Carrier-to-noise ratio

<h2 id="definition">Definition</h2>
The carrier-to-noise ratio is defined as the ratio of the received modulated carrier signal <a href="/facts/Power_(physics)/mkaEyRnn">power</a> 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 <a href="/facts/Characteristic_impedance/oUg0mhah">impedance</a>, 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 <a href="/facts/Root_mean_square/Cfmg7dws">root mean square</a> (RMS) voltage levels of the carrier signal and noise respectively.
C/N ratios are often specified in <a href="/facts/Decibel/0LyxAPXh">decibels</a> (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)}

<h2 id="measurements-and-estimation">Measurements and estimation</h2>
The C/N ratio is measured in a manner similar to the way the <a href="/facts/Signal-to-noise_ratio/qohClhyG">signal-to-noise ratio</a> (S/N) is measured, and both specifications give an indication of the quality of a communications channel.
In the famous <a href="/facts/Shannon%E2%80%93Hartley_theorem/nlWW6VAy">Shannon–Hartley theorem</a>, the C/N ratio is equivalent to the S/N ratio. The C/N ratio resembles the <a href="/facts/Carrier-to-interference_ratio/lBQVMXmC">carrier-to-interference ratio</a> (C/I, CIR), and the <a href="/facts/Carrier-to-noise-and-interference_ratio/lBQVMXmC">carrier-to-noise-and-interference ratio</a>, C/(N+I) or CNIR.
C/N estimators are needed to optimize the receiver performance.<a class="footnote-ref" id="fnref:1" href="#fn:1">1</a> 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 <a href="/facts/Estimation/dsztTYcy">estimation</a> techniques are timely and important.

<h2 id="carrier-to-noise-density-ratio">Carrier-to-noise density ratio</h2>

In <a href="/facts/Satellite_communications/y5RXPMDT">satellite communications</a>, carrier-to-noise-density ratio (C/N0) is the <a href="/facts/Ratio/mFmhQt7T">ratio</a> of the <a href="/facts/Carrier_signal/ae98pBlY">carrier</a> <a href="/facts/Power_(physics)/mkaEyRnn">power</a> C to the <a href="/facts/Noise_power_density/WAGesbqr">noise power density</a> N0. When considering only the <a href="/facts/Receiver_(radio)/5olDTxkg">receiver</a> 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 <a href="/facts/Encoded/CSntvnEo">encoded</a> in the <a href="/facts/Signal_(electrical_engineering)/41YqUJ8c">signal</a> can be retrieved, given the amount of noise present in the received signal. The carrier-to-receiver noise density ratio is usually expressed in <a href="/facts/Decibels/0LyxAPXh">decibels</a>.
The receiver noise power density, N0, has dimension of power per frequency (units of watts per <a href="/facts/Hertz/6Wshj5qm">hertz</a>, W/Hz). It can be written as N0=kT (in joules or watts-second, J=W ⋅ s), the product of the <a href="/facts/Boltzmann_constant/5DIejyR3">Boltzmann constant</a> k (in joules per <a href="/facts/Kelvin/E3trzC4C">kelvin</a>) and the <a href="/facts/Noise_temperature/t3Ecsmg5">noise temperature</a> T (in kelvins).
In the <a href="/facts/Quotient/JekSq1Ko">quotient</a> between carrier power (in watts, W) and noise density (in W/Hz), the two units of watt <a href="/facts/Cancelling_out/8zP00Eyj">cancel out</a>, resulting in units of hertz (Hz). When expressed in logarithmic scale, the reference value for decibels, 1 Hz, is often denoted "<a href="/facts/DB-Hz/0LyxAPXh">dB-Hz</a>".

<h2 id="see-also">See also</h2>
<ul><li>C/I: <a href="/facts/Carrier-to-interference_ratio/lBQVMXmC">carrier-to-interference ratio</a></li>
<li><a href="/facts/Eb/N0/DU5sMhd6">Eb/N0</a> (energy per bit relative to noise power spectral density)</li>
<li><a href="/facts/Es/N0/DU5sMhd6">Es/N0</a> (energy per symbol relative to noise power spectral density)</li>
<li><a href="/facts/Signal-to-interference_ratio/lBQVMXmC">Signal-to-interference ratio</a> (SIR or S/I)</li>
<li><a href="/facts/Signal-to-noise_ratio/qohClhyG">Signal-to-noise ratio</a> (SNR or S/N)</li>
<li><a href="/facts/SINAD/gl00Pxox">SINAD</a> (ratio of signal-plus-noise-plus-distortion to noise-plus-distortion)</li></ul>

This article incorporates <a href="/facts/Copyright_status_of_works_by_the_federal_government_of_the_United_States/Q1jvr96g">public domain material</a> from <a href="https://web.archive.org/web/20220122224547/https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm">Federal Standard 1037C</a>. <a href="/facts/General_Services_Administration/Np3opv9x">General Services Administration</a>. Archived from <a href="https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm">the original</a> on 2022-01-22. (in support of <a href="/facts/MIL-STD-188/D5rsvdsW">MIL-STD-188</a>).

<h2 id="further-reading">Further reading</h2>
<ul><li><a href="https://web.archive.org/web/20160304080134/http://www.broadcom.com/collateral/wp/CMTS-WP101-R.pdf">Digital Transmission: Carrier-to-Noise Ratio, Signal-to-Noise Ratio, and Modulation Error Ratio</a> at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a> (archived March 4, 2016)</li>
<li><a href="https://insidegnss.com/measuring-gnss-signal-strength/">Measuring GNSS Signal Strength</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn: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. <a href="978-1-4244-1798-8" target="_blank">978-1-4244-1798-8</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
</ol>

Carrier-to-noise ratio open-in-new

Carrier-to-noise ratio