This paper explores the application of fractional programming (FP) in communication system design, focusing on power control, beamforming, and energy efficiency maximization. The main theoretical contribution is a novel quadratic transform technique for solving multiple-ratio concave-convex FP problems, which decouples the numerator and denominator of each ratio term. This technique is particularly useful for coordinated resource optimization in wireless cellular networks. The paper demonstrates that the proposed quadratic transform can significantly facilitate the optimization involving ratios by transforming nonconvex problems into a sequence of convex problems, leading to an efficient iterative optimization algorithm with provable convergence to a stationary point. The paper also discusses the connections between the proposed FP approach and other well-known algorithms, such as fixed-point iteration and weighted minimum mean-square-error beamforming. The discrete case, which is more challenging, is addressed in Part II of the paper.This paper explores the application of fractional programming (FP) in communication system design, focusing on power control, beamforming, and energy efficiency maximization. The main theoretical contribution is a novel quadratic transform technique for solving multiple-ratio concave-convex FP problems, which decouples the numerator and denominator of each ratio term. This technique is particularly useful for coordinated resource optimization in wireless cellular networks. The paper demonstrates that the proposed quadratic transform can significantly facilitate the optimization involving ratios by transforming nonconvex problems into a sequence of convex problems, leading to an efficient iterative optimization algorithm with provable convergence to a stationary point. The paper also discusses the connections between the proposed FP approach and other well-known algorithms, such as fixed-point iteration and weighted minimum mean-square-error beamforming. The discrete case, which is more challenging, is addressed in Part II of the paper.