Carrier-to-Noise Density Ratio (C/N0) Explained

What is Carrier-to-Noise Density Ratio (C/N0)?

Carrier-to-noise density ratio (C/N0) is the ratio of carrier power to noise power density and denotes the strength of the power of carrier wave relative to the noise.

C/N0 is often used in calculating link budget, and it describes the clarity of signal.

Thus, the receiver should keep the value of C/N0 to the available level by reducing the loss of the receiver system.

Derivation of Carrier-to-Noise Density Ratio (C/N0)

Let’s assume the free space (imaginary space where no matter exists), the power of carrier wave \(C\) is

\[C = P_r = P_tG_tG_r\left(\frac{\lambda}{4\pi d}\right)^2\]

where \(P_t\) is the transmission power, \(G_t\) is the gain of transmission antenna, \(G_r\) is the gain of the reception antenna, \(P_r\) is the reception power, \(\lambda\) is wave length, and \(d\) is the distance between antennas.

Please refer to the following article for this derivation.


Also, noise power \(N\) is

\[N = kT_sB\]

where \(k\) is Boltzman constant, \(T_s\) is the system noise temperature, \(B\) is the bandwidth.

Thus, the carrier-to-noise ratio can be written as

\[\frac{C}{N} = \frac{P_tG_tG_r}{kT_sB}\left(\frac{\lambda}{4\pi d}\right)^2\]

where the noise power \(N\) is, using noise spectral density \(N_0\),

\[N = N_0B\]

C/N0 can be written as

\[\frac{C}{N_0} = \frac{P_tG_tG_r}{kT_s}\left(\frac{\lambda}{4\pi d}\right)^2\]

This is also converted to

\[\frac{C}{N_0} = \frac{\mathrm{EIRP}}{L_{fsp}}\frac{G_r}{T_s}\frac{1}{k}\]

EIRP meaning and calculation

Converting this equation to dB,

\[\mathrm{C/N_0} = \mathrm{EIRP}-L_{fsp}+G/T+228.6\]

Eb/N0 Explained