1

Interference-Aware Energy Efficiency Maximizationin 5G Ultra-Dense Networks

Chungang Yang∗, Jiandong Li∗, Qiang Ni†, Alagan Anpalagan‡, Mohsen Guizani§

Abstract—Ultra-dense networks can further improve the spec-trum efficiency (SE) and the energy efficiency (EE). However, theinterference avoidance and the green design are becoming morecomplex due to the intrinsic densification and scalability. It isknown that the much denser small cells are deployed, the morecooperation opportunities exist among them. In this work, wecharacterize the cooperative behaviors in the Nash bargainingcooperative game-theoretic framework, where we maximize theEE performance with a certain sacrifice of SE performance.We first analyze the relationship between the EE and the SE,based on which we formulate the Nash-product EE maximizationproblem. We achieve the closed-form sub-optimal SE equilibria tomaximize the EE performance with and without the minimumSE constraints. We finally propose a CE2MG algorithm, andnumerical results verify the improved EE and fairness of thepresented CE2MG algorithm compared with the non-cooperativescheme.

Index Terms—Cooperative game; Energy efficiency (EE);Ultra-dense networks; Spectrum efficiency (SE).

I. INTRODUCTION

The fifth generation (5G) mobile communication systemsare facing novel challenges due to promising mobile Internetand Internet of Things applications [1]. 5G should be withboth spectrum efficiency (SE) and energy efficiency (EE) [2],[3], [8]–[12]. Increasing network densification is regarded asone of the powerful ways to jointly enhance them in a cost-effective manner [1], [4], [5]. However, ultra-dense deploy-ment of small cells also introduces novel technical challenges,e.g., the interference. In order to avoid the interference andincrease the SE, some useful observations of interferencemanagement were reported in [6], e.g., the more irregularand denser deployment of small cells, the higher gains ininterference mitigation.

However, the interference and green design problems in theultra-dense networks are becoming more complex due to the

∗ C. Yang and J. Li are with the State Key Lab. of ISN, Xidian University,Xi’an, 710071 China. (chgyang2010@163.com; jdli@xidian.edu.cn); C. Yangis also supported by National Mobile Communications Research Laboratory,Southeast University.

† Q. Ni is with School of Computing and Communications, LancasterUniversity, Lancaster, UK. (q.ni@lancaster.ac.uk)

‡ A. Anpalagan is with the Department of Electrical and ComputerEngineering, Ryerson University, ON, Canada (email: alagan@ee.ryerson.ca).

§ M. Guizani is with Electrical and Computer Engineering DepartmentUniversity of Idaho, Idaho, USA. (email: mguizani@ieee.org).

This work was supported in part by the National Science Foundation ofChina under Grant 61201139, 61231008; by the Open Research Fund ofNational Mobile Communications Research Laboratory, Southeast University(No.2014D10); by the Fundamental Research Funds for the Central Uni-versities under Grant JB150111; by the ISN02080001; by the 111 Projectunder Grant B08038; by the EU FP7 under Grant Number PIRSES-GA-2013-610524; and by the Shaanxi Province Science and Technology Research andDevelopment Program (2011KJXX-40).

intrinsic densification and scalability. On one hand, ultra-densesmall cells underlay the macrocell, which introduces complexinterference. It is hard to analyze the interactive behaviors andstrategic decision-making among different small cell eNBs(SeNBs). Meanwhile, the scalability is also challenging inspecific hotspots. On the other hand, distributed resourcemanagement and interference control will be more effectivein ultra-dense networks. However, the signaling overhead willalways be high, which challenges and burdens the backhaulof the networks.

Different from the existing research on interference miti-gation by improving the SE performance only, in this work,we study the EE maximization problem by exploring andexploiting various cooperative diversity gains. First, it isknown that the denser the small cells are, the more cooperativediversity gains can be explored to mitigate interference, thusimproving the SE and the EE performance [19]. Second, toexplore the intrinsic characteristics of ultra-dense networks,game theory can well characterize the interactive behaviorsand strategic decision-making among different small cellplayers. Meanwhile, game theory also facilitates the designof distributed resource management and interference control.To characterize the cooperative behaviors, we turn to thebargaining cooperative games. The main contributions aresummarized as follows:

• We implement the mean field approach to characterizeand mitigate the complex interference influence. Thisapproach can be applied in the ultra-dense networks witheasier analysis of the relationship between the EE and theSE.

• With the known interference scenario, we provide closed-form relationships between the SE and the EE in differentcases. This clarifies the bargaining cooperative optimiza-tion problem formulated in this work.

• We propose a distributed cooperative interactive algo-rithm to approximate the optimal solutions, where boththe efficiency and the fairness can be guaranteed.

The remainder of this article is structured as follows. InSection II, we illustrate the typical ultra-dense networks andclarify the technical challenges. In Section III, we analyze theoptimal tradeoff between the SE and the EE, and discoverhow much revenues can be gained in the cooperative way. Weformulate the cooperative EE maximization game (CE2MG)model in Section IV. The SE optimization to maximize theenergy efficiency is analyzed without multiple constraints inSection V, and then with constraints in Section VI, respec-tively. Based on these analysis, we propose a distributed

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CE2MG algorithm. Finally, in Section VII we provide exten-sive numerical results to verify the improved EE performanceand the fairness of the presented CE2MG algorithm comparedwith the non-CE2MG algorithm. We conclude this work inSection VIII.

II. TRADEOFF, DENSIFICATION, AND COOPERATIVEBARGAINING GAMES

There are many seminal research attempting for the EEand the SE maximization, or tradeoff optimization, and wesurveyed them in [28]. Meanwhile, various interference-awaremanagement strategies have been designed for either SEor EE optimization [7]–[12]. However, it is not simple tosimultaneously optimize both the EE and the SE [8], [12],[13]. Generally speaking, the optimal EE performance oftenleads to lower SE performance, and vice versa. Therefore,there exists an inherent tradeoff between the EE and the SEoptimization. Existing studies on the tradeoff of the EE andthe SE optimization can be divided into two categories: oneis to characterize a closed-form relationship between the EEand the SE [15]; the other is to maximize the EE with theSE requirement or to maximize SE with an EE requirement.There have been several studies on the SE and the EE inultra-dense networks, for instance, authors in [17] analyzedthem with extreme densification levels of both indoor andoutdoor scenarios. Authors in [18] investigated the downlinkperformance of coordinated scheduling among different smallcells. It was shown that given the number of antennas, the EEis a decreasing function with the increasing user density.

Most of surveyed work in this area concentrate on the trade-off between the spectrum and the energy efficiency, and theresource sharing, power control, or scheduling, cell zooming,and other traffic-aware techniques are designed to achieveit. However, in our paper, we take a different perspectiveto maximize the EE performance by sacrificing some SEperformance, which is motivated by the fact that sacrificinga certain spectrum efficiency can significantly improve theenergy efficiency [29].

Moreover, we investigate the problem in ultra-dense net-works [30], thus it is necessary to firstly know the desificationconcept. By now, there is not a standard concept of ultra-dense networks. Ultra-dense networks can be defined as thosenetworks, where there are more cells than active users [31].In other words, λb ≫ λu, where λb is the density of accesspoints, and λu is the density of users. Another definition ofultra-dense networks was solely given in terms of the celldensity, irrespective of the users density. Authors in [31]provided a quantitative measure of the density at which anetwork can be considered ultra-dense when the density ofaccess points λb ≥ 103cells/km2 . In fact, the first definitionconverges to the second given that the active users densityconsidered in dense urban scenarios is upper bounded by about600 active users/km2 [31].

In our previous work, we have studied the resource com-petition problem between primary and secondary users, wherewe formulated the interference-aware power control problemas a bargaining game in [20]. Meanwhile, joint channel and

power allocation were investigated in [21], and [22] surveyedthe problems which were modeled as a cooperative game in 5Gheterogeneous cellular networks. More details of the advancedgame models and their applications in wireless communica-tions can be found in [26]. Previously, in [23], we presentedan overview of the basics of the celebrated Nash bargainingsolution and its extensions with geometric interpretations tohelp understand them and facilitate distributed algorithm de-sign. Then, both symmetric and asymmetric cooperative game-theoretic frameworks were formulated with different tradeoffsincorporating an asymmetric unified -coefficient determinedcooperative game model [20]. As a use case, a preferencefunction was designed firstly incorporating both the SE andthe EE.

As stated above, the SE and the EE are coupled with eachother, and the complex interference influences should be wellinvestigated to maximize the EE performance. To solve theEE maximization problem, we formulate a novel cooperativegame-theoretic framework in this work. Different from thecurrent investigations of tradeoff and optimization between theEE and the SE [24], [25], we answer two important questions:

• What are the characteristics of the optimal tradeoffbetween the EE and the SE with known interferencesituations;

• How to maximize the EE without sacrificing much of theSE, that is what the achievable SE performance is whilemaximizing the EE.

We formulate a novel cooperative energy efficient maxi-mization game (CE2MG) model and propose a distributedCE2MG algorithm to achieve the optimal SE solution tomaximize the EE performance for each small cell.

III. ULTRA-DENSE NETWORKS AND CHALLENGES

In this section, we illustrate ultra-dense networks, anddiscuss the characteristics of the SE and the EE, and clarify theinterference and high energy consumption challenges affectingthe SE and the EE performance.

A. Ultra-Dense Networks and Characteristics of SE and EE

We illustrate the ultra-dense heterogeneous small cell net-works (ultra-dense networks) in Fig. 1. We assume that overthe macrocell coverage, the small cells are densely deployed.SeNBs with the omni-directional antenna, coexist with themacrocell eNB (MeNB) via a shared spectrum access. Weassume that L SeNBs share bandwidth with the MeNB, wheresevere inter-tier interference and intra-tier interference existand thus impact the overall system performance. There are Lcooperating SeNBs, and the concerned SeNBs are interchange-ably called players in this paper.

In the ultra-dense networks, we omit the effects and analysisof the MeNB on the dense SeNBs in Fig. 1. We concentrate onthe investigation of the tradeoff between the EE and the SE,and the way to approach the EE maximization point withoutsacrificing much of SE of each SeNBℓ, where ℓ ∈ L andL = {1, ..., L}. Meanwhile, here we assume that all L-SeNBsform a grand coalition, which is proved to be the most socialoptimal in the cooperative game theoretic discipline [26].

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TABLE ISUMMARY OF THE KEY NOTATIONS AND DEFINITIONS.

Notation MeaningL, and ℓ The SeNB set also called the player set L = {1, ..., L}, and the index of each SeNBℓ, ℓ ∈ L

mℓ, and pcstℓ The number of SUEs, and the fixed energy consumption in each SeNBℓ, ℓ ∈ L

cmℓ , wmℓ , and gmℓ The downlink capacity, undesirable power, and channel gain of SUEm in the SeNBℓ, ℓ ∈ L

pℓ, ϖℓ, and cℓ The downlink transmission power, normalized undesirable power, and the system capacity of the SeNBℓ, ℓ ∈ Lπℓ, and ηℓ The spectrum and energy efficiency of the SeNBℓ, ℓ ∈ L

0 200 400 600 800 1000 1200 1400 1600 1800 2000-500

0

500

1000

1500

2000

2500

MeNB

Boundary

SeNB

Fig. 1. A sketch of ultra-dense heterogeneous and small cell networks.

Then, we formulate the cooperative bargaining game theoreticframework of the EE maximization in ultra-dense networks.

As shown in Fig. 1, there exist several hotspots, whichcan represent a residential community or an office building.Each hotspot can be a grand coalition constituted by multipleSeNBs, where each SeNB is also called a player in a game.Each SeNBℓ, ℓ ∈ L, will pursue the EE maximization withsuitable SE settings. Without loss of generality, we use aspecific SeNB as an example. For SeNBl, l ∈ L serving ml

small cell user equipments (SUEs), we assume that all the ml

SUEs can achieve a similar performance due to the limitedcoverage of the SeNBs. The downlink capacity of the mthSUE served by the SeNBl can be approximately representedby the Shannon capacity function as

cmℓ = W ln

(1 +

pℓgmℓ

ωmℓ

), (1)

where W , pℓ, gmℓ are the spectrum bandwidth, the downlinktransmission power, and the channel gain of the mth SUEserved by the SeNBℓ. ωm

ℓ is the sum of inter- and intra-tierinterference plus noise power, which is perceived by the mthSUE served by the SeNBℓ. To simplify the following analysis,here we use the natural logarithm to compute the capacity,which results in the unit of Mnat/s/User. Furthermore, thecapacity of each small cell can be expressed

cmℓ = W ln

(1 +

pℓϖℓ

), (2)

where ϖℓ is termed as the average normalized undesirable

power, which is given by

ϖℓ =1

mℓ

∑m

ωmℓ

gmℓ. (3)

Here, ϖℓ is the average normalized undesirable power withrespect to the total number mℓ of associated SUEs with theSeNBℓ.

With the above assumption of the similar capacity achievedby all associated SUEs in the small cell, it is known that ifSeNBl serves ml SUEs, then the total per-small cell capacityis

cℓ = mℓcmℓ . (4)

In the ultra-dense small cell networks, as the number ofsmall cells is very large, the distance between the small cellbase station and the user is very small. Therefore, the channelcondition and cell capacity for different small cells is veryfamiliar with each other. Thus, we assume that there is notmuch difference for the capacity of different cells in the smallcell network. In this paper, for simplicity of expression andhighlighting the contribution of our work, we assume all usersreceive with similar capacity.

Certainly, this assumption also leads to other benefits. It canreduce the analysis, or in other words we can derive the closed-form solution to reflect the relationship between the EE andthe SE. Based on which, the designed distributed algorithmcan reduce the signaling overhead. Finally, this is in line withthe cooperative game settings, where all the players rationallyexpect the utility maximization.

Most of the small cells are deployed by individual sub-scribers or the service providers, therefore each small cellowner cares more about the per-cell SE performance andthe system EE performance. To investigate the relationshipbetween them and to maximize the EE performance, we shouldfirst define the cell-specific spectrum and the energy efficiencyas follows.

Definition 1: The SE πℓ of the SeNBℓ can be defined as

πℓ =cℓW

, (5)

where cℓ (Mnat/s) is the small cell capacity defined in (4), W(MHz) is the bandwidth, and the SE πℓ (nat/s/Hz).

The EE is another critical performance metric in densenetworks due to rapidly rising costs and carbon footprint ofenergy consumption. Below we define the EE performancemetric.

Definition 2: Without loss of generality, we define the EEηℓ of the SeNBℓ as

ηℓ =cℓ

ϵℓpℓ + pcstℓ

, (6)

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where ϵℓ represents the effectiveness of the power amplifier inthe SeNBℓ, where 0 ≤ ϵℓ ≤ 1. The term pcstℓ is the constantcircuit power consumption.

In the next section we clarify serious interference and highenergy consumption challenges affecting the SE and EE per-formance metrics. Then, we identify the potential opportunitiesin ultra-dense networks through the metric analysis.

B. Summary of Research Challenges

We summarize the research challenges for the ultra-densedeployment of small cells as follows:

• Intra-tier interference among different small cells: For afull co-channel deployment, the fact of having multiplesmall cells close to each other increases interference,thereby degrading the achievable SE.

• High energy consumption: Increasing the number ofsmall cells leads to an increase in the global energyconsumption of the system. A high energy consumption isnot desirable in the ultra-dense networks due to its impacton the environment and its high operating expenses.

Serious intra-tier interference and high energy consumptionsignificantly affect the performance of both the SE and the EE.With interference-awareness of small cells, we characterizethe relationship between the SE and the EE with interferenceand circuit energy consumption consideration for an individualsmall cell. Accordingly, we formulate an EE maximizationproblem via a cooperative game theoretic framework, whichconsists of the following contents in this work.

IV. TRADEOFF ANALYSIS AND OPPORTUNITIES OFCOOPERATION GAINS

In this section, we first derive the tradeoff relationshipbetween the SE and the EE, which will help us explore oppor-tunities of cooperation gains, and realize the EE-maximizationproblem.

A. Tradeoff Analysis between SE and EE

We have the SE and the EE definitions in (5) and (6)respectively. It is useful to clarify the relationship betweenthem, which can help us design an energy efficient ultra-densenetwork.

Theorem 1: The tradeoff relationship between spectrumand energy efficiency of each player ℓ, ℓ ∈ L can besummarized as

ηℓ =πℓ

ϵℓϖℓ

W

(e

πℓmℓ − 1

)+

pcstℓ

W

. (7)

Proof: Observed from (4) and (5), it is easy to concludethat

Wπℓ = mℓcmℓ , (8)

with the assumptions of similar capacity achieved by all theSUEs associated to the SeNBℓ. At this time, we compute thetransmission power pℓ via (2) with cmℓ = Wπℓ

mℓaccording to

(8). At last, we achieve a closed-form transmission power pℓas

pℓ = ϖℓ

(e

πℓmℓ − 1

). (9)

Furthermore, with (5) we know cℓ =πℓ

W . Substituting (9) into(6), and with necessary normalized transformation with respectto bandwidth W , we conclude this proof.

Observing the closed-form of tradeoff relationship betweenthe spectrum and the energy efficiencies in (7), we know thatit is important and different from the literature, e.g., [34],because it characterizes the relationship between the EE andthe SE. Meanwhile, here we can clearly see the effects of thenumber of small cells, the interference, and circuit power onthe tradeoff. Moreover, we have the following conclusions.

• When pcstℓ = 0, if SE πℓ → 0, then the EE ηℓ → 0;if SE πℓ → ∞, then ηℓ → 0. Therefore, the EE ηℓ isa first-increasing and then finally decreasing function ofSE πℓ.

• When pcstℓ = 0, if SE πℓ → 0, then the EE ηℓ = Wmℓ

ϵℓϖℓ;

if SE πℓ → ∞, then ηℓ → 0.Meanwhile, if we can always attain the optimal SE π⋆

ℓ , ℓ ∈L, then the transmission rate of the SeNBℓ is c⋆ℓ = Wπ⋆

ℓ canbe determined with the above assumptions. Furthermore, theTheorem 1 leads to various cooperative gains to mitigate theinterference, save the energy, and balance the traffic.

V. COOPERATIVE ENERGY EFFICIENCY MAXIMIZATIONGAME (CE2MG) AND PROBLEM FORMULATION

With the above listed technical challenges, we have foundthat the identified cooperation benefits could deal with them. Inthis section, we explore such kinds of rich cooperation diver-sities to combat these challenges via a bargaining cooperativegame theoretic framework. We formulate a cooperative energyefficient maximization game (CE2MG) model and proposea distributed CE2MG algorithm to achieve the optimal SEsolution of each player maximizing system EE. Bargaining-based cooperative game can guarantee the performance of boththe efficiency and the fairness among different SeNBs.

A. Cooperative Energy Efficiency Maximization Game(CE2MG)

It is known that the optimal Nash cooperative bargainingsolution (NBS)-based control will achieve an optimal tradeoffbetween Nash fairness and Nash axiomatic efficiency underthe framework of Nash axiomatic theory, which has beenverified in our previous NBS-formulated work of [20]–[22].In summary, the cooperative EE maximization game can beachieved by solving the Nash-product problem of {π⋆

1 , π⋆2} =

maxη1≥ηmin1 ,η2≥ηmin

2(η1−ηmin

1 )(η2−ηmin2 ), where ηmin

1 andηmin2 are regarded as the disagreement points. Generally, ηmin

1

and ηmin2 are set as the minimal energy efficiency requirements

of the participating players.With these basic statements of Nash bargaining game of

a two-player case, we define the L-player cooperative EEmaximization game as follows.

Definition 3: The L-player cooperative EE maximizationgame (CE2MG) is formulated as CE2MG = {L,S,U},with L = {1, 2, ..., L} as the player set, and L-SeNBs inultra-dense networks are regarded as the players; S is the

Cartesian product action space defined as S =L∏

ℓ=1

Sℓ, where

5

Sℓ represents the available set of player ℓ, which will be further

given with multiple constraints; U =L∏

ℓ=1

uℓ is systematic

utility function, which characterizes the player’s EE preferenceregarding the tradeoff between EE and SE as described in (7).

The optimal total utility in the Nash-product form definedin the presented (CE2MG) framework guarantees both theefficiency and the fairness, which has been proved in [20]–[22]. In the following, we first define the cooperative bargain-ing solution of the CE2MG and investigate its properties. Weuse the straightforward achieved definition in game theory todescribe the equilibrium behaviors.

Definition 4: An SE profile π⋆ = {π⋆ℓ , ℓ ∈ L} is a Nash

cooperative bargaining solution if and only if no player canimprove its utility by deviating unilaterally, i.e.,

uℓ(π⋆ℓ , π

⋆−ℓ) ≥ uℓ(πℓ, π

⋆−ℓ), ∀ℓ ∈ L, ∀πℓ ∈ Sℓ, πℓ = π⋆

ℓ .

Nash cooperative bargaining solutions for the CE2MG can beguaranteed by following the best response function.

Definition 5: We define the best response function (BRF) ofplayer ℓ ∈ L as the optimal SE profile that maximizes the EEutility when any SE profiles {π−ℓ,−ℓ ∈ L,−ℓ = ℓ} of otherplayers are given. Mathematically, it is represented as

ρ(π−ℓ) = arg maxπℓ∈Sℓ

uℓ(πℓ, π−ℓ).

Based on the definition of the BRF, it is known that the Nashcooperative bargaining solution of player ℓ ∈ L is

π⋆ℓ = ρ(π⋆

−ℓ).

At this time, the problem is transferred to derive the BRFto approach the cooperative bargaining equilibrium solutionof player ℓ ∈ L. We will formulate the Nash-product EEmaximization problem to achieve such a BRF.

B. Problem Formulation

In the general cooperative bargaining game-theoretic frame-work, the CE2MG is formulated as the following optimizationproblem

P1 : max u =L∏

ℓ=1

(ηℓ − ηmin

ℓ

), (10a)

subject to π ≤L∑

ℓ=1

πℓ, (10b)

πℓ ≤ πmaxℓ , ℓ = 1, ..., L. (10c)

Objective (10a) is the Nash product function of the EE functiondefined in (7) and the minimum EE of the player ℓ, which isin line with the Nash bargaining game-theoretic framework.Constraint (10b) represents the summation of SE that is largeror equal to a minimum SE requirement π. πℓ and πmax

ℓ are theSE and maximum SE of player ℓ, respectively. Each player isconstrained by the individual rate limit in (10c).

This equivalent re-formulation is widely used to transferthe Nash product-based objective function into the utility-summation form using the logarithmic function [22]. It isknown that this process does not change the convexity of theprime objective function in (10).

Moreover, and according to [22], the equivalent model of(10) is given by

P2 : max u =

L∑ℓ=1

ln(ηℓ − ηmin

ℓ

), (11a)

subject to (10b) and (10c), (11b)

where we compute u = ln(u) as a natural logarithmictransformation that will not change the convexity of u. Wewill analyze the problem to achieve the specific BRF withoutand with the constraints in the following two sections.

VI. OPTIMAL SPECTRAL EFFICIENCY ANALYSIS WITHOUTCONSTRAINTS

In this section, we first study the optimal SE to maximize theEE, where we omit the individual and system SE requirements.Then, some intrinsic characteristics between the EE and theSE are provided in this section.

We first characterize the optimal tradeoff between the EEand the SE aware of the interference situation. We will intro-duce the corresponding methods to estimate the interferencepower in the simulation section.

With (7) and to simplify the following expressions, werepresent the EE as

ηℓ =πℓ

φℓ + σℓ, (12)

where φℓ = µℓ

(e

πℓmℓ − 1

)is a function of the SE πℓ, and

here µℓ = ϵℓϖℓ

W is the effective interference plus noise powerspreading over all the bandwidth W , and σℓ =

pcstℓ

W is the nor-malized circuit power consumption. For each implementationof the EE maximization, we assume that both the normalizedstatic power consumption σℓ and the normalized interferencepower µℓ are determined.

Finally, according to (11a), we have the following optimiza-tion problem without multiple constraints.

P3 : max u =L∑

ℓ=1

ln

(πℓ

φℓ + σℓ− ηmin

ℓ

). (13)

Furthermore, we analyze the possible existence properties andthe closed-form of SE to maximize the EE.

Theorem 2: There always exist optimal solutions of SE tomaximize the EE with the known σℓ, µℓ, and fixed number ofSUEs, mℓ, ℓ ∈ L in P3 defined in (13).

Proof: With the known σℓ, µℓ, and fixed number ofSUEs, mℓ, ℓ ∈ L in P3 defined in (13), the individual EE-related utility function uℓ = ln

(πℓ

φℓ+σℓ− ηmin

ℓ

)is a unimodal

function with respect to πℓ. The detailed proof can be foundin the Appendix A.

With the above conclusion, it is known that there alwaysexist optimal solutions of the spectrum efficiency to maximizethe EE. We further derive the optimal closed-form solutions.

Theorem 3: The optimal SE π⋆ℓ , ℓ ∈ L to maximize the

system EE can be mathematically achieved by solving thefollowing equation:

πℓ = mℓ

(1− µℓ − σℓ

µℓe− πℓ

mℓ

), (14)

6

when πℓ = ηminℓ (φℓ + σℓ).

Proof: Here, we know that φℓ = µℓ

(e

πℓmℓ − 1

), and

we can compute first-order partial differential function withrespect to πℓ, yielding

∂φℓ

∂πℓ=

1

mℓµℓe

πℓmℓ =

φℓ + µℓ

mℓ. (15)

Further, we compute the partial differential function of theindividual utility function uℓ with respect to SE πℓ, which isshown as

∂uℓ

∂πℓ=

(φℓ + σℓ)− πℓ∂φℓ

∂πℓ(πℓ − ηmin

ℓ (φℓ + σℓ))(φℓ + σℓ)

(16)

=(φℓ + σℓ)− πℓ

mℓ(φℓ + µℓ)(

πℓ − ηminℓ (φℓ + σℓ)

)(φℓ + σℓ)

.

In the above derivation process of (16), we use the resultof (15). According to Theorem 2, we know that the opti-mal solutions always exist. Therefore, we conclude that ifπℓ − ηmin

ℓ (φℓ + σℓ) = 0, which can be also represented asπℓ = ηmin

ℓ (φℓ + σℓ), then we know that

(φℓ + σℓ)−πℓ

mℓ(φℓ + µℓ) = 0, (17)

will guarantee ∂uℓ

∂πℓ= 0 in (16). At last, with (17) we know

that

πℓ = mℓφℓ + σℓ

φℓ + µℓ. (18)

We compute φℓ+µℓ = µℓeπℓmℓ and φℓ+σℓ = µℓe

πℓmℓ +µℓ−σℓ

according to φℓ = µℓ

(e

πℓmℓ − 1

), and substitute these two

equations to (18), which concludes the proof.Theorem 4: If the attained average SE πℓ

mℓof each SeNBℓ,

ℓ ∈ L is large enough in the ultra-dense networks, then weconclude that the optimal SE π⋆

ℓ = mℓ

√σℓ

µℓ.

Proof: If the attained average SE πℓ

mℓof each SeNBℓ,

ℓ ∈ L is large enough in the ultra-dense networks, then weknow that

e− πℓ

mℓ ≈ 1− πℓ

mℓ(19)

with the first-order series approximation to e− πℓ

mℓ . Substituting(19) into (14), we conclude the proof.

In summary, we conclude from Theorem 4 that moreassociated SUEs (mℓ), higher circuit power consumption (σℓ),and less normalized undesirable power (µℓ) mean the SeNBℓ

should pursue more SE (πℓ) to maximize the EE.

VII. ANALYSIS OF OPTIMAL SPECTRAL EFFICIENCY TOMAXIMIZE ENERGY EFFICIENCY

In this section, we solve the CE2MG problem with boththe individual and the system SE constraints among differentSeNB-players. We try to find the optimal SE of each playerto maximize the system EE. We analyze the dual problem ofpredefined problem P2 in (11), based on which we analyzethe proposed CE2MG algorithm and the solution properties.

A. The Denoted Problem

In this section, we solve the problem P2 in (11) by solvingits Lagrangian relaxation problem, shown as

P4 : maxλ≥0,κℓ≥0,ℓ∈L

ξ, (20a)

subject to πℓ ∈ Sℓ, ℓ ∈ L, (20b)

where

Sℓ =

{π ≤

L∑ℓ=1

πℓ, πℓ ≤ πmaxℓ , ℓ ∈ L

}, (21)

and ξ represents the Lagrangian function associated with P2.ξ is defined in (22).

B. Analysis of SE to Maximize EE

It is critical to derive the detailed best response function forthe CE2MG model via solving (22).

Theorem 5: Again with all σℓ, µℓ, ℓ ∈ L as constants, weconclude that

πℓ = mℓ(φℓ + σℓ) (λ− κℓ) η

minℓ + 1

φℓ+µℓ

φℓ+σℓ+mℓ (λ− κℓ)

, (23)

where we assume that the Lagrangian parameters λ, and κℓ,ℓ ∈ L are pre-determined according to KKT conditions of

λ

(π −

L∑ℓ=1

πℓ

)= 0 (24)

L∑ℓ=1

κℓ (πℓ − πmaxℓ ) = 0.

Proof: With respect to the SE πℓ, we derive the first-orderderivation of the Lagrangian relaxed function in (22), whichyields

∂ξ

∂πℓ=

(φℓ + σℓ)− πℓ

mℓ(φℓ + µℓ)(

πℓ − ηminℓ (φℓ + σℓ)

)(φℓ + σℓ)

− (λ− κℓ) . (25)

We solve the equation ∂ξ∂πℓ

= 0, and then with necessarycalculation and we have

πℓ

mℓ=

(φℓ + σℓ) + (λ− κℓ) ηminℓ (φℓ + σℓ)

2

φℓ + µℓ +mℓ (λ− κℓ) (φℓ + σℓ)(26)

=(φℓ + σℓ) (λ− κℓ) η

minℓ + 1

φℓ+µℓ

φℓ+σℓ+mℓ (λ− κℓ)

.

With (26), therefore, we know (23) holds with KKT conditionsof the Lagrangian parameters constrains of λ, and κℓ, ℓ ∈ Lin (24).

Here, Theorem 5 is a general conclusion, with Theorem 3as a special case of λ = κℓ = 0, for all ℓ ∈ L.

7

ξ =

L∑ℓ=1

ln

(πℓ

φℓ + σℓ− ηmin

ℓ

)− λ

(π −

L∑ℓ=1

πℓ

)−

L∑ℓ=1

κℓ (πℓ − πmaxℓ ) (22)

=L∑

ℓ=1

{ln

(πℓ

φℓ + σℓ− ηmin

ℓ

)+ (λ− κℓ)πℓ

}+

(L∑

ℓ=1

κℓπmaxℓ − λπ

)

C. Distributed CE2MG Algorithm

With the above analysis, a distributed CE2MG algorithm ispresented to achieve the optimal SE of each SeNBℓ, ℓ ∈ L tomaximize the EE. The detailed implementation of the proposeddistributed CE2MG algorithm is described as follows:

• Initialization: Initialize the related parameters includingthe total number (L) of SeNBs in the considered ultra-dense networks, the number of SUEs (mℓ) associatedto each SeNBℓ, the circuit power consumption pcstℓ , theshared bandwidth W , the effectiveness of the poweramplifier ϵℓ, the minimum EE requirement ηmin

ℓ , and theintroduced Lagrangian factors of λ0 , κ0

ℓ of the SeNBplayer ℓ ∈ L.

• Observation: To achieve the awareness of the interfer-ence environment, it is critical for each SeNB playerℓ ∈ L to attain the undesirable power ϖℓ =

1mℓ

∑m

ωmℓ

gmℓ

in the form of (3) and σℓ =pcstℓ

W . The critical estimationof ωm

ℓ is given in Appendix B.• Decision: Each SeNB player ℓ ∈ L repeats the following

steps until the convergence to achieve the optimal SE(π⋆

ℓ ), ℓ ∈ L:– First, estimate the initial SE via

πtℓ = ln(1 +

ptℓϖt

ℓ

).

– Second, calculate the best response function

φtℓ = µt

ℓ

(e

πtℓ

mℓ − 1

),

where µtℓ = ϵℓ

ϖtℓ

W .– Third, calculate the next available SE via

πt+1ℓ = mℓ

(φtℓ + σℓ) (λ

t − κtℓ) η

minℓ + 1

φtℓ+µℓ

φtℓ+σℓ

+mℓ (λt − κtℓ)

– Finally, update the Lagrangian multipliers using

λt+1 = λt + α

(π −

L∑ℓ=1

πtℓ

), (27)

and

κt+1ℓ = κt

ℓ + β(πtℓ − πmax

ℓ

), (28)

where α and β are the adjustable step factors, whichsensitively affect the convergence properties of theCE2MG algorithm.

• Convergence: Determine the termination condition using∥∥λt+1 − λt∥∥ ≤ ε1, (29)

and ∥∥κt+1ℓ − κt

ℓ

∥∥ ≤ ε2, (30)

where ε1 and ε2 are convergence precision settings.

For the proposed distributed CE2MG algorithm, we havethe following remarks:

• First, the iteration equations of the Lagrangian multipliers(27) and (28) are achieved by the sub-gradient deriva-tions.

• Second, with the convergence settings of (29) and (30)the proposed distributed CE2MG algorithm can convergeafter limited iterations, which is verified via numericalsimulation.

• Third, in the observation step, each SeNB can achieve thereal undesirable power in the form of (3) via the similarinterference estimation method in [27], which is given inAppendix B.

VIII. NUMERICAL RESULTS

In this section, we first illustrate the simulation scenariosand the basic settings with multiple parameters. Then, we ver-ify the convergence property, the effectiveness condition, andthe improved performance of the proposed distributed CE2MGscheme. Finally, we evaluate the scheme with more settings,including the interference situation, different requirements, andextremely dense players.

A. Basic Simulation Settings

In this section, we present simulation results for aninterference-limited downlink OFDMA ultra-dense networkand observe the performance of the proposed algorithm inequilibrium. We set the system parameters as the bandwidthW = 20MHz, background noise power is 2e−13 Watt withthe noise power spectrum density as -174dBm/Hz. The averagechannel gain is 2.5e−10, which is determined with the fadingmodel of 148+40log10[d], where d is the maximum coverageradius of various SeNBs in the unit of km. The average numberof SUE mℓ = 5 associated to each SeNBℓ, the effectivenessof the power amplifier ϵℓ = 0.8, the minimum EE requirementηminℓ = 1, and the introduced Lagrangian factors of λ0 = 1,κ0ℓ = 0.5 of the SeNB player ℓ ∈ L. If it is not specified in

the following subsection, then the numerical results are withthese basic system settings. However, we will change someof them during the following simulations to reflect improvedperformance using the proposed algorithm.

8

B. Convergence VerificationFirst, we illustrate the iteration process of the proposed

CE2MG scheme, where we use the settings of mℓ = 5, ηminℓ =

1 as the benchmark case. Meanwhile, we choose mℓ =10, ηmin

ℓ = 1, and mℓ = 5, ηminℓ = 2 as another two cases

to reflect the effects of increasing number of SUEs and theincreasing minimum EE requirement of the SeNBℓ on the finalperformance and the convergence rate. The EE performance ofthe proposed CE2MG scheme with the above different settingsis described in Fig. 2 with respect to multiple iterations.

� � �� ���

����

���

����

���

����

���

����

����� ����

����� �������

�

�

����

����

Fig. 2. Convergence verification and effectiveness.

Observing Fig. 2, several conclusions can be made asfollows:

• The proposed CE2MG scheme guarantees the conver-gence with different settings, different numbers of SUEsand various minimum energy efficiency requirements ofthe SeNBℓ. We can see that the proposed CE2MG schemewill converge to a steady region of convergence aroundless than 1000 iterations.

• Increasing the number of SUEs in a specific SeNBℓ

will help enhance the EE, which can be found from theperformance curves of the settings of mℓ = 5, ηmin

ℓ = 1and mℓ = 10, ηmin

ℓ = 1. Also, increasing more SUEswill make the convergence rate slow down since moreimplementations occur.

• An increasing minimum EE requirement of the SeNBℓ

will help to improve the final performance, and there islittle effect on the convergence rate, which can be foundfrom the performance curves of the settings of mℓ =5, ηmin

ℓ = 1 and mℓ = 5, ηminℓ = 2.

Second, we investigate the tradeoff relationships of theproposed CE2MG scheme with different assumptions of fixedeffective interference plus noise power µℓ and the normalizedstatic power consumption σℓ, which is illustrated in Fig. 3.

Fig. 3 demonstrates three tradeoff relationships of the pro-posed CE2MG scheme with different assumptions of (µℓ, σℓ),(2 × µℓ, σℓ), and (µℓ, 2 × σℓ). We can make the followingconclusions:

• Specific SeNBℓ, e.g., (2× µℓ, σℓ), that bears more inter-ference will achieve a low tradeoff between SE and EE,

0 10 20 301

2

3

4

5

πl (nats/s/Hz)

ηl (

Mn

ats

/Jo

ule

)

(µl, σ

l)

(2 × µl, σ

l)

(µl, 2 × σ

l)

Fig. 3. Tradeoff relationships of the proposed CE2MG scheme with differentassumptions.

compared with the least value, e.g., (µℓ, σℓ). On the onehand, more interference means lower EE with the sameSE, e.g., when specific SE πl = 10, specific SeNBℓ, e.g.,(µℓ, σℓ) that bears less interference can achieve a 33% EEimprovement, compared with the case of (2×µℓ, σℓ). Onthe other hand, more interference means lower SE withthe same EE, e.g., when specific EE ηl = 4, specificSeNBℓ, e.g., (µℓ, σℓ) that bears less interference canachieve a 40% SE improvement, compared with the caseof (2× µℓ, σℓ).

• Specific SeNBℓ, e.g., (µℓ, 2 × σℓ) that consumes morepower will achieve a low tradeoff between SE and energyefficiency, compared with the least value, e.g., (µℓ, σℓ).On the one hand, more power consumption means lowerEE with the same SE, e.g., when specific SE πl = 10,specific SeNBℓ, e.g., (µℓ, σℓ) that is with less powerconsumption can achieve a 100% EE improvement, com-pared with the case of (µℓ, 2 × σℓ). On the other hand,more power consumption means lower SE with the sameEE, e.g., when specific EE ηl = 3, specific SeNBℓ, e.g.,(µℓ, σℓ) that consumes less power can achieve a 25%spectrum efficiency improvement, compared with the caseof (µℓ, 2× σℓ).

C. Performance Evaluation with Dense Deployments of SmallCells

In this subsection, we first characterize the effects of densi-fication (e.g., the increasing number L of small cells) on thesystem EE η and the average EE ηℓ of specific SeNBℓ, ℓ ∈ L.At last, we investigate the fairness among different SeNBs,and the optimal tradeoff of our proposed CE2MG schemecompared with the selfish non-CE2MG scheme.

First, we observe the effects of densification (e.g., theincreasing number L of small cells) on system EE η andaverage energy efficiency ηℓ of specific SeNBℓ, ℓ ∈ L. Withoutloss of generality, we illustrate both the system EE and the

9

0 200 400 600200

400

600

800

1000

L-number of SeNBs(a) System EE

η (M

na

ts/J

ou

le)

0 200 400 6000

50

100

150

200

250

L-number of SeNBs(b) Average individual EE

ηl (

Mn

ats

/Jo

ule

)

Fig. 4. Effects of densification on the system EE (a) and the average EE (b).

average EE performance with respect to the increasing numberL of small cells via Fig. 4.

We conclude that the system EE η keeps increasing with theincreasing number L of small cells, which can be seen in Fig.4; however, the rate and the speed are not the same. At first,a dramatic increment of the system EE η until the number(L) of small cells is about 200 and after that, there is littleincrement in the SE. On the other hand, we depict the curveof the individual average energy efficiency (ηℓ) with respect tothe increasing number (L) of small cells. We can see that ηℓkeeps decreasing and then reaches a flat performance, whichcan be seen in Fig. 4.

Second, we investigate the fairness among different SeNBs,and the optimal tradeoff of our proposed CE2MG schemecompared with the selfish Non-CE2MG scheme. Here, thenon-CE2MG scheme can be regarded as the conventional non-cooperative method. Here, we assume that the SeNBs alwaysselfishly expect more spectrum efficiency have the same strat-egy as the non-cooperative players in the CE2MG model. Inaddition, the corresponding scheme is termed as Non-CE2MGscheme. When analyzing the formulated CE2MG, fairness isan important issue in the multiple players case. Here, in thispaper, fairness means that L SeNB players will achieve afair improved performance with respect to either energy orspectrum efficiency. Here, we use Jain’s fairness index as thecriterion of fairness. This is mathematically computed as

J =

(L∑

ℓ=1

ηℓ

)2

LL∑

ℓ=1

η2ℓ

,

where we use the achieved EE η as the measurement metric.Here, we compute the fairness index of J from L = 1, andthen we compute it again with one SeNB participating intothe CE2MG gaming process until the total number of SeNBsis 200. The fairness index of the proposed CE2MG schemeand the benchmark Non-CE2MG are illustrated in Fig. 5.

Here, we conclude that both the presented CE2MG schemeand the Non-CE2MG scheme will achieve decreasing fairnessdue to the increasing number of small cells. Meanwhile,the presented CE2MG scheme always outperforms the Non-CE2MG scheme. For instance, the presented CE2MG schemewill achieve a 30% fairness improvement compared with theNon-CE2MG scheme when the number of small cells is 200.Furthermore, we can see that the presented CE2MG schemewill maintain this advantage with a larger number of smallcells.

At last, we show the tradeoffs in the measurement of ηµ

in Fig. 5. Also, here the presented CE2MG scheme signifi-cantly outperforms the Non-CE2MG scheme. For instance, thepresented CE2MG scheme will achieve at least 30% tradeoffimprovement compared with the Non-CE2MG scheme whenthe number of small cells is 150. Also, we can see that thepresented CE2MG scheme will maintain this advantage witha larger number of small cells. Overall, with an increasingnumber of players, both the fairness and the tradeoff decrease;however, the presented CE2MG scheme significantly outper-forms the Non-CE2MG scheme due to the exploring of thecooperation gains.

IX. CONCLUSION

Ultra-dense networks enhance the system capacity via ex-ploring both spatial and frequency diversities. The interferenceand green design problems were more complex due to theintrinsic densification and scalability, and at the same time itrequires distributed control with reduced signaling overhead.Different from the popular research on interference mitigationon improving the SE performance, in this work, we studiedthe energy efficiency maximization problem by exploring andexploiting various cooperative diversity gains. In this work,we formulated a cooperative energy efficiency maximizationgame (CE2MG) model and proposed a distributed CE2MG al-gorithm to achieve the optimal SE solution of each small cellsto maximize the system energy efficiency. We characterized

10

0 50 100 150 200 250

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

L-number of SeNBs(a) Jain's fairness index

J

CE2MG

Non-CE2MG

0 50 100 150 200 2500.8

1

1.2

1.4

1.6

1.8

2

L-number of SeNBs(b) Ratio of EE and SE

η/π

CE2MG

Non-CE2MG

Fig. 5. Performance of the Jain’s fairness index (a) and the EE vs. SE tradeoffs (b).

the optimal tradeoff relationship between energy efficiency andspectrum efficiency with the emphasis of circuit power con-sumption of small cell and the known interference situations.Based on the derived tradeoff function, we proposed an energyefficiency utility function to maximize energy efficiency with-out sacrificing more spectrum efficiency. Numerical resultsverified the convergence properties, the tradeoff relationship,the improved system energy efficiency performance and thefairness of the presented CE2MG algorithm compared withnon-CE2MG solution.

APPENDIX AUNIMODAL FUNCTION PROOF OF THE FORMULATED

UTILITY FUNCTION

We can prove the designed utility function is a unimodalfunction, which guarantees the existence of the maximumpoint. For the designed utility function uℓ = ln( πℓ

ϕℓ+σℓ−

ηminℓ ), we know the spectrum efficiency πℓ = cℓ

W , andπℓ ≥ 0; at the same time, ϕℓ = µℓ(e

πℓmℓ − 1) ≥ 0, and

µℓ = εℓϖℓ

W ≥ 0, σℓ =pcstℓ

W ≥ 0, and mℓ ≥ 0. In thedesigned utility function uℓ = ln( πℓ

ϕℓ+σℓ− ηmin

ℓ ), we knowπℓ

ϕℓ+σℓ

ϕℓ+σℓ>0> ηmin

ℓ ⇒ πℓ > (ϕℓ + σℓ)ηminℓ , which can help

first determine the value range of πℓ = cℓW . We define the

function F (πℓ) = πℓ − (µℓ(eπℓmℓ − 1) + σℓ)η

minℓ , and then we

have ∂F (πℓ)∂πℓ

= 1− µℓηminℓ

mℓe

πℓmℓ with πℓ

mℓ≥ 0. There exist two

cases:• Case 1: when µℓη

minℓ

mℓ≥ 1, we know ∂F (πℓ)

∂πℓ< 0 always

holds. It is known that πℓ

ϕℓ+σℓ− ηmin

ℓ |πℓ=0 ≤ 0 whenπℓ = 0, which tells that there does not exist πℓ > 0 toachieve the uℓ > 0.

• Case 2: when µℓηminℓ

mℓ< 1, we have ∂F (πℓ)

∂πℓ= 1 −

µℓηminℓ

mℓe

πℓmℓ = 0. We obtain πℓ = mℓ ln(

mℓ

µℓηminℓ

), and we

can see that ∂F (πℓ)∂πℓ

will decrease with πℓ. Meanwhile,we know ∂F (πℓ)

∂πℓ|πℓ=0 > 0, which leads to F (πℓ) is a

unimodal function.

In this case 2, with πl = ml ln(ml

µlηminl

), we haveF (πl)|πl=ml ln(

mlµlη

minl

) = ml ln(ml

µlηminl

) − ml + µlηminl −

σlηminl . This concludes that when F (πl)|πl=ml ln(

mlµlη

minl

) ≥ 0,

F (πl) will exist with the potential πl.As follows, we further prove the designed utility function

ul = ln( πl

ϕl+σl− ηmin

l ) is a unimodal function. We assumethat G(πl) − ηmin

l > 0, where G(πl) = πl

ϕl+σl, thus leading

to ul = ln(G(πl)− ηminl ). We have ∂ul

∂πl= 1

G(πl)−ηminl

∂G(πl)∂πl

.

Here, we know G(πl) − ηminl > 0; therefore, if ∂ul

∂πl> 0,

then ∂G(πl)∂πl

> 0. Furthermore, ∂G(πl)∂πl

= ϕl+σl−(∂ϕl/∂πl)πl

(ϕl+σl)2=

K(πl)(ϕl+σl)2

.By now the problem is to prove whether the numerator is

larger than 0. We further have K(πl) = µl(1− πl

ml)e

πlml −µl+

σl, and we know ∂K(πl)∂πl

= [ 1ml

eπlml −( 1

mle

πlml + πl

m2le

πlml )]µl =

−πlµl

m2le

πlml < 0. It is easy to conclude that K(πl) is a

monotonic function. Meanwhile, with the definition of K(πl),we know when πl = 0, K(πl) = σl > 0; when πl → −∞,K(πl) → −∞. We can conclude that G(πl) = πl

ϕl+σla

unimodal function.In summary, we know the designed utility function ul =

ln( πl

ϕl+σl− ηmin

l ) is a unimodal function.

APPENDIX BESTIMATION OF UNDESIRABLE INTERFERENCE POWER

Here, we estimate the undesirable interference power valueof ωm

ℓ in a mean field approach [27]. We have

ωmℓ =

L∑ℓ′=1,ℓ′ =ℓ

p′ℓgmℓ′,ℓ = (L− 1) p′ℓg

mℓ′,ℓ,

where p′ℓ, gmℓ′,ℓ represent the downlink power of other SeNBs

ℓ′ ∈ L, ℓ′ = ℓ except the SeNBℓ, and the interference gainfrom the SeNB′

ℓ to the SeNBℓ. In addition, p′ℓ is the known

11

test transmit power, and gmℓ′,ℓ defines the mean interferencechannel gain, which can be estimated by the following idea.

If we test using p′ℓ, then the received power at SeNBℓ is

p′Rℓ = p′ℓgmℓ′,ℓ + ωm

ℓ ,

where gmℓ′,ℓ is the known effective channel gain, and p′ℓgmℓ′,ℓ

is the effective received power, and ωmℓ is the received

interference power from all the other SeNBs ℓ′ ∈ L, ℓ′ = ℓ.With the above two equations we can derive the only

unknown variable gmℓ′,ℓ as

p′Rℓ = p′ℓgmℓ′,ℓ + (L− 1) p′ℓg

mℓ′,ℓ,

and we have

gmℓ′,ℓ =p′Rℓ − p′ℓg

mℓ′,ℓ

(L− 1) p′ℓ.

That is, each SeNB can achieve the undesirable power in theform of (3) via the interference estimation method in [27].This method can approximate the real interference with theincreasing number of SeNBs.

REFERENCES

[1] J. G. Andrews, S. Buzzi, W. Choi, S. Hanly, A. Lozano, A. Soong, andJ. C. Zhang, “What will 5G be?,” IEEE Journal on Selected Areas inCommunications, vol. 32, no. 6, pp. 1065-1082, 2012.

[2] C. L. I, C. Rowell, S. Han, Z. Xu, G. Li, and Z. Pan, “Toward Greenand Soft: A 5G Perspective,” IEEE Communications Magazine, vol. 52,no. 2, pp. 66-73, 2014.

[3] S. Han, C. Yang, and Andreas F. Molisch, “Spectrum and EnergyEfficient Cooperative Base Station Doze,” IEEE Journal on SelectedAreas in Communications, vol. 61, no. 5, pp. 1258-1271, 2013.

[4] N. Bhushan, J. Li, D. Malladi, et al, “Network Denzification: The Dom-inant Theme for Wireless Evolution into 5G,” IEEE CommunicationsMagazine, vol. 52, no. 2, pp. 82-89, 2014.

[5] M. Bennis, S.M. Perlaza, P. Blasco, Z. Han, and H.V. Poor, “Self-Organization in Dense Small Cells: A Reinforcement Learning Ap-proac,” IEEE Transactions on Wireless Communications, vol. 12, no.7, pp. 3202- 3212, 2013.

[6] B. Soret, K.I. Pedersen, N.T.K. Jrgensen, and V. Fernandez-Lopez,“Interference Coordination for Dense Wireless Network,” IEEE Com-munications Magazine, vol. 53, no. 1, pp. 102-109, 2015.

[7] Y. Wang, X. Wang, J. Shi, “A Stackelberg Game Approach for Energy-Efficient Resource Allocation and Interference Coordination in Hetero-geneous Networks,” IEEE CIT, 2014.

[8] C. Yang, J. Yue, M. Sheng, J. Li, “Tradeoff between energy-efficiencyand spectral-efficiency by cooperative rate splittin,” Journal of Commu-nications and Networks, vol. 16, no. 2, pp. 121-129, 2014.

[9] X. Ge, X. Huang, Y. Wang, M. Chen, Q. Li, T. Han, and C.-X. Wang,“Energy Efficiency Optimization for MIMO-OFDM Mobile MultimediaCommunication Systems with QoS Constraint,” IEEE Transactions onVehicular Technology, vol. 63, no. 5, pp. 2127-2138, 2014.

[10] F. S. Haider, C.-X. Wang, H. Haas, E. Hepsaydir, and X. Ge, “Energy-Efficient Subcarrier-and-Bit Allocation in Multi-User OFDMA System,”in IEEE Vehicular Technology Conference (VTC-Spring), Yokohama,Japan, 2012.

[11] X. Ge, T. Han, Y. Zhang, G. Mao, C-X. Wang, J. Zhang, B. Yang,and S. Pan, “Spectrum and Energy Efficiency Evaluation of Two-TierFemtocell Networks with Partially Open Channels”, IEEE Transactionson Vehicular Technology, vol. 63, no. 3, pp. 1306-1319, 2014.

[12] R. Q. Hu and Y. Qian, “An Energy Efficient and Spectrum EfficientWireless Heterogeneous Network Framework for 5G Systems,” IEEECommunications Magazine, vol. 52, no. 5, pp. 94-101, 2014.

[13] G. He, S. Zhang, Y. Chen, and S. Xu, “Spectrum Efficiency andEnergy Efficiency Tradeoff for Heterogeneous Wireless Networks,”IEEE Wireless Communications and Networking Conferenc, pp. 2570-2574, 2013.

[14] L. Deng, Y. Rui, P. Cheng, et al., “A Unified Energy Efficiencyand Spectral Efficiency Tradeoff Metric in Wireless Networks,” IEEECommunications Letters, vol. 17, no. 1, pp. 55-58, 2013.

[15] O. Onireti, F. Heliot, and M. A. Imran, “On the energy efficiency-SE trade-off in the uplink of CoMP system,” IEEE Trans. WirelessCommun., vol. 11, no. 2, pp. 556-561, 2012.

[16] C. Xiong, G. Y. Li, S. Zhang, Y. Chen, and S. Xu, “Energy-andSE tradeoff in downlink OFDMA networks,” IEEE Trans. WirelessCommun., vol. 10, no. 11, pp. 3874-3886, 2011.

[17] S. Yunas, M. Valkama, and J. Niemela, “Spectral and Energy Efficiencyof Ultra-Dense Networks under Different Deployment Strategies,” IEEECommunications Magazine, vol. 53, no. 1, pp. 90-100, 2015.

[18] X. Zhang, S. Zhou, Z. Niu, and X. Lin, “Energy-Efficiency andSpectrum-Efficiency Tradeoff in Coordinated Small-Cell Networks,”2014 IEEE/CIC International Conference on Communications in China,pp. 241-245, 2014.

[19] J. Xu, J. Wang, Y. Zhu, et al., “Cooperative Distributed Optimizationfor the Hyper-Dense Small Cell Deployment,” IEEE CommunicationsMagazine, vol. 52, no. 5, pp. 61-67, 2014.

[20] C. Yang, J. Li, and Z. Tian, “Optimal Power Control for Cognitive RadioNetworks with Coupled Interference Constraints: A Cooperative Game-Theoretic Perspective,” IEEE Transactions on Vehicular Technology, vol.59, no. 4, pp. 1696-1706, 2010.

[21] Q. Ni and C. Zarakovitis, “Nash Bargaining Game Theoretic Schedulingfor Joint Channel and Power Allocation in Cognitive Radio Systems,”IEEE Journal on Selected Areas in Communications, vol. 30, no. 1, pp.70-81, 2012.

[22] C. Yang, J. Li, and A. Anpalagan, “Cooperative Bargaining Game-Theoretic Methodology for 5G Wireless Heterogeneous Networks,”Transactions on Emerging Telecommunications Technologies, Accepted,2016.

[23] C. Yang, J. Li, A. Anpalagan, and M. Guizani, “Joint Power Coordi-nation for Spectral-and-Energy Efficiency in Heterogeneous Small CellNetworks: A Bargaining Game-Theoretic Perspective,” IEEE Transac-tions on Wireless Communications, vol. 15, no. 2, pp. 1364-1376, 2016.

[24] G. Miao, N. Himayat, G. Li, and S. Talwar, “Distributed interference-aware energy-efficient power optimization,” IEEE Trans. Wireless Com-mun., vol. 10, no. 4, pp. 1323lC1333, 2011

[25] E. Bjornson, E. Jorswieck, M. Debbah, and B. Ottersten, “Multi-objective signal processing optimization: The way to balance conflictingmetrics in 5G systems,” IEEE Signal Process. Mag. vol. 31, no. 6, pp.14lC23, 2014.

[26] Z. Han, D. Niyato, T. Basar, Game Theory in Wireless and Communica-tion Networks: Theory, Models, and Applications, Cambridge UniversityPress, 2012.

[27] A. Al-Zahrani and F. Yu, M. Huang, “A Joint Cross-Layer and Co-Layer Interference Management Scheme in Hyper-Dense HeterogeneousNetworks Using Mean-Field Game Theory”, IEEE Transactions onVehicular Technology, accepted, 2015.

[28] C. Yang, J. Li, and M. Guizani, “Cooperation for spectral and energyefficiency in ultra-dense small cell networks,” IEEE Wireless Communi-cations, vol. 23, no. 1, pp. 64-71, Feb. 2016.

[29] D. Zhang, R. Shinkuma and N. B. Mandayam, “Bandwidth exchange:an energy conserving incentive mechanism for cooperation,” IEEETransactions on Wireless Communications, vol. 9, no. 6, pp. 2055-2065,June 2010.

[30] X. Ge, S. Tu, G. Mao, C. X. Wang, and T. Han, “5G Ultra-Dense CellularNetworks,” IEEE Wireless Communications, vol. 23, no. 1, pp. 72-79,2016.

[31] D. David Lopez-Perez, M. Ding, H. Claussen, and A. Jafari, “Towards1 Gbps/UE in cellular systems: Understanding ultra-dense small celldeployments,” IEEE Commun. Surveys Tuts., vol. 17, no. 4, pp. 2078-2101, 2015.

[32] M. Ding, D. Lopez-Perez, G. Mao, P. Wang, and Z. Lin, “Will the areaspectral efficiency monotonically grow as small cells go dense?” IEEEGlobal Communications Conf., San Diego, CA,pp. 1-7, 2015.

[33] J. Deissner and G. Fettweis, “A study on hierarchical cellular structureswith inter-layer reuse in an enhanced GSM radio network,” Workshopon Mobile Multimedia Communications, San Diego, CA, pp. 243-251,Nov. 1999.

[34] F. Heliot, E. Katranaras, O. Onireti, and M. A. Imran, “Green Communi-cations Theoretical Fundamentals Algorithms and Applications: On theEnergy Efficiency-Spectral Efficiency Trade-off in Cellular Systems,”CRC press, Sep. 2012.

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Chungang Yang (S’09-M’12) is currently an as-sociate professor at Xidian University, where Dr.Yang leads the research team of "GUIDE, Game,Utility, Intelligent computing Design for Emergingcommunications". Dr. Yang received his Bachelorand Doctoral Degree at Xidian University, Xi’an,China, in 2006 and 2011, respectively. Between Sep.2010 and March 2011, he held the visiting scholarposition in the department of electrical and computerengineering at Michigan Technological University.Between March 2015 and March 2016, he held

the visiting scholar position in the department of electrical and computerengineering at University of Houston. He has edited two books: Game TheoryFramework Applied to Wireless Communication Networks (IGI Global, 2016),Interference Mitigation and Energy Management in 5G Heterogeneous Cellu-lar Networks (IGI Global, 2017). His research interests include resource andinterference management, network optimization, and mechanism design forcognitive radio networks, heterogeneous cellular networks, and game theoryfor wireless communication and computing networks.

Dr. Yang serves as an Editor for the KSII Transactions on Internet andInformation Systems, and an editor of special issue of Green and EnergyHarvesting Wireless Networks, Wireless Communications and Mobile Com-puting.

Jiandong Li (SM’05) was graduated from XidianUniversity with Bachelor Degree, Master Degree andPh. D in Communications and Electronic Systemrespectively in 1982, 1985 and 1991. He is withXidian University from 1985, an associate professorfrom 1990 to 1994, professor from 1994, Ph.Dstudent supervisor from 1995, and Dean of Schoolof Telecommunication Engineering, Xidian Univer-sity from 1997 respectively. Now, he also servesas Executive Vice Dean Graduate School, XidianUniversity.

Dr. Li is a senior member of IEEE and China Institute of Electronics(CIE) and the fellow of China Institute of Communication (CIC). He wasthe member of PCN specialist group for China 863 Communication hightechnology program between Jan. 1993 and Oct. 1994 and from 1999 to 2000.He is also the member of Communication specialist group for The Ministry ofInformation Industry. His current research interest and projects are funded bythe 863 High Tech Project, NSFC, National Science Fund for DistinguishedYoung Scholars, TRAPOYT, MOE and MOI.

Qiang Ni (M’04-SM’08) received his Ph.D. degreein Engineering from Huazhong University of Sci-ence and Technology, Wuhan, in 1999. He is cur-rently a Full Professor and the Head of Communica-tion Systems Research Group at the School of Com-puting and Communications, Lancaster University,Lancaster, UK. His research interests include futuregeneration communications and networking systems,energy and spectrum efficient green wireless com-munications, 5G, SDN, game theory, heterogeneousnetworks, cognitive radio network systems, ultra-

dense networks, cloud networks, energy harvesting, IoTs, vehicular networks,big data analytics, etc. He had published more than 180 research papers ininternational journals and conferences. He was an IEEE 802.11 WirelessStandard Working Group Voting Member and a Contributor to the IEEEWireless Standards.

Alagan Anpalagan (S’98-M’01-SM’04) receivedthe B.A.Sc., M.A.Sc., and Ph.D. degrees in elec-trical engineering from the University of Toronto,Canada. He joined with the ELCE Department, Ry-erson University, Canada in 2001, and was promotedto Full Professor in 2010. He served the Depart-ment as Graduate Program Director (2004-2009) andthe Interim Electrical Engineering Program Direc-tor (2009-2010). During his sabbatical (2010-2011),he was a Visiting Professor at Asian Institute ofTechnology, Thailand, and Visiting Researcher at

Kyoto University, Japan. His industrial experience includes working for threeyears with Bell Mobility, Nortel Networks, and IBM. He directs a researchgroup working on radio resource management (RRM) and radio access andnetworking (RAN) areas within the WINCORE Laboratory. He also completeda course on Project Management for Scientist and Engineers at the Universityof Oxford CPD Center, Oxford, U.K. He has coauthored three edited books:Design and Deployment of Small Cell Networks (Cambridge University Press,2016), Routing in Opportunistic Networks (Springer, 2013), Handbook onGreen Information and Communication Systems (Academic Press, 2012) anda book: Game-theoretic Interference Coordination Approaches for DynamicSpectrum Access (Springer, 2016). His research interests include 5G wirelesssystems, energy harvesting and green communications technologies, cognitiveradio resource management, wireless cross layer design and optimization,cooperative communication, M2M and sensor communication, small cell, andheterogeneous networks.

Dr. Anpalagan served as an Editor for the IEEE COMMUNICATIONSSURVEYS AND TUTORIALS (2012-2014), IEEE COMMUNICATIONSLETTERS (2010-2013), and EURASIP Journal of Wireless Communicationsand Networking (2004-2009). He also served as Guest Editor for six specialissues in IEEE WIRELESS COMMUNICATIONS,IEEE ACCESS, and so on.He was also the recipient of IEEE M.B. Broughton Central Canada ServiceAward (2016), Exemplary Editor Award from IEEE ComSoc (2013) andEditor-in-Chief Top10 Choice Award in Transactions on Emerging Telecom-munications Technology (2012) and, a coauthor of a paper that received IEEESPS Young Author Best Paper Award (2015). He is a Registered ProfessionalEngineer in the province of Ontario, Canada and Fellow of the Institution ofEngineering and Technology (FIET).

Mohsen Guizani (S’85-M’89-SM’99-F’09) re-ceived the B.S. (with distinction) and M.S. Degreesin electrical engineering and the M.S. and Ph.D.degrees in computer engineering from Syracuse Uni-versity, Syracuse, NY, USA, in 1984, 1986, 1987,and 1990, respectively. He is currently a Professorin Electrical and Computer Engineering DepartmentUniversity of Idaho, Idaho, USA. He was a Profes-sor and the Associate Vice President for GraduateStudies with Qatar University, Doha, Qatar. He wasthe Chair of the Computer Science Department at

Western Michigan University, Kalamazoo, MI, USA, from 2002 to 2006 andthe Chair of the Computer Science Department at the University of WestFlorida, Pensacola, FL, USA, from 1999 to 2002. He has held academicpositions at the University of Missouri-Kansas City, MO, USA; the Universityof Colorado-Boulder, CO, USA; Syracuse University, Syracuse, NY, USA;and Kuwait University, Kuwait City, Kuwait. His research interests includecomputer networks, wireless communications and mobile computing, andoptical networking. He currently serves on the editorial board of six technicaljournals and is the Founder and the Editor-in-Chief of the "Wireless Communi-cations and Mobile Computing" Journal published by John Wiley (http://www.interscience.wiley.com/jpages/1530-8669/). He is the author of eight booksand more than 300 publications in refereed journals and conferences. He guestedited a number of special issues in IEEE Journals and Magazines. He alsoserved as a member, Chair, and General Chair of a number of conferences. Dr.Guizani served as the Chair of the IEEE Communications Society WirelessTechnical Committee and the Chair of TAOS Technical Committee. He wasan IEEE Computer Society Distinguished Lecturer from 2003 to 2005. He isa Senior Member of the ACM.