SNR vs CNR: Signal-to-Noise Ratio and Carrier-to-Noise Ratio Explained

This article clarifies the difference between Signal-to-Noise Ratio (SNR) and Carrier-to-Noise Ratio (CNR), both crucial concepts in telecommunications and RF engineering.

What is C/N Ratio (CNR)?

CNR, short for Carrier-to-Noise Ratio, is measured after modulation. It represents the power of the carrier signal relative to the power of the noise in the channel.

What is S/N Ratio (SNR)?

SNR, or Signal-to-Noise Ratio, is measured before modulation. It reflects the power of the original signal compared to the power of the noise affecting it.

SNR Equation

The S/N ratio can be mathematically expressed as:

S/N = Psignal/Pnoise = [Asig(rms)/Anoise(rms)]²

In decibels (dB), the formula is:

(S/N)dB= 10 log(Psignal/Pnoise)

Both CNR and SNR are commonly expressed in decibels (dB).

Relation Between C/N Ratio (CNR) and Eb/N0 Ratio

Eb/N0 (Energy per bit to noise power spectral density ratio) is related to CNR as follows:

Eb/N0 = ((C/Fb )/ (N/BW))

Where:

• Fb is the bit rate.
• C is the total carrier power.
• N is the total noise power.
• BW is the bandwidth of the modulated signal.

Eb/N0 and S/N Ratio for WiMAX

The following table illustrates the Eb/N0 and S/N ratios required for various Modulation and Coding Schemes (MCS) used in WiMAX systems:

Practical Applications

Understanding SNR vs CNR is crucial for RF field engineers. It aids in analyzing complex power spectrums using spectrum analyzers and interpreting readings obtained from satellite modems used in VSAT (Very Small Aperture Terminal) systems.