Price-Based Resource Allocation for Spectrum-Sharing Femtocell Networks: A Stackelberg Game Approach

Abstract: This paper investigates the price-based resource allocation strategies for the uplink transmission of a spectrum-sharing femtocell network, in which a central macrocell is underlaid with distributed femtocells, all operating over the same frequency band as the macrocell. Assuming that the macrocell base station (MBS) protects itself by pricing the interference from the femtocell users, a Stackelberg game is formulated to study the joint utility maximization of the macrocell and the femtocells subject to a maximum tolerable interference power constraint at the MBS. Especially, two practical femtocell channel models: sparsely deployed scenario for rural areas and densely deployed scenario for urban areas, are investigated. For each scenario, two pricing schemes: uniform pricing and non-uniform pricing, are proposed. Then, the Stackelberg equilibriums for these proposed games are studied, and an effective distributed interference price bargaining algorithm with guaranteed convergence is proposed for the uniform-pricing case. Finally, numerical examples are presented to verify the proposed studies. It is shown that the proposed algorithms are effective in resource allocation and macrocell protection requiring minimal network overhead for spectrum-sharing-based two-tier femtocell networks.

• The paper introduces a price-based Stackelberg game model where a macrocell sets interference prices while femtocell users adjust power to maximize their utilities.
• It compares uniform and non-uniform pricing schemes, showing that non-uniform pricing maximizes macrocell revenue while uniform pricing favors femtocell throughput.
• A distributed algorithm is proposed to achieve Stackelberg equilibrium with minimal network overhead, as validated by numerical simulations in diverse deployment scenarios.

Price-Based Resource Allocation for Spectrum-Sharing Femtocell Networks: A Stackelberg Game Approach

This paper proposes a novel approach to tackle the problem of resource allocation in spectrum-sharing femtocell networks by leveraging a price-based model grounded in the Stackelberg game theory framework. The research addresses the interference management challenges in two-tier heterogeneous networks, where a macrocell and multiple femtocells coexist within the same frequency band.

Game-Theoretical Framework

The authors model the interaction between a macrocell base station (MBS) and the femtocell users (FUs) as a Stackelberg game. In this framework, the MBS acts as a leader by imposing prices on the interference power from the FUs, while the FUs are seen as followers optimizing their uplink transmit power to maximize their utilities considering the interference prices.

The main objective is to achieve joint utility maximization for the MBS and FUs. The utility for MBS is defined as the revenue from selling interference quotas, whereas the FUs aim to maximize their individual utilities defined by a tradeoff between data rate and interference cost.

Key Contributions

1. Interference Pricing Schemes: The paper introduces two pricing schemes—uniform pricing and non-uniform pricing. In uniform pricing, the same interference price is applied to all FUs; in non-uniform pricing, different prices are assigned to individual FUs.
2. Stackelberg Equilibrium: The authors theoretically compute the Stackelberg equilibriums for both schemes under different deployment scenarios—sparsely and densely deployed femtocell networks. They derive closed-form solutions for optimal interference prices and power allocations in the sparsely deployed scenario.
3. Distributed Algorithm: For the uniform pricing scenario, a distributed interference price bargaining algorithm is proposed, which allows the attainment of Stackelberg equilibrium with minimal network overhead.
4. Numerical Characterization: Numerical simulations are conducted to verify the effectiveness of the proposed models and algorithms. The results highlight the tradeoffs in MBS revenue and FU sum-rate under different pricing schemes and deployment scenarios.

Noteworthy Numerical Results

The simulation results demonstrate that the non-uniform pricing scheme maximizes the MBS revenue while minimizing the sum-rate of FUs, illustrative of the tradeoff between revenue maximization for the MBS and sum-rate maximization for FUs. Conversely, uniform pricing is shown to favor the sum-rate of FUs, suggesting its utility in scenarios prioritizing overall user throughput.

Additionally, in the context of densely deployed femtocell networks, the derived lower and upper bounds of MBS revenue provide insight into optimal resource allocation even when cross-femtocell interference is considered.

Theoretical and Practical Implications

The research comprehensively bridges the concept of interference pricing as applied in cognitive radio networks (CRNs) with spectrum-sharing femtocell networks—a transition not commonly explored previously due to the lack of sensing and power-adaptation capabilities in femtocell devices. Introducing interference power constraints effectively shifts the responsibility of managing interference to the MBS through pricing, ensuring sustained macrocell performance without imposing excessive requirements on femtocell users.

Future Directions

Potential future work may involve extending these principles to broader and more complex femtocell network scenarios, including multi-tier configurations and the incorporation of advanced interference suppression technologies. Exploration of dynamic pricing algorithms and their convergence properties would complement the proposed solutions, enhancing adaptability to network condition changes. Additionally, incorporating machine learning techniques to predict interference patterns and adjust pricing dynamically can further optimize resource allocation in real-time.

This paper contributes significantly to the understanding and practical implementation of game-theory-based approaches for optimizing resource allocation in heterogeneous wireless networks, providing both theoretical rigor and applicability. Heterogeneous network designers and communication theorists would benefit from leveraging the methodologies and results presented in this study.