Fractional Programming for Communication Systems--Part II: Uplink Scheduling via Matching (1802.10197v2)

Abstract: This two-part paper develops novel methodologies for using fractional programming (FP) techniques to design and optimize communication systems. Part I of this paper proposes a new quadratic transform for FP and treats its application for continuous optimization problems. In this Part II of the paper, we study discrete problems, such as those involving user scheduling, which are considerably more difficult to solve. Unlike the continuous problems, discrete or mixed discrete-continuous problems normally cannot be recast as convex problems. In contrast to the common heuristic of relaxing the discrete variables, this work reformulates the original problem in an FP form amenable to distributed combinatorial optimization. The paper illustrates this methodology by tackling the important and challenging problem of uplink coordinated multi-cell user scheduling in wireless cellular systems. Uplink scheduling is more challenging than downlink scheduling, because uplink user scheduling decisions significantly affect the interference pattern in nearby cells. Further, the discrete scheduling variable needs to be optimized jointly with continuous variables such as transmit power levels and beamformers. The main idea of the proposed FP approach is to decouple the interaction among the interfering links, thereby permitting a distributed and joint optimization of the discrete and continuous variables with provable convergence. The paper shows that the well-known weighted minimum mean-square-error (WMMSE) algorithm can also be derived from a particular use of FP; but our proposed FP-based method significantly outperforms WMMSE when discrete user scheduling variables are involved, both in term of run-time efficiency and optimizing results.

• The paper reformulates challenging discrete uplink scheduling problems in wireless cellular systems using fractional programming techniques for distributed combinatorial optimization.
• It introduces FP-based approaches for joint optimization of user scheduling with either power control (SISO) or beamforming (MIMO) in uplink cellular networks.
• Numerical comparisons show that the proposed FP framework significantly outperforms traditional algorithms like WMMSE, especially when discrete scheduling variables are involved.

Insightful Overview of "Fractional Programming for Communication Systems—Part II: Uplink Scheduling via Matching"

The second part of the series "Fractional Programming for Communication Systems" by Kaiming Shen and Wei Yu addresses the challenging domain of discrete optimization problems involving uplink scheduling in communication systems. This paper extends the fractional programming (FP) techniques introduced in the first part, leveraging them to solve discrete and mixed discrete-continuous problems, which are notably more complex than their continuous counterparts due to the inherent difficulty in recasting them as convex problems.

Central to this work is a novel approach that deviates from the traditional method of relaxing discrete variables. Instead, it reformulates user scheduling problems in wireless cellular systems using fractional programming, making them amenable to distributed combinatorial optimization. The paper focuses specifically on the uplink coordinated multi-cell user scheduling problem, which is inherently more complex than downlink scheduling due to the need to consider interference across neighboring cells—a challenge the authors effectively address by integrating discrete scheduling decisions with continuous optimization variables such as transmit power levels and beamformers.

Key Contributions and Methodology

This paper introduces an innovative approach for joint optimization of user scheduling and power control in uplink cellular networks through FP-based reformulations:

1. Joint Uplink Scheduling and Power Control: The problem is formulated as maximizing network utility through coordinated scheduling and power allocation across multiple cells in a SISO network. The proposed method leverages an FP-based model to couple power control dynamically with scheduling, delivering promising results both in terms of solution quality and computational efficiency.
2. Joint User Scheduling and Beamforming: Extending the approach to MIMO networks, the paper formulates a joint uplink scheduling and beamforming problem, demonstrating the versatility and robustness of FP in handling both power and vector optimization in a distributed manner across multiple cells. A nearest point projection scheme is also proposed for scenarios with discrete beamforming requirements.
3. Comparison with WMMSE: The FP framework is juxtaposed with the renowned WMMSE algorithm, which traditionally addresses beamforming from a minimum mean-square-error perspective. This paper reveals that the proposed FP method significantly outperforms WMMSE, especially when discrete scheduling variables are involved.

Implications and Future Directions

The methodologies put forth in this paper present clear numerical advantages over existing heuristics and conventional algorithms like WMMSE. By handling the uplink scheduling problem through a fractional programming lens, the work demonstrates improved efficiency in resource allocation tasks, a critical component as wireless systems scale further in complexity and size.

From a theoretical standpoint, the paper's contribution lays in redefining how complex interactions in cellular interference can be decoupled and managed across distributed systems. Practically, its implications extend toward more efficient infrastructure management, latency reduction, and enhanced service quality—all pivotal to modern communication networks catering to large user bases.

Looking forward, the adaptability of FP in solving complex, discrete, and mixed optimization problems could be further explored in other domains where similar interference and scheduling issues persist, such as device-to-device communication and full-duplex systems. The successful application of the FP methods addressed in this paper suggests an exciting horizon for fractional optimization techniques, potentially reshaping aspects of network management and resource allocation in upcoming cellular technologies.

The rigorous approach undertaken by Shen and Yu provides both a solid foundation and a springboard for further investigation into the application of FP across a gamut of complex network scenarios, potentially extending the boundaries of current methodologies in network optimization and control.