# Joint Base Station Activation and Coordinated Downlink Beamforming for HetNets: Efficient Optimal and Suboptimal Algorithms

## TL;DR

This paper proposes efficient algorithms for joint base station activation and coordinated downlink beamforming in HetNets, optimizing power consumption with guaranteed optimality and polynomial-time approximations.

## Contribution

It introduces a novel Benders' decomposition approach for optimal solutions and a dual-subgradient method for fast approximate solutions in HetNet beamforming design.

## Key findings

- Optimal solution guarantees convergence.
- Polynomial-time approximate algorithm demonstrated.
- Framework generalizes to robust and multi-cell scenarios.

## Abstract

In cellular heterogeneous networks (HetNets), a number of distributed base stations cooperatively provide services to multiple mobile users. This paper addresses joint base-station activation and coordinated beamforming design for downlink transmission in HetNets. To this end, a mixed integer program is formulated to optimize the total power consumption of a HetNet. A novel approach based on Benders' decomposition is then put forth to obtain the optimal solution for the problem of interest with guaranteed convergence. Building on our new formulation, a dual-subgradient algorithm is also proposed to find an approximate solution in polynomial time. The proposed approaches can be generalized to more general setups, including robust beamforming designs under channel uncertainty, and coordinated beamforming for multi-cell scenarios.