Practical algorithms for a family of waterfilling solutions

By D. P. Palomar, Javier Rodríguez Fonollosa. IEEE Transactions on Signal Processing, 2005

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Optimum power allocation for parallel Gaussian channels with arbitrary input distributions (2006, background): “Power allocations that can be viewed as multidimensional waterfillings have been derived as solutions to a number of constrained optimization problems involving various uncoded performance criteria [13]–[ 20 ].”
MIMO Transceiver Design via Majorization Theory (2007, methodology): “The numerical evaluation of such waterfilling solutions can be done efficiently in practice either by bisection or by hypothesis testing as explored in detail in [108, 112].”
Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems (2013, background): “Note that, in the presence of the power budget constraint only (as in [23], [29], [30]), reduces to a scalar quantity such that , whose solution can be obtained using the classical bisection algorithms (or the methods in [42]).”
Convex Optimization in Signal Processing and Communications (2009, unknown): “, [65] for practical algorithms to compute the waterlevel μq,X in (1.”
Framework for Link-Level Energy Efficiency Optimization with Informed Transmitter (2011, methodology): “The solution is water-filling, wher e the water level is a function of the dual variable, which can be computed using known algorithms [27].”