  User scheduling, beamforming and energy coordination are investigated in
smart-grid powered cellular networks (SGPCNs), where the base stations are
powered by a smart grid and natural renewable energy sources. Heterogeneous
energy coordination is considered in SGPCNs, namely energy merchandizing with
the smart grid and energy exchanging among the base stations. A long-term
grid-energy expenditure minimization problem with proportional-rate constraints
is formulated for SGPCNs. Since user scheduling is coupled with the beamforming
vectors, the formulated problem is challenging to handle via standard convex
optimization methods. In practice, the beamforming vectors need to be updated
over each slot according to the channel variations. User scheduling needs to be
updated over several slots (frame) since the frequent scheduling of user
equipment can cause reliability issues. Therefore, the Lyapunov optimization
method is used to decouple the problem. A practical two-scale algorithm is
proposed to schedule users at each frame, and obtain the beamforming vectors
and amount of exchanged natural renewable energy at each slot. We prove that
the proposed two-scale algorithm can asymptotically achieve the optimal
solutions via tuning a control parameter. Numerical results verify the
performance of the proposed two-scale algorithm.
