  The application of renewable energy is a promising solution to realize the
Green Communications. However, if the cellular systems are solely powered by
the renewable energy, the weather dependence of the renewable energy arrival
makes the systems unstable. On the other hand, the proliferation of the smart
grid facilitates the loads with two-way energy trading capability. Hence, a
hybrid powered cellular system, which combines the smart grid with the base
stations, can reduce the grid energy expenditure and improve the utilization
efficiency of the renewable energy. In this paper, the long-term grid energy
expenditure minimization problem is formulated as a stochastic optimization
model. By leveraging the stochastic optimization theory, we reformulate the
stochastic optimization problem as a \mbox{per-frame} grid energy plus weighted
penalized packet rate minimization problem, which is NP-hard. As a result, two
suboptimal algorithms, which jointly consider the effects of the channel
quality and the packet reception failure, are proposed based on the successive
approximation beamforming (SABF) technique and the \mbox{zero-forcing}
beamforming (ZFBF) technique. The convergence properties of the proposed
suboptimal algorithms are established, and the corresponding computational
complexities are analyzed. Simulation results show that the proposed SABF
algorithm outperforms the ZFBF algorithm in both grid energy expenditure and
packet delay. By tuning a control parameter, the grid energy expenditure can be
traded for the packet delay under the proposed stochastic optimization model.
