Robust {MISO Transmit} Optimization under Outage-Based QoS Constraints in Two-Tier Heterogeneous Networks

To improve wireless heterogeneous network service via macrocell and femtocells that share certain spectral resources, this paper studies the transmit beamforming design for femtocell base station (FBS), equipped with multiple antennas, under an outage-based quality-of-service (QoS) constraint at the single-antenna femtocell user equipment characterized by its signal-to-interference-plus-noise ratio. Specifically, we focus on the practical case of imperfect downlink multiple-input single-output (MISO) channel state information (CSI) at the FBS due to limited CSI feedback or CSI estimation errors. By characterizing the CSI uncertainty probabilistically, we formulate an outage-based robust beamforming design. This nonconvex optimization problem can be relaxed into a convex semidefinite programming problem, which reduces to a power control problem when all CSI vectors are independent and identically distributed. We also investigate the performance gap between the optimal transmission strategy (that allows maximum transmission degrees of freedom (DoF) equal to the number of transmit antennas) and the proposed optimal beamforming design (with the DoF equal to one) and provide some feasibility conditions, followed by their performance evaluation and trade-off through simulation results.