Waterfilling algorithm

Power allocation for the maximization of sum rate in parallel Gaussian channels

% the water-filling process
% x: a vector with each component representing noise power
% P: total power
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% The returned vector p maximizes the total sum rate given by
% sum(log(1 + p./x)), subject to the power constraint sum(p)== P, p>=0.
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% The return a vector p also minimizes
% norm(p+x)
% subject to the constraints
% sum(p)==P; p>=0
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% The second output "level" is the water level
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% Sample usage:
% Three parallel Gaussian channels with noise powers 1, 2 and 3.
% The total power is 2.
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% >> waterfill([1 2 3],2)
% ans =
% 1.5000 0.5000 0
%
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% Author: Kenneth Shum, 2010
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% Reference:
% T. M. Cover and J. A. Thomas, "Elements of Information Theory", John Wiley & Sons, 2006