  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.
