Joint user association power control and beamforming in HetNets via distributed SOCP

We consider in this paper an uplink coordinated beamforming problem for multi-cell heterogeneous networks (HetNets) whereby base stations are densely and co-channel deployed. A joint user-base station association, power control and beamforming scheme is presented for HetNets to minimize the power consumption. Such joint optimization is formulated as a mixed-integer second-order conic programming (MI-SOCP). To cope with this intractable problem, we develop two polynomial-time distributed methods. The first method is a two-stage solution, while the second method is a customized distributed solution by dual decomposition. The optimal tradeoff between data link gain and control link consumption using coordinated beamforming is able to be achieved by the two presented algorithms. Numerical results also show that, these two algorithms are efficient, and low complexity that consume much less run time comparing to the standard mixed-integer solver Gurobi.