Graph water injection theorem power distribution diagram
In the figure, the solid curve represents the reciprocal of the SNR corresponding to different frequencies within the channel bandwidth. A representation of the SNR is S/N, which is proposed in the Shannon formula C=Blog2(1+S/N). . When N is large, S/N is small, and according to noise power+signal power=constant, the available signal power is correspondingly small. At this time, the corresponding channel capacity C is small. The total channel capacity ∑C is correspondingly reduced because C=∑Ci. Realizing the maximum channel capacity is like injecting water into a bowl represented by a solid curve. The larger the signal-to-noise ratio, ie, the smaller the N, the more signal power is obtained. In the problem of power allocation, the channel capacity can only be maximized if the water filling theorem is satisfied. In the figure, when the bottom of the bowl is reached, that is, the N/S is the minimum, the power allocated by the channel is large, and the channel capacity can be maximized at this time. At this time, the signal to noise ratio is the highest. This is the famous water filling theorem.
The water injection algorithm is an optimal power allocation strategy. It can inject water separately in time, frequency and space. It is also possible to combine these types of water injection and optimize water injection. When the average signal-to-noise ratio is low, the channel capacity can be greatly improved by the water injection method, but the calculation is more complicated and is not very practical in reality.
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