiver section: antenna gain (dBi), antenna noise temperature (K), feed/cable loss (dB), receiver noise figure (dB), system noise temperature (K), G/T (dB/K), noise bandwidth (MHz), noise power (dBW), received signal power (dBW), C/N (dB). Performance section: required Eb/No (dB), spectral efficiency (bits/s/Hz), required C/N (dB), link margin (dB). Each parameter has a nominal value and a worst-case value. The link budget is calculated for both conditions. The worst-case margin must be positive for the design to be acceptable.
- Performance verification: confirm specifications against the application requirements before finalizing the design
- Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
- Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades
Propagation Modeling
For a satellite repeater system: the end-to-end C/N is determined by both the uplink (earth station to satellite) and downlink (satellite to earth) C/N values: 1/(C/N)_total = 1/(C/N)_up + 1/(C/N)_down + 1/(C/N)_intermod (for a transponder operating in multicarrier mode). In dB: (C/N)_total is approximately 1-2 dB less than the weaker of uplink and downlink C/N. Design strategy: balance the uplink and downlink C/N so neither is significantly weaker than the other. Typical design: uplink C/N is 5-10 dB higher than downlink C/N (uplink earth station has high EIRP and the satellite receives with moderate G/T; downlink satellite has limited EIRP and the ground VSAT has moderate G/T). The downlink is usually the limiting path.
Frequently Asked Questions
What is the difference between C/N and SNR?
C/N (carrier-to-noise ratio) is measured at the receiver input or IF stage, before demodulation. It is the ratio of the modulated carrier power to the noise power in the receiver bandwidth. SNR (signal-to-noise ratio) is measured after demodulation, at the baseband output. For digital systems: SNR after a matched filter equals C/N only if the filter bandwidth equals the symbol rate (matched condition). For analog FM systems: SNR after demodulation is much higher than C/N due to FM processing gain. In practice: C/N is the standard metric in RF link budgets; SNR is used in audio/video quality assessment after demodulation.
How do I account for interference in the C/N calculation?
Replace C/N with C/(N+I) or equivalently SINR: C/(N+I) = C / (N + I_total), where I_total is the sum of all interference powers at the receiver. In dB: C/(N+I) = C - 10×log10(N + I). If the interference sources are known: calculate each interferer signal level at the receiver (using a separate link budget for each interferer), sum them (in linear), and add to the noise. Common interference sources in satellite links: adjacent satellite interference (C/I specified by coordination agreements, typically >25 dB), cross-polarization interference (antenna cross-pol discrimination >25 dB), and terrestrial interference (particularly at C-band: 5G deployment conflicts). The overall C/(N+I): 1/(C/(N+I)) = 1/(C/N) + 1/(C/I_1) + 1/(C/I_2) + ...
Can C/N be negative in dB?
Yes. A negative C/N (in dB) means the carrier power is below the noise power. The signal is buried in noise. For uncoded narrowband systems: this means the signal cannot be detected. For systems with processing gain: signals below the noise floor can be detected. Spread spectrum: a CDMA signal can operate at C/N = -10 to -20 dB because the despreading process provides 10-20 dB of processing gain. GPS: the received signal is at -130 dBm in a 2 MHz bandwidth, giving C/N ≈ -17 dB. After despreading (10.23 MHz chip rate / 50 bps data rate = 53 dB processing gain): the effective Eb/No ≈ 36 dB (far above the minimum for detection). For coded systems: modern LDPC codes can operate at C/N as low as -2 to -3 dB (in the code bandwidth), enabling near-Shannon-limit performance.