## 1 Introduction
Finally, in fuzzy cell zooming scheme, as an extension of the discrete scheme, a BS transmit power is increased with a small amount from each discrete level. In [12], the authors proposed an energy-saving small cell zooming scheme in a two-tier cellular network, where small cell BSs dynamically select turning on, turning off, zooming in, and zooming out based on varying traffic load, the speed of UE, and the location of UE, while satisfying data rate requirements of UEs. Figure 1: Activation and deactivation of base stations (BSs). (a) Activation; (b) deactivation. Figure 2: Operation of cell zooming: (a) zooming-in; (b) zooming-out. In order to save the energy of BSs and efficiently serve UEs, work on state management has recently drawn a lot of attentions [13; 14; 15]. Although turning off BSs can save a significant amount of BSs' energy, it introduces long delay to respond to the users' traffic demand, since BSs should activate first from the _off_ state to serve UEs and this takes a relatively longer time. In order to solve the long delay problem of a deactivated BS, the BS does not turn off all the components but turns off most of the components in order to save energy and quickly reacts to the users' demand by entering into _sleep_ state instead of entering into _off_ state. In [13], the authors classified the state of a BS as _on_, _standby_, _sleep_, and _off_ states based on the activity and energy consumption of the BS. In the _on_ state, a BS consumes the largest power since all of the operations of a BS are active. In _standby_ state, the BS can move to _on_ state very rapidly when it is needed, since only the radio frequency (RF) and temperature compensated crystal oscillators (TCXO) heater of a BS are inactive. A BS in _standby_ state consumes less power than that in the _on_ state but it consumes more power than that in the _sleep_ or _off_ state. In the _sleep_ state, which is very similar to the low power mode in [14], a BS consumes less power than that in the _on_ or _standby_ state. A BS in _sleep_ state only activates the power supply, backend connection, and central processing unit (CPU) core and thus the transition time to _on_ from _sleep_ state is longer than the transition time from _standby_ state to _on_ state, but it is much shorter than the transition time from _off_ to _on_ state. If the traffic load of a BS is very low, _sleep_ state is more favorable. On the other hand, if the traffic load is high, the _on_ state is more favorable. In the _off_ state, a BS consumes no power since all of the operations of a BS are inactive. The transition time from _off_ state to _on_ state is the longest. In [15], the authors analyzed the relationship between the energy efficiency of a BS for varying traffic load and concluded that _sleep_ state is more efficient if the traffic load is low. The authors also obtained an appropriate threshold value to make a transition to the _sleep_ state. In [16], the authors analyzed the relationship between power efficiency and residence time in the _sleep_ state. In parallel to the study of the energy efficiency related to the BS states, there have been attempts to save the BS energy using new network architecture. In conventional heterogeneous network architecture, a number of small cells are overlaid on a macro cell. Small cells are introduced to accommodate the varying traffic distribution and increasing data traffic load. However, in the conventional heterogeneous network, energy efficiency is not significant since all the BSs in the macro cell and small cell should deal with both the control signal and data traffic, and thus should always be awake. In a heterogeneous network architecture with overlapped macro cell BSs and small cell BSs, if small BSs are not used they are turned off to save energy [17]. In [18], the activation and deactivation of small cell BSs are controlled by a macro cell BS using the traffic load and position of UEs but it has high signaling overhead [18].