Carrier-to-noise Ratio - Wikipedia

Signal-to-noise ratio of a modulated signal

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In telecommunications, the carrier-to-noise ratio, often written CNR or C/N, is the signal-to-noise ratio (SNR) of a modulated signal. The term is used to distinguish the CNR of the radio frequency passband signal from the SNR of an analog base band message signal after demodulation. For example, with FM radio, the strength of the 100 MHz carrier 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 or PSK) are basically made of two CW carriers (the I 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.

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

Definition

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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:

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

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

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

where V C {\displaystyle V_{C}} and V N {\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):

C N R d B = 10 log 10 ⁡ ( C N ) = C d B m − N d B m {\displaystyle \mathrm {CNR_{dB}} =10\log _{10}\left({\frac {C}{N}}\right)=C_{dBm}-N_{dBm}}

or in term of voltage:

C N R d B = 10 log 10 ⁡ ( V C V N ) 2 = 20 log 10 ⁡ ( V C V N ) {\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)}

Measurements and estimation

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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.

Carrier-to-noise density ratio

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In satellite communications, carrier-to-noise-density ratio (C/N0) is the ratio of the carrier power C to the noise power density N0. 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 decibels.

The receiver noise power density, N0, has dimension of power per frequency (units of watts per hertz, W/Hz). It can be written as N0=kT (in joules or watts-second, J=W⋅s), the product of the Boltzmann constant k (in joules per kelvin) and the noise temperature T (in kelvins).

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

See also

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• C/I: carrier-to-interference ratio
• Eb/N0 (energy per bit relative to noise power spectral density)
• Es/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)

References

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1. ^ Islam, A. K. M. Najmul; Lohan, E. S.; Renfors, M. (Mar 2008). "Moment based CNR estimators for BOC/BPSK modulated signal for Galileo/GPS". 2008 5th Workshop on Positioning, Navigation and Communication. pp. 129–136. doi:10.1109/WPNC.2008.4510366. ISBN 978-1-4244-1798-8. S2CID 8008857.

 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).

Further reading

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• 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

v t e Noise (physics and telecommunications)
General	Acoustic quieting Distortion Noise cancellation Noise control Noise measurement Noise power Noise reduction Noise temperature Phase distortion
Noise in...	Audio Buildings Electronics Environment Government regulation Human health Images Radio Rooms Ships Sound masking Transportation Video
Class of noise	Additive white Gaussian noise (AWGN) Atmospheric noise Background noise Brownian noise Burst noise Cosmic noise Flicker noise Gaussian noise Grey noise Infrasound Jitter Johnson–Nyquist noise (thermal noise) Pink noise Quantization error (or q. noise) Shot noise White noise Coherent noise Value noise Gradient noise Worley noise
Engineering terms	Channel noise level Circuit noise level Effective input noise temperature Equivalent noise resistance Equivalent pulse code modulation noise Impulse noise (audio) Noise figure Noise floor Noise shaping Noise spectral density Noise, vibration, and harshness (NVH) Phase noise Pseudorandom noise Statistical noise
Ratios	Carrier-to-noise ratio (C/N) Carrier-to-receiver noise density (C/kT) dBrnC Eb/N0 (energy per bit to noise density) Es/N0 (energy per symbol to noise density) Modulation error ratio (MER) Signal, noise and distortion (SINAD) Signal-to-interference ratio (S/I) Signal-to-noise ratio (S/N, SNR) Signal-to-noise ratio (imaging) Signal-to-interference-plus-noise ratio (SINR) Signal-to-quantization-noise ratio (SQNR) Contrast-to-noise ratio (CNR)
Related topics	List of noise topics Acoustics Colors of noise Interference (communication) Noise generator Spectrum analyzer Thermal radiation
Denoise methods	General Low-pass filter Median filter Total variation denoising Wavelet denoising 2D (Image) Gaussian blur Anisotropic diffusion Bilateral filter Non-local means Block-matching and 3D filtering (BM3D) Shrinkage Fields Denoising autoencoder (DAE) Deep Image Prior