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Intelecommunications, thecarrier-to-noise ratio, often writtenCNR orC/N, is thesignal-to-noise ratio (SNR) of amodulated signal. The term is used to distinguish the CNR of the radio frequencypassband signal from the SNR of an analogbase band message signal afterdemodulation. For example, with FM radio, the strength of the 100 MHzcarrier wave with modulations would be considered for CNR, whereas the audio frequency analogue message signal would be for SNR; in each case, compared to the apparent noise. If this distinction is not necessary, the term SNR is often used instead of CNR, with the same definition.

Digitally modulated signals (e.g.QAM orPSK) are basically made of twoCW carriers (theI and Q components, which are out-of-phase carriers). In fact, the information (bits or symbols) is carried by given combinations of phase and/or amplitude of the I and Q components. It is for this reason that, in the context of digital modulations, digitally modulated signals are usually referred to as carriers. Therefore, the term carrier-to-noise-ratio (CNR), instead of signal-to-noise-ratio (SNR), is preferred to express the signal quality when the signal has been digitally modulated.

HighC/N ratios provide good quality of reception, for example lowbit error rate (BER) of a digital message signal, or high SNR of an analog message signal.

The carrier-to-noise ratio is defined as the ratio of the received modulated carrier signalpowerC to the received noise powerN after the receiver filters:

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

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

${\displaystyle \mathrm{C}\mathrm{N}\mathrm{R}={\left(\frac{V_C}{V_N}\right)}^2}$,

where${\displaystyle V_C}$ and${\displaystyle V_N}$ are theroot mean square (RMS) voltage levels of the carrier signal and noise respectively.

C/N ratios are often specified indecibels (dB):

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

or in term of voltage:

${\displaystyle \mathrm{C}\mathrm{N}{\mathrm{R}}_{\mathrm{d}\mathrm{B}}=10{\log }_{10}{\left(\frac{V_C}{V_N}\right)}^2=20{\log }_{10}\left(\frac{V_C}{V_N}\right)}$

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

In the famousShannon–Hartley theorem, theC/N ratio is equivalent to theS/N ratio. TheC/N ratio resembles thecarrier-to-interference ratio (C/I,CIR), and thecarrier-to-noise-and-interference ratio,C/(N+I) orCNIR.

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 CNRestimation techniques are timely and important.

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Insatellite communications,carrier-to-noise-density ratio (C/N₀) is theratio of thecarrierpowerC to thenoise power densityN₀. When considering only thereceiver as a source of noise, it is calledcarrier-to-receiver-noise-density ratio.

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

The receiver noise power density,N₀, has dimension of power per frequency (units of watts perhertz, W/Hz). It can be written asN₀=kT (in joules or watts-second, J=W⋅s), the product of theBoltzmann constantk (in joules perkelvin) and thenoise temperatureT (in kelvins).

In thequotient between carrier power (in watts, W) and noise density (in W/Hz), the two units of wattcancel out, resulting in units of hertz (Hz). When expressed in logarithmic scale, the reference value for decibels, 1 Hz, is often denoted "dB-Hz".

• 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 orS/I)
• Signal-to-noise ratio (SNR orS/N)
• SINAD (ratio of signal-plus-noise-plus-distortion to noise-plus-distortion)

 This article incorporatespublic domain material fromFederal Standard 1037C.General Services Administration. Archived fromthe original on 2022-01-22. (in support ofMIL-STD-188).

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

• Noise (electronics)
• Engineering ratios
• Radio frequency propagation
• Radio resource management
• Interference

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