Carrier-to-noise ratio

The carrier-to-noise ratio is defined as the ratio of the received modulated carrier signal power C to the received noise power N after the receiver filters:

${\displaystyle \mathrm {CNR} ={\frac {C}{N}}}$ .

When both carrier and noise are measured across the same impedance, this ratio can equivalently be given as:

${\displaystyle \mathrm {CNR} =\left({\frac {V_{C}}{V_{N}}}\right)^{2}}$ ,

where ${\displaystyle V_{C}}$  and ${\displaystyle V_{N}}$  are the root mean square (RMS) voltage levels of the carrier signal and noise respectively.

C/N ratios are often specified in decibels (dB):

${\displaystyle \mathrm {CNR_{dB}} =10\log _{10}\left({\frac {C}{N}}\right)=C_{dBm}-N_{dBm}}$ 

or in term of voltage:

${\displaystyle \mathrm {CNR_{dB}} =10\log _{10}\left({\frac {V_{C}}{V_{N}}}\right)^{2}=20\log _{10}\left({\frac {V_{C}}{V_{N}}}\right)}$ 

The C/N ratio is measured in a manner similar to the way the signal-to-noise ratio (S/N) is measured, and both specifications give an indication of the quality of a communications channel.

In the famous Shannon–Hartley theorem, the C/N ratio is equivalent to the S/N ratio. The C/N ratio resembles the carrier-to-interference ratio (C/I, CIR), and the carrier-to-noise-and-interference ratio, C/(N+I) or CNIR.

C/N estimators are needed to optimize the receiver performance.^[1] Typically, it is easier to measure the total power than the ratio of signal power to noise power (or noise power spectral density), and that is why CNR estimation techniques are timely and important.

In satellite communications, carrier-to-noise-density ratio (C/N₀) is the ratio of the carrier power C to the noise power density N₀, expressed in dB-Hz. When considering only the receiver as a source of noise, it is called carrier-to-receiver-noise-density ratio.

It determines whether a receiver can lock on to the carrier and if the information encoded in the signal can be retrieved, given the amount of noise present in the received signal. The carrier-to-receiver noise density ratio is usually expressed in dB-Hz.

The noise power density, N₀=kT, is the receiver noise power per hertz, which can be written in terms of the Boltzmann constant k (in joules per kelvin) and the noise temperature T (in kelvins).

• C/I: carrier-to-interference ratio
• E_b/N₀ (energy per bit relative to noise power spectral density)
• E_s/N₀ (energy per symbol relative to noise power spectral density)
• Signal-to-interference ratio (SIR or S/I)
• Signal-to-noise ratio (SNR or S/N)
• SINAD (ratio of signal-plus-noise-plus-distortion to noise-plus-distortion)

  This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22. (in support of MIL-STD-188).

• Digital Transmission: Carrier-to-Noise Ratio, Signal-to-Noise Ratio, and Modulation Error Ratio at the Wayback Machine (archived March 4, 2016)
• Measuring GNSS Signal Strength