Many engineering problems that can be formulated
as constrained optimization problems result in solutions
given by a waterfilling structure; the classical example is the
capacity-achieving solution for a frequency-selective channel.
For simple waterfilling solutions with a single waterlevel and a
single constraint (typically, a power constraint), some algorithms
have been proposed in the literature to compute the solutions
numerically. However, some other optimization problems result in
significantly more complicated waterfilling solutions that include
multiple waterlevels and multiple constraints. For such cases, it
may still be possible to obtain practical algorithms to evaluate the
solutions numerically but only after a painstaking inspection of
the specific waterfilling structure. In addition, a unified view of
the different types of waterfilling solutions and the corresponding
practical algorithms is missing.
The purpose of this paper is twofold. On the one hand, it
overviews the waterfilling results existing in the literature from a
unified viewpoint. On the other hand, it bridges the gap between
a wide family of waterfilling solutions and their efficient implementation
in practice; to be more precise, it provides a practical
algorithm to evaluate numerically a general waterfilling solution,
which includes the currently existing waterfilling solutions and
others that may possibly appear in future problems.
CitationPérez Palomar, D.; Rodríguez Fonollosa, J. Practical algorithms for a family of waterfilling solutions. IEEE Transactions on Signal Processing, 2005, vol. 53, núm. 2, p. 686-695.
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