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Water-filling solutions play an important role in the designs for wirelesscommunications, e.g., transmit covariance matrix design. A traditional physicalunderstanding is to use the analogy of pouring water over a pool withfluctuating bottom. Numerous variants of water-filling solutions have beendiscovered during the evolution of wireless networks. To obtain the solutionvalues, iterative computations are required, even for simple cases with compactmathematical formulations. Thus, algorithm design is a key issue for thepractical use of water-filling solutions, which however has been given marginalattention in the literature. Many existing algorithms are designed on acase-by-case basis for the variations of water-filling solutions and/or withcomplex logics. In this paper, a new viewpoint for water-filling solutions isproposed to understand the problem dynamically by considering changes in theincreasing rates on different subchannels. This fresh viewpoint provides usefulmechanism and fundamental information in finding the optimization solutionvalues. Based on the new understanding, a novel and comprehensive method forpractical water-filling algorithm design is proposed, which can be used forsystems with various performance metrics and power constraints, even forsystems with imperfect channel state information (CSI).

New Viewpoint and Algorithms for Water-Filling Solutions in Wireless Communications