This paper considers the optimal energy efficient association for HetNets by applying almost blank subframes (ABSs) techniques. Aiming at maximizing energy efficiency (EE) without the quality of service (QoS) constraints, we obtain a closed-form optimal solution, which indicates that the optimal choice of blank resource block (RB) fraction for EE maximization is binary without individual user QoS requirements. We further incorporate QoS constraints and equivalently transform the corresponding complicated fractional EE optimization problem to a single linear program (LP) by introducing some new auxiliary variables. Finally, we confirm the validity of the assumption that a user is served by at most one BS in a given RB both in theory and by numerical results.

In this paper, we investigate robust beamforming to improve the energy efficiency (EE) of wireless networks when only imperfect or partial channel state information (CSI) is available at the transmitter. Due to CSI quantization errors and/or limited feedback information, CSI imperfections can be well modeled by a bounded uncertainty region. We focus on the worst case robust beamforming strategy to optimize the EE of downlink transmission under the deterministic bounded channel model, which merely assumes a maximal channel error magnitude. We start with a single-user single-cell MIMO system and obtain a closed-form design for robust beamforming. For a multicell network, robust beamforming is in a nonconvex fractional form, and the solution cannot be directly extended from the single-cell scenario. To solve this problem efficiently, we resort to a lower bound, instead of the primal problem, and cast it as a semidefinite program (SDP). The robustness and efficiency of the proposed beamforming design are confirmed by computer simulation results.