How do SNR, Eb/N0 and channel capacity relate?
Signal-to-noise ratio (SNR) is signal power divided by noise power in a stated bandwidth. Digital links are often specified by Eb/N0, energy per bit over noise spectral density, which relates to SNR by SNR = (Eb/N0)·(Rb/B). Shannon’s theorem bounds error-free capacity at C = B·log2(1 + SNR).[1]
What is C/N0?
Carrier-to-noise-density ratio C/N0 (dB-Hz) is bandwidth-independent: C/N0 = Pr(dBm) + 174 − NF at 290 K. Then SNR = C/N0 − 10·log10(B) and Eb/N0 = C/N0 − 10·log10(Rb). GNSS receivers commonly report C/N0 near 35–50 dB-Hz.
What does the Shannon limit say?
As bandwidth grows without limit, the minimum Eb/N0 for reliable communication approaches ln 2, or −1.59 dB.[1] Practical coded systems with LDPC or turbo codes operate within about 1 dB of capacity at moderate spectral efficiency.
What SNR does a modulation need?
It depends on modulation, coding and target error rate. Uncoded BPSK needs about 9.6 dB Eb/N0 for a bit error rate of 10−5; higher-order QAM needs more. Standards specify sensitivity tests at a defined packet or bit error rate. See modulation and sensitivity.[2]
Frequently asked questions
Is SNR the same as CNR?
Often used interchangeably; CNR usually refers to the RF carrier before demodulation, SNR after.
What is Eb/N0 in dB?
10·log10 of the ratio of bit energy to noise spectral density.
Can a link work below 0 dB SNR?
Yes, spread-spectrum systems such as GPS operate below 0 dB SNR before despreading.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “A Mathematical Theory of Communication”. C. E. Shannon, Bell System Technical Journal, vol. 27. 1948.
- “Wireless Communications: Principles and Practice, 2nd ed.”. T. S. Rappaport, Prentice Hall. 2002.