waterfilling

Waterfilling is a method used in information theory and communications to allocate a limited transmit power across multiple parallel channels in order to maximize the total achievable data rate under a total power constraint. The visualization treats each channel as a vessel with a base level set by its noise and channel gain; power is added like water, raising the level until a common “water line” is reached. Channels with poorer conditions receive little or no power, while better channels receive more.

For a system with K parallel Gaussian channels, each with an effective noise level η_i (which incorporates the channel gain and noise) the optimal power allocation P_i follows the rule P_i = max(0, μ − η_i), where μ is the water level chosen so that the sum of P_i equals the total available power P_total. In practice, η_i is often written as the inverse of the channel-to-noise ratio for channel i, so the allocation increases for channels with higher gains. The water level μ is determined by the total power constraint and the set of channel conditions.

Waterfilling also extends to more complex settings. In MIMO systems, the problem reduces to allocating power across the eigenmodes of the channel matrix after a suitable decomposition. In OFDM or wideband systems, it amounts to distributing power across subcarriers. The approach assumes channel state information at the transmitter; without CSI, power may be allocated uniformly or by other rules. Waterfilling provides the capacity-maximizing distribution for Gaussian channels under a sum-power constraint and is a standard result in communications theory.