7.1 Introduction

Great advancements in wireless communications services have resulted in high energy consumption by network operators and mobile users. In the literature, there have been several proposals for designing an energy aware infrastructure in wireless communications networks. Energy awareness in wireless communications networks has been studied for a long time in mobile devices and wireless sensors, due to their limited power capabilities. Recently, such awareness has been extended to cellular network BSs due to financial and environmental considerations. In this regard, researchers have proposed to exploit the traffic load (temporal and spatial) fluctuations, by switching off some of the available radio resources when the traffic load is light. Such an approach is known as dynamic planning. The investigated resources can be the radio transceivers of active BSs [195]. When a BS is in its active mode, power supply, processing circuits and air conditioning consume up to of the total energy [34]. Therefore, significant energy saving can be achieved if the entire BS is switched off when the traffic load is light [34]. In this chapter, three research directions will be investigated, namely dynamic planning with dense small-cells, network cooperative dynamic planning and balanced dynamic planning. These approaches will be the major focus of this chapter.

A heterogeneous wireless network includes a mix of various cell sizes and shapes, such as high-power macro cells and low-power nodes such as pico cells and relays. It is expected that a dense deployment of low-power BSs (small-cells) will be implemented in the near future. However, the dense deployment of low-power BSs raises several fundamental issues in terms of energy consumption. Particularly, key issues for energy efficient deployment of dense small-cells include finding the optimal cell-zooming techniques (i.e. expanding and shrinking the cell size) and sleep policies (i.e. on–off switching of BSs) for both macro and small (pico) BSs depending on the traffic pattern. In this chapter, we present optimal energy-efficient and QoS-aware dynamic cell-zooming and BS-switching policies for dense small-cell deployment subject to constraints on user data rate requirements and outage probability [196].

Most of the dynamic planning solutions are limited to the operation of a single network (as described in the previous paragraph). Consequently, the proposed solutions for service provision for the off cells rely on the active resources of such a network. This in turn leads to an increase in the transmission power, and hence an increase in inter-cell interference, and may result in coverage holes. Furthermore, most of the dynamic planning solutions in the literature focus on switching off either some of the BSs or some of the radio resources of the BSs. In this chapter, we present an optimal resource (BSs and radio channels) on–off switching framework that enables network operators with BSs of overlapped coverage in a given geographical region to cooperate among each other to achieve energy saving [12].

Finally, the existing research focuses only on improving energy efficiency for network operators and does not account for the incurred energy consumption for the mobile users in the uplink. In practice, dynamic planning can lead to higher energy consumption for mobile users in the uplink due to switching off nearby BSs and hence MTs suffer from larger transmission distances. As a result, MTs suffer from battery drain at a higher rate and hence are subject to call droppings. In this chapter, we present a dynamic planning approach that can capture and balance the trade-off in energy efficiency between network operators (in the downlink) and mobile users (in the uplink) [197 198].

7.2 Dynamic Planning with Dense Small-Cell Deployment

Several works have addressed energy-efficient cell-zooming mechanisms and sleep policies for heterogeneous networks with dense small-cell deployment. In particular, energy minimization in macro-relay networks has been studied in [199] and [200]. However, both these contributions are restricted to a single macro cell scenario. The energy consumptions of a two-hop relaying scheme (LTE type 1 relay) and a multicast cooperative scheme (LTE type 2 relay) are studied in [201]. In spite of the interesting results presented in the above studies, the energy-efficient cell-zooming and BS-switching policies in the previousworks do not guarantee the minimum data rate requirements and outage probability of end user. Moreover, these techniques cannot be generalized to dense small-cell deployment scenarios. We present a dynamic planning approach to optimally associate users to access nodes (pico and macro BSs) by adjusting the coverage area of these BSs. The objective of the optimal cell zooming and user association is to reduce the traffic load at some BSs and let them enter into sleep mode, while ensuring the user data rate demand.

Consider a downlink dense macro–pico network consisting of macro BSs, low-power pico BSs and MTs. An overview of a dense macro–pico network is shown in Figure 7.1. Denote the sets of macro BSs, pico BSs and MTs by , and , respectively. Let be a binary variable representing the association between BS and MT . The achieved data rate in the downlink for MT is given by

7.1

where denotes the received SINR at the MT and is a real variable representing the allocated bandwidth to MT from BS . The total bandwidth available at BS is . Let represent user required data rate. The total load at BS is given by

7.2

The BS power consumption model is given by

7.3

where is the minimum power consumed when the BS is in idle mode and depends on the transceiver electronics, cooling and so on; denotes the power amplifier efficiency of BS and is the maximum RF output power of BS at full load and . Let denote a binary variable representing BS operation mode, where represents an active BS and denotes an inactive BS. Furthermore, is a real variable representing the cell-zooming condition of BS by dynamically controlling BS transmission power based on the power requirements of the farthest user in the cell.

7.2.1 Energy-Efficient and QoS-Aware Cell Zooming

Next, we present an analytical model for optimizing the cell size in a dense macro–pico heterogeneous network to minimize energy consumption while maintaining the end user quality of service [196]. The adjustment of physical cell parameters such as transmission power can help to implement cell zooming. In particular, cells can zoom in by decreasing the transmission power of BSs and viceversa.

The first constraint we introduce in the optimization framework concerns capacity and radio resource allocation, where the amount of allocated bandwidth by each BS cannot exceed the BS total available bandwidth, that is,

7.4

Furthermore, no MT can be associated with an inactive BS, that is,

7.5

In addition, each active user should be associated with only one BS at a time, that is,

7.6

The allocated data rate to MT should satisfy the user-required data rate, that is,

7.7

In order to serve cell edge MTs (at the maximum distance ), the cell-zooming mechanism should satisfy

7.8

where represents the received power required for the farthest user at distance, denotes a proportionality constant and denotes the path loss exponent.

In the dynamic cell-zooming mechanism, the transmission power is adjusted according to a desired cell radius; therefore, a user may experience outage when it is out of a BS coverage area due to its movement during the cell-zooming operation. Formally, the outage probability is defined as

7.9

where denotes the SINR threshold.

The optimization framework objective is to minimize the total power consumed by the network while satisfying the users' target QoS, and it is expressed as [196]

7.10

The energy-efficient dynamic cell-zooming linear program (LP) problem in (7.10) can be solved optimally using the state-of-the-art CPLEX mixed integer program (MIP) solver. However, large instances of the above problem are difficult to be solved optimally. It turns out from the objective function and constraints in (7.10) that the total number of terms inside the constraints can increase significantly with the increase in the number of macro BSs, pico BSs and users due to the fact that the number of connection opportunities among different nodes increases with a growth in the density of nodes. Therefore, the computational complexity for finding the CPLEX MIP optimal solution increases dramatically as larger clusters of cells are considered. The increased computational complexity issue requires designing approximate solution strategies. In this regard, a practical and effective approach is to apply a distributed technique for finding the solution, in which repetitive uses of small-cell clusters can be made to deal with a larger cluster [196]. For small-cell clusters, the problem can be solved efficiently in a distributed manner. Then, one can merge the distributed solutions to obtain the network-wide solution. Clearly, a dramatic reduction in computational complexity comes at the cost of aperformance gap between the optimal CPLEX solution and the distributed solution.

7.2.2 Performance Evaluation

In this section, we evaluate the performance of the energy-efficient cell-zooming mechanism. The parameter values used in the analysis are reported in Table 7.1. The first scenario consists of a seven-cell macro–pico network with hotspot and uniformly distributed users.

Parameter	Value
Carrier frequency	2 GHz
Bandwidth	20 MHz
Thermal noise PSD	dBm/Hz
Carrier frequency	2 GHz
	40 W
	712 W
	14.5
	1 W
	14.9 W
	8
MT transmission power	23 dBm
Antenna configuration	TX-1, RX-1
(): Macro-MT link
(): Macro-MT link
(): Pico-MT link
(): Pico-MT link
Inter-site distance	500 m

Figure 7.2 depicts the effect of the density of pico BSs on the number of active macro base stations in operation. From the plot depicted in Figure 7.2, it can be seen that the dynamic cell -zooming algorithm for a dense macro–pico network can offload the traffic from macro BSs by increasing the coverage area of pico BSs and switching off most of the lightly loaded macro base stations. Moreover, it is evident from Figure 7.2 that more macro BSs are switched off by increasing the density of pico BSs in the network.

Figure 7.3 depicts that there is a trade-off between outage probability and energy consumption. It must be mentioned here that in this plot the energy consumption is normalized to 100 if all the BSs are in active mode. It is evident from Figure 7.3 that the outage probability decreases by increasing the density of pico BSs. However, this decrease in outage probability comes at the cost of slightly increased energy consumption. We also compare the performance of the dynamic cell-zooming algorithm with a static cell-zooming algorithm, which reduces the coverage area of BSs to , or of the maximum coverage. Figure 7.3 shows that the dynamic cell-zooming algorithm performs better than the static algorithm. Moreover, the dynamic cell-zooming algorithm is more flexible as it can freely leverage the trade-off between outage probability and energy consumption.

A plot of the area energy efficiency against the total offered traffic load for different dense small-cell scenarios is depicted in Figure 7.4. The bar labelled optimal dense macro–pico network in Figure 7.4 represents the scenario where we take into account transmission and circuit energy of macro and pico base stations in active mode, which are obtained by solving the problem in (7.10) using CPLEX. Moreover, the bar labelled distributed dense macro–pico network represents the scenario where we solve the problem in (7.10) using a cluster based distributed approach. The bar labelled dense macro–pico network without sleep mode represents the scenario where we consider transmission and circuit energy of all macro base stations in the network together with the deployed pico cells. Finally, the bar macro only refers to the scenario where we consider only macro BSs, and all macro BSs are assumed in the active mode. It is evident from Figure 7.4 that the macro–pico network has the best area energy efficiency compared with other cases. Figure 7.4 illustrates that the area energy efficiency of the optimal dense macro–pico solution is significantly higher than that corresponding to the macro-only case. The rationale behind this fact is that most of the macro BSs are operating in an inactive mode in the optimal dense macro–pico network, as shown in Figure 7.4, as compared with other small-cell scenarios.

The user association for a seven-cell dense macro–pico network powered by a stand-alone power grid is depicted in Figure 7.5. It turns out that the dynamic cell-zooming algorithm adjusts the transmission power from the macro and pico BSs in such a way that more users connect to the pico BSs than to the macro BSs with an increase in the density of pico BSs in the network.

7.3 Dynamic Planning with Cooperative Networking

While BS on–off switching can avoid resource over-provision in a low-traffic load condition and hence achieve energy saving, the radio coverage and service provision for the off cells face several challenges. Since most of the dynamic planning solutions are limited to the operation of a single network, the proposed solutions for service provision for the off cells rely on the active resources of such a network, as mentioned in the previous section. Consequently, an increase in the transmission power of the active BSs is required to increase the radii of its cells to provide radio coverage for the off cells. This may also result in coverage holes if the maximum allowed transmission power of the remaining active BSs cannot achieve radio coverage for the switched-off cells, and therefore, service disruption is expected in these areas. Also, an increase in the transmission power may result in inter-cell interference in the case that more than one active BS tries to achieve radio coverage for the switched-off cells. Consequently, additional interference management schemes are needed. With the existence of different network operators with overlapped coverage among different BSs, network cooperation can achieve energy saving and avoid the dynamic planning shortcomings. In addition, the dynamic planning solutions proposed in the literature focus on either switching off some of the BSs or switching off some of the radio resources of the BSs. It is more beneficial to combine both strategies and not only switch off some BSs but also switch off some of the radio resources of an active BS to further improve the amount of energy saving. In this case, an optimal resource (BSs and radio channels) on–off switching framework is required to determine the operation mode of BSs and radio channels that adapts to the fluctuations of the traffic load and maximizes the amount of energy saving under service quality constraints, assuming a cooperative networking environment.

Consider a geographical region with two network operators [12]. The first network operator offers 4G cellular services while the second operator offers WiMAX services. The cellular network covers the whole geographical region. In regions with a high service demand, WiMAX BSs are deployed to provide high capacity. Let denote the set of cellular network cells covered by the WiMAX network BS, as shown in Figure 7.6. An MT in the overlapped coverage can be served by either of the two networks, that is, no multi-homing is allowed. Let denote the number of channels available in a cellular network BS. The WiMAX network BS has channels. Each channel has a fixed bandwidth . For simplicity of illustration, assume that a call requires one channel from one of the networks for its service. A network BS working mode variable for the cellular network BS () is represented by a binary digit “0” to indicate an inactive (off) BS or “1” to indicate an active (on) BS. Similarly, the binary variable is used for the WiMAX network BS to represent its on/off states. There is always at least one active network in the overlapped coverage area to guarantee service provision. Let denote a vector of BS working modes in the overlapped coverage area. The total power consumption of a BS is denoted by () for WiMAX (cellular) network, and consists of two components. A fixed component which accounts for the BS power supply and air conditioning is represented by () for a WiMAX (cellular) network. The variable component depends on the number of active channels in the BS, and accounts for the power amplifier, feeder loss and transmitted power, and is represented by () for WiMAX (cellular) network. The number of active channels in cell is given by () for WiMAX (cellular) network, . The power consumption of an inactive/sleep WiMAX (cellular) network BS is denoted by (). When a BS changes its working mode from inactive to active, more energy is required to start up the BS power supply, circuits, and air conditioning. The switching cost is represented by an additional power consumption of the BS fixed-power component.

The following traffic and mobility assumptions are made: (A1) The aggregate traffic arrivals (new and handoff calls) to the cell are modelled by a Poisson process with mean arrival rate ; (A2) The channel-holding time in the cell (the minimum of the user cell dwell time and the call duration) follows an exponential distribution with mean .

7.3.1 Optimal Resource On–Off Switching Framework

Network cooperation in green radio communications exploits the temporal fluctuations in the traffic load to save energy. This is achieved by alternately switching on and off the available resources from BSs of different networks in regions with overlapped coverage, according to the traffic load condition. In general, two types of traffic load fluctuations can be distinguished: (i)large-scale fluctuation, in which the traffic load varies significantly from one period to another along the day and (ii) small-scale fluctuation, in which the traffic load varies slightly around some average value. Hence, we partition the time into a set of periods of constant duration (h) that can capture the large-scale fluctuations in the traffic load along the day, . Each period is further partitioned into a set of smaller periods each of duration to capture the small-scale fluctuations of the traffic load during that period, . The large-scale fluctuations in the traffic load can be exploited to turn off some BSs in a light-load condition and transfer the traffic load to the remaining active networks to save energy. On the contrary, the small-scale fluctuations can be exploited to switch off some of the radio channels in each active BS to further reduce the amount of energy consumption.

Decisions on the BS working mode are made at the initial moment of each period . While BS on–off switching can save energy, a switching action that is not compatible with the traffic load during a given period will result in a high call-blocking probability. An appropriate switching decision should maximize the amount of saved energy during that period and, at the same time, should achieve acceptable service quality, for example, as in terms of call-blocking probability. Also, it is desirable to minimize the frequency at which a BS changes its working mode from inactive to active to avoid the switching cost due to the additional energy consumption required for the BS start-up. The aggregate traffic arrival rate for each period is estimated using the data of traffic arrivals observed in previous days, as the traffic load, in general, follows a repeating pattern every day. Call arrivals follow a Poisson distribution and call departures follow an exponential distribution. The call-blocking probability is calculated using the Erlang B loss model. The optimal BS on–off switching decision for a given period can be obtained by carrying out the following optimization problem [12]

7.11

The objective function in (7.11) represents the total power saving in the overlapped coverage area. The variables and denote the BS powerconsumption for the cellular and WiMAX network, respectively, and depend on the BS working mode. Hence, if , and otherwise. Similarly, if , and otherwise. The variables and denote the additional power consumption required for the BS to start up. Hence, if the cellular network BS changes its working mode from inactive to active, and otherwise. Similarly, if the WiMAX BS changes its working mode from inactive to active, and otherwise. From the objective function definition, there exists a trade-off between the amount of energy saving achieved by switching on or off different BSs and the switching cost due to the additional energy consumption required for a BS to start up when its working mode changes from inactive to active. The parameter is a weighting factor that models the relative importance between energy saving and the BS start-up switching cost. The variable represents the required number of channels in cell , . The first constraint in (7.11) guarantees an acceptable service quality in terms of call-blocking probability not larger than a required upper bound , where the value of for a given is the largest aggregate traffic arrival rate over in that . The WiMAX BS working mode rule is given in the second constraint in (7.11), while the number of required active BSs from the cellular network is given in the last constraint in (7.11), with . The BS operation rules are designed to satisfy the service demand in each cell for a given and ensure radio coverage in the overlapped area. Hence, (7.11) results in the optimal BS working mode for the WiMAX and cellular network in the geographical region, which maximizes the amount of energy saving during some period , limits the frequency at which BSs change their working mode and provides a satisfactory call-blocking probability. A search algorithm can be used to solve (7.11). In this case, the values of , which violate the service quality constraint in (7.11), are excluded from the search space. Different working mode vector values can be composed from the feasible values using the BS operation rules in (7.11). Hence, the working mode vector , which maximizes the objective function value of (7.11), can be found. If the large-scale optimization problem results in more than one optimal BS working mode vector , the working mode vector is chosen from these optimal vectors such that the cells with the lowest traffic loads are switched off.

For each active BS, we can further exploit the small-scale fluctuations in the traffic load to find the optimal number of active channels that maximizes the percentage energy saving for the active BS and achieves an acceptable call-blocking probability. This is calculated at the beginning of each period using the following cost function [12]

7.12

where and are obtained from the solution of (7.11). The optimization problem (7.12) is subject to the service quality constraint in (7.11), where is defined for each . With a larger coverage area of the WiMAX BS, it is assumed that the power consumption of each active radio channel in the WiMAX BS is not less than that of a cellular network BS (i.e. ). In this case, in order to further improve the amount of energy saving, when the BSs of both networks are active, more radio channels from the cellular network are utilized. As a result, we let and when BSs from both networks are active; otherwise, the active number of radio channels from the active BS is equal to . The time sequence of optimization events is illustrated in Figure 7.7.

7.3.2 Performance Evaluation

In this section, we evaluate the performance of the cooperative networking dynamic planning approach using the framework depicted by (7.11) and (7.12). The geographical region under consideration is given in Figure 7.6 with the coverage of 3 cellular BSs that overlap with the coverage area of a WiMAX BS. It is assumed that the initial BS working mode vector is . The system parameters are given in Table 7.2. The number of available radio channels in the cellular network and WiMAX BSs are chosen in a way that reflects the higher capacity of the WiMAX BS. The total number of available radio channels in the region are determined such that the peak traffic load does not violate the target level of the call-blocking probability. The different power components of the WiMAX BS are chosen such that they are larger than that of a cellular BS, to reflect the fact that a WiMAX BS has more channels and covers a larger area than that of a cellular BS. The value of gives equal importance for maximizing the amount of energy saving and reducing the BSs on–off switching cost.

Parameter	Value	Parameter	Value	Parameter	Value
	10		400 W		1 h
	72		250 W		15 min
	1,500 W		10 W		0.5
	400 W		3		0.1
	30 W		2.4 min		0.01

Figure 7.8 shows the aggregate traffic mean arrival rate over the 24 h of a day for each cell. The values capture the traffic load fluctuations during the day. Variable exhibits a peak value in the middle of the day, while it assumes small values at early morning and late night periods.

The optimal decisions regarding the BS working mode for different periods are given in Table 7.3. The BS working mode varies in accordance with the traffic load fluctuations in each cell such that the optimal number of BSs is selected to maximize the amount of energy saving and yield a satisfactory quality of service.

Period	1–5	6–12	13–14	15–19	20	21–23	24
	1110	0001	1001	1101	0101	0001	1110

The daily percentage of energy saving when all radio channels are active for the WiMAX BS is , while for the cellular network BSs in cells 1, 2 and 3, the energy savings are , and , respectively. With an optimized number of active channels, the daily percentage of energy saving for the WiMAX BS is , and for the cellular network BSs in cells 1, 2 and 3 is , and , respectively. This shows that the small-scale optimization problem significantly improves the amount of energy saving for the WiMAX BS.

Figure 7.9 shows the call-blocking probability in each cell when the number of channels is optimized. The call-blocking probability in each cell has a desired maximum value .

7.4 Balanced Dynamic Planning Approach

The main goal of dynamic planning is to reduce the BS energy consumption while ensuring an acceptable downlink service quality for mobile users. However, no attention is paid to the relation between the mobile users' perceived service quality and their incurred uplink energy consumption. Consequently, the BSs' switch-off decisions can result in energy-inefficient user associations from the mobile users' standpoint. As shown in Figure 7.10, accounting only for the downlink performance, MTs with uplink traffic can be associated to a faraway BS, due to a switched off nearby BS. Because of the long transmission distance, a high energy consumption in the MTs in the uplink is expected, which leads to energy depletion for MTs at a higher rate. Although energy consumption for MTs is not that much compared with the BS energy consumption, a high rate of battery depletion for MTs results in a higher rate of dropped services in the uplink, which jeopardizes the mobile users' perceived service quality. Dynamic planning approaches, if not carefully designed, can lead to higher energy consumption for the MTs in the uplink. In such a case, dynamic planning would only shift the energy consumption burden from the BSs to the MTs, which results in battery drain for MTs at a higher rate. Consequently, this will degrade the service quality perceived by the mobile users, for example, lower throughput, higher call dropping rate and so on. Hence, the future designs of dynamic planning should capture and balance the trade-off in energy efficiency among network operators and mobile users.

One challenge of dynamic planning is that the switching decisions of BSs are coupled with MT associations. Particularly, when a BS is switched off, the associated MTs will need to perform a handover process to another BS. Similarly, when a BS is turned on, the nearby MTs can perform a handover process to this BS. Also, newly incoming MTs are associated to a subset of active BSs to get service. However, the BS operation (i.e. on–off switching) does not occur at the same rate as the MT association. Hence, dynamic planning is a two-timescale problem. At a high level, the BS operation occurs at a low rate (with scale of hours) that depends on the call traffic load density. At a low level, the MT association takes place at a higher rate (with scale of minutes) based on user arrivals and departures. When only downlink traffic is considered, as in the existing research, the decisions at both levels are determined based only on the BS energy consumption, as shown in the previous two sections. With coexistence of uplink and downlink traffic, the decisions at both levels are determined based on the expected energy consumption at BSs and MTs.

When uplink traffic is considered, the BS switch-off decision criteria should be revised. Particularly, the switch-off decision criteria should capture the impact of MTs' battery drain on the uplink service degradation, for example, lower throughput, higher latency, higher call dropping rate and so on. Hence, the uplink service degradation is due to two factors, namely unavailability of radio resources at the BSs (due to BS switch-off) and MTs' battery drain (due to communicating with faraway BSs). The BS switch-off decision metric should balance the BS energy consumption with the uplink service quality due to MTs' battery drain. Similarly, the existing mechanisms employ the call traffic load increase as a wake-up decision criterion for a switched off BS [64]. However, in the presence of uplink traffic, the wake-up decision criteria should include, besides the call traffic load measure, a measure of MTs' service degradation due to battery drain. As a result, if the MTs' service quality is degraded due to battery drain, a nearby inactive BS should be turned on to avoid MTs' battery depletion and dropping of uplink calls.

Consider a geographical region that can be covered by a cluster of BSs from different networks, as shown in Figure 7.11, . The BSs of different networks operate in separate frequency bands, and there is no interference among them. Consider a cooperative networking scenario where different operators alternately switch on and off their BSs to save energy while providing service coverage, as in the previous section. Let denote the distance between BSs and , and define by the height of BS , where . BSs control their coverage areas through antenna tilting [34]. For BS , the tilting angle index is given by , which corresponds to BS coverage area An inactive BS has .

Both uplink and downlink video call traffic loads are considered. Mobile users who capture live videos on their MTs and transmit them for online posting represent the uplink traffic [25]. On the contrary, mobile users performing video streaming represent the downlink video traffic. Let and denote the user arrival rates for uplink and downlink call traffic loads, respectively. The user arrival rates vary over the day and present peak values by mid-day and low values at early morning or late night periods [12]. Let and denote the average duration of the user service time in the uplink and downlink traffic, respectively. Each BS can simultaneously support a maximum of and users in the uplink and downlink, respectively. Let and denote the minimum required data rate for uplink and downlink users, respectively. The BSs operate in frequency division duplex (FDD) mode, and variables and denote the available bandwidth for uplink and downlink users, respectively.

Let and denote the number of MTs served by BS in the downlink and uplink, respectively, and . Let and be the number of MTs in the geographical region with downlink and uplink traffic, respectively. The spatial distributions of MTs in the geographical region are described by the PMFs and for MTs with downlink and uplink traffic, respectively. The PMFs give the distribution of users in the proximity of each BS , that is, in with . For instance, gives the number of MTs with downlink traffic in the proximity of the first BS.

Let and denote the average channel power gain in the uplink and downlink, respectively. The average channel power gain is characterized by the path loss model [202]

7.13

where represents the distance between the transmitter and receiver; denotes the carrier frequency and , and are model-dependent constants. The average path loss is determined based on the BS coverage area. Hence, for , as shown in Figure 7.11, in (7.13) is dominated by , while for , is dominated by , where represents the BS that lies in BS coverage, as shown in Figure 7.11. The average channel power gain is given by .

The average power consumption of BS depends on its mode of operation, which is given by Auer et al. [39]

7.14

where is the BS fixed power consumption, which accounts for the power supply, cooling, backhaul and other circuits, represents the slope of the load-dependent power consumption, denotes the BS average transmission power and denotes the BS sleep power. For BS to support MTs in the downlink with minimum required data rate , its downlink transmission capacity should at least be . Using Shannon formula, the minimum BS average transmission power is expressed as

7.15

In (7.15), is a function of due to the effect of on . The BS power consumption admits the maximum value .

In order for BS to support MT in the uplink with the minimum required data rate , the BS uplink transmission capacity should at least be . Using Shannon's formula, the minimum average power consumption of a given MT that is associated with BS in the uplink is given by

7.16

where denotes the MT circuit power consumption and the second part of (7.16) represents the average transmission power. The MT power consumption admits the maximum value of .

7.4.1 Two-Timescale Approach

In dynamic planning, the BS-switching decisions are coupled with the MT association decisions [35]. However, the BS operation and MT association decisions do not occur with the same rate. The BS operation decisions follow a low rate, with the scale expressed in hours, depending on the call traffic load density variation over the day. On the contrary, the MT association decisions occur at a high rate, with a scale expressed in minutes, depending on the user arrivals and departures. A two-timescale decision problem formulation can capture such a behaviour, as described in the previous section. Consequently, time is divided into slow and fast scales, as shown in Figure 7.12. At the slow timescale, time is partitioned into a set of periods with fixed duration . Set covers the 24 h of the day and captures the variations in the call arrival rates, that is, and (per unit ) are fixed during period and vary from one period to another. Each period is further partitioned into a set of periods of equal duration , . represents the fast timescale, and it captures the mobile users' arrivals and departures, that is, and are fixed during period and may vary from one period to another. The elements of the slow and fast timescale decision problems, namely states, actions, transition probabilities and cost will be explained next.

7.4.1.1 Slow Timescale

The slow timescale consists of a set of periods that covers the 24 h of the day, each period having a long duration . The slow timescale decision problem is to control the BS operation (on and off) to minimize (and balance) the total expected energy consumption of network operators and mobile users.

The slow timescale system state yields the uplink and downlink call traffic load densities, where , and . The call traffic load densities can be inferred from the historical load patterns [12 34]. Since the large-scale variations over the day are finite, the slow timescale system presents a finite set of states.

Given the system state, the slow timescale action specifies the BS mode of operation and the antenna tilting for the current period . The action should not violate a target call-blocking probability for the uplink and downlink traffic, that is, it should satisfy and , where and denote the call-blocking probabilities during period in the uplink and downlink, respectively, and and are the target upper bounds in the uplink and downlink, respectively. Hence, the chosen action can be described by

7.17

Two constraints are implicit in (7.17). First, all BSs in cannot be switched off simultaneously. Second, active BSs must provide radio coverage for mobile users in inactive cells.

Given the system state , the next state transition probability is independent of the action , that is,

7.18

In addition, the transition probability is deterministic and inferred from the historical traffic patterns.

The slow timescale cost function is determined based on the fast timescale actions, a topic that will be addressed in the next subsection.

7.4.1.2 Fast Timescale

The fast timescale decision problem is to control the transmission powers of BSs and MTs to minimize (and balance) the total expected energy consumption. Since , the fast timescale is an infinite horizon decision problem.

The fast timescale state represents the number of mobile users with uplink and downlink traffic in the geographical region, that is, . The fast timescale system behaves as a discrete queuing system. Within period , the arrivals of mobile users with uplink and downlink traffics follow Bernoulli processes with probabilities and in the uplink and downlink, respectively. The uplink and downlink service processes follow geometric distributions with parameters and , respectively, where and are expressed in per unit . A maximum of () MTs can be served simultaneously in the uplink (downlink), (), where denotes the indicator function. Hence, the uplink and downlink queues can be described by and queues, respectively [203]. Define as the probability that MTs have completed their uplink service out of MTs in the uplink. It follows that

7.19

Let and denote the steady-state probabilities of having and MTs in the uplink and downlink, respectively. The balance equations for the uplink queue are given by

7.20

Similar equations can be written for the downlink queue. Using the balance equations, one can easily derive the steady-state probabilities and and the transition probabilities and by solving a set of linear equations. In finding , the blocking probabilities and are given by and , respectively, for the current time period arrival rates and .

Given the slow timescale action and the fast timescale state , the fast timescale action controls the transmission powers of the BSs and MTs, that is,

7.21

Given the system state , the next-state transition probability is independent of the action , and is given by

7.22

Given the actions taken at period , the BSs' expected energy consumption is

7.23

and the expected energy consumption for the MTs at the uplink is given by

7.24

Since we aim to minimize (and balance) the total expected energy consumption, the cost function is expressed as

7.25

where is a weighting factor.

We derive the optimal BS-switching decisions and transmission power control for MTs and BSs in the next subsection.

7.4.1.3 Optimal Decisions

Given the system state and action in period , the fast timescale decision framework total value function is given by

7.26

where is the initial system state in period and denotes the expectation, which is taken over the system state and is the policy of the fast timescale decision problem in period . Hence, is a set of actions taken for all at a given , with a policy space . The immediate cost of the slow timescale decision problem given the fast timescale policy in period is expressed as

7.27

where the expectation is taken over the initial system state . Let denote the slow time scale policy, which admits the policy space of . The dynamic planning approach with balanced energy efficiency follows the policies and for all and minimizes the total uplink and downlink expected energy cost, that is,

7.28

and the expectation is over the states .

The optimal solution for (7.28) is a sequence for all that minimizes the expected total energy consumption expressed by Ismail et al. [198]

7.29

The approach is to find the optimal fast timescale policy that minimizes the expected total energy consumption, given some action taken at the slow timescale. For different actions , different MT associations can be deployed, leading to different cost values . Therefore, in the second step, we determine the optimal slow timescale action that minimizes the expected total energy consumption .

7.4.2 Performance Evaluation

In this subsection, we evaluate the performance of the proposed dynamic planning approach with balanced energy efficiency through comparison with a traditional dynamic planning approach that does not account for the energy consumption of the mobile users (i.e. with ). The system model is given in Figure 7.11. The two BSs are identical and the system parameters are given by m, m, , , Mbps, MHz, W, and W, h, min and . The fast time scale arrival rate in the downlink is 0.5, and the average service duration is 0.2 for both the uplink and downlink.

Figure 7.13a and b show the expected downlink energy consumption for both balanced and unbalanced dynamic planning. The unbalanced dynamic planning energy consumption performance does not vary with the weighting factor since it does not account for the MTs' incurred energy consumption. It is affected only by the arrival rate. At low arrival rates , only one BS is kept active to serve the MTs, while at higher arrival rates higher than , both BSs are switched on to satisfy the target service quality in terms of minimum required data rates (and hence upper bound on call-blocking probabilities). On the contrary, the balanced dynamic planning energy consumption performance is affected by both and arrival rate. For low arrival rates and low , a single BS is kept active to serve the MTs. As the arrival rate increases, a second BS is switched on to satisfy the users target service quality (in terms of minimum required data rate and call-blocking probabilities). In addition, large values force the second BS activation to avoid uplink service degradation (e.g. a higher call-dropping rate and lower throughput) due to MTs' battery depletion. At low arrival rate values, the second BS activation is dominated by large values since the uplink service degradation due to MTs' battery depletion is more pronounced than users' call blocking due to limited radio resources, and the opposite is true at high arrival rate values. In Figure 7.14a and b, when a single BS is switched on at arrival rates and to 1,400, respectively, the balanced approach decides which BS should be kept active based on the spatial distribution of the uplink users. Hence, for the balanced approach, the second BS is kept active while the first BS is switched off. However, for the unbalanced approach, the expected energy consumption of the uplink users is not accounted for, and hence, the first BS is kept active while the second BS is switched off. Even if the unbalanced approach follows a random or round-robin BS switching off policy to decide which BS should be switched off, the unbalanced approach still will lead to a higher expected uplink energy consumption compared with the balanced approach.

Figure 7.15 shows the expected uplink energy consumption versus the spatial distribution of uplink users near the proximity of the first BS. The arrival rate for the uplink users is fixed at 0.4. Due to the low arrival rate, only a single BS is kept active (Figure 7.13a). As shown in Figure 7.15, with more uplink users concentrated around the second BS (), the balanced dynamic planning approach keeps the second BS active and switches off the first BS, resulting in low expected energy consumption for the uplink users, unlike the unbalanced approach which keeps the first BS active and switches off the second BS. As uplink users become more concentrated around the first BS (), the balanced approach switches off the second BS and keeps the first BS active to keep the expected energy consumption of the uplink users as minimum as possible.

7.5 Summary

At a low call traffic load, network operators are expected to save energy by switching off some of their BSs. In this context, two approaches can be adopted to serve the mobile users. The first approach relies on the same network resources, and hence, a dense macro–pico architecture is implemented and optimal cell zooming techniques (i.e. expanding and shrinking the cell size) and sleep policies (i.e. on–off switching of BSs) for both macro and pico BSs are deployed depending on the traffic pattern. In such a case, it is imperative to satisfy the users' target QoS while saving energy for the network operator. The second approach that can be adopted to serve the mobile users while switching off lightly loaded BSs relies on cooperative networking, where network operators with overlapped coverage among different BSs alternately switch on and off their BSs to achieve energy saving and avoid the dynamic planning shortcomings as mobile users are served by the active network operator. In all cases, it is beneficial to combine both switching off BSs and switching off some of the radio resources of an active BS to further improve the amount of energy saving. Finally, dynamic planning should capture and balance the trade-off in energy efficiency between network operators (in the downlink) and mobile users (in the uplink) to save energy for network operators while not jeopardizing the mobile users' perceived service quality due to a high rate battery depletion for MTs which results in a high rate of dropped services in the uplink.