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 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:
.
When both carrier and noise are measured across the same
impedance
, this ratio can equivalently be given as:
,
where
and
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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/95a3d7d4316cdb7f89cbb0c8e02c523ab44a0f05)
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)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a44291e43d17230a5f1c53d55d0ff042b998ecd)
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/N
0
) is the
ratio
of the
carrier
power
C
to the
noise power density
N
0
, 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,
N
0
=
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).
See also
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References
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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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]
Noise
(physics and telecommunications)
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General
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Noise in...
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Class of noise
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Engineering
terms
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Ratios
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Related topics
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Denoise
methods
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