Some facts you may want to know about water-filling solutions

Optimizations for wireless communications have been greatly developed in the past two decades. The amount of the related research outputs is so enormous that summaries are becoming more and more desired. The authors believe that a revisit on the extensively studied topic to reveal some negligible problems is necessary and important for future research on this topic. Water-filling solutions are the most famous result in wireless network optimizations, but it may be a theoretical result once familiar and strange as many details in its derivation are neglected or omitted in the existing works. In this work, we investigate some easily overlooked facts for water-filling solutions e.g., turning off effects, related complex matrix derivatives and so on. These facts are very fundamental and important for the implementation of water-filling solutions. This work can give you a better understanding of water-filling solutions.