Joint Admission Control, Mode Selection and Power Allocation in D2D Communication Systems

0018-9545 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TVT.2015.2487220, IEEE Transactions on Vehicular Technology

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX,XXXX 2015 1

Joint Admission Control, Mode Selection andPower Allocation in D2D Communication SystemsMuhammad Azam, Mushtaq Ahmad, Muhammad Naeem,Member, IEEE, Muhammad Iqbal, Ahmed Shaharyar

Khwaja, Member, IEEE, Alagan Anpalagan,Senior Member, IEEEand Saad Qaiser,Senior Member, IEEE

Abstract—Device to device (D2D) communications can helpin achieving the higher data rate targets in emerging wirelessnetworks. The use of D2D communication imposes certainchallenges such as interference with the cellular and D2D users.A well designed joint admission control, network mode selection,and power allocation technique in a cellular network withD2D capability can improve overall throughput. The proposedtechnique jointly maximizes the total throughput and numberof admitted users in cellular networks under quality of serviceand interference constraints. The joint admission control, modeselection and power allocation problem falls into a class ofmixed integer non-linear constraint optimization problems whichare generally NP-hard. Due to the combinatorial nature of theproblem, its optimal solution needs exhaustive search of integervariables whose complexity increases exponentially with the num-ber of user pairs. In this paper, we invoke outer approximationapproach (OAA) based linearization technique to solve the jointadmission control, mode selection and power allocation problem(JACMSPA). The proposed method gives guaranteedε-optimalsolution with reasonable computational complexity. Simulationresults verify the effectiveness of the proposed approach method.

Index Terms—Device-to-Device communication, admissioncontrol, mode selection.

I. I NTRODUCTION

Demand for higher data rates in future cellular networks isbeing witnessed globally. Data hungry applications on mobiledevices such as multimedia downloading, video streaming, on-line gaming and large file sharing among users are forcingcellular operators to adopt new technologies. These technolo-gies allow the operators to satisfy customers’ demand ofenhanced data rates and increase their revenues. The policyformulating entities and regulators around the globe are also

Manuscript received November 07, 2014; revised April 06, 2015 and July04, 2015; accepted September 12, 2015.

Copyright (c) 2015 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

M. Azam, is with Foundation University Institute of Engineering andManagement Sciences, Islamabad, Pakistan.

M. Ahmad and M. Iqbal are with Department of Electrical Engineering,COMSATS Institute of Information Technology, Wah Campus, Pakistan.

M. Naeem is with the Department of Electrical Engineering, COMSATSInstitute of Institute of Information Technology, Wah Campus, Pakistanand with the Department of Electrical and Computer Engineering, RyersonUniversity, ON, Canada. (email:[email protected])

A. S. Khwaja and A. Anpalagan are with the Department of Elec-trical and Computer Engineering, Ryerson University, ON, Canada.(email:[email protected])

S. Qaiser is with School of Electrical Engineering and Computer Science(SEECS), NUST, Pakistan

This work was supported in part by NSERC Discovery Grants.

following this trend. Rightly realizing the importance of higherdata rates, the 3rd generation partnership project (3GPP) hasstressed the need to increase the bandwidth requirement ofIMT-Advanced1 systems up to 100 MHz by the incorporationof new technological components [1]. The IMT-Advancedsystems promise to improve local area services through effi-cient utilization of scarce radio resources. Long term evolution(LTE) technologies are designed to provide high data rates [2]–[4]. Ref. [1] presents the concept of D2D communication inlong term evolution advanced (LTE-A) to meet higher datarate demands.

D2D communication in advanced cellular networks is avery promising technique wherein user equipments share thesame radio resources used by cellular users to enhance thethroughput of the cellular systems. According to [5], differ-ent techniques are possible for the controlled managementof resources by the evolved node-B (eNB). Non-orthogonalfrequency sharing method is more suitable to enhance spectralefficiency. A lot of work has been done through wireless localarea networks and wireless personal area networks. Althoughtechnologies such as bluetooth and ultra wide band providehigher data rates, they require manual peering and have nocontrol over interference. However, in D2D communication,due to the controlled assignment of radio resources by the basestation (BS) or eNB in the licensed band, problems such asmanual peering and interference among users are alleviatedto a greater extent [1]. According to [5], benefits of D2Dcommunication include: reduction in end-to-end latency dueto reduced number of hops, higher bit rates due to proximityof users, low power consumption thereby enhancing batterylife of devices, wireless cellular network evolving towardthe advanced and intelligent architectures to achieve betternetwork capacity, coverage and quality of service.

The use of D2D communication imposes certain challengessuch as interference with cellular and D2D users while reusingthe same radio resources with the cellular users. To achievehigher data rate of future wireless networks while simultane-ously satisfying the quality of service with power constrainedis a challenging task. A well designed joint admission control,mode selection2 and power allocation (JACMSPA) techniquein cellular network with D2D capability can improve overallthroughput of cellular network. Various techniques have been

1International Mobile Telecommunications-Advanced (IMT-Advanced) arerequirements issued by the the International Telecommunication Union (ITU)for future generation mobiles phone and Internet access service.

2Mode selection determines whether the user pair will communicate directlyin a point to point fashion or communicate with the help of cellular eNB.



2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX,XXXX 2015

TABLE ICOMPARISONOF DIFFERENTREFERENCES. AC = ADMISSIONCONTROL, MS = MODE SELECTION, PA = POWER ALLOCATION

Ref AdmissionControl

Mode Se-lection

Power Al-location

JACMSPA Algorithm Remarks

[7] X Heuristic Mode selection without the knowledge of perfect CSI[10] X Heuristic Graph theory based resource allocation[11] X Greedy Radio resource allocation based on greedy algorithm

and successive interference cancellation in Device-to-Device (D2D) communication

[12] X Traditional con-vex optimizationtechniques

System throughput maximization for cellular networkwith D2D capability.

[14] X X Greedy scheme Empirical D2D results for underlay WINNNER IIproject

[15] X Power optimization for orthogonal amd non-orthogonalresource sharing modes between cellular and D2D com-munication.

[16] X Best-effort Successive Interference Cancelation algo-rithm, canceling interfering signals.

[17] X X AdaptiveApproximationAlgorithms

This admission control is without mode selection.

[18] X X Robustoptimizationalgorithm

Utility Maximization and Admission Control for aMIMO Cognitive Radio Network.

[19] X X Linear Program-ming


[20] X X Convex Approx-imation


[22] X X Heuristic Distributed power control and set based admission con-trol

[23] X X Greedy Channel assignment and mode selection in OFDMAbased cellular network.

[25] X X Heuristic Subcarrier allocation for D2D multicast system withOFDMA scheme.

[28] X X X Evolutionary Al-gorithm

GA based resource allocation in D2D network.

[30] X Coverage analysis and calculation of erotic capacity incellular D2D network.

[32] X X Heuristic A bipartite matching based resource allocation.[34] X X Heuristic Resource allocation as a coalition formation game.[36] X X Heuristic Resource allocation in cooperative two-way cellular

D2D network.

suggested in the literature to enhance data rates of futurecellular networks. Currently, local services prefer to reusethe spectrum to increase the system throughput. Unlike thetraditional cellular network, D2D can establish a direct link inuser equipments by sharing the same resource blocks withother cellular users, thereby improving spectral efficiency.However, cellular users experience interference from the D2Dtransmitters. To control the interference level efficiently, eNBwill be in charge of assigning the resource blocks to theD2D devices. Literature review and some design challengesrelated to resource allocation and spectrum sharing betweencellular and D2D users to enhance the efficiency of networkis discussed in next section.

II. L ITERATURE REVIEW

In [11], the authors propose a greedy algorithm and suc-cessive interference cancelation (SIC), which allows the co-existence of three pairs of D2D user equipments and cellularusers in a channel. SIC approach maximizes the performanceof D2D links and reduces the interference from D2D usersto cellular users. Fractional frequency reuse (FFR) is usedto reduce the interference with co-channel cells [12]. They

suggest that if user equipments are in outer cell region,then D2D and cellular user equipments experience a tolera-ble interference. In [23], the authors investigate power andchannel allocation using a greedy method. In [13], the authorssuggest to improve the spectrum utilization and optimize theperformance by maximizing the weighted sum rate of D2Dand cellular users. Several efficient algorithms were analyzedon the basis of complexity and overall performance. To opti-mize different parameters of future cellular networks, powercontrol is considered in [14], [22] whereas [15] examines bothadmission and power control in D2D and cellular networks.A distance dependent mode selection is investigated in [24].In OFDMA based systems, in order to guarantee quality ofservice (QoS), the authors in [25] propose a resource allocationscheme while considering signal to interference plus noiseratio (SINR) threshold value for cellular users. The authorsdivides the scheme into two steps: In the first step, subcarriersare assigned under the premise of ensuring the minimum datarate of the D2D multicast groups and the second step involvesQoS of cellular users.Literature review and some design challenges related to spec-trum sharing between cellular and D2D users to enhance the



SHELL et. al:M. NAEEM 3

Fig. 1. A cellular system with D2D capability

energy efficiency are discussed in [26]. In [27], the authorspropose a new spectrum sharing protocol. It allows the D2Duser equipments to communicate bi-directionally with oneanother while supporting two-way communications betweenthe BS and cellular users. In [28], the authors investigatedthe resource reusing mechanism in more than one D2D pairallowing to share the multiple resource blocks to obtainhigher sum-rates. Mode selection is also performed basedon evolutionary algorithm. In [29], the authors presenteddistributed implementation. The sum-rate of D2D system ismaximized by maximizing the transmission rate using gametheory. An interference management strategy is proposed in[30] to increase the overall capacity of cellular users and D2Dsystem. A conventional technique is used that limits maximumtransmit power of D2D transmitter, so that it does not generateharmful interference from D2D user to cellular users. In D2Dcommunication, the decision to assign a part of resource todownlink or uplink is very important. It should be done onpriority to enable the reuse of resources for higher systemcapacity. Ref. [31] proposes interference control in downlinkmode to limit the BS interference to D2D user equipmentsby selecting cellular users that are closer to BS. To improvethe QoS of both D2D and cellular users, a three-step schemeis proposed in [32], which involves admission control andsubsequent power allocation for each selected D2D pair and itspotential cellular user partners. D2D needs intelligent resourcesharing as suggested in [33] to optimize the spectrum utiliza-tion. Ref. [34] investigates resource sharing issue to optimizethe system performance in D2D communication in cellularnetworks from a cooperative and distributive perspective.Inthis scheme, utility function is maximized for each user andprovides incentive to cooperate with other users to form astrong group to increase the likelihood to win its preferredspectrum resource.

A. Contributions

Based on the literature review and a closed look at Table Ireveal that a joint user, mode selection with power allocation is

TABLE IINOTATIONS

Symbol DefinitionK Set of user pairsc Cellular moded D2D modeR Radius of D2D transmissionCul

kCapacity of thekth cellular user in uplink

Cdlk

Capacity of thekth cellular user in downlinkCc

kCapacity of the kth cellular user pair-i.e.,1

2min(Cul

k, Cdl

k)

Cdk

Capacity of thekth D2D usersPmaxeNB Maximum power of eNB

Pmaxc,k

Maximum power of thekth user in cellular modePmind,k

Minimum power threshold of thekth user in D2D modeoutside radiusR

pdk

Power of thekth in D2D modepulk

Power of thekth in uplink cellular modepdlk

Power of thekth in downlink cellular modexk Binary indicator for D2D or cellular modeCmin

kMinimum rate requirement of thekth user

hk Channel gain between thekth user and eNB link(uplink)

fk Channel gain between thekth receiver and eNB link(downlink)

gk Channel gain between thekth D2D user pairφc Set of selected users in cellular modeφd Set of selected users in D2D Modeφ Set of all selected Users-i.e.,φc ∪ φd

do Reference distance for the antenna far fieldd Distance between secondary transmitter and receiverhk Rayleigh random variable associated with thekth SUξ Log normal shadowingU A utility function to maximize the joint user admission

and throughputUS A utility function to maximize the admitted usersUT A utility function to maximize the throughputpc Probability of cross overpm Probability of mutationps Probability of selection

an open area of research. There are some papers in the litera-ture that claim joint admission control and power allocation butthey always try to solve the user selection and power allocationseparately. Since the user selection and power allocation arenot separable and in addition to joint user selection and power




allocation, we are also jointly determining the mode selection.In [17]–[21], authors proposed different joint admission andpower control schemes for wireless systems. All these workdo not include the mode selection in their formulation. Asper the best knowledge of the authors, the literature reviewreveals that there is no throughput maximization scheme incellular network with D2D capability that jointly controlsthe admission of the users, mode selection (whether to bein cellular or D2D mode) and power allocation under QoSand interference constraint. The existing work focuses onindividual aspects as shown in the self explanatory TableI. The closest possible existing work is done in [28]. Theauthors apply genetic algorithm (GA) for admission controland mode selection. The main difference between [28] and ourformulation is joint admission control and mode selection.In[28], authors proposed separate admission control and modeselection where as in this paper, we propose a joint admissioncontrol and mode selection scheme. For a fair comparison,in this paper, we also compare the results of GA with ourproposed algorithm. The scope of the proposed work fillsthe gap and tries to maximize the throughput consideringJACMSPA mechanism. The main contribution of this paperare summarized as follows:

1) We formulate a constrained JACMSPA optimization prob-lem that maximizes the overall throughput of the futurecellular networks by jointly controlling admission ofthe users, satisfying mode selection and power controlconstraints of the users and base station.

2) The JACMSPA is a class of mixed integer non-linear con-straint optimization problems, which are generally NP-complete. Due to the combinatorial nature of JACMSPA,the optimal solution needs exhaustive search of integervariables whose complexity increases exponentially withthe number of user pairs. In this paper, we apply alinearization technique that uses outer approximation ap-proach (OAA) to solve this NP-complete JACMSPA. Theproposed OAA gives guaranteedε-optimal results withfinite convergence. Inε-optimal solution, for anyε > 0,theε-optimal algorithm gurantee the solution withinε ofthe optimal. We also compare the OAA algorithm withgenetic algorithm. The results show that performance ofOAA is much better than GA.

3) Theε-optimal solution is analysed in detail with the helpof simulation results.

Throughout this paper, we useA, a, and a to representmatrix, vector and an element of a vector respectively. Thispaper is organized as follows: The system model and problemstatement are described in section III. In section IV, wepresent JACMSPA solution technique using OAA method. Thesimulation results are analyzed in section V and finally weconclude this paper in section VI.

III. SYSTEM MODEL AND PROBLEM FORMULATION

We consider a cellular network having D2D communicationcapability as shown in Fig. 1. There are two possible modesof communication, (a) cellular mode and (b) D2D mode. Weassume that the users selected for D2D communication use

non-orthogonal sharing mode. In this mode, the D2D userswill re-utilize cellular network resources. LetK be the set ofuser pairs that want to communicate with one another. Wedenote bypulk , pdlk andpdk, thekth user’s transmitted power inuplink (to eNB), thekth user’s transmitted power in downlink(to the kth receiver) and thekth user power in D2D mode.The channel gain between thekth user pair isgk. We denotehk andfk as the channel gains between transmitting user-eNBlink (uplink) and eNB- receiving user (downlink) respectively.Let the antenna gain beGo and ξ = 10

ξo10 be the log normal

shadowing, whereξo is zero mean Gaussian random variablewith standard deviationσ [37]. The channelhk is modeled as[39]:

hk = hkξGo

(

do

d

)α

, (1)

wheredo andd are the antenna far field reference distance anddistance between the receiver and transmitter, respectively. Thepath loss exponent is denoted byα and hk is the Rayleighrandom variable. The channel capacity of thekth user isdefined asCk = log(1 + pkhk

N0). A summary of symbol

notations is shown in Table II. In cellular mode, the eNB willact like a relay and the communication between the cellularuser pair needs two time slots. The possible rate of thekthuser in cellular mode isCck = 1

2min

(

Culk , Cdlk)

. The rate for

kth pair in D2D communication isCdk = log(1 +pdkgkN0

). Formode selection, we define a binary mode selection indicatoras:

xk =

{

1, Cellular mode0, D2D mode.

To meet the QoS of thekth user pair, the pair must satisfyits minimum rateCmink . For any power constraint, wirelessnetwork satisfying every user’s rate requirement is not alwayspossible3. Traditional admission control schemes generallyselect the users that can give higher aggregate throughput.Inthis paper, we propose a framework for joint admission controland mode selection that not only maximizes the throughputbut also maximizes the number of admitted users under theminimum rate and power constraints. Letφ be the set ofadmitted users. One admitted user can only be served eitherin cellular or D2D mode and the set of admitted usersφ isthe union of admitted cellular and D2D users. Mathematically,this is written as:

φ = φc ∪ φd

φc ∩ φd = ∅

(2)

We introduce a utility function that maximizes admitted usersand throughput as:

U(

φ,x,pd,pul,pdl)

= US (φ)∑

k∈φ

UT(

xk, pdk, p

ulk , pdlk

)

(3)

where US = |φ||K| and UT

(

xk, pdk, p

ulk , pdlk

)

= xkCck +

(1− xk)Cdk . The utility function U

(

φ,x,pd,pul,pdl)

en-sures that if cellular mode is selected for any admitted user,

3There are a number of reasons for this-e.g., channel may be bad, batteryis low, increase in power may increase interference to others etc.




then the terms related to D2D mode should be zero andvice versa. Mathematically, we can write the joint admissioncontrol, mode selection and power allocation constrained op-timization problem as:

maxφ,x,pd,pul,pdl

U(

φ,x,pd,pul,pdl)

subject to

C1 : UT(

xk, pdk, p

ulk , pdlk

)

≥ Cmink , ∀k ∈ φ

C2 : pdk ≤ (1 − xk)RαPmind,k , ∀k ∈ φ

C3 : pulk ≤ xkPmaxc,k , ∀k ∈ φ

C4 :∑

k∈φ

xkpdlk ≤ PmaxeNB

C5 : φ = φc ∪ φd

C6 : φc ∩ φd = ∅

C7 : xk ∈ {0, 1}, ∀k ∈ K

C8 : pdk ≥ 0, pulk ≥ 0, pdlk ≥ 0 , ∀k ∈ K

(4)

The objective function in (4) is a max-min problem. Byintroducing a new variabletk, k ∈ K, we can rewrite anequivalent maximization problem as

maxt,φ,x,pd,pul,pdl

Ut(

t, φ,x,pd,pul,pdl)

subject to

C1-C8 of (4)

C9 : Culk ≥ tk, ∀k ∈ φc

C10 : Cdlk ≥ tk, ∀k ∈ φc

(5)

where

Ut(

t, φ,x,pd,pul,pdl)

= US (φ)∑

k∈φ

UT,t(

t, xk, pdk, p

ulk , pdlk

)

(6)and

UT,t(

t, xk, pdk, p

ulk , pdlk

)

= xktk + (1− xk)Cdk (7)

The utility function in the above optimization problem max-imizes the admitted users and total throughput. ConstraintC1 is the minimum rate constraint of each user. If any usercan not meet the rate constraint condition, then that user isnot selected for transmission. ConstraintsC2, C3 and C4are power constraints for D2D, cellular uplink and cellulardownlink mode respectively. ConstraintC2 ensures that incase of D2D communication, the power experienced by anyother cellular or D2D user beyond radiusR should be lessthan a threshold powerPmind,k . ConstraintC3 is the uplinkpower constraint andC4 is the downlink sum power constraint.ConstraintsC2, C3 and C4 also ensure that the respectivepower should be zero if respective mode is not selected.ConstraintsC5 and C6 ensure that D2D and cellular usersare mutually exclusive.

The formulation in (5) is a non-convex mixed integer non-linear programming problem. To prove the hardness of (5), wecan reduce the multiple-choice multiple-dimensional knapsackproblem to the JACMSPA optimization problem.

Theorem 1. JACMSPA for D2D cellular network is NP-complete.

Proof: The proof is given in the Appendix A.Due to NP-complete nature of JACMSPA, determining opti-

mal solution in polynomial time is not possible. An exhaustivesearch algorithm for (5) would enumerate all the users andmode selection options, which increases its computationalload exponentially with the number of users. The structure ofoptimization problem in (5) is very interesting. With knowndiscrete variables, the objective function of (5) is a concavefunction in power, and all the constraints are either linearorconvex. By exploiting this special structure, in the next section,we will present a branch and bound based outer approximationalgorithm (OAA) to solve (5).

IV. PROPOSEDAPPROACH TO ASOLUTION

As mentioned in the previous section, the coupling of inte-ger domain, with the continuous domain and non-linearitiesinthe problem make the class of problem mentioned in (5) verychallenging. As the integer variables (user admission and modeselection in our case) increase, the complexity analysis resultstend towards NP-completeness. Despite all these challenges,the optimization problem in (5) has a very special structure. Byexploiting this special structure, in this section we will presentan OAA method to solve (5). The OAA solves (5) in a finitesequence of alternately nonlinear programming sub-problems(by fixing the discrete variablesφ andx) and relaxation of amixed integer linear program based master problem (MILP-MP). The solution of the sub-problem provides a point thatwill generate supporting hyperplanes of the objective andconstraint functions. The OAA method adds one linearizationfor each constraint and the objective function for every sub-problem. These linearizations of the problem are collectedina MILP-MP. The solution of the master program determines anew set of discrete variables that will be used for next iteration[40].

A. Algorithm description

Let us denoteUψ as the set of constraintsC1 to C10 in (5),P = {t,pd,pul,pdl} andΘ = φ ∪ x. We can easily provethat (5) satisfies the following propositions:

Proposition 1. P is compact, nonempty, convex set and theobjective functionUt andUψ are convex inP for fixed valuesof Θ.

Proposition 2. Ut andUψ are once continually differentiable.

Proposition 3. A constraint qualification holds at the solutionof each nonlinear continuous sub-problem obtained by fixingthe values ofΘ.

Proposition 4. The nonlinear programming problem obtainedby fixingΘ can be solved exactly.

These propositions make the problem in (5) a special classof problems that can be solved using OAA method [38]. Theconvexity of (5) ensures that the linearization of constraint andobjective function produces outer approximation. Although




Algorithm 1 : OAA1: j ← 12: Initialize Θj

3: ε← 10−3

4: Convergence← FALSE

5: while Convergence == FALSE do

6: Pj ←

{

arg minP

−Ut(

Θj,P)

subject to Uψ(

Θj ,P)

≤ 0;7: UpperBound← Ut

(

Θj ,P∗)

8: (Θ∗,P∗, η∗)←

arg minΘ,P,η

η

subject toη ≥ −Ut

(

Θj ,Pj)

−∇Ut(

Θj,Pj) (

P−Pj

0

)

Uψ(

Θj,Pj)

−∇Uψ(

Θj,Pj) (

P−Pj

0

)

≤ 09: LowerBound← η

10: if UpperBound− LowerBound≤ ε then11: Convergence← TRUE

12: else13: j ← j + 114: Θj ← Θ∗

15: end if16: end while

the algorithm proposed in the later section is also applicableto non-convex objectives, it can give local optimal solutioninstead of global optimal solution. Proposition 3 is usefulas many nonlinear programming solvers use Kuhn-Tuckerconditions, which require a constraint qualification to hold.The OAA uses sequence of non-increasing upper and non-decreasing lower bounds for mixed integer problems thatsatisfy the propositions 1 to 4. The OAA converges in a finitenumber of iterations withε-convergence capability [40]. Thesequence of upper and lower bounds are obtained by solvingprimal and master problem, respectively. The primal problemis obtained by fixingΘ variables. At thejth iteration of OAA,let the values of integer variable beΘj . We can write theprimal problem as:

minP− Ut

(

Θj ,P)

subject to: Uψ(

Θj,P)

≤ 0.(8)

Solution of this problem will give thePj that will be usedfor master problem. Primal problem gives the upper boundand the master problem will give the lower bound. The masterproblem is derived with the help of primal solution, i.e.,Pj

and is based upon linearization (outer approximation) of thenon-linear objectiveUt and constraintsUψ around the primalsolution Pj [41], [42]. The solution of the master problemprovides the information for the next set of integer variablesΘj+1. As the iteration proceeds, these two bounds come closeto each other. The algorithm will terminate when the differencebetween the two bounds is less thanε. The master problem isderived in two steps: In the first step, we need projection of(5) onto the integer space-Θ. We can rewrite the problem (5)

as:

minΘ

minP− Ut

(

Θj ,P)

subject to: Uψ(

Θj,P)

≤ 0;(9)

We can also write (9) as

minΘ− υ (Θ) (10)

where

υ (Θ) = minP− Ut

(

Θj ,P)

subject to Uψ(

Θj,P)

≤ 0(11)

The problem (10) is the projection of (5) onΘ space. Sincea constraint qualification holds at the solution of every primalproblem (8) for everyΘj , the projection problem has the samesolution as the problem below:

minΘ

minP− Ut

(

Θj ,Pj)

−∇Ut(

Θj ,Pj)

(

P − Pj

Θ−Θj

)

subject to

Uψ(

Θj,Pj)

−∇Uψ(

Θj,Pj)

(

P − Pj

Θ−Θj

)

≤ 0

(12)

By introducing a new variableη, we can rewrite an equiv-alent minimization problem as:

minΘ,P,η

η

subject to

η ≥ −Ut(

Θj ,Pj)

−∇Ut(

Θj ,Pj)

(

P − Pj

Θ−Θj

)

Uψ(

Θj ,Pj)

−∇Uψ(

Θj,Pj)

(

P − Pj

Θ−Θj

)

≤ 0

(13)

2 3 4 5 6 710

5

106

107

108

Sum

Rat

e (b

/s)

Number of users

OAAESA

6 6.01 6.02 6.03

107.08

107.09

Number of users

Fig. 2. Performance of OAA with exhaustive search algorithm(ESA) fordifferent number of users

This is the master problem used to generate lower bound.Under the propositions 1, 2 and 3, (13) is equivalent to (5).Problem (13) is now a mixed integer linear programmingproblem and can be solved using iterative framework. Apseudo code for OAA is given in Algorithm 1.




2 3 4 5 6 7 8 9 10

107

Sum

Rat

e (b

/s)

Number of users

OAA Rate Threshold = 100kbpsOAA Rate Threshold = 200kbpsGA Rate Threshold = 100kbpsGA Rate Threshold = 200kbps

(a) Performance of OAA for different number of users withPmaxeNB

=4W,Pmax

c,k= 0.5W .

10 15 20 25 3010

7

108

109

Sum

Rat

e (b

/s)

Number of users

OAA Rate Threshold = 1MbpsOAA Rate Threshold = 2MbpsGA Rate Threshold = 1MbpsGA Rate Threshold = 2Mbps

(b) Performance of OAA for different number of users withPmaxeNB

=20W,Pmax

c,k= 2W .

5 10 15 200

5

10

15

20

25

30

35

Spe

ctra

l Effi

cien

cy(b

/s/H

z)

Number of Users

GAOAA

(c) Performance of OAA and GA for different number of users

1 2 3 4 50

2

4

6

8

10

12

Spe

ctra

l Effi

cien

cy(b

/s/H

z)

OAA K = 4GA K = 4OAA K = 8GA K = 8

Rate Req = 25kb/s Rate Req

= 50kb/sRate Req = 100kb/s

Rate Req = 200kb/s

Rate Req = 150kb/s

(d) Performance of OAA and GA for different data rates

Fig. 3. Comparison of OAA and GA

B. Discussion on Algorithm optimality and convergence

If the problem holds all four prepositions and the discretevariables (Θ) are finite, then the Algorithm 1 terminates ina finite number of steps at anε -optimal solution [40]. Asmention earlier, in anε -optimal solution, for anyε > 0, ε-optimal algorithms guarantee the solution withinε of optimalsolution. Lower values ofε mean high degree of accuracy.The main reason forε -optimal solution of OAA is its branchand bound like architecture. In branch and bound procedure,any combination of discrete variable (Θ in our case, whichis the union of users and mode selection variable) will neverbe used twice. The optimality ofP in (13) implies thatηis greater thanUt

(

Θj,Pj)

for any feasible point in (13). Ifthe value ofη is less thanUt

(

Θj ,Pj)

, it means that themaster problem has no feasible solution for the choice ofdiscrete variablesΘj. If there is no feasible solution for anyparticularΘj in (13), then the algorithm excludes that valueof Θj from any subsequent master problems. It means thatthe algorithm is finitely converging. The optimality of the

algorithm follows from the convexity of the objective andconstraints for any fixed values ofΘ. It is proven in themixed integer programming literature that the convergencerate of OAA is linear [42]. A detailed convergence proof of ageneral OAA algorithm is given in [38]. An exhaustive searchalgorithm (ESA) for (5) would enumerate all the user andmode selection options, which increases its computationalloadexponentially with the number of users. In this paper, we havecompared the results of the proposed OAA with ESA and GA.The simulation results show that the performance of OAA isalmost same as optimal solution obtained and ESA and betterthan GA. One more advantage of OAA is its guaranteedε-optimal results. The problem with the GA is that it cannotguarantee any optimal orε-optimal solution. GA can give goodresult but there is no proven convergence criterion for GAwhere as OAA has proven convergence toε-optimal solution.




1 2 3 4 5 610

0

101

102

103

104

105

106

107

Users Index

Rat

e of

eac

h us

er (

b/s)

U

UT

(a) Comparison ofU and UT with PmaxeNB

= 4W,Pmaxc,k

= 0.5W andCmin

k= 100kbps. Sum-rate forU andUT is same.

1 2 3 4 5 6 7 8 9 1010

0

101

102

103

104

105

106

107

Users Index

Rat

e of

eac

h us

er (

b/s)

U

UT

(b) Comparison ofU and UT with PmaxeNB

= 2W,Pmaxc,k

= 0.5W andCmin

k= 200kbps. Sum-rate forU = 1.68Mbps andUT = 4.33Mbps

1 2 3 4 5 6 7 8 9 1010

0

101

102

103

104

105

106

107

Users Index

Rat

e of

eac

h us

er (

b/s)

U

UT

(c) Comparison ofU and UT with PmaxeNB

= 4W,Pmaxc,k

= 0.5W andCmin


Fig. 4. Comparison ofU andUT

TABLE IIISIMULATION PARAMETERS

Parameter ValuePmaxeNB {2,4}Watts

Pmaxc,k

{0.5,0.75}WattsPmind,k

100mWCmin

k{100,200}kbs

do 20eNB coverage 1000md Uniformly distributed distanceξo 10dBGo 50ps 0.90pm 0.10pc 0.50

V. SIMULATION RESULTS

In this section, we show simulation results to demonstratethe performance of the proposed OAA scheme. The resultsshow the effect of number of users on the total throughputand also analyze the effectiveness of joint admission controland mode selection utility. The system parameters used in thesimulation are shown in Table III. We use Basic Open SourceNonlinear Mixed Integer Programming (BONMIN) softwarefor OAA. We compare the results of OAA with standardcontinuous GA [43].

In the simulation, the eNB maximum coverage is set to 1000meters. The maximum eNB powerPmaxeNB is set to{2, 4}Watts.The coverage distance for D2D is 20 meters. In cellular modePmaxc,k = {0.5, 0.75} Watts. In all the simulation results,do =20 meters,Go = 50 andξo = 10dB. We assume that distanced is greater thando. For convergence,ε is set to0.00001. In allsimulations, for GA, probability of cross over,pc, probabilityof mutation,pm and probability of selection,ps are set to 0.9,0.1 and 0.5 respectively. Elitist selection and uniform crossover rules with global best value adaptation are used to gethigh quality GA solutions. We apply GA for discrete variables(user and mode selection), and for each realization of discretevariables a conventional convex optimization algorithm isusedto get the optimal power allocation. In the simulation results,U represents a utility function that jointly maximizes thethroughput and users admission considering mode selectionwhere asUT represents a utility function that only maximizesthe throughput considering mode selection.

In Fig. 2, we compare results of optimal solution obtainedby ESA and OAA for different number of users. For ESAapproach, we need to22K enumeration of discrete variables4

and for each realization of discrete variable, there is a needto solve one non-linear convex optimization problem. Thecomputational complexity of ESA increases exponentially.Thats makes ESA unsuitable for such kind of problems. Theresult in Fig. 2 shows that the performance of OAA is almostsimilar to the optimal ESA algorithm. To get one result usingESA required a lot of time, for brevity, we only present oneresult of ESA in this paper.

Figs. 3(a), 3(b), 3(c) and 3(d) investigate the performanceofOAA and GA for joint user and throughput maximization on

4K variables for admission control andK variables for mode selection




5 10 15 20 25 3010

0

101

102

103

104

105

106

107

Users Index

Rat

e of

eac

h us

er (

b/s)

U

UT

(a) Comparison ofU and UT with PmaxeNB

= 4W,Pmaxc,k

= 0.75W andCmin


5 10 15 20 25 3010

0

101

102

103

104

105

106

107

Users Index

Rat

e of

eac

h us

er (

b/s)

U

UT

(b) Comparison ofU and UT with PmaxeNB

= 4W,Pmaxc,k

= 0.5W andCmin


2 4 6 8 10 12 14 16 18 2010

0

101

102

103

104

105

106

107

108

Rat

e of

eac

h us

er (

b/s)

Users Index

U

UT

(c) Comparison ofU and UT with PmaxeNB

= 20W,Pmaxc,k

= 2W andCmin

k= 1Mps. Sum-rate forU = 123Mbps andUT = 110.41Mbps

Fig. 5. Comparison ofU andUT

.

100 200 300 400 500 600 700 800 900 100010

6

107

108

109

Sum

Rat

e (b

/s)

Coverage Distance (m)

K = 5K = 10K = 15K = 20

Fig. 6. Coverage distance versus Sum throughput comparisonfor differentnumber of users.

the cellular network. Fig. 3(a) shows a plot of sum-rate versusthe number of users with the parameters

{

PmaxeNB , Pmaxc,k

}

=

{4, 0.5} and{20, 2} watts respectively. The results present thecomparison of different rate thresholds for a power constraintcellular network with D2D capability using OAA and GA.As there is an increase in the rate requirement, for sameconstraints, the sum-rate decreases. This is because less num-ber of users are admitted due to high rate requirement andstringent power constraint in D2D mode. In Fig. 3(c), wepresent the comparison results of OAA and GA in terms ofspectral efficiency and in Fig. 3(d), we show the OAA andGA results for different data rates. All the results highlight theeffectiveness of OAA over GA. This is because ofε-optimalnature of OAA algorithm. Due to stochastic nature of GA,there is no guarantee that the GA will give optimal solution.

Figs. 4(a), 4(b) and 4(c) investigate the effect of joint userand throughput maximization (in log scale) on the cellularnetwork. These figures compare the throughput obtained byusers usingU and UT utilities. The straight horizontal lineshows the rate requirement. In Fig. 4(a) with parametersPmaxeNB = 2W,Pmaxc,k = 0.75 watts andCmink = 200kbps, theperformance both utilities is almost same. Sum-rate forU andUT is same. In the figure, fifth user is not selected due to badchannel conditions.

For Figs. 4(b) and 4(c), we set the parameters asPmaxeNB =2W,Pmaxc,k = 0.5W,Cmink = 100kbps and PmaxeNB =

4W,Pmaxc,k = 0.5W,Cmink = 200kbps, respectively. In Fig.4(b), we can see that six users are admitted withU utilitywhile only two users are selected forUT utility. Sum-rate forU = 1.68 Mbps andUT = 4.33 Mbps. Similarly for Fig. 4(c)four users are admitted withU utility while three users areselected forUT utility. Sum-rate forU = 2.574 Mbps andUT= 3.2 Mbps. We can see that although sum-rate forUT is high,it is at the cost of low number of admitted users.

Figs. 5(a), 5(b) and 5(c) compare the throughput obtainedby users usingU and UT utilities for 30 users with param-




eters asPmaxeNB = 4W,Pmaxc,k = 0.75W,Cmink = 100kbps,PmaxeNB = 4W,Pmaxc,k = 0.5W,Cmink = 200kbps andPmaxeNB =20W,Pmaxc,k = 2W,Cmink = 1Mbps, respectively. Fig. 6 showsthe effect of eNB coverage area the throughput. In Fig. 5(a),21 users are admitted withU utility while only 18 users areadmitted withUT utility. With the increase in rate requirementfor Fig. 5(b), 17 users are admitted withU utility while only13 users are admitted withUT utility. We can conclude fromthe results that for cellular system with D2D capability, jointadmission control and mode selection add more fairness ascompared to sum-rate maximization.

VI. CONCLUSION

In this paper, we presented a computationally viable solutionfor solving the joint admission control, mode selection andpower allocation problem in D2D communication. We madeuse of the special structure of this problem to propose asolution based on branch and bound outer approximationapproach. The proposed OAA method gives guaranteedε-optimal results and has a reasonable computational complexity.We verify the effectiveness of the proposed approach methodby simulations that demonstrated the effect of number of userson the total throughput and also analyzed the effectivenessofjoint admission control and mode selection utility.

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APPENDIX APROOF OFTHEOREM 1

We prove that even with known uplink and downlink powersthe joint admission control, network mode selection, andpower allocation is a NP-complete problem. One exampleof known power is equal power distribution among selectedusers. We first show that the JACMSPA is equivalent to the0-1 multiple-choice multiple-dimensional knapsack problem(MCMDKP). We will start by describing the input, out-put formal description of decision problem associated withMCMDKP and JACMSPA.

Problem 1. The MCMDKP problem is to select the itemsxj,q in disjoint classes to maximize the total profit such thatan item can only be selected by at most one class subject tosatisfaction ofW resource constraints.

Instance: J disjoint classes,Q items andW resource con-straints (capacity of knapsack withW dimensions). Theqthitem of classj has profitfj,q and weightwj,q [44].Output: A selection of itemsX .Decision problem associated with MCMDKP: TheMCMDKP decision problem is to determine, for a givenprofit F , whether it is possible to load the multidimensionalknapsack so as to keep the total weight in each dimension nogreater thanW , while making the total profit at least equal toF .

Problem 2. The JACMSPA problem is to select the disjointsubsets of users that are either using D2D or eNB forcommunication such that: 1) the total data rate (sum-capacity)of the system is maximized and 2) Data rate of each selecteduser must be more than or equal to a predefined threshold.

Instance: The number of usersK, rate thresholdRk, k =1, 2, · · · ,K; channel gainshk, fk, gk of the kth user, andarbitrary users’ power.Output: An selection of users and their respective mode.Decision problem associated with JACMSPA:The decisionproblem associated with the JACMSPA is to determine, for agiven throughputC, whether it is possible to select multipleusers multiple mode ( cellular or D2D) such that the rate ofeach selected users with any specific mode is more thanR.

Lemma 1. The JACMSPA problem is polynomial time verifi-able.

Proof. We can easily observe that if we are given a set ofselected users which represents the mapping between D2Dand cellular mode, we can verify in polynomial time that thetotal throughput of the selected users is at leastC and the rateof each selected user is more thanR. Since the dimensionof the matrix for users and mode selection is2 × K, so itslength is polynomial in the size of the input. We can writean algorithm that can verify the result inO(2K) iterations,which shows polynomial time verification.

Lemma 2. MCMDKP is polynomial time reducible toJACMSPA.

Proof. We can do reduction by simple equivalence. We makethe K users as disjoint classes, the items as mode. TheRkrate of selected users is the same as capacity of knapsackwith W dimensions. We make the channelshk, fk, gk as itemprofit. For any given instance,J , Q, W , fj,q of MCMDKP,if there is a matrixX with entries of selected itemsxj,qthat maximizes the total profit such that an item can onlybe selected by at most one class subject to satisfaction ofW

resource constraints, then there will be a user-mode selectionmatrix that maximizes the the total data rate (sum-capacity)of the system such that a user can only operate in one modesubject to rate constraint. This reduction by simple equivalencemeans every yes-instance of MCMDKP implies yes-instanceof JACMSPA in polynomial time.

Lemma 1 and Lemma 2 implies the NP-completeness ofjoint admission control, mode selection and power allocationproblem.

Muhammad Azam received the B.Sc. degree inElectronics Engineering from University of Engi-neering and Technology Taxila, Pakistan in 2012,and M.Sc. degree in Electrical Engineering fromCOMSATS Institute of Information Technology Pak-istan, in 2015. Currently, he is a Lab Engineerin Electrical Engineering Department, FoundationUniversity Islamabad (Rawalpindi Campus) His re-search interests include Wireless communications,Resource Allocation in 5G Networks, Optimizationin Energy-Communication Systems, Smart Grid, and

related topics.




Mushtaq Ahmad received the BSc , MS in Electri-cal Engineering and Masters of TelecommunicationManagement from University of Engineering andTechnology Lahore, University of Michigan Ann Ar-bor, USA and Institut National Des Telecom Francein 1990, 1994 and 1999 respectively. Possessingdouble Masters’ degree both in the field of Elec-trical Engineering and Telecom Management fromrenowned universities of the world , the author hasdiverse working experience with Incumbent operatorPTCL, regulator PTA, policy formulation experience

in the capacity of Member Telecom at Ministry of InformationTechnology andexperience in the capacity of Chief Executive Officer of reputable public andprivate institutions. The author is currently working as a Principal Engineerat Comsats Institute of Information Technology Wah, Pakistan and pursuinghis PhD degree from same institution . His main research areas are ResourceAllocation in next generation networks.

Muhammad Naeem (S’09-M’12) received the BS(2000) and MS (2005) degrees in Electrical En-gineering from the University of Engineering andTechnology, Taxila, Pakistan. He received his PhDdegree (2011) from Simon Fraser University, BC,Canada. From 2012 to 2013, he was a PostdoctoralResearch Associate with WINCORE Lab. at Ryer-son University, Toronto, ON, Canada. Since August2013, he has been an assistant professor with theDepartment of Electrical Engineering, COMSATSInstitute of IT, Wah Campus, Pakistan and Research

Associate with WINCORE Lab. at Ryerson University. From 2000 to 2005, hewas a senior design engineer at Comcept (pvt) Ltd. At the design departmentof Comcept (pvt) Ltd, Dr. Naeem participated in the design and developmentof smart card based GSM and CDMA pay phones. Dr. Naeem is also aMi-crosoft Certified Solution Developer (MCSD). His research interests includeoptimization of wireless communication systems, non-convex optimization,resource allocation in cognitive radio networks and approximation algorithmsfor mixed integer programming in communication systems. Dr. Naeem hasbeen the recipient of NSERC CGS scholarship.

Muhammad Iqbal was born on October 15, 1976 inMultan. He got B.Sc. Electrical Engineering degreein 1999 from University of Engineering and Tech-nology, Lahore. After completing B.Sc. ElectricalEngineering, he served in the state owned telecom-munication company for more than seven years.In 2007 he completed his MS TelecommunicationEngineering from the University of Engineering andTechnology, Peshawar. After completing PhD byJuly, 2011 from Beijing University of Posts andTelecommunications, P.R. China, he rejoined COM-

SATS and till this date working as Assistant Professor, Electrical EngineeringDepartment, CIIT, Wah Campus. His research interests include signal andinformation processing, wireless communication, smart grid and appliedoptimization.

Ahmed Shaharyar Khwaja received the Ph.D. andM.Sc. degrees in signal processing and telecommu-nications from the University of Rennes 1, Rennes,France, and B. Sc. degree in electronic engineeringfrom Ghulam Ishaq Khan Institute of EngineeringScience and Technology, Topi, Pakistan. Currently,he is a postdoctoral research fellow with WINCORELab. at Ryerson University, Toronto, ON, Canada.His research interests include compressed sensing,remote sensing and optimization problems in wire-less communication systems.

Alagan Anpalagan received the B.A.Sc. M.A.Sc.and Ph.D. degrees in Electrical Engineering fromthe University of Toronto, Canada. He joined theDepartment of Electrical and Computer Engineeringat Ryerson University in 2001 and was promotedto Full Professor in 2010. He served the depart-ment as Graduate Program Director (2004-09) andthe Interim Electrical Engineering Program Director(2009-10). During his sabbatical (2010-11), he wasa Visiting Professor at Asian Institute of Technologyand Visiting Researcher at Kyoto University. Dr.

Anpalagan’s industrial experience includes working at Bell Mobility, NortelNetworks and IBM Canada. Dr. Anpalagan directs a research group workingon radio resource management (RRM) and radio access & networking (RAN)areas within the WINCORE Lab. His current research interests includecognitive radio resource allocation and management, wireless cross layerdesign and optimization, cooperative communication, M2M communication,small cell networks, and green communications technologies.

Dr. Anpalagan serves as Associate Editor for the IEEE CommunicationsSurveys & Tutorials (2012-), IEEE Communications Letters (2010-13) andSpringer Wireless Personal Communications (2009-), and past Editor forEURASIP Journal of Wireless Communications and Networking(2004-2009).He also served as Guest Editor for two EURASIP SI in Radio ResourceManagement in 3G+ Systems (2006) and Fairness in Radio Resource Manage-ment for Wireless Networks (2008) and, MONET SI on Green Cognitive andCooperative Communication and Networking (2012),. He co-authored of threeedited books, Design and Deployment of Small Cell Networks,CambridgeUniversity Press (2014), Routing in Opportunistic Networks, Springer (2013),Handbook on Green Information and Communication Systems, AcademicPress (2012).

Dr. Anpalagan served as TPC Co-Chair of: IEEE WPMC’12 WirelessNetworks, IEEE PIMRC’11 Cognitive Radio and Spectrum Management,IEEE IWCMC’11 Workshop on Cooperative and Cognitive Networks, IEEECCECE’04/08 and WirelessCom’05 Symposium on Radio Resource Manage-ment. He served as IEEE Canada Central Area Chair (2013-14),IEEE TorontoSection Chair (2006-07), ComSoc Toronto Chapter Chair (2004-05), IEEECanada Professional Activities Committee Chair (2009-11). He is the recipientof the Dean’s Teaching Award (2011), Faculty Scholastic, Research andCreativity Award (2010), Faculty Service Award (2010) at Ryerson University.Dr. Anpalagan also completed a course on Project Managementfor Scientistand Engineers at the University of Oxford CPD Center. He is a registeredProfessional Engineer in the province of Ontario, Canada.

Saad Qaisar received his Masters and Ph.D. de-grees in Electrical Engineering from Michigan StateUniversity, USA in 2005 and 2009, respectively,under supervision of Dr. Hayder Radha (Fellow,IEEE). He is currently serving as an Assistant Pro-fessor at School of Electrical Engineering ComputerScience (SEECS), National University of SciencesTechnology (NUST), Pakistan. He is the lead re-searcher and founding director of CoNNekT Lab:Research Laboratory of Communications, Networksand Multimedia at National University of Sciences

Technology (NUST), Pakistan. As of September 2011, he is thePrincipalInvestigator or Joint Principal Investigator of multiple research projectsspanning cyber physical systems, applications of wirelesssensor networks,network virtualization, communication and network protocol design, wirelessand video communication, internet measurements analysis,multimedia codingand communication. He has published over 50 papers at reputed internationalvenues. He is also serving as the chair for Mobile-Computing, Sensing andActuation for Cyber Physical Systems (MSA4CPS) workshop inconjunctionwith International Conference on Computational Science and Its Applications(ICCSA). He is the lead researcher on a joint internet performance measure-ments study in Pakistan with Georgia Institute of Technology, current head ofa core working group for establishment of Pakistan IXP, technical consultantto United Nations Food and Agriculture Organization (UNFAO), lead architectfor Pakistan Laboratory Information Management System project and activelyengaged with projects funded by King Abdullah City of Science Technology(KACST).

Documents

Joint Admission Control, Mode Selection and Power Allocation in D2D Communication Systems