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Cellular networks are undergoing transformation from conventional homogeneous macro Base Stations (BSs) to Heterogeneous Network (HetNet). This new paradigm not only offers a significant improvement in the overall network capacity or user data rate; it also promises an improvement in the overall network Energy Efficiency (EE). In this study, a theoretical model for evaluating the EE in HetNet is developed. A HetNet generally consists of different types of Base Stations (BSs) which operate in harmony towards a set of common goals defined by the network operator such as coverage and capacity improvement. Each BS may differ in terms of transmit power, achievable data rate, coverage, BS density and EE, under different network deployment scenarios. The results show that the picocell strongly impacts the Energy Efficiency (EE) of the HetNet as compared to microcell. More specifically it is observed that certain ratios of microcells and picocells per macro BS will result in sub-optimal of Area Energy Efficiency (AEE). It is shown that the AEE of HetNet also increases as the percentage area of macro BS overlaid by smaller cells and the density of micro/picocells increases.


INTRODUCTION
According to Cisco (2012) the number of mobileconnected devices will exceed global population by the end of 2012 and by 2016, there will be 1.4 mobile devices per person. At the same time, mobile data traffic will grow at a Compound Annual Growth Rate (CAGR) of 78 percent from 2011 to 2016, indicating the need for a new infrastructure to cope with the capacity requirement (Ling and Chizhik, 2012). It is certain that smaller base stations or Low Power Nodes (LPN) will play a major role in such infrastructure since they have higher capacity per area. On the other hand, the amount of energy consumed by this dramatic increase of traffics poses great challenges to network operators in preserving energy cost as well as environmental preservation. To address both capacity and energy challenges, future cellular networks will need to consider Network Energy Efficiency (EE) as a key performance indicator. EE not only considers energy consumed by the base station, but also features and properties related to capacity and coverage of the network (Tao et al., 2010). Some research works on cellular network planning mainly focus on the practical deployment algorithm design (Panayiotis et al., 2012;Amaldi et al., 2008). A survey of green mobile networks and an overview of some promising approaches and methods for improving the EE in HetNet is provided in Ayad et al. (2012a) and Xiaofei et al. (2012). This study extends the work to cover multi-user and multicell cases as well as considering the practical issues. In this regard, Richter et al. (2009) introduce a metric known as area power consumption APC. For a given average area spectral efficiency, the authors show that moderate power saving can be achieved through heterogeneous deployments using micro and macro base stations. In theirstudy however, only two types of BSs were considered, a uniform user distribution was assumed under full traffic load scenarios and there was no optimization on the specific location of the micro-cells (Richter et al., 2009). The study in Ayad et al. (2012b) looks into the relationship between percentage requirements of coverage area and optimal inter site distances (or macrocell radius) in homogeneous macrocell network. The authors in Miao et al. (2011) investigate multi-cell interference-limited uplink OFDMA cellular network scenarios and develop a non-cooperating game for energy-efficient power optimization. Wang and Shen (2010) analyzes the energy efficiency and area energy efficiency AEE of two-tier networks with macro and pico cells. In their study, the maximum achievable data transmission rate for each user is obtained with the knowledge of receiving SNR. In this study, a theoretical model of energy efficiency that reinforces the key deployment solutions in heterogeneous cellular networks considering three types of base stations has been derived and the network performance in terms of EE has been evaluated. The EE of HetNet is defined as the ratio of the total sum of achievable data rate at user's terminals within all BSs to the sum of power consumed by these BSs. The achievable data rate is calculated as a function of the received power at User Equipment (UE) for different locations.

SYSTEM MODELS
Propagation model: Commonly, deterioration of signal quality due to propagation is related to several factors such as Path-Loss (PL), penetration loss (β), antenna pattern (Ah) in the case of directional antennas and shadowing effect ( Ψ ). The received signal power, P rx , of the nth user from a base station BS at a distance r and angle θ from the antenna's main lobe can be modeled in term of BS transmitted power as Tesfay et al. (2011): where, Ptx is the transmitted power and ALF is the aggregate signal attenuation factor due to Path Loss (PL), outdoor-indoor penetration loss (β) and radiation pattern (Ah) as well as shadowing effect, ALF for the nth user can be written as: These factors can be obtained by choosing the appropriate path loss model (e.g., (3GPP, 2009)). The propagation model (1) provides the basis for the more realistic models presented in 3GPP (2009), which incorporate path loss dependency on carrier frequency, Line of Sight (LOS) conditions as well as shadowing deviations. Furthermore, they also consider UE and BS height, where the latter differs significantly between macro, micro and pico cells (Richter et al., 2009).

Coverage model:
A cellular coverage is designed based on an average received power P rx (R) at the cell boundary with cell radius R. The cell coverage area can be defined as the fraction of cell area where received power is above a given level P min , which is also referred as receiver sensitivity. The cell coverage area C can be written as (Goldsmith, 2005): where, the Q-function is defined as the probability that a Gaussian random variable X with mean 0 and variance 1 is greater than z (see Appendix A) P min is the minimum power received at which a throughput requirement is fulfilled. The throughput is equal or higher than 95% of the maximum throughput for a specified reference measurement channel and can be expressed as Stefania et al. (2011): where, kTB represents the thermal noise level in a specified noise bandwidth BW, where BW = N RB * 180 (kHz) as defined in 3GPP (Stefania et al., 2011). N RB is the number of Resource Blocks (RB) and 180 kHz is the bandwidth of one RB. NF is the prescribed maximum noise figure for the receiver. SINR req is the signal to interference plus noise ratio requirement for the chosen Modulation and Coding Scheme (MCS). IM is the implementation margin and the G d represents the diversity gain (Stefania et al., 2011). Note that a = 0, when the minimum received power, P min is equal to target average power, P rx (R) at the cell boundary with radius R. σ ψdB is the standard deviation of shadow fading. The outage probability of the cell is defined as the percentage of area within the cell that does not meet its minimum power requirement P min ; namely P out = p(P rx (r) < P min ) =1-C (Goldsmith, 2005).
Hence, the coverage area of a cell is a function of receiver sensitivity P min , carrier frequency f, transmitted power P tx , path losses exponent α and shadowing standard deviation σ ψdB . By limiting the coverage area to a certain size, the network performance in terms of achievable data rates and efficiencies within each base station can be estimated. The lower and upper bounds for coverage area, C can be written as: The detailed proof of this derivation is given in Appendix A. Also by optimizing the coverage area according to actual user distribution within the cellular network, cell congestion can be reduced.
Power model: Analyses of data traffic in wireless networks reveal that for current network design and operation, the power consumption is mostly insensitive and can be considered independent of the traffic load carried by the network Micallef et al., 2012;Skillermark et al., 2011). Assuming static power consumption across all traffic loads, the average power consumption of a base station Pci can be defined as Richter et al. (2009): where, N sec and N ant denote the BS's number of sectors and the number of antennas per sector, respectively. Pc i is the average total power per base station and P tx is the power fed to the antenna as defined in (1). The coefficient A i accounts for the part of the power consumption that is proportional to the transmitted power (e.g., Radio Frequency (RF) amplifier power including feeder losses), while B i denotes the power that is consumed independent of the average transmit power (e.g., signal processing, site cooling). These factors are the most important elements that provide energy efficiency within the stations (Bambos and Rulnick, 1997). For small cell site which has an optical Small-form Factor Pluggable (SFP) interface connected to an Ethernet switch port at the aggregation site, a coefficient P BHi is added to represent the power consumption of the SFP used to transmit over the backhauling fiber if exist (Tombaz et al., 2011). In order to evaluate the power consumption of the network corresponding to its size and for a given cell power consumption P C, the APC is used and can be expressed as Richter et al. (2009): where, AC is the cell area Energy efficiency model : Energy Efficiency (EE) is defined as the ratio of the total amount data delivered and total power consumed PC T (Chockalingam and Zorzi, 1998), which is expressed as: The unit of EE is then bits per sec per Watt, namely bits per Joule, which has been frequently used in literature for energy efficient communications. Bit/Joule is expected as the main EE metric for next generation cellular systems and beyond (Tao et al., 2010). R T is the overall data rate which can be defined for one user as: where, K is the total number subchannels assigned for user n (in LTE, subchannels can be considered as resource blocks, RB), hence the total data rate for all users can be written as Miao et al. (2011): Since the maximum data for each user is a function of the received power, i.e., where, Prx n is the received signal and IN n represents interference plus noise and BW n is the assigned bandwidth for the nth user. The Shannon capacity bound in Eq. (11) cannot be reached in practice due to several limitations in the implementation. To represent these loss mechanisms, the following modified Shannon capacity formula for LTE is used (Mogensen et al., 2007): where, η BW accounts for the system bandwidth efficiency of LTE and η SNR accounts for the SNR implementation efficiency of LTE. LTE generally achieves 1.6~2 dB lower than the Shannon capacity bound because η SNR is not constant and it changes with the geometry factor (G-factor). It was shown that this impact can be accounted for using the fudge factor, η, multiplied with the η BW parameter. The factor η is a correction factor which nominally should be equal to one (Harri and Antti, 2009). Eq. (12) can also be rewritten as: where, N RB,n is the number of allocated RBs to the nth user and BW RB is the RB bandwidth (Quintero, 2008). The resource block is the smallest entity that can be scheduled in the frequency domain (in downlink and uplink). This means in the frequency domain, one UE can receive or transmit in one resource block or integer multiples of one resource blocks only. In other words, it is not possible to assign less than 12 subcarriers to one terminal. The resource block size of 12 subcarriers (180 kHz) is the same for all bandwidths. A feasible starting point is to allocate equal RBs to each user, i.e. RB k =N RB /N and the sum of RBs allocated to all users equals N RB : For a 20 MHz channel, there are 100 Resource Blocks (RB) that can carry user traffic. This means the BS can theoretically serve a maximum number of 100 simultaneous users every 1 ms interval. In practice, different users will have different dynamic bandwidth requirements so that the number will be less 100. For simplicity, it is assumed that each RB is assigned for one user. Let η i = η BW η BW RB and substitute (1) in (11) Hence, the total data rate of all users within a specific BS, i can be written as: In order to assess the EE the network relative to its size, the notion of Area Energy Efficiency (AEE) which is defined as the bit/Joule/unit area is introduced. The AEE for a certain base station can be expressed as: where, EE i and A BS, i denote the energy efficiency in bit/Joule and the area covered by a certain station with the unit of km 2 respectively (Wang and Shen, 2010 where, A Het denotes the total area of the heterogeneous cellular network.

RESULTS AND ANALYSES
In the following sections, the simulation setup and the results are analyzed.
Simulation setup: A straightforward model for HetNet would consist of a mix of macro, micro and pico BSs as shown in Fig. 1. BSs are uniformly placed in the area according to the cell radius; where each BS may differ in terms of transmit power, achievable data rate, coverage and EE. The cell radius for each type of BS is calculated based on a cell coverage requirement of C = 95% by setting the transmit powers for macro, micro and pico to 46, 35 and 30dBm, respectively. UEs are assumed to be uniformly distributed within the cell and the bandwidth for the investigated LTE downlink scenario is set to 10 MHz at carrier frequency of 2.6 GHz. It is worth mentioning that the path loss model  Simulation results: In this section, some simulation results to verify the theoretical analysis and the effectiveness of the suggested approaches are presented. The performance of the HetNet from EE perspective is presented. The proposed model for energy efficiency of the heterogeneous network has been verified through extensive simulations under various practical configurations. The methodology for evaluating the energy efficiency, considering heterogeneous cellular network can be more understood through the flow chart in Fig. 2.

Effects on area power consumption:
The area power consumption of a network with different types of BSs is shown in Fig. 3. In order to achieve C=95% in correspondence to their transmitted powers, the radius of macro, micro BS and pico BS are found to be  together. On other hand, the pico BS provides better bit per joules than micro BS within the coverage area. For instance, the energy efficiency of pico BS is greater than the micro BS at their cell edge as shown in Fig. 4 Effects on area energy efficiency: While there are different cell sizes in a HetNet which comprises of macro, micro and picocells, there are different data rates for each base station according to its size and therefore EEs. Moreover, the coverage area of each cell varies according to the implementation environment. Thus, the Area Energy Efficiency (AEE) is used to evaluate the EE of HetNet relative to its size. The EE of the network corresponding to its size and deployment can be assessed by comparing AEE performance under different sector radius and scenarios. The AEE of HetNet as a function of macro BS' radius with different deployments is shown in Fig. 5. It is clearly shown that AEE decreases as the macrocell BS' radius increases. When considering the APC metric, the difference of AEE between a HetNet with 5 micros and one pico and HetNet with one micro and 10 picos becomes evident. For instance, at macro cell radius of 1000 m, the AEE of the network with 5 micros and one pico is about 4340 bites/joule/km 2 while for one micro and 10 picos the AEE is equal to 29347 bites/joule/km 2 which is greater than the previous scenario. The number of picocell in HetNet has a more dramatic impact on the AEE of the network as compared with microcell because picocells provide data rate within their coverage higher than the macro and micro BSs.
In addition, picocells provide better cell-edge performance than large cells because of their size are much more power efficient in providing broadband coverage. The AEE improves as the number of microcells and picocells increases this is because the capacity improves as the number of pico stations increases. The AEE as a function of the number of micro and picos is shown in Fig. 6. It is obvious that the AEE improves as the number of picos increases. Also, for each combination of micro and pico BSs, there is a certain AEE. Moreover, as the microcell is larger than a picocell, the number of picos is more influencing on AEE than the micros and maximum the AEE is achieved with minimum number of micros and maximum number of pico BS. However, the number of micros and picos overlay traditional macrocell networks should be chosen according to the required percentage of the macro BS area which needed to be covered and according to the user density.     The AEE of the heterogeneous networks is plotted in Fig. 7 in correspondence to different percentage of overlapping i.e. the needed percentage of the macro coverage area to be overlaid with multiple smaller cells or LPN.
It can be observed that AEE increases as the percentage area of macro BS overlaid by LPN is increases. For example, the maximum AEE is less than 1973 (bits/joule/km 2 ) when 20% of macro coverage area overlaid by LPN while the AEE becomes 58682 (bits/joule/km 2 ) when the coverage area of the macro BS is around 90%. Table 2. shows all the possible maximum number of micros and picos that can be deployed to the macro area and the corresponding AEE of the whole network. From Table 2 it can be deduced that AEE decreases as the number of micro increases and the number of pico decreases. Basically the maximum AEE can be achieved with a minimum number of micros and maximum number of picos. In other hand, AEE decreases as the required percentage of macro area decrease, the maximum AEE as well as the maximum number of simultaneous users can be obtained when the original macro area is 100% filled by small cells or LPNs as it is demonstrated in Table 3.

CONCLUSION
In this study, the Energy Efficiency (EE) of a heterogeneous cellular network HetNet has been investigated, particularly for a LTE network of macrocell base stations overlaid by randomly distributed microcells and picocells. The main contribution is the simulation results which are reinforced by the theoretical expressions that reinforce the key deployment solutions. First, the analytical expressions of the EE have been derived. Then the network performance in terms of EE has been evaluated. From the numerical results which support the analytical framework, it can be concluded that there exists an optimal micro-pico per macro density that maximizes the overall EE of HetNet. It has been shown that the APC metric cannot be the exclusive metric describing the EE in HetNet since it does not take into account the provided higher network capacity. The picocells have a dramatic impact on the AEE of the network as compared with microcell because the picocells provide higher data rate within their coverage than the macro and micro BS. Also, there is an optimal number of microcells and picocells per macro BS that achieve the maximum AEE. Moreover, the AEE of the HetNet increases as the percentages area of macro BS overlaid by smaller cells is increases. Using this model, the EE of different deployment scenarios involving HetNet can be obtained and hence providing insights on how to deploy a greener HetNet. Interference issues are not taken into account in this study, which needs to be addressed in future works.

ACKNOWLEDGMENT
This study was collaboratively carried out by Power Engineering Center, Universiti Tenaga Nasional and MIMOS Berhad.
Appendix A: In this appendix, the derivation of the analytical form of the expected percentage of locations within a cell where the received power at these locations is above a given minimum has been given. Precisely, formula (2) has been derived. The aim is to prove that: where, (3) Now by using the following substitution: y = α = b 1n(r/R) Therefore, at r = 0 → y = − ∞, also at r = R → y = a. Moreover we have r = R exp(y -α/b) and dr = R/bexp(y -α/b) dy. Substituting all these elements in the first line of Eq. (1) the result will be arrived at: Next; using integration by parts, which can be explained as follows: For any two differentiable functions u, v: In order to apply the rule (5) to (4), it can be assumed that u = Q(y) and v = (b/2) exp (2y/b): It is worth reminding that exp (-1) = 0. The next task is to find the last integral in (6). For doing so, next step is to find the explicit form of dQ (y) as: For the last integral we substitute β = -(y -2/b). This leads to that at y = -∞ → β = ∞; at y = a →β = (2-ab)/b. Also dy = -dβ. Invoking all these elements into (10) we obtain: For the last integral, by means of the definition of Q function (2) it can be simplified as: By substituting (12) into (11) relation (1) can be obtained . The Q-function is not an elementary function. However, the bounds: