B.5 SIGNAL-TO-NOISE RATIO

In communications, we are not just interested in the strength of a signal, but we are also interested in the noise that is present. For example, a strong signal in the presence of strong noise may not be much more useful than a weak signal in the presence of weak noise. We are therefore interested in maximizing the signal while minimizing the noise. The measure most commonly used to describe this is the signal-to-noise ratio (SNR):

S N R = \frac{S}{N}

(B.10)

where S is the signal power and N is the noise power.

In decibels (see Appendix C), the SNR is:

{S N R}_{d B} = 10 \log_{10} (\frac{S}{N})

(B.11)

In most communications systems, noise is modeled as random additive Gaussian white noise (AGWN), and SNR is calculated using average signal and noise powers measured over a specified bandwidth.