Fractional Programming for Communication Systems—Part I: Power Control and Beamforming

Abstract

Fractional programming (FP) refers to a family of optimization problems that involve ratio term(s). 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. Index Terms-Fractional programming (FP), quadratic transform, power control, beamforming, energy efficiency I. OVERVIEWO PTIMIZATION is a key aspect of communication system design [3], [4]. This two-part work explores the application of fractional programming (FP) in the design and optimization of communication systems. FP refers to a family of optimization problems containing ratio term(s). Its history can be traced back to an early paper on economic expansion [5] by von Neumann in 1937; it has since been studied extensively in broad areas in economics, management science, information theory, optics, graph theory, and computer science [6]- [8]. For example, FP has recently been applied in [9]-[12] to solve the energy efficiency maximization problem for wireless communication systems.

Spectral Efficiency and Energy Efficiency Tradeoff in Massive MIMO Downlink Transmission With Statistical CSIT

“…A total of K = 8 UTs are randomly distributed in the cell sector. The pathloss is set as −120 dB for all UTs [48]. The antenna array topology ULA is adopted for the BS and each UT k, with the numbers of antennas being M = 128 and N k = 4(∀k), respectively, and the spacing between antennas is a half wavelength.…”

Efficiency Maximization for UAV-Enabled Mobile Relaying Systems With Laser Charging

“…It cannot be directly solved by standard convex optimization techniques. Moreover, neither the Dinkelbach's transformation [43] nor the fractional programming technique [44] can be directly applied to solve this problem, since the former cannot deal with objective functions with multiple-ratio terms and the latter is not designed to handle coupling constraints. A feasible approach for problem (8) is the AO-based algorithm, which alternating between power optimization and trajectory optimization, however, no optimality (e.g., to stationary solutions) can be theoretically declared for such an algorithm as has been shown in [3], [45], [46], etc.…”

Energy Efficiency Optimization for Downlink Massive MIMO With Statistical CSIT

“…In this paper, Dinkelbach's algorithm is used to solve F (ℓ) 3 , owing to its advantage of not having additional constraints compared with Charnes-Cooper algorithm [34]. Specifically, F (ℓ) 3 is equivalently solved by a series of concave subproblems in the following…”

“…Note that the parametric problem in (17) required to be addressed in each iteration is concave, thereby, it can be handled by applying classical convex optimization approaches [35]. Moreover, it can be readily proved that the Dinkelbach-based method can converge to the globally optimal solution of the fractional problem F (ℓ) 3 [34]. We can conclude that the sequence of the objective values generated by F (ℓ) 3 converges, which follows from the convergence properties of MM method [33].…”