Shannon Capacity Forulula

Shannon Capacity Forulula

Nyquist's formula indicates that, all other things being equal, doubling the bandwidth
doubles the data rate. Now consider the relationship among data rate, noise,
and error rate. The presence of noise can corrupt one or more bits. If the data rate is
increased, then the bits become "shorter" in time, so that more bits are affected by a
given pattern of noise. Thus, at a given noise level, the higher the data rate, the
higher the error rate.
Figure 2.9 is an example of the effect of noise on a digital signal. Here the
noise consists of a relatively modest level of background noise plus occasional larger
spikes of noise. The digital data can be recovered from the signal by sampling the
received waveform once per bit time. As can be seen, the noise is occasionally sufficient
to change a 1 to a 0 or a 0 to a 1.
All of these concepts can be tied together neatly in a formula developed by the
mathematician Claude Shannon. As we have just illustrated, the higher the data
rate, the more damage that unwanted noise can do. For a given level of noise, we
would expect that a greater signal strength would improve the ability to receive data
correctly in the presence of noise. The key parameter involved in this reasoning is