Editing Channel capacity (section)

===Bandlimited AWGN channel===
{{main|Shannon–Hartley theorem}}
[[File:Channel Capacity with Power- and Bandwidth-Limited Regimes.png|thumb|AWGN channel capacity with the power-limited regime and bandwidth-limited regime indicated. Here, <math>\frac{\bar{P}}{N_0}=1</math>; ''B'' and ''C'' can be scaled proportionally for other values.]]

If the average received power is <math>\bar{P}</math> [W], the total bandwidth is <math>W</math> in Hertz, and the noise [[power spectral density]] is <math>N_0</math> [W/Hz], the AWGN channel capacity is

:<math>C_{\text{AWGN}}=W\log_2\left(1+\frac{\bar{P}}{N_0 W}\right)</math> [bits/s],

where <math>\frac{\bar{P}}{N_0 W}</math> is the received signal-to-noise ratio (SNR). This result is known as the '''Shannon–Hartley theorem'''.<ref>{{cite book|title=The Handbook of Electrical Engineering|year=1996|publisher=Research & Education Association|isbn=9780878919819|page=D-149|url=https://books.google.com/books?id=-WJS3VnvomIC&q=%22Shannon%E2%80%93Hartley+theorem%22&pg=RA1-SL4-PA41}}</ref>

When the SNR is large (SNR ≫ 0&nbsp;dB), the capacity <math>C\approx W\log_2 \frac{\bar{P}}{N_0 W} </math> is logarithmic in power and approximately linear in bandwidth. This is called the ''bandwidth-limited regime''.

When the SNR is small (SNR ≪ 0&nbsp;dB), the capacity <math>C\approx \frac{\bar{P}}{N_0 \ln 2} </math> is linear in power but insensitive to bandwidth. This is called the ''power-limited regime''.

The bandwidth-limited regime and power-limited regime are illustrated in the figure.