  We consider a small cell network (SCN) consisting of N cells, with the small
cell base stations (SCBSs) equipped with Nt \geq 1 antennas each, serving K
single antenna user terminals (UTs) per cell. Under this set up, we address the
following question: given certain time average quality of service (QoS) targets
for the UTs, what is the minimum transmit power expenditure with which they can
be met? Our motivation to consider time average QoS constraint comes from the
fact that modern wireless applications such as file sharing, multi-media etc.
allow some flexibility in terms of their delay tolerance. Time average QoS
constraints can lead to greater transmit power savings as compared to
instantaneous QoS constraints since it provides the flexibility to dynamically
allocate resources over the fading channel states. We formulate the problem as
a stochastic optimization problem whose solution is the design of the downlink
beamforming vectors during each time slot. We solve this problem using the
approach of Lyapunov optimization and characterize the performance of the
proposed algorithm. With this algorithm as the reference, we present two main
contributions that incorporate practical design considerations in SCNs. First,
we analyze the impact of delays incurred in information exchange between the
SCBSs. Second, we impose channel state information (CSI) feedback constraints,
and formulate a joint CSI feedback and beamforming strategy. In both cases, we
provide performance bounds of the algorithm in terms of satisfying the QoS
constraints and the time average power expenditure. Our simulation results show
that solving the problem with time average QoS constraints provide greater
savings in the transmit power as compared to the instantaneous QoS constraints.
