Water-filling solutions play an important role in the designs for wireless communications, e.g., transmit covariance matrix design. A traditional physical understanding is to use the analogy of pouring water over a pool with fluctuating bottom. Numerous variants of water-filling solutions have been discovered during the evolution of wireless networks. To obtain the solution values, iterative computations are required, even for simple cases with compact mathematical formulations. Thus, algorithm design is a key issue for the practical use of water-filling solutions, which however has been given marginal attention in the literature. Many existing algorithms are designed on a case-by-case basis for the variations of water-filling solutions and/or with complex logics. In this paper, a new viewpoint for water-filling solutions is proposed to understand the problem dynamically by considering changes in the increasing rates on different subchannels. This fresh viewpoint provides a useful mechanism and fundamental information for finding the optimization solution values. Based on this new understanding, a novel and comprehensive method for practical water-filling algorithm design is proposed, which can be used for systems with various performance metrics and power constraints, even for systems with imperfect channel state information (CSI).

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无线通信中注水解决方案的新观点和算法

加水解决方案在无线通信设计中发挥着重要作用，例如传输协方差矩阵设计。传统的物理理解是使用将水倒在底部波动的水池上的类比。在无线网络的发展过程中，已经发现了许多不同的注水解决方案。为了获得解值，需要迭代计算，即使对于具有紧凑数学公式的简单情况也是如此。因此，算法设计是注水解决方案实际使用的关键问题，但在文献中却很少受到关注。许多现有算法是根据具体情况设计的，用于注水解决方案的变化和/或具有复杂的逻辑。在本文中，提出了一种新的注水解决方案，通过考虑不同子通道上增加速率的变化来动态理解问题。这种新观点为寻找优化解值提供了有用的机制和基本信息。基于这种新的理解，提出了一种新颖而全面的实用注水算法设计方法，该方法可用于具有各种性能指标和功率约束的系统，甚至是信道状态信息 (CSI) 不完善的系统。