  This two-part paper explores the use of FP in the design and optimization of
communication systems. Part I of this paper focuses on FP theory and on solving
continuous problems. The main theoretical contribution is a novel quadratic
transform technique for tackling the multiple-ratio concave-convex FP
problem--in contrast to conventional FP techniques that mostly can only deal
with the single-ratio or the max-min-ratio case. Multiple-ratio FP problems are
important for the optimization of communication networks, because system-level
design often involves multiple signal-to-interference-plus-noise ratio terms.
This paper considers the applications of FP to solving continuous problems in
communication system design, particularly for power control, beamforming, and
energy efficiency maximization. These application cases illustrate that the
proposed quadratic transform can greatly facilitate the optimization involving
ratios by recasting the original nonconvex problem as a sequence of convex
problems. This FP-based problem reformulation gives rise to an efficient
iterative optimization algorithm with provable convergence to a stationary
point. The paper further demonstrates close connections between the proposed FP
approach and other well-known algorithms in the literature, such as the
fixed-point iteration and the weighted minimum mean-square-error beamforming.
The optimization of discrete problems is discussed in Part II of this paper.
