This paper addresses the challenge of load balancing in heterogeneous cellular networks (HetNets) by optimizing user association to maximize long-term rates. The authors propose a distributed algorithm that converges to a near-optimal solution with low complexity, bridging the gap between theoretical optimization and practical implementation. The key contributions include: 1. **Problem Formulation**: The authors formulate a utility maximization problem for user association and resource allocation, considering both unique and fractional associations. They assume a logarithmic utility function to encourage load balancing and fairness. 2. **Optimal Resource Allocation**: For single-BS association, they show that equal resource allocation is optimal, leading to a convex optimization problem. This simplifies the joint cell association and resource allocation problem. 3. **Distributed Algorithm**: A primal-dual distributed algorithm is proposed using Lagrangian dual decomposition. This algorithm converges to a near-optimal solution with low complexity, making it suitable for HetNets. 4. **Range Expansion (Biasing)**: The authors investigate the effectiveness of range expansion, a simple approach where users are associated with BSs based on biased received power. They derive optimal biasing factors for SINR and rate, showing that these factors are insensitive to the deployment of BSs and users. 5. **Performance Evaluation**: Numerical results demonstrate significant throughput gains for cell-edge users and median users, with rate gains of up to 3.5x and 2x, respectively, compared to max-SINR association. The biasing schemes achieve performance close to the optimal load-aware association. The paper provides a comprehensive solution for load balancing in HetNets, offering both theoretical guarantees and practical implementation details.This paper addresses the challenge of load balancing in heterogeneous cellular networks (HetNets) by optimizing user association to maximize long-term rates. The authors propose a distributed algorithm that converges to a near-optimal solution with low complexity, bridging the gap between theoretical optimization and practical implementation. The key contributions include: 1. **Problem Formulation**: The authors formulate a utility maximization problem for user association and resource allocation, considering both unique and fractional associations. They assume a logarithmic utility function to encourage load balancing and fairness. 2. **Optimal Resource Allocation**: For single-BS association, they show that equal resource allocation is optimal, leading to a convex optimization problem. This simplifies the joint cell association and resource allocation problem. 3. **Distributed Algorithm**: A primal-dual distributed algorithm is proposed using Lagrangian dual decomposition. This algorithm converges to a near-optimal solution with low complexity, making it suitable for HetNets. 4. **Range Expansion (Biasing)**: The authors investigate the effectiveness of range expansion, a simple approach where users are associated with BSs based on biased received power. They derive optimal biasing factors for SINR and rate, showing that these factors are insensitive to the deployment of BSs and users. 5. **Performance Evaluation**: Numerical results demonstrate significant throughput gains for cell-edge users and median users, with rate gains of up to 3.5x and 2x, respectively, compared to max-SINR association. The biasing schemes achieve performance close to the optimal load-aware association. The paper provides a comprehensive solution for load balancing in HetNets, offering both theoretical guarantees and practical implementation details.