## Channel capacity restriction due to noise – the Shannon–Hartley theorem

#### As the number of symbol states M increases, the ability of the receiver to distinguish between symbols in the presence of noise and/or interference/distortion decreases. Hence the ratio of signal power S to noise power N will be a crucial factor in determining how many symbol states can be utilized and still achieve error-free communication.

#### The 'duration' of each symbol is also key in determining the noise tolerance of a receiver system, with longer symbols giving the receiver more time to average out the effects of noise than shorter symbols. The combined effects of finite bandwidth B and finite signal to noise ratio S/N on channel capacity are governed by a very famous relationship known as the Shannon–Hartley capacity limit. The mathematical basis for this expression was first put forward in Shannon (1948a, 1948b) |

#### The Shannon–Hartley capacity limit for error-free communication is given by: #### Channel capacity C = B.log2(S / N + 1) bits/second