Chapter 8
Greening the Cell Edges
Heterogeneous networks (HetNets) are envisioned to enable the next-generation cellular networks with higher spectral and energy efficiency. This chapter presents a two-tier HetNet, where small-cell BSs (SBSs) are arranged around the edge of the reference macro-cell such that the resultant configuration is referred to as cell-on-edge (COE). Each mobile user in a small-cell is considered to be capable of adapting its uplink transmission power according to a location-based slow power control (PC) mechanism. The COE configuration is observed to increase the uplink area spectral efficiency (ASE) and energy efficiency, while reducing the co-channel interference power. A moment-generating function (MGF)-based approach is presented to derive the analytical bounds on the uplink ASE of the COE configuration. The derived expressions are generalized to any composite fading distribution and closed-form expressions are presented for the generalized-
fading channels. Simulation results are included to support the analysis and show the spectral and energy efficiency improvements of the COE configuration. A comparative performance analysis is also provided to demonstrate the improvement in the performance of cell-edge users of the COE configuration compared to macro-only networks and other unplanned deployment strategies. Moreover, the COE deployment guarantees the reduction in carbon footprint of the mobile operations by employing adaptive uplink power control. In order to calibrate the reduction in 
emissions, this chapter provides a description of the ecological and associated economical impacts of energy savings in the proposed deployment.
8.1 Introduction
The telecommunications industry is currently witnessing a remarkable increase in the data and voice traffic, particularly with the introduction of smartphones, tablet computers and other portable smart devices. Today, the mobile data volume corresponding to 4.5 billion mobile subscribers (which represents 67% of the world population) is 45 million TB/year, and is expected to reach 623 million TB/year by 2020. The exponential growth in the data rates is due to not only an increase in the number of broadband mobile subscribers, but also bandwidth-consuming activities such as distribution of videos, online meetings, e-government services and facilities and other peer-to-peer information and content exchange services. A direct solution is to densify the BS deployment. Adding a BS to the sparsely deployed areas does not have much impact on the interference, and thus cell splitting gains are easy to achieve. Nonetheless, adding a BS to the densely deployed urban area generates severe interference per channel, and therefore, the cell-splitting gains get reduced significantly. In addition, the site acquisition cost in a capacity-limited dense urban area may also get prohibitively expensive.1
The demand for high data rates is also expected to increase (i) the network energy consumption by 16–20%; (ii) network operational expenses by 20–30% and (iii) carbon footprint of mobile communication industry by 10%, by 2020 [9, 60, 205–207]. The contributing factors behind the increase in energy consumption and carbon footprint include, but are not limited to, production, operation, distribution and maintenance of the mobile communications networks, devices and services. Therefore, the wireless network operators are facing a huge challenge to meet the escalated demands of mobile users while minimizing the energy consumption and cost of the wireless networks.
In this regard, heterogeneous networks are emerging as the most influential solution that guarantees higher data rates, offloading of macro-cell traffic and reduction of CAPEX and OPEX, while providing dedicated capacity to homes, enterprises or urban hot spots. In addition to macro-cell networks, HetNets include various kinds of small-cells, such as outdoor/indoor femto cells, relays and micro and pico cells, with radii of about 30–200 m. The small-cells are short-range, low-power and low-cost BSs that guarantee spectral and energy efficiency by reducing the propagation distance between the BS and the mobile users in the small-cells [208–212].
8.1.1 Why Cell-on-Edge Deployment?
In LTE-Advanced, the focus is on increased peak data rates, higher spectral and energy efficiency, increased number of simultaneously active mobile users and improved performance at the cell-edges. The spectral efficiency of the cell-edge mobile users is often very poor due to the higher path-loss effects and thereby degrades the overall network coverage and capacity. Due to this reason, the network operators are striving to facilitate the cell-edge mobile users in a cost-effective manner. Several small-cell deployment strategies are currently under consideration where the performance is calibrated with respect to the profitability, spectral and energy efficiency, link quality and outage probability [213–216]. However, providing coverage to the cell-edge mobile users in a spectral and energy-efficient manner is still a challenge.
Limitations in cellular coverage, particularly at the cell-edge, can be overcome by positioning small-cell BSs at the cell-edge or in a coverage hole to compensate for the drastic path-loss experienced at the cell-edge. In this context, this chapter focuses on the cell-edge deployment of the small-cells by the operator and the resultant configuration is referred to as COE configuration. The main aim of this deployment strategy is to provide the required network coverage and capacity for the cell-edge mobile users by reducing the distance between the transmitting BS and the cell-edge mobile users in an energy-efficient manner.
The COE configuration is expected to produce significant gains compared with two competitive network configurations, namely (i) HetNets, where the small-cells are uniformly distributed across the macro-cells, that is, uniformly distributed small-cells (UDC) and (ii) macro-only network (MoNet). Typically, UDC is considered as one of the standard approaches that allow unplanned deployment of the small-cells in the current infrastructure [217–219]. Even though, considering the UDC deployment may be more close to realistic deployments, the considered COE deployment is simple, easy to assess, analytically tractable, helps to conduct rapid performance assessment studies and excels UDC in the following aspects:
- Energy Consumption: Due to the limited battery power constraint and uplink power control, mobile users located close to the serving BS can achieve their desired signal to interference ratio (SINR) while minimizing their transmission power. Whereas, the cell-edge mobile users are highly likely to transmit with their maximum powers to achieve as high data rates as possible. In this context, the COE deployment reduces the transmission power of the cell-edge mobile users while allowing them to achieve their desired signal quality levels.
- Spectral Efficiency: The spectral efficiency of the HetNets increases with the increase of deployment density of small-cells. The small-cell deployment guarantees the reduction in path-loss between the mobile user and the small-cell BS, and thereby improves the link quality. The uplink spectral efficiency improvement is expected to be significant in the COE deployment, as the absence of such a configuration forces the cell-edge mobile users to get connected to the macro-cell BS via poorer channel conditions.
- Interference Reduction: In the case of a MoNet, the cell-edge mobile users are highly likely to transmit with their maximum power to achieve and maintain the desired SINR. The co-channel interference due to such cell-edge mobile users may cause significant degradation in the network performance with aggressive frequency reuse. The COE configuration enables a reduction of transmission power of the cell-edge mobile users due to the reduction in terms of distance between the transmitter and receiver, which in turn diminishes the co-channel interference with limited spectral resources.
8.1.2 Background Work
Some recent simulation-based studies investigated the performance of micro cell and pico cell deployments in terms of downlink area power consumption and spectral efficiency metrics [218–220]. The investigations in [218, 219] have shown that the power savings from the deployment of micro BSs at the macro cell-edges are moderate in full-load scenarios and strongly depend on the offset power consumption of both macro and micro sites. It has been further shown in [220] that the deployment of residential pico cells can reduce the total network energy consumption by 60% in urban areas. Nonetheless, it is important to note that all of these studies are focused on downlink performance analysis, and there is no explicit framework that investigates uplink spectral and energy efficiency of HetNets with small-cells on the edge. Since the uplink power consumption is directly related to the user's channel conditions, the type of uplink power control employed and battery power constraint, and therefore, the conclusions for downlink networks may not be directly applicable to the uplink scenarios. Moreover, it is also worth mentioning that the deployment of small-cells does not directly lead to a reduction in power consumption, rather it depends on the type of uplink power control employed and required quality of service (QoS) at mobile user's end. The higher QoS and traffic loads certainly lead to higher power consumption and consequently results in reduced power efficiency.
8.2 Two-Tier Small-Cell-on-Edge Deployment
This section presents the network layout, bandwidth partition and random mobile user distribution.
8.2.1 Network Layout
Consider a two-tier HetNet as illustrated in Figure 8.1, where the integration of macro-cell and small-cell networks is illustrated. For the sake of simplicity, the considered configuration has only the central macro-cell of the macro-cell network tier. However, it is assumed that there are 
interfering co-channel macro-cells near the reference macro-cell. The first tier of the considered HetNet comprises circular macro-cells, each of radius 
[m] with a BS 
deployed at the centre and equipped with an omni-directional antenna. Each macro-cell is assumed to have 
mobile users uniformly distributed over the region bounded by 
and 
, where 
denotes the minimum distance between the macro-cell mobile user and its serving BS.
Figure 8.1 Graphical illustration of the two-tier HetNets, where a macro-cell is surrounded by 
small-cells around the edge of the reference macro-cell
The second tier of the HetNet consists of 
circular small-cells (e.g. outdoor femto cells) each of radius 
[m] with low-power low-cost operator deployed BSs 
located at the centre of each small-cell. It is considered that the small-cells are distributed around the edge of the reference macro-cell. The resultant small-cell deployment is referred to as COE configuration. For practical reasons, the number of small-cells per macro-cell can be calculated as follows:
where 
, 
, 
denotes the ceiling function and the factor 
is referred to as the cell population factor (CPF), which controls the number of small-cells per macro-cell, that is,
2 The number of mobile users in each small-cells is expressed as 
, where 
and 
. In the COE deployment, 
out of 
mobile users are assumed uniformly distributed over the region bounded by 
and 
, whereas the remaining mobile users, that is, 
, are reserved for 
small-cells. Moreover, the frequency allocated to a reference macro-cell is reused in the neighbouring macro-cells at a reuse distance 
[m], where 
represents the network resource reuse factor. Here, the reuse distance is calculated based on the circular coverage of the macro-cells such that the network resource reuse factor is given by 
, where 
is the conventional frequency reuse factor given by 
. An aggressive frequency reuse factor, 
has been assumed for the pair 
[222]. The total bandwidth allocated to the small-cell tier is reused in each small-cell within a given macro-cell.
8.2.2 Bandwidth Partition and Channel Allocation
The spectrum partition strategy will be employed for the considered HetNets, which include COE and UDC configurations. Moreover, the spectrum partition is based on the proportion of the number of mobile users in the macro-cell and small-cells. The spectrum-splitting strategy has been considered to avoid cross-tier interference issues, that is, the interference between macro-cells and small-cells. However, this is not a limitation as it can be applied to spectrum sharing scenarios as well, by conducting a more comprehensive mathematical analysis. If 
[Hz] is the total bandwidth of the available spectrum per cell, then the total bandwidth may be divided as
where 
[Hz] and 
[Hz] represent the amount of the spectrum dedicated to the macro-cell and small-cells, respectively, based on the proportion of active mobile users. The macro-cell and small-cell bandwidth are divided further into sub-channels, where each sub-channel can be allocated to one mobile user at a time and there will not be any mobile user, who cannot be serviced by the respective macro-cell or small-cell BS. The number of active serviced channels available per macro-cell and small-cells can then be expressed as 
and 
, respectively.3 Each sub-channel is allocated to any user randomly without considering the channel conditions, that is, strictly a fair scheduling strategy is considered.
8.2.3 Mobile User Distribution
All of the mobile users in macro-cell and small-cell networks are considered as mutually independent and uniformly distributed in their respective cells. The PDF of the location of a macro-cell mobile user located at 
from the serving macro-cell BS is expressed as
where 
and 
. Similarly, the PDF of the location of a small-cell mobile user located at 
from the serving SBS can be expressed as
where 
and 
(see Fig. 8.1 for a geometrical representation of 
and 
).
8.3 Energy-Aware Transmission Design
The radio environment of a typical wireless cellular network is subject to (i) distance-dependent path-loss, (ii) shadowing and (iii) multipath fading. The radio wave propagation in small-cells is complicated due to strong LOS conditions between the transmitter and receiver. Several models can be employed for this purpose [223]. However, it has been shown that a simple path-loss model does not fit well the measurements for strong LOS environments [224]. Motivated by this fact, this chapter considers a two-slope (or commonly known as dual-slope) path-loss model, which is shown to be suitable for strong LOS conditions [223].
8.3.1 Path-Loss Model for Strong LOS Conditions
The dual-slope path-loss model considers two separate path-loss exponents 
and 
, which are referred to as basic and additional path-loss exponents, respectively. These path-loss exponents are used to characterize two different propagation environments, together with a breakpoint distance 
between them, where propagation changes form one regime to the other. The signal attenuates with the basic path-loss exponent 
before break point and attenuates with the additional path-loss exponent 
after break point. For 
, the path-loss can be modelled as 
, whereas for 
, it can be modelled as 
, where 
[m] is the break point of a path-loss curve and it depends on the macro-cell or small-cell BS's (receiver in uplink) antenna height 
[m], the antenna height of the mobile user (transmitter in uplink) 
[m] and wavelength of the carrier frequency 
. Constant 
represents the path-loss constant.
The dual-slope path-loss model can be written in a generalized form as 
, where 
.
The received signal power at macro-cell or small-cell BS from the corresponding mobile user is expressed as
where 
[W] denotes the average received signal power at the reference macro-cell or small-cell BS from the desired mobile user, which is located at a distance of 
from the same reference BS, 
is the composite shadowing and fading over the link between the mobile user and respective macro-cell or small-cell BS and 
[W] defines the mobile user transmission power, which is equal to the maximum power 
for a macro-cell user and is expressed for a small-cell user according to the slow power control (PC) mechanism as follows [225–228]:
where 
is the cell-specific parameter and it is used to control the target SINR. Using (8.7) and (8.6) can be expressed as
8.3.2 Composite Fading Channel for Strong LOS Conditions
In wireless channels, the phenomena of shadowing and fading can be jointly modelled by the composite fading distribution. Nakagami-m is a generic fading distribution, which includes Rayleigh distribution for 
(typically used for non-LOS conditions) and can well approximate the Ricean fading distribution for 
(typically used for strong LOS conditions) [229 230]. Shadowing is usually modelled by a log-normal distribution. However, due to the unavailability of a closed-form expression, log-normal-based composite fading models further complicate the analysis. Recently, it has been shown that the Nakagami log-normal distribution can be modelled by the generalized-
distribution, where the average power variations due to shadowing are closely approximated by gamma distribution [231].
Figure 8.2 shows the summary of uplink transmission power per mobile user over the range of desired target SINR for HetNets and other competitive networks, namely MoNets with and without PC, HetNets with UDC deployment and HetNets with COE configuration. The mobile users in traditional MoNets without PC transmit with the maximum power over the link, while the mobile users in MoNets with PC transmit with the minimum required power to meet the desired SINR. Similarly, the mobile users in HetNets adapt their power intelligently and transmit with the minimum power required to meet the quality of the link. The adaptive mobile user transmission power in HetNets represents the average of the minimum transmission power of the macro-cell and small-cell mobile users. The transmission power of the mobile user increases with the rise in the desired target SINR. The reduction in transmission power due to PC is significant in HetNets due to the shorter distances. Moreover, the power consumption of the HetNets with COE deployment is lower than that corresponding to the UDC deployment, since under the UDC deployment mobile users are located around the edge of the cell while transmitting with their maximum power.
Figure 8.2 Summary of uplink transmission power adaptation for several competitive networks configurations
8.4 Area Spectral Efficiency of HetNets
ASE 
of typical macro-cell and small-cell networks is mathematically defined as follows [222 232]:
where 
, 
denotes the frequency reuse factor and 
denotes the total achievable Shannon capacity of two-tier HetNets, which is given by
where 
and 
[bps/Hz] are the mean achievable capacity of the 
macro-cell and 
small-cells, respectively, 
denotes the Shannon capacity of the 
mobile user in the 
macro-cell and 
represents the capacity of the 
mobile user in the 
small-cell. More explicitly, 
is given by
where 
denotes the PDF of 
, which represents the SINR of the 
macro-cell mobile user in the 
macro-cell:
In (8.13)), 
denotes the thermal noise power, 
denotes the received power level at the reference macro-cell BS 
from the 
desired mobile user and 
represents the sum of the individual interfering power levels received at the reference macro-cell BS 
from the interfering mobile users 
, which are located in each of the interfering macro-cell. As an example, the geometrical illustration of the macro-cell-level interference model is shown in Figure 8.3. Substituting (8.6) into4 (8.13), the SINR of the macro-cell mobile user can be re-written as
where 
is the composite fading statistics of the interference from the 
mobile user in the 
macro-cell to the 
BS of interest.
Figure 8.3 Geometrical illustration of the macro-cell-level interference problem, where the interfering mobile user is located at 
in one of the 
co-channel macro-cells at a reuse distance 
Similarly, for the second tier of small-cells, 
in (8.10) can be expressed as
where 
denotes the SINR of the 
mobile user located in the 
small-cell, which is given by
where 
denotes the received power level at the reference small-cell BS 
from the 
desired mobile user and 
denotes the sum of the individual interfering power levels received at the reference small-cell 
from the interfering mobile users located in the 
interfering macro-cell. Figure 8.4 illustrates the geometrical representation of the considered small-cell interference, where the interfering signals are considered from the mobile users 
located in two adjacent small-cells. However, this effect is considered only for analytical tractability and it does not affect the overall significance of COE configuration as it will be shown later through simulation results. Substituting (8.6) into5 (8.17), 
can be expressed as
Figure 8.4 Geometrical illustration of the small-cell-level interference problem where the interfering mobile users are located at 
, that is, mobile users are located in two adjacent small-cells of the reference small-cell
Figure 8.5 shows the ASE of four different types of network configurations: (i) MoNet (solid curve with triangle markers); (ii) COE configuration with interference from two adjacent small-cells (solid curve with square markers); (iii) COE configuration with interference from 
small-cells (dotted curve with square markers) and (iv) UDC configuration with interference from 
small-cells (solid curve with circle markers). The interference from 
co-channel macro-cells is also considered in each of these configurations. It is clear that the ASE of the COE configuration has been significantly improved when the small-cells are active in the macro-cell compared with the MoNet and UDC configurations (compare the solid curve with triangle markers with the rest of the curves with circle and square markers). This is due to the fact that the COE deployment restricts only the cell-edge mobile users to communicate with the small-cells, which enhances the overall network ASE compared with UDC and MoNet configurations. More precisely, the UDC configuration allows the small-cell BSs to be deployed in the cell centre, which causes an under-utilization of the macro-BS capabilities (under-utilization of existing infrastructure). Thus, the performance degradation due to the cell-edge mobile users still exist in the UDC configuration. Due to the weaker channel gains of the mobile users in the large macro-cells, the degradation of ASE with 
is also evident.
Figure 8.5 Comparison of the ASE of MoNet with two different HetNet configurations: (i) COE configuration and (ii) UDC configuration as a function of the reference macro-cell
8.5 Analytical Bounds on ASE of HetNets
This section first calculates the analytical bounds on the mean achievable capacity of COE deployment and then it proceeds with the derivation of the lower and upper bounds on ASE.
8.5.1 Mean Achievable Capacity Based on MGF Approach
The dependence of the distribution of SINR on the distribution of the interfering user locations and their fading channels leads to multifold convolutions. Recently, an MGF-based generalized framework has been developed in [233] to evaluate the system capacity, given the MGF of the desired signal and interference random variables. Using the efficient capacity lemma, the exact capacity of a desired macro-cell mobile user can be evaluated as follows:
where 
and 
denote the MGF of the macro-cell interference and joint MGF of the received signal and interference, respectively. In particular, 
and 
can be expressed as 
and 
, respectively. Similarly, for small-cell networks, the capacity of a desired small-cell user can be expressed as
where 
and 
denote the MGF of the macro-cell interference and joint MGF of the received signal and interference, respectively. In particular, 
and 
are defined as 
and 
, respectively. Because of the computational complexity of (8.19) and (8.20), this section focuses on finding analytical bounds on the capacity, and thereby bounds on the ASE of two-tier HetNets. It is important to note that determining the statistics of SINR for the two-slope path-loss model is computationally intensive mainly due to the arbitrary locations of interferers.
8.5.2 Assumptions to Derive Upper and Lower Bounds
This section first lists the assumptions used to derive the analytical bounds for the ASE of the COE deployment. Nonetheless, such constraints have been relaxed in simulations to provide a fair comparison. Next, a well-known established method for computing upper and lower bounds is utilized by fixing the distance of the macro-cell and small-cell interferers [233]. Since a location-based power control is employed, fixing the distance of interferers ultimately leads to fixing the transmission power of the interferers. Nonetheless, the second assumption of fixed transmission powers is not considered deliberately, rather it is a consequence of the previously considered assumption of fixed distance of the interferers. The worst (near) and best (far) location of the interferers refers to the upper and lower bounds, respectively.
Figure 8.6 illustrates the geometrical model of the uplink interference in both macro-cell and small-cell networks showing the worst and best case distances of interferers to derive lower and upper bounds for the ASE of HetNet.
Figure 8.6 Geometrical illustration of uplink interference showing the worst- and best-case distance of the interferers in both macro and small cellular networks
The mobile users in the small-cell networks adapt their transmission power according to (8.7), which is significantly less than the maximum transmitting power of the mobile
users 
. The magnitude of the uplink interference signal received at the small-cell BS depends significantly on the transmission powers of the small-cell mobile users (or more explicitly interferers), which, in turn, depend on their battery power, target signal quality level and employed power control scheme. For example, the transmission power of a small-cell mobile user with 
m, 
W and 
W is anticipated to be less than 0.5 mW by using (8.7). Due to such low uplink transmission powers, the interference level received from the interfering 
small-cells, particularly those deployed far away from the reference small-cell is significantly weak and can be considered negligible. On the basis of this reason, the interference only from adjacent small-cells is considered to derive the bounds.6
At this point, it is important to stress further that the considered assumption of the interference coming from only the adjacent small-cells instead of the 
interfering small-cells is significantly useful in improving the analytical tractability while providing clean closed-form bounds for the ASE of COE configuration. Regarding the macro-cell network, it is considered that the interfering signal is received from the worst and best interfering mobile users in each of the 
macro-cells. This simplification facilitates evaluating the bounds for the worst and best case interference scenarios in the most efficient manner.
- Upper Bound: Consider a macro-cell best interference configuration which corresponds to the case where all co-channel interferers are located on the far boundary of their respective cells, that is, at a distance given by
from the desired mobile BS and transmitting with power
. Similarly, thesmall-cell interferers are considered to be located at a distance given byThe interferers are considered to transmit with the fixed transmitting powers applicable at the cell edge of small-cell,
. The desired small-cell mobile user is considered to transmit with an adaptive transmission power. - Lower Bound: Consider a macro-cell worst interference configuration which corresponds to the case where all the co-channel interferers are located near the boundaries of their respective cells, that is, at a distance given by
from the desired mobile BS and transmit with power
. Similarly, small-cell interferers are considered to be located at a distanceThe interferers transmit with fixed transmitting powers applicable at the cell edge of the small-cell,
. The desired small-cell mobile user is considered to transmit with an adaptive transmission power.
8.5.3 Analytical Bounds on the Capacity of Macro-cell Network
By assuming the worst and best interfering mobile users in a macro-cell network, the SINR of the macro-cell mobile user can be evaluated by substituting (8.21) and (8.23) into (8.14) as follows:
where 
denotes the desired signal power and 
represents the bounded cumulative interference received at the BS of interest of macro-cells. The bounds for (8.19) can be expressed as
where 
denotes the lower and upper bounds for the MGF of the bounded cumulative interference received at the BS of interest and 
denotes the exact MGF of the desired signal in the macro-cell networks. By assuming i.i.d interfering mobile users in 
interfering macro-cells, the MGF of the bounded cumulative interference 
can be evaluated as follows:
Similarly, the MGF of the received signal, 
can be derived by the use of the scaling property of MGF as follows:
Moreover, the joint MGF is given by 
.
The expression in (8.26) represents the generalized bounds on the mean achievable capacity of the desired mobile user in macro-cell networks over any type of fading channel that assumes knowledge of the MGF of the composite fading distribution.
8.5.4 Analytical Bounds on the Capacity of Small-Cell Networks
By assuming the worst and best interfering mobile users in a small-cell network, the SINR of the macro-cell mobile user can be derived by substituting (8.22) and (8.24) into (8.18) as follows:
where 
denotes the desired signal power and 
denotes the bounded cumulative interference received at the BS of interest of a small-cell. The bounds on (8.20) can be derived as follows:
where 
denotes the lower and upper bounds on the MGF of the bounded cumulative interference received at the BS of interest and 
denotes the exact MGF of the desired signal in small-cell networks. As stated earlier, the location of the worst and best interferers in small-cell networks is shown in Figure 8.6. In general, 
can be expressed by using the scaling property of MGF as follows:
Similarly, the MGF of the desired signal, 
can be expressed as
The expressions in (8.31) represent the generalized bounds on the mean achievable capacity of the desired mobile user in small-cell networks over any type of fading channel that assumes knowledge of the MGF of the composite fading distribution.
8.6 Analytical Bounds on ASE over Generalized-
Fading Channel
The CDF and MGF of the generalized-
distribution involves Meijer-G and Whittaker functions, respectively, which reduce the analytical tractability because of their computational complexity. However, in order to avoid the associated computational difficulties, the authors in [229] proposed an accurate approximation of the generalized-
distribution by a more tractable gamma distribution using the moment-matching method, that is, 
. By matching the first and second moments of the two distributions, the corresponding values of 
and 
are given by Al-Ahmadi and Yanikomeroglu [229]
where 
represents the adjustment factor. Let 
and 
denote the fading severity (shape) and scale parameter, respectively, for the desired mobile users, which are located in both the macro-cell and small-cell networks. Similarly, let 
and 
denote the fading severity (shape) and scale parameter, respectively, for the interfering mobile users, located in both the macro-cell and small-cell networks.
The analytical bound of (8.19) over a generalized-
fading channel is evaluated by using (8.26), where the MGFs of the bounded cumulative interference 
and the desired signal 
in the macro-cell network are determined by using (8.28) and (8.29), respectively:
Similarly, the analytical bound of (8.20) over the generalized-
fading channel is determined by using (8.31), where the MGFs of the bounded cumulative interference 
and the desired signal 
in the small-cell network are derived by using (8.33) and (8.34), respectively, as follows:
The desired and interference signals in both the macro-cell and small-cell networks assume a gamma distribution with different shape and scale parameters. Therefore, in order to derive a closed-form expression for the conditioned capacity, next a general result is derived, which is applicable to both macro-cells and small-cells.
By substituting (8.39) into (8.26) and (8.40) into (8.31), the bounds on the mean achievable capacity of the desired mobile user in the macro-cell and small-cell networks are obtained under the interference-limited regime. Also, the bounds for (8.9) for a COE configuration is given by
where 
, 
and 
.
Figure 8.7 illustrates the best and worst bounds on the ASE of MoNet and COE configuration. The bounds provide insights into the gain and loss in the ASE of the desired mobile user in the best and worst case interference conditions, respectively. It is observed that the analytical upper bound on the ASE of the COE configuration is quite tight in the presence of interferers from adjacent cells. Also, the analytical bounds are observed to be useful in capturing the ASE of COE and UDC configurations with 
interferers. The lower bound is comparatively loose. However, it illustrates the worst-case ASE when the macro-cell and small-cell interferer's location is in the neighbourhood of the desired cell centre. Despite the ASE degradation, the achieved ASE is higher than that corresponding to MoNet.
Figure 8.7 Analytical bounds on the ASE of (i) COE configuration considering that the interferers are located at the worst and best distances in each of the two adjacent small-cells and 
co-channel macro cells and (ii) MoNet configuration as a function of the radius of the macro-cell
8.7 Energy Analysis of HetNets
This section quantifies the energy improvements of HetNets in terms of energy consumption, energy savings and associated energy economics. The mapping between the power consumption/savings to energy consumption/savings can be understood from the following relationship:
where 
denotes the number of hours per day a mobile user is active under full-load conditions.
8.7.1 Energy Consumption of Two-Tier HetNets
In general, energy consumption is defined as the power consumption per unit time such that the uplink power consumption can be directly calculated using (8.7) and the associated energy consumption can be calculated using (8.42).
Figure 8.8a depicts the energy consumption per user for HetNets with COE deployment as a function of small-cell radius. It can be seen clearly that the energy consumption of the COE deployment outperforms the energy consumption of (i) UDC deployment and (ii) MoNets (compare the solid curve with dashed and dotted curves). The significant improvement is due to the fact that the small-cells around the edge of the macro-cell ensure a reduction in the number of edge mobile users of the macro-cell that transmit at their maximum power.7 At this point, it is important to emphasize that MoNet is a state of the COE deployment when small-cells are inactive. The resultant coverage radius of the macro-cell is 
given the geometrical illustration shown in Figure 8.1. Therefore, with the increase in the small-cell radius 
more mobile users will be located around the edge of the cell, and will transmit with the maximum power. This is the primary reason of increase in energy consumption for MoNet when the small-cells are inactive. The same reason applies to Figure 8.8b as well. The comparative summary on the performance of HetNets with COE deployment with respect to the two competitive network deployments is next presented.
- Comparison with MoNets: Energy consumption of the COE deployment outperforms the energy consumption of the MoNets due to (i) the deployment of the small-cells and (ii) reduction in the number of cell-edge mobile users who transmit with their maximum power. As an example, for
m, the energy consumption of the COE deployment reduces to 1 kWh per user, which offers a 
reduction in energy consumption compared with MoNets. - Comparison with the UDC deployment: Energy consumption of the COE deployment outperforms the UDC deployment mainly due to the reduction in the cell-edge mobile users who transmit with their maximum power, for example, for
m, the COE deployment offers a 
reduction in energy consumption compared with the UDC deployment.
Figure 8.8 Summary of energy analysis per user as a function of small-cell radius. (a) Energy consumption; (b) spectral and energy gains
8.7.2 Energy Savings of Two-Tier HetNets
Power savings per mobile user is assessed by using (8.7) as 
. The associated energy savings is calculated by using the relationship introduced in (8.42).
Figure 8.8b depicts the amount of energy saved by the mobile users who transmit with an adaptive power, for example, the energy savings offered by the COE deployment at 
m is 4 kWh, which is more than double the savings that the network can achieve at 
m and which is 1.9 kWh. In addition, Figure 8.8b quantifies the average capacity achieved per user as a function of 
. It can be observed that the HetNets with the COE deployment remain spectrally efficient over medium to high range of values for 
(for more detailed results, discussions and mathematical interpretations, see [235]).
8.8 Ecology and Economics of HetNets
This section presents the ecological impact of energy consumption and energy savings of the HetNets in terms of 
emissions and the associated economics of the networks.
8.8.1 
Emissions and Reduction in 
Emissions
In order to determine the ecological impact of the energy consumption of HetNets, this section calculates the corresponding 
emissions in mega tonnes [Mtonnes]. The conversion factor used to convert the energy consumption into 
emissions is 1 kWh 
kg 
emissions, and it represents the energy used at the point of final consumption [236].
Figure 8.9a illustrates the uplink 
emissions for (i) MoNets; (ii) HetNets with UDC deployment and (iii) HetNets with COE deployment, where all mobile users are transmitting with their adaptive power to maintain the desired SINR of the link. The 
emissions of the systems under consideration are compared with the 
emissions of the MoNets without PC, that is, the network where the mobile users are transmitting with the maximum power and the small-cells are inactive. It can be seen clearly that the 
emissions of the HetNets are reduced significantly in comparison with the MoNets without PC. As an example, the 
emissions of the MoNets without PC in 2016 is approximately 
Mtonnes. The MoNets with PC reduce the estimated 
emissions to 
Mtonnes (
reduction). This can be further reduced to 8 Mtonnes (
reduction) by introducing small-cells in HetNet with COE deployment. Finally, the significant reduction in 
emissions can be achieved by introducing small-cells around the edge of the macro-cells. The proposed HetNets with COE deployment guarantees the reduction of the 
emission to 
Mtonnes (
reduction). Therefore, the mobile communications industry can enforce effective policies to reduce the global carbon footprint emissions.
Figure 8.9 Summary of carbon footprint of HetNets. (a) Uplink 
emissions for several networks; (b) Daily 
emissions profile corresponding to various traffic loads
8.8.2 Daily 
Emissions Profile
The daily 
emissions profile quantifies the amount of 
emissions corresponding to the various mobile traffic loads, that is, percentage of the active mobile users at different times of the day. Figure 8.9b depicts the daily 
emissions profile of an European country corresponding to the daily mobile traffic loads profile presented in [60]. It can be seen clearly that the 
emissions of MoNets without PC are significantly higher during peak times of the day. Moreover, the 
emissions of the HetNets with COE deployment improve significantly during the peak periods of the day compared with the other two competitive network deployments (MoNets with PC and HetNets with UDC deployment). As an example, the maximum number of active users is 
at 9 pm. The corresponding daily 
emissions of MoNets without PC is estimated as 142 Mtonnes, and it decreases to 120 Mtonnes in the presence of PC. Moreover, the UDC deployment contributes 60 Mtonnes to daily 
emissions. In addition, HetNet with COE deployment reduces the daily 
emissions to 47.5 Mtonnes. Therefore, the daily 
emissions profile clearly shows that the proposed HetNets with COE deployment improves the energy savings, and thereby they establish green HetNets by contributing less amounts of 
emissions to the environment.
8.8.3 Low-Carbon Economy
The world economy has witnessed three economic transformations: (1) the industrial revolution, (2) the technological revolution and (3) the modern era of globalization. At present, the world economy stands at the edge of the next transformation: the age of green economy. The green economy is an economic development based on ecological sustainability and knowledgeable decisions. Most of the developing and emerging economies are struggling to balance the economical and environmental resources, at both local and global scales. The ICT and mobile communication industries are required to act now and contribute toward mitigating the effects of climate change and reducing the global carbon footprint.
The low-carbon economy index (LCEI) is generally defined as the amount of 
emissions released per capita gross domestic product (GDP) and is fundamentally dependent on several factors including energy efficiency, 
emissions, population density and economic infrastructure. In particularly, the LCEI of a mobile user is the measure of 
emissions corresponding to the energy consumed over the uplink per capita GDP. Figure 8.10 shows the LCEI of a mobile user under several competitive network configurations, namely (i) macro-only networks without PC, (ii) macro-only networks with PC, (iii) HetNets with COE and (iv) HetNets with UDC. Here, per capita GDP is assumed as $ 12,000 as mentioned in the World Bank statistics [237]. It can be seen clearly that LCEI of the heterogeneous networks can be reduced significantly in comparison with the LCEI of the macro-only networks. The improvement in LCEI is due to the fact that the mobile users in HetNets adapt their transmission power, and thereby reduce the energy consumption and 
emissions of the uplink. However, the LCEI of HetNets with COE deployment is much less than other competitive networks, including HetNets with UDC deployment. Under the COE deployment, the cell-edge mobile users transmit with a much reduced power than the UDC deployment, where a significant number of mobile users transmit with the maximum power to meet the desired target SINR.
Figure 8.10 Low carbon economy index (LCEI) for several competitive network configurations
8.9 Summary
In this chapter, we discussed the uplink performance of two-tier HetNets, where small-cells are arranged at the edge of the macro-cell, that is, the COE configuration, which is shown to facilitate the cell-edge mobile users with a guaranteed high-quality link, and thereby it tends to increase the ASE compared with the other two competitive configurations, namely the UDC and MoNet configurations. The channel propagation model explicitly considers the strong LOS conditions that exist mainly in the small-cell scenario. Analytical bounds are derived to illustrate the ASE of HetNets under the worst and best interference scenarios. The bounds are generalized for any composite fading distribution and closed-form expressions are presented for generalized-
fading channels. It is shown that significant energy savings can be achieved by (i) deploying small-cells around the edge of macro-cells and (ii) employing PC in the uplink where each mobile user transmits with adaptive power. It is shown further that the 
emissions of the COE deployment is reduced to 82% in comparison with the 
emissions of the MoNets without employing PC. Therefore, the reduction in 
emissions is considered as a cornerstone in designing and planning environment-friendly wireless networks.
APPENDIX A - Simulation Parameters
Table 8.1 Simulation parameters for COE deployment in HetNet
| Simulation parameter | Small-cell | Macro-cell |
Transmission power  |
1 W | 1 W |
Cell radius ( ) |
50 m | 150–500 m |
Path-loss exponent ( ) |
1.8 | 2.0 |
Path-loss exponent ( ) |
3.6 | 4.0 |
Additional path-loss exponent ( ) |
1.8 | 2.0 |
BS antenna height ( ) |
12.5 m | 25 m |
Mobile antenna height ( ) |
2 m | 2 m |
Reference distance ( ) |
1 m | |
Target power received  |
0.008 mW | |
Breakpoint distance ( ) |
1,300 m | 500 m |
System bandwidth ( ) |
20 MHz | |
Reuse factor ( ) |
2 | |
| Small-cell population factor (CPF) | 1 | |
Thermal noise power ( ) |
 W/Hz |
|
| Macro-cell user density | 0.005  |
|
APPENDIX B - Proof of (8.38)
Considering the integral representation of the bounded capacity conditioned on the location of the desired user (8.38) in the presence of a gamma composite fading channels, one can infer that
and simple algebraic manipulations show that (8.43) can be re-written as follows:
Applying the binomial expansion formula in the factor 
present in the numerator of (8.44), it follows that
Substituting the value from (8.45) into (8.44), the integral in (1.44) can be written as follows:
and (8.46) can be further simplified to
Now, by using the identity [238][3.197/1], that is, 
and carrying out simple algebraic manipulations, the integral in (8.43) can be evaluated and simplified to (8.38).
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