Water-filling algorithm: Difference between revisions

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The '''water-pouringfilling algorithm''' is a technique used in [[digital communications]] systems for allocating power among different channels in multicarrier schemes. It was described by R. C. Gallager in 1968<ref name="gallager">{{cite book |last=Gallager |first=R. C. |publisher=Wiley |year=1968 |title=Information Theory and Reliable Communications}}</ref> along with the '''water-pouringfilling theorem''' which proves its optimality for channels having [[Additive White Gaussian Noise]] (AWGN) and [[intersymbol interference]] (ISI).

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For this reason, it is a standard baseline algorithm for various digital communications systems, such as [[MIMO|MIMO wireless systems]].<ref>{{ cite patent

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| discuss =Talk:Water filling algorithm#Merge proposal: Water-pouring algorithm

| target =Water-filling algorithm

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| date =2025-07-23

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{{In use}}

'''Water filling algorithm''' is a general name given to the ideas in [[communication systems]] design and practice for [[adaptive equalizer|equalization]] strategies on [[channel (communications)|communications channels]]. As the name suggests, just as water finds its level even when filled in one part of a vessel with multiple openings, as a consequence of [[Pascal's law]], the amplifier systems in communications network repeaters, or receivers amplify each channel up to the required power level compensating for the channel impairments. See, for example, channel power allocation in [[MIMO]] systems.

==Single channel systems==

In a single-channel communication system the deamplification and loss present on them can be simplistically taken as attenuation by a percentage ''g'', then amplifiers restore the signal power level to the same value at transmission setup by operating at a gain of 1/ (1&nbsp;−&nbsp;''g''). E.g. if we experience 6&nbsp;dB attenuation in transmission, i.e. 75% loss, then we have to amplify the signal by a factor of 4''x'' to restore the signal to the transmitter levels.

==Multichannel systems==

Same ideas can be carried out in presence impairments and a multiple-channel system. Amplifier nonlinearity, crosstalk and power budgets prevent the use of these waterfilling algorithms to restore all channels, and only a subset can benefit from them.

==See also==

* [[Water-pouring algorithm]]

* [[Zero-forcing equalizer]]

* [[Robert Lucky]]

* [[Amplifier system]]

* [[EDFA]]

==References==

* Proakis, Digital Communication Systems, 4th Ed., McGraw Hill, (2001).

[[Category:Telecommunication theory]]

[[Category:Error detection and correction]]

[[Category:Information theory]]

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=Water-pouring algorithm=

The '''water-pouring algorithm''' is a technique used in [[digital communications]] systems for allocating power among different channels in multicarrier schemes. It was described by R. C. Gallager in 1968<ref name="gallager">{{cite book |last=Gallager |first=R. C. |publisher=Wiley |year=1968 |title=Information Theory and Reliable Communications}}</ref> along with the '''water-pouring theorem''' which proves its optimality for channels having [[Additive White Gaussian Noise]] (AWGN) and [[intersymbol interference]] (ISI).

For this reason, it is a standard baseline algorithm for various digital communications systems.<ref>{{ cite patent

| country = USA

| number = 6973122

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To allocate power, imagine pouring water into this container (the amount depends on the desired maximum average transmit power). After the water level settles, the largest amount of water is in the deepest sections of the container. This implies allocating more power to the channels with the most favourable SNR. Note, however, that the ratio allocation to each channel is not a fixed proportion but varies nonlinearly with the maximum average transmit power.

==See also==

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* [[Zero-forcing equalizer]]

{{cite journal |last= |first= |title= |journal= |volume= |year= |month= |page= |doi= }}

* [[Robert Lucky]]

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* [[EDFA]]

==References==

* Proakis, Digital Communication Systems, 4th Ed., McGraw Hill, (2001).

<references/>

{{telecomm-stub}}

[[Category:Telecommunications]]

[[Category:Error detection and correction]]

[[Category:Information theory]]

[[Category:Information theoryTelecommunications]]

{{Telecomm-stub}}

[[Category:Telecommunication theory]]