SPECIAL SECTION ON ADVANCES IN INTERFERENCE MITIGATION TECHNIQUES FORDEVICE-TO-DEVICE COMMUNICATIONS

Received January 31, 2018, accepted March 7, 2018, date of publication March 19, 2018, date of current version April 18, 2018.

Digital Object Identifier 10.1109/ACCESS.2018.2817189

Energy-Aware Radio Resource Management inD2D-Enabled Multi-Tier HetNetsSYED AHSAN RAZA NAQVI1, HARIS PERVAIZ 2, SYED ALI HASSAN 1, LEILA MUSAVIAN 3,QIANG NI 4, MUHAMMAD ALI IMRAN5, (Senior Member, IEEE),XIAOHU GE 6, (Senior Member, IEEE),AND RAHIM TAFAZOLLI2, (Senior Member, IEEE)1School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Islamabad 44000, Pakistan2Institute of Communication Systems, Home of 5GIC, University of Surrey, Guildford GU2 7XH, U.K.3School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, U.K.4School of Computing and Communications, Lancaster University, Lancaster LA1 4YW, U.K.5School of Engineering, University of Glasgow, Glasgow G12 8QQ, U.K.6School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, China

Corresponding author: Haris Pervaiz (h.pervaiz@surrey.ac.uk)

This work was supported by the ESPRC U.K. Global Challenges Research Fund allocation under Grant EP/P028764/1.

ABSTRACT Hybrid networks consisting of both millimeter wave (mmWave) and microwave (µW )capabilities are strongly contested for next-generation cellular communications. A similar avenue of currentresearch is device-to-device (D2D) communications, where users establish direct links with each other ratherthan using central base stations. However, a hybrid network, where D2D transmissions coexist, requiresspecial attention in terms of efficient resource allocation. This paper investigates dynamic resource sharingbetween network entities in a downlink transmission scheme to maximize energy efficiency (EE) of thecellular users (CUs) served by either (µW ) macrocells or mmWave small cells while maintaining a minimumquality-of-service (QoS) for the D2D users. To address this problem, first, a self-adaptive power controlmechanism for the D2D pairs is formulated, subject to an interference threshold for the CUs while satisfyingtheir minimum QoS level. Subsequently, an EE optimization problem, which is aimed at maximizing theEE for both CUs and D2D pairs, has been solved. Simulation results demonstrate the effectiveness of ourproposed algorithm, which studies the inherent tradeoffs between system EE, system sum rate, and outageprobability for various QoS levels and varying densities of D2D pairs and CUs.

INDEX TERMS Device-to-device (D2D) communication, energy efficiency, fifth generation (5G) network,heterogeneous network, millimeter wave, multi objective optimization and radio resource management.

I. INTRODUCTIONThe next generation wireless technology will consist of amixture of network tiers of different sizes, transmissionpower levels, backhaul capabilities, and radio access tech-nologies (RATs) [2], [3]. In recent years, traditional cel-lular networks have been utilizing sub-6GHz bands whichare insufficient enough to meet the data demands of nextgeneration networking, such as 5G, due to spectrum scarcity.Millimeter wave (mmWave) is considered as a key enablingtechnology for future generation networks due to its higheravailable bandwidth (in the range of 1-2 GHz) and the possi-bility of larger antenna arrays due to the smaller wavelengthof mmWave signals [4]–[6].

Device-to-device (D2D) communication is a paradigmshift allowing its coexistencewithin the cellular infrastructure

with a potential to enhance network performance, throughputand power utilization. It enables a dedicated direct link for thedevices in close proximity to establish a connection [7]–[10],whereas in traditional cellular communication the entire traf-fic is routed through base stations (BSs). D2D communica-tion systems have the potential to improve spectral resourceutilization and reduce energy consumption, while providingsupport to new peer-to-peer and location-based applicationsand services [10], [11], such as public safety networks [12].

Recently, a lot of attention has been given to the radioresource management in traditional heterogeneous networks(HetNets) [13]–[18], where the small cells coexist with themacrocell both operating on µW band covering the samegeographical area. Another facet of future 5G networks is theuse of mmWave resources alongwith theµW resources.With

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the extreme shortage of available spectrum and demand forhigher data rates, mmWave communication has triggered agreat deal of interest. Indeed, the realization of a reliable com-munication network can only be achieved when mmWavenetwork coexist with conventional µW networks. In past,the use of mmWave spectrum was not considered suitablefor wireless communication due to its sensitivity to block-ing and strong directionality requirements [19]. Moreover,[20], [21] summarizes the distinct characteristics of mmWavenetworks ranging from blockage models, initial accessdesign, beamforming and radio resource management issues.In the recent literature, the coverage and rate trends areanalyzed in mmWave cellular networks as outlined in [22].It is also shown in [22] that the mmWave networks operatein noise limited regime in comparison to the traditional cel-lular networks operating in an interference limited regime.Furthermore, a cloud radio access network (CRAN) mayalso be considered a suitable candidate for 5G systems. It isenvisioned that a 5G ultra dense cloud small cell network(UDCSNet) comprises densely deployed small cells and aCRAN. Zhang et al. [23] have highlighted the network archi-tecture of such systems, laying special emphasis on theirfronthaul infrastructure.

Another promising solution to improve the network capac-ity for the future generation network is the integration ofD2D communication within the cellular infrastructure. Thechallenge in D2D communication is to devise a mode strategythat allows users to dynamically choose between either com-municating directly or via the central access point (or BS).Lin et al. [24] have tackled this mode selection problem andhave presented a tractable hybrid network model to derive ananalytical rate expressions for the two D2D spectrum sharingscenarios, i.e., underlay and overlay. This work highlightsthat at higher D2D mode selection thresholds, the optimalspectrum partition is almost independent of the proportionof possible D2D users in the overlay spectrum sharing sce-nario. Similarly, the design of innovative and novel powercontrol strategies for D2D links are of paramount importancein improving the performance of the D2D-enabled systems.In this respect, [25] puts forth a random network model for aD2D underlaid cellular network to develop a centralized anddistributed power control strategies. Here, the former strategyrestricts the aggregate received interference from the D2Dpairs whereas the latter strategy maximizes the sum-rate of itsusers. For instance, [26] studies such a systemmodel in whichD2D pairs coexist with the multiple-input multiple-output(MIMO)-enabled cellular infrastructure. This work investi-gates the spectral efficiency of both cellular and D2D tiersunder the estimation errors in the channel state information(CSI) and it concludes that the spectral efficiency of cellulartier is affected by the underlay D2D tier.

Several investigations have been carried-out into variousaspects of D2D communications [27]–[35]. For example,in [30], the resource allocation scheduling is modeled asan approximate dynamic programming algorithm which pro-vides significant gains in terms of overall throughput, energy

efficiency and quality-of-experience (QoE) for the users incontrast to the conventional techniques used in cellular sys-tems. A context-aware and self-organizing algorithm is mod-eled as a matching game in [31] to optimize the resourceutilization and traffic offloading using the social and wirelesscontextual information of the wireless users in D2D-enabledsmall cell networks to reduce the traffic congestion on thebackhaul links. Similarly, Hoang et al. [32] have proposedthe non-orthogonal dynamic spectrum sharing scheme inD2D underlaid cellular network and utilize the graph theoryto maximize the weighted system capacity. Two possibleapproaches, namely iterative rounding algorithm and opti-mal branch-and-bound (BnB) algorithm, have been used toprovide solution to the aforementioned problem. An energy-efficient power scheme is investigated for D2D communi-cations underlaying within a cellular infrastructure, wherethe resources in the uplink transmission scheme reservedfor the cellular users are shared among the multiple D2Dpairs [33]. The original EE optimization problem is non-concave, which is transformed into the difference of two con-cave functions, following which the authors have proposed asub-optimal approach with reasonable complexity to providea near-optimal solution.

Zhou et al. [34] have studied the simultaneous wire-less information and power transfer (SWIPT)-based D2Dunderlay networks to jointly investigate power and spectrumresource allocation problem. The joint optimization problemis formulated as a two-dimensional energy-efficient stablematching scheme and the solution is obtained using the Gale-Shapley (GS) algorithm. The energy efficient resource shar-ing procedure in the downlink (DL) transmission schemeis proposed to maximize the system EE with the aid of amatching scheme in D2D underlying cellular networks asoutlined in [35].

A. APPROACH AND CONTRIBUTIONSIn this paper, we consider a network of multiple radio accesstechnologies (RATs) where D2D pairs can share resourceswith CUs. Therefore, in order to enhance the QoS of CUs adynamic power control strategy has been proposed for D2Dpairs to satisfy a predefined interference threshold.

It is worthwhile to note that the original problem proposesto maximize the EE of both CUs and D2D pairs. However,it has been broken down into two independent subproblems,i.e., the the radio resource management of D2D pairs in orderto satisfy their minimum QoS, and the predefined interfer-ence threshold set for the CUs. In the second subproblem,we aim to jointly optimize the two conflicting objectives,i.e., maximizing the system EE and maximizing the systemsum rate, in light of the resource allocation to the D2Dpairs. The transformed radio resource allocation problem isformulated as a multi-objective optimization problem (MOP)to derive an optimal power allocation strategy for the CUs.The MOP is transformed into a single-objective optimizationproblem using the weighted-Tchebycheff method in order toachieve a Pareto-optimal solution resulting in a complete

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FIGURE 1. A snapshot of BS and user deployment.

Pareto-Frontier curve by tuning the weights of both conflict-ing objectives. Furthermore, the mmWave-based small cellsare assumed to operate exclusively in the mmWave bandwith a chosen power control strategy to maximize the sumrate of their associated users. Using the formulated approach,the optimal power allocation for the CUs are computed andthe Hungarian method has been utilized to select the bestavailable subcarriers for the CUs. The simulation resultsdemonstrate the relationship between the coverage probabil-ity of D2D pairs and the system EE for a varying minimumQoS for both CUs and D2D pairs. Finally, the impact ofdensity ratios of D2D pairs to CUs on the system sum rate andsystem EE has also been investigated. The results illustratethe effectiveness of our proposed mechanism in comparisonto the traditional rate maximization and power minimizationschemes.

The rest of the paper is organized as follows. Section II out-lines the system model, whereas Sections III and IV providedetailed information on power allocation mechanisms for theD2D pairs and the CUs. Section V describes the simulationresults and Section VI concludes the paper.

II. SYSTEM MODELConsider a DL transmission scheme consisting of kb µWmacro-cells, distributed using a Poisson point process (PPP)with density 8b, overlaid with 4 kb mmWave (mmWave)small base stations (SBSs), with |M| CUs with density 8mand D D2D pairs with density8d as shown in Fig. 1. The setof CUs, denoted byM, consists of U wireless virtual realityusers and C normal wireless users such that M = U ∪ C.The BSs operating on µW and mmWave frequency bandsare denoted by B = {1, . . . ,B} and W = {1, . . . ,W },respectively such that L = B ∪W . Each µW BS has NµWsubcarriers, whereas each mm small BS has Nmm subcarrierssuch that NµW = Nmm = N . The set of subcarriers for eachBS l ∈ L is denoted by Nl = {1, 2, · · · ,N }, the set of allCUs by M = {1, . . . ,M} and the set of all D2D pairs byD = {1, . . . ,D}. Moreover, each user m ∈M must satisfy aminimumQoS, which is given by R(m)min. In addition, (µW BSsand mm SBSs) operate independently of each other which

aids in finding their optimal power allocation in a distributedmanner. It should be noted that one of the major objectivesof this work is to provide a framework where each BS canchoose whether to maximize its own throughput or EE andthe D2D transmitters dynamically adjust their transmissionpower in order to protect the QoS of cellular users. In thiswork, it is assumed that themmWave BSswill maximize theirown throughput whereas the µW BSs will maximize theirown energy efficiency.

Herein, we provide some of our antenna assumptions spe-cially for mmWave SBSs. It is assumed that the transmittersand receivers are perfectly aligned with each other and havean antenna gain of Gmax whereas a misaligned beam has anantenna gain of Gmin. Therefore, the effective antenna gainGym,w for y ∈ {t, r}, where t and r represents the transmitterand receiver, respectively, can be described as follows

Gtm,w=

Gmax=2π−

(2π−1ωtw

)Gmin

1ωtw, if |θ tm,w|≤

1ωtw

2Gmin, Otherwise.

(1a)

and

Grm,w=

Gmax=2π−

(2π−1ωrm

)Gmin

1ωrm, if |θ rm,w|≤

1ωrm

2Gmin, Otherwise.

(1b)

In this work, it is assumed that each subcarrier is exclu-sively assigned to a single CU within the same BS. Theachievable rate of user m ∈ M on subcarrier n ∈ Nassociated with µW BS b ∈ B is given by

r (b)m,n = 2bBwblog2(1+ γ(b)m,n × p

(b)m,n), (2)

where the proportion of bandwidth allocated to each sub-carrier by µW BS b is denoted by 2b, Bwb indicates thetotal bandwidth available to the µW BS b and p(b)m,n indicatesthe power allocated to user m associated with µW BS bon subcarrier n. The signal-to-interference plus noise ratio(SINR) of user m on subcarrier n associated with µW BS b,γ (b)m,n is defined as

γ (b)m,n =

|g(b)m,n|2/PLbm(N02bBwb + I

(b)m,n)

=|g(b)m,n|2/PLbm

(σ 2 + Pmind,n × g(m)d,n)

, (3)

where |g(b)m,n|2 follows a Nakagami distribution at subcarrier

n between CU m, and µW BS b, N0 is the noise spectraldensity and the total cross-tier interference caused due to thesubcarrier n ∈ Nb being reused by a D2D pair within thecoverage area of µW BS b is given by I (b)m,n = Pmin

d,n × g(m)d,n.More details about the computation of Pmin

d,n can be found inSection III. The path loss of a userm at carrier frequency fµW ,

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associated with µW BS, denoted by PLµWm , can be expressedas

PLµWm = 20 log(

4πλµW

)+ 10αµW log(d)+ εµW , (4)

where λµW is the wavelength, αµW is the path loss exponentfor the µW frequency band, d is the distance between userm and µW BS, and εµW represents the shadowing (in dB)which is a Gaussian random variable with zero mean andvariance ξ21 .

Similarly, the achievable rate of user m ∈M on subcarriern ∈ N associated with mmWave SBS w ∈W is given by

r (w)m,n =

(1−

τm,w

T

)2wBwwlog2

(1+ γ (w)

m,n × p(w)m,n

), (5)

where the proportion of bandwidth allocated to each subcar-rier by mmWave SBS w is denoted by 2w, Bww indicatesthe total bandwidth available to the mmWave SBS w andp(w)m,n indicates the power allocated to user m associated withmmWave SBS w on the subcarrier n. The beam alignmentoverhead τm,w between user m and mmWave SBS w can bedefined as

τm,w(1ωtw,1ω

rm)=1stw1s

rmTp

1ωtw1ωrm, (6)

where it should be noted that 1ωtw1ωrm ≥

Tp1stw1srm

Tin

order to make sure that τm,w ≤ T and Tp is the duration of thepilot transmission. From this condition, we can infer that the

minimum value of 1ω is given by 1ωlower ,Tp1stw1s

rm

T.

Since the beam level alignment takes place within the sectorlevel beamwidths, therefore, 1ωtw ≤ 1s

tw and 1ωrm ≤ 1s

rm.

From these conditions, we can infer that the maximum valueof 1ω is given by 1ωupper , 1stw1s

rm. Since we assume

that the multi-user interference is negligible, the joint opti-mization of operating beamwidths for all mmWave SBS-CUpairs can be simplified to be the independent optimizationfor each mmWave SBS-CU pair. Hence, the feasible regionof optimal beam-level beamwidth1ω∗ for each SBS-CU pairto maximize the throughput defined in (5) can be given by

Tp1stw1srm

T≤ 1ω∗ ≤ 1stw1s

rm,

Lemma 1: The signal-to-noise ratio (SNR) of a user m onsubcarrier n associated withmmWave BSw is denoted by γ (w)

m,nand is given by

γ (w)m,n ,

(|g(w)m,n|

2/PLwm) (

�1ω+ G2

min

)N02wBww

. (7)

Proof: We assume that the multi-user interference isnegligible due to the pseudo-wired abstraction of mmWavecommunications. The SNR of a user m on subcarrier n asso-ciated with mmWave BS w can be defined as

γ (w)m,n =

(|g(w)m,n|

2/PLwm)Gtm,wG

rm,w

N02wBww

=

(|g(w)m,n|

2

PLwm

)(2π−(2π−1ωtw)Gmin

1ωtw

)(2π−(2π−1ωrm)Gmin

1ωrm

)N02wBww

=

(|g(w)m,n|

2

PLwm

)(�1/2+1ωtwGmin1ωtw

) (�1/2+1ωrmGmin1ωrm

)N02wbw

=

(|g(w)m,n|

2

PLwm

)(�1/2

1ωtw+ Gmin

) (�1/2

1ωrm+ Gmin

)N02wBww

=

(|g(w)m,n|

2

PLwm

)(�1ω+

�1/2Gmin1ωrm

+�1/2Gmin1ωtw

+ G2min

)N02wBww

=

(|g(w)m,n|

2

PLwm

)(�1ω+

�1/2Gmin(1ωtw+1ωrm)

1ωtw1ωrm

+ G2min

)N02wBww

=

(|g(w)m,n|

2

PLwm

)(�1ω+

�1/2Gmin(1ωtw+1ωrm)

1ω+ G2

min

)N02wBww

γ (w)m,n ,

(|g(w)m,n|

2

PLwm

) (�1ω+ G2

min

)N02wBww

,

if Gmin(1ωtw +1ω

rm)� �1/2,

where � = (2π − 2πGmin)2 and 1ω = 1ωtw1ω

rm.

The path loss of a user m located associated with mmWaveSBS w, at carrier frequency fw, denoted by PLwm is givenby [38],

PLmmWm =

{ρ + 10αmmW

L log(d)+ εmmWL , if Link is LoS,

ρ + 10αmmWN log(d)+ εmmW

N , Otherwise.

(8)

In (8), εmmWL and εmmW

N represent the shadowing in mmWband (in dB) for the line-of-sight (LoS) and non line-of-sight (NLoS) links, respectively. The εmmW

L and εmmWN are

Gaussian random variables with zero mean and variancesξ2z , where z ∈ {LoS,NLoS} model the effects of blockages,ρ = 32.4+ 20 log(fmmW).

The total rate of a user m, associated with either µW BSb or mmWave SBS w, can be written as,

Rm =∑l∈L

∑n∈Nm

σm,lr (l)m,n, ∀m (9)

Similarly, the total power consumed by user m is denoted byPm and given by

Pm =∑l∈L

∑n∈Nm

σm,lp(l)m,n. (10)

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Similarly, the system EE can be defined as

ηEE =

∑m∈M

Rm +∑d∈D

Rd∑m∈M

Pm + (B+W )× PC + D× P(d)C +

∑d∈D

P(∗)d,

(11)

where Rd is the total rate of D2D pair d , PC is the circuitpower for both µW and mmWave BSs, P(d)C is the circuitpower for the D2D transmitter. More information about P(∗)dare described in detail later in Section III. Each user depend-ing on their category has a minimum QoS requirement asdetailed below:

R(m)min =

Rmin, ∀m ∈ U(npixels × spixels × urate

)crate

, ∀m ∈ C.(12)

where npixels is the number of pixels for a panoramic image,spixels is the number of bits used to store each pixel, urate isthe refresh rate of the image and crate is the compression rate.

III. SELF-ADAPTIVE POWER CONTROLSTRATEGY FOR D2D PAIRSIn order to preserve the QoS of the CUs associated withµW BS, a maximum predefined interference threshold It isimposed for the D2D transmitter reusing the same subcarrierwith the CUs. The transmission power of the D2D transmitteris also constrained such that the CUs can satisfy their mini-mum QoS and can be given as,

log2

1+p(b)m,n|g

(b)m,n|

2(σ 2 +

Pd,nPLµWd,m|g(d)m,n|

2

)PLµWm

≥ R(m)min (13)

Pd,n ≤PLµWd,m

|g(d)m,n|2

(p(b)m,n|g

(b)m,n|

2

(2R(m)min − 1)PLµWm

− σ 2

), (14)

wherePd,n is the transmission power of the d th D2D transmit-ter at subcarrier n, which it shares with CU m and p(b)m,n is thecellular power transmitted by the BS at the given subcarriern to the CU m.

The D2D transmission power is also limited due to a pre-determined interference threshold, It . Due to this provision,the transmit power of the D2D transmitter can be computedas

Pd,n ≤It PL

µWd,m

|g(d)m,n|2, (15)

where Pd,n is the transmit power of the d th D2D transmittercorresponding to It and PLµWd,m is the path loss between thed th D2D transmitter and themth CU sharing the same subcar-rier n. Similarly, each D2D pair needs to transmit at a specificpower level in order to achieve its minimum QoS which is

given by,

Pmind,n =

PLd|gd,n|2

(2R

(m)min − 1

)(σ 2+p(b)m,n|g

(d)m,n|

2

PLµWm,d

), (16)

where PLd is the path loss between the transmitter andreceiver of a D2D pair. Hence, the final constrained trans-mission power of d th D2D pair is then given by,

P(∗)d,n=

{min

(Pd,n,max

(Pd,n,Pmin

d,n

),Pmax

d

), if 3≥Pmin

d,n ,

Infeasible, Otherwise,(17)

where 3 = min(Pd,n,Pd,n

). Finally, the total sum rate of a

D2D pair is given by

Rd =Nd∑n=1

rd,n =Nd∑n=1

σd,n log2(1+ P(∗)d,nγd,n

), (18)

where γd,n =|hd,n|2(

σ 2 + Id,n)PLd

. The allocation of subcarriers

for D2D pairs can also be obtained using the Hungarianalgorithm.

IV. PROPOSED ENERGY AWARE RADIO RESOURCEMANAGEMENT PROCEDURE IN D2D-ENABLEDMULTI-TIER HETNETSThe objective of this work is to jointly maximize the achiev-able rate and EE of all the CUs, subject to a maximuminput power constraint and minimum QoS requirement. Thisformulated problem is equivalent to maximizing the sum rateand minimizing the total power consumption. The proposedoptimization problem is formulated as a MOP which is fur-ther transformed into a single objective optimization problem(SOP) using the weighted-Tchebycheff method by normal-izing the two objectives by Rnorm and Pnorm, respectively,to ensure a consistent comparison as shown below:

(P1) maxp,σ,1ω

φ

∑l∈L

∑m∈M

∑n∈N

σ(l)m,nr

(l)m,n

Rnorm− (1− φ)

PPnorm

,

subject to C1:∑m∈M

∑n∈N

p(l)m,n ≤ Pmaxl ,∀l

C2: Rm ≥ R(m)min, ∀m,

C3: p(l)m,n ≥ 0, ∀m, ∀n, ∀l.

C4: σ (l)m,n ∈

[0, 1

], ∀m, ∀n, ∀l (19)

The optimization problem (P1) as outlined in (19) canbe decomposed into two subproblems. Firstly, optimizingover the operating beamwidth and transmission power forall BS-CU pairs to find their optimal transmission powerp(l,opt)m,n which is dependent on the SINR, which is defined asthe function of the operating beamwidth as depicted in (7).Each BS-CU pair can optimize its own operating beamwidthindependently due to the negligible multi-user interference inorder to maximize its achievable throughput at the expense

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of reduced beam alignment overhead. Finally, substitutingp(l,opt)m,n into a reformulated optimization problem as outlinedlater in (P1-2) to find the optimal allocation for the CUs. Thejoint optimization problem of operating beamwidth and trans-mission power in DL transmission scheme can be formulatedas

(P1− 1) maxp,1ω

φ

∑l∈L

∑m∈M

∑n∈N

r (l)m,n

Rnorm− (1− φ)

PPnorm

,

subject to C1-C3 (20)

From (20), we can also observe that the formulated prob-lem (P1-1) can be transformed into a power minimizationproblem by setting φ = 0. Similarly, the formulated problem(P1-1) can be varied from the power minimization problemto the rate maximization problem by dynamically adjustingthe weighting coefficient from φ = 0 to 1 to obtain acomplete Pareto-optimal solution. It is important to mentionthat an energy efficient solution of the problem (P1-1) can beobtained by selecting φ = φEE.Using [36], the Lagrangian function of problem (P1-1)

subject to the constraints C1 – C3 can be written as,

T (p,µ, η,1ω) =φ

Rnorm

∑l∈L

∑m∈M

∑n∈N

r (l)m,n −(1− φ)Pnorm

P

+

∑l∈L

µl

(Pmaxl −

∑m∈M

∑n∈N

p(l)m,n

)+

∑m∈M

ηm(Rm − R(m)min), (21)

where Pmaxl is the maximum transmit power of BS l, µ is the

Lagrange multiplier vector of dimensions L correspondingto the minimum data requirement of CUs, η is the Lagrangemultiplier vector of dimensionsM corresponding to the max-imum transmission power constraint of BS and 1ω is thevector of beam-level beamwidth for all the links within thesystem with a dimension of M × W . Using (2), (21) can berewritten as (22), shown on the bottom of the next page. Thecorresponding Lagrangian dual function is

t (µ, η) = maxp,1ω

T (p,µ, η,1ω) , (23)

and the dual problem is

minµ,η

t (µ, η)

subject to µ ≥ 0, η ≥ 0. (24)

It is worthwhile to highlight that since the dual problem isconvex, hence the dual decompositionmethod is used to solvethis problem. This dual problem can be decomposed into Nindependent sub-problems as

t (µ, η) = maxp,1ω

{∑n∈N

tn (µ, η)−(1− φ) (L × PC )

Pnorm

+

∑l∈L

µlPmaxl −

∑m∈M

ηmR(m)min

}, (25)

where

tn (µ, η) =∑l∈L

∑m∈M

[(1+ ηm)2lBwl log2

(1+ γ (l)

m,np(l)m,n

)−

(µl +

(1− φ)Pnorm

)p(l)m,n

]It should be noted that tn (µ, η) is convex with respect to

p(l)m,n and these N subproblems can be solved independently.Using the Karush-Kuhn-Tucker (KKT) conditions, the opti-mal power allocation for µW BS l ∈ L and mmWave BS l ∈W can then be computed respectively as (26a)-(26c), shownon the bottom of the next page, where

[y]+= max (0, y) and

p(l,opt)m,n ∈[0, p(l,max)

m,n].

The transmission power of the D2D transmitter cannotexceed Pmax

d which can also limit the maximum permissibletransmission power of the CUs which is denoted by p(l,max)

m,n .This quantity may be computed as follows:

p(l,max)m,n = min

{Pmaxd ,

PLµWm,d

|g(d)m,n|2

|gd,n|2Pmax

d

PLd(2R

(m)min − 1

) − σ 2

}

The optimal power allocation for users associated withµW BS l ∈ B as shown in (26b) is in the form of multi-level water filling where the water-level depends on both dualvariables µ and η, both rate and power normalization factors,i.e.,Rnorm andPnorm, weighting factor φ and the channel gain.Similarly, the optimal power allocation for users associatedwith mmWave BS l ∈ W as shown in (26c) is in the formof multi-level water filling where the water-level depends onthe beam-level beamwidth for both transmitter and receiver,i.e.,1w , 1ωtw1ω

rm, side lobe antenna gain Gmin, both dual

variables µ and η, both rate and power normalization factors,i.e.,Rnorm andPnorm, weighting factor φ and the channel gain.Further details about the joint optimal beam-level beamwidthand optimal power allocation mechanism for D2D-enabledMulti-Tier HetNets are given in Algorithm 1.

Then, substituting the p(l,opt)m,n as an optimal power alloca-tion solution from (26) corresponding to (P1-1) for the CUsassociated with l ∈ L, the subcarrier allocation problem foreach BS l can be modeled as below:

(P1− 2) maxσ

∑l∈L

∑m∈M

∑n∈N

σ (l)m,np

(l,opt)m,n ,

subject to C4: σ (l)m,n ∈

[0, 1

], ∀m, ∀n, ∀l. (27)

It can be shown that (27) is a linear assignment problem withrespect to σ (l)

m,n and can be effectively solved optimally usingthe standard integer point methods. The problem (P1-2) canbe solved using the Hungarian Algorithm [37] for each BSl ∈ L, resulting in σ =

[σ (1), σ (2), · · · , σ (L)

]where σ (L) is a

subcarrier allocation indicator matrix for BS L whose size isML ×NL . It is worthwhile to mention that the constraint (C4)that was not considered in the partial Lagrangian are includedin (27). The obtained solution is an asymptotically optimalsolution.

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Algorithm 1 Joint Optimal beamwidth and Power AllocationMechanism for D2D-Enabled Multi-Tier HetNets1: Set i = 0, j = 0, imax = 104 and jmax = 104, initializeδ = 10−4, p(l)m,n = 10−6, ηm = min

l∈L,n∈N

(|g(l)m,n|

2)+ δ,

∀m and µl = δ, ∀l.

2: Set 1ωlower =Tp1stw1s

rm

Tand 1ωupper = 1stw1s

rm

3: while(|ηEE (i+ 1)− ηEE (i) ||ηEE (i+ 1) |

)≤ 10−4 do

4: 1ω =1ωlower +1ωupper

25: while ηm and µb have not converged or j < jmax do6: Compute p(l,opt)m,n by substituting 1ω = 1ω

using (26)7: Update µl(j+ 1) according to (29a)8: Update ηm(j+ 1) according to (29b)9: end while10: Calculate ηEE (i+ 1) using (11)11: if (ηEE (i+ 1) > ηEE (i))12: 1ωlower = 1ω

13: Else14: 1ωupper = 1ω

15: End if16: go to Step 317: end while18: End

After computing the optimal power allocation and subcar-rier allocation, the dual problem can be solved using subgra-dient method. The subgradients of the dual function in (23)are given as follow:

1µl (j) = Pmaxl −

∑m∈M

∑n∈N

σ (l)m,np

(l)m,n, ∀l, (28a)

1ηm (j) = σ (l)m,n2lBwl log2

(1+ γ (l)

m,np(l)m,n

)− R(m)min, ∀m,

(28b)

The dual variables in the j+ 1th iteration are updated by

µl (j+ 1) =[µl (j)− s1 (j)×1µl (j)

]+, ∀l, (29a)

ηm (j+ 1) =[ηm (j)− s2 (j)×1ηm (j)

]+, ∀m, (29b)

where s1 (j) and s2 (j) are the appropriate positive small stepsizes, respectively, according to the non-summable diminish-ing step length policy. It is assumed that s1 (j) = s2 (j) = 0.5

√i,

where i denotes the iteration index. We also like to mentionthat the subgradient method can guarantee a globally opti-mum solution only for the convex optimization problem forsmall step size.

In this work, we have utilized the dual decompositionmethod to solve (24). In the dual decomposition method,the inner subproblem is first solved in order to obtain thesubcarrier and power allocation variables using the given val-ues of dual variables (or Lagrangian multipliers) such as µland ηm. The outer problem is solved to update the Lagrangianmultipliers using the obtained values of subcarrier and powerallocation variables. This procedure is repeated until the con-vergence is achieved.

V. PERFORMANCE EVALUATIONThe simulations consider actual building locations from theNUST campus, Islamabad, Pakistan, in order to incorporatereal blockage effects and environmental geometry. In the con-sidered setup, there areK mmWave SBSs randomly deployedat the cell edge of each µW BS. The simulation parametersand their considered values are shown in Table I. It should benoted that 0m = 2Rmin,t − 1, for t ∈ {U , C}.Fig. 2 demonstrates the variation of achievable system

EE versus varying 0m for different power control strategies.The power minimization strategy (φ = 0) ensures that allCUs achieve their minimum QoS, i.e., they strictly operateat 0m. The rate maximization strategy (φ = 1) allocates

T (p,µ, η,1ω) =φ

Rnorm

∑l∈L

∑m∈M

∑n∈N

2lBwl log2(1+ γ (l)

m,np(l)m,n

)−

(1− φ)Pnorm

(∑l∈L

∑m∈M

∑n∈N

p(l)m,n + L × PC

)

+

∑l∈L

µl

(Pmaxl −

∑m∈M

∑n∈N

p(l)m,n

)+

∑m∈M

ηm

(∑l∈L

∑n∈N

2lBwl log2(1+ γ (l)

m,np(l)m,n

)− R(m)min

)(22)

dtn (µ, η)

dp(l)m,n= 0, (26a)

p(l,opt)m,n =

(

φRnorm+ ηm

)2lBwl(

µl +1−φPnorm

)ln(2)

−

(N02lBwl + I

(l)m,n

)PLlm

|g(l)m,n|2

+ , ∀l ∈ L, (26b)

p(l,opt)m,n =

(

1Rnorm+ ηm

)2lbl

µl ln(2)−

N02lBwlPLlm|g(l)m,n|2

(�1ω+ G2

min

)+ , ∀m ∈M,∀n ∈ N ,∀l ∈W, (26c)

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TABLE 1. Simulation parameters.

FIGURE 2. System energy efficiency versus target SINR for various powercontrol mechanisms.

the transmission power such that each CU attains its max-imum possible rate. Finally, the EE maximization strategy(φ = φEE) allocates transmission power to each subcarrieraccording to the optimal power allocation strategy definedin (26). The achievable system EE curve remains constantirrespective of 0m for φ = 1. At a target SINR of 10 dB,the power minimization curve approaches the achievable sys-tem EE curve of the EE maximization strategy (φ = φEE).The curve for φ = φEE has an achievable system EE which

FIGURE 3. System energy efficiency versus rmaxd for various power

control mechanisms.

is approximately 60% greater than the φ = 1 curve at 0m =-30 dB. Moreover, for 0m > 9 dB, the curves for φ = φEEand φ = 0 follow a similar trend.

Fig. 3 depicts the system EE versus variation in the max-imum proximity distance between the D2D pair rmax

d at8d/8m = 0.2 and 0m =5 dB for the three proposed powercontrol strategies. The power minimization power controlstrategy (φ = 0) results in an achievable EE of approxi-mately 34 b/J/Hz and it decreases with an increase in rmax

d .The same trend can also be observed for the remaining twopower control strategies as well. The EEmaximization powercontrol strategy (φ = φEE) achieves better performance interms of achievable EE in comparison to the other two powercontrol strategies irrespective of the rmax

d . On the other hand,the rate maximization power control strategy (φ = 1) attainsfar higher rate of 8 kb/s/Hz in contrast to the two other powercontrol strategies as shown in Fig. 4. It is also evident thatthe achievable rate of the powerminimization control strategyalways remains constant irrespective of the variation in rmax

das each user is only interested in achieving its minimum QoSrequirement. The achievable rates of the other two powercontrol strategies show a non-increasing trend with respectto an increase in rmax

d . These simulation results demonstratethat the rmax

d can be tuned in order to attain a specific levelof achievable rate and EE. For example, in order to attain anachievable EE of 28 b/J/Hz (or achievable rate of 5.3 kb/s/Hz)for a given 0m=5 dB and 8d/8m = 0.2, the rmax

d can bechosen as 30 m.

Fig. 5 analyzes the system EE versus the interferencethreshold, It , with rmax

d at 8d/8m = 0.2 and 0m =5 dBfor various power control mechanisms. As the interferencethreshold It increases, the achievable rate of the priorityusers, i.e., CUs, decreases due to the fact that the maximumallowable transmission power of D2D transmitter is limitedby It as shown in (15). An increase in It allows the trans-mission power of the non-priority users (or D2D pairs) to be

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FIGURE 4. System sum rate versus rmaxd for various power control

mechanisms.

FIGURE 5. System EE versus interference threshold It for various powercontrol mechanisms with rmax

d = 25 m.

increased which can help them satisfy their minimum QoSlevel, resulting in better connectivity as depicted in (15) and(16) at the expense of reduced achievable rates of the CUs.As the density of the CUs 8m is 5 times greater than thedensity of D2D pairs 8d , the system EE decreases with anincrease in It for all the proposed power control mechanisms.It is important to mention that a decrease in the system EE isquite gradual as the primary objectives of both priority andnon-priority users are to satisfy their minimum QoS levelreducing the impact of increase in It for the case of powerminimization scheme (φ = 0). We can also observe that aftera certain value of It , the power minimization scheme (φ = 0)outperforms in comparison to the EE maximization scheme(φ = φEE) and rate maximization scheme (φ = 1).

The impact of the interference threshold It on the systemsum rate with rmax

d at 8d/8m = 0.2 and 0m =5 dB for vari-ous power control mechanisms are illustrated in Fig. 6. The

FIGURE 6. System sum rate versus interference threshold, It , for variouspower control mechanisms with rmax

d = 25 m.

FIGURE 7. Average rate of CUs versus interference threshold It forvarious D2D pair to CU density ratio 8d/8m with rmax

d = 25 m.

achievable rates of both CUs and D2D pairs increase with anincrease in It for all the proposed power control mechanisms.The rate maximization scheme (φ = 1) outperforms the othertwo proposed power control schemes as the D2D transmit-ters are allowed to transmit with more transmission powerresulting in their high achievable data rates without degradingthe QoS of CUs below the minimum acceptable level. Thisphenomenon results in an increased system power consump-tion which increases the system sum rate irrespective of theselected power control scheme (as depicted in Fig. 6) at theexpense of a decrease in the achievable system EE as shownin Fig. 5.

Fig. 7 describes the average achievable rate of CUs versusIt for various 8d/8m ratios with rmax

d = 25 m. As the inter-ference threshold It increases, the average achievable rateof CUs decreases due to the increased maximum allowableinterference threshold from the D2D pairs. The CUs willneed more allocated power from the access point in order

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FIGURE 8. Outage probability of D2D pairs and system energy efficiencyversus target SINR at different It for φ = φEE.

FIGURE 9. System energy efficiency and system sum rate versus the D2Dpair to CU density ratio with rmax

d = 25 m.

to achieve their minimum rate requirement. This figure pin-points that the average achievable rate of CUs decreases withan increase in It at a given fixed 8d/8m. It is also importantto mention that decreasing8d/8m, (i.e., decreasing the totalnumber of CUs) results in decreasing the average achievablerate of the CUs. For example, the average achievable rateof CUs increases from 3.1 b/s/Hz to 3.8 b/s/Hz at It =10−10 W by decreasing the ratio from 8d/8m = 0.5to 8d/8m = 0.2.

Fig. 8 analyzes the relationship between outage probabilityof D2D pairs and the achievable system EE versus It forvarious values of 0m. We can also observe that the coverageprobability decreases with an increase in 0m for various

values of interference thresholds It . It can also be seen thatthe probability of D2D pairs being in outage is higher at lowervalues of It . The figure highlights that in order to maintainan outage probability of 20%, the network operators caneither tune the network parameters such as It = 10−16 Wand 0m = −20 dB whereas the same outage probabilitycan also be achieved for 0m = 0 dB and 0m = 20 dBat It = 10−14 W and It = 10−12 W, respectively. It canalso be observed from Fig. 8 that the achievable system EEgenerally decreases with an increase in 0m. It also demon-strates that the achievable system EE also decreases withan increase in It . In fact, the system EE can achieve nearly25% gain at 0m = 10 dB with the help of interferencemitigation techniques, i.e., reducing from It = 10−16 Wto It = 10−12W.

Fig. 9 investigates the achievable systemEE and the systemsum rate versus the ratios of densities, i.e.,φd/φm. The systemsum rate increases with an increase in φd/φm. However, forall the values of density ratios, the system EE optimizationapproach offers the greatest achievable SEE, followed bythe power minimization and rate maximization approaches.In order to achieve a system EE of 26 b/J/Hz for the powerminimization strategy, i.e., φ = 0, the optimal φd/φm densityratio should be 0.41, which will result in the achievablesystem sum rate of 2 Kb/s/Hz.

VI. CONCLUSIONAlthough 5G networks are anticipated to provide enhanceddata rates and seamless connectivity, they pose critical chal-lenges related to the resource allocation between variousnetwork entities. The problem becomes more pronouncedespecially if the network is truly heterogeneous in termsof diverse frequency bands, cell sizes, and modes of usercommunication. This article studied the resource allocationproblem for such a network where D2D communicationscoexist with cellular communications and the BSs and CUscan operate on both sub 6 GHz as well as above 6 GHzfrequency bands. Optimization routines have been developedto maximize both energy and spectral efficiencies of cellularas well as D2D users while guaranteeing a minimum QoS.The results heavily depend upon total power budget and thedensity of CUs and D2D pairs in the system. Future worksinclude analyzing the system with more practical path lossmodels such as dual-slope models to cater for the effectsof irregular patterns and geometry of cells. Similarly, userassociation for decoupled uplink/downlink can be studiedwhere a CU can make disparate connections to different BSsin uplink and downlink, respectively.

ACKNOWLEDGMENTThe authors would like to thank the support of the Universityof Surrey 5GIC (http://www.surrey.ac.uk/5gic) members forthis paper. This paper was presented at the IEEE GlobalCommunications Conference [1].

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SYED AHSAN RAZA NAQVI received thebachelor’s degree in electrical engineering fromthe National University of Sciences and Tech-nology (NUST), Pakistan, in 2015. He was aResearch Assistant with the Information Pro-cessing and Transmission Lab, NUST. As aGraduate Research Assistant, he was primarilyfocused on the enabling technologies for 5G net-works. His research interests include cooperativecommunication, millimeter-wave technology, anddevice-to-device communication.

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HARIS PERVAIZ received the M.Sc. degree ininformation security from the Royal HollowayUniversity of London in 2005, the M.Phil. degreein electrical and electronic engineering from theQueen Mary University of London in 2011, andthe Ph.D. degree from the School of Computingand Communication, Lancaster University, U.K.,in 2016. From 2016 to 2017, he was an EPSRCDoctoral Prize Fellow with the School of Comput-ing and Communication, Lancaster University. He

is currently a Research Fellow with the 5G Innovation Centre, Universityof Surrey, U.K. His main research interests include green heterogeneouswireless communications and networking, green communications, controldata separation architecture, 5G and beyond systems, Internet of Things,UAV, and millimeter-wave communication.

SYED ALI HASSAN received the B.E. degree(Hons.) in electrical engineering from the NationalUniversity of Sciences and Technology (NUST),Pakistan, in 2004, the M.S. degree in electri-cal engineering from the University of Stuttgart,Germany, in 2007, and the M.S. degree in math-ematics and the Ph.D. degree in electrical engi-neering from the Georgia Institute of Technology,Atlanta, GA, USA, in 2011. He was a ResearchAssociate with Cisco Systems Inc., CA, USA. He

is currently an Assistant Professor with the School of Electrical Engineeringand Computer Science, NUST, where he is also the Director of InformationProcessing and Transmission Research Group, which focuses on variousaspects of theoretical communications. His research interest is signal pro-cessing for communications. He has co-authored over 75 publications ininternational conferences and journals. He served as a technical committeemember and a symposium chair for various conferences/workshops. Heserved as a guest editor for various journals.

LEILA MUSAVIAN received the Ph.D. degreein telecommunications from the King’s CollegeLondon, U.K., in 2006. From 2006 to 2008, shewas a Post-Doctoral Fellow with the NationalInstitute of Scientific Research-Energy, Materials,and Telecommunications, University of Quebec,Canada. From 2009 to 2010, she was with Lough-borough University, where he investigated adap-tive transmission techniques for delay quality ofservice (QoS) provisioning in cognitive radio net-

works (CRNs). From 2010 to 2012, she was a Research Associate withthe Department of Electrical and Computer Engineering, McGill University,where she was involved in developing energy-efficient resource allocationtechniques for multiuser wireless communications systems. From 2012 to2016, she was a Lecturer in communications with InfoLab21, School ofComputing and Communications, Lancaster University. She is currently aReader with the School of Computer Science and Electronics Engineering,University of Essex, U.K. Her research interests lie in the area of wirelesscommunications and include radio resource management for next genera-tion wireless networks, CRNs, green communication and energy-efficienttransmission techniques, and cross-layer design for delay QoS provisioningin spectrum-sharing channels.

QIANG NI received the B.Sc., M.Sc., andPh.D. degrees from the Huazhong University ofScience and Technology, China, all in engineer-ing. He led the Intelligent Wireless Communica-tion Networking Group with Brunel UniversityLondon, U.K. He is currently a Professor and theHead of the Communication Systems Group withInfoLab21, School of Computing and Communi-cations, Lancaster University, Lancaster, U.K. Hismain research interests lie in the areas of wire-

less communications and networking, including green communications,cognitive radio systems, 5G, IoT, and vehicular networks. He was a IEEE802.11Wireless Standard Working Group Voting Member and a Contributorto the IEEE Wireless Standards.

MUHAMMAD ALI IMRAN (M’03–SM’12)received the B.Sc., M.Sc. (Hons.), and Ph.D.degrees from the Imperial College London, U.K.,in 2002 and 2007, respectively. From 2007 to2016, he was a Visiting Professor with the 5GIC,University of Surrey, Surrey, U.K. He is currently aProfessor in communication systems with the Uni-versity of Glasgow, the Vice Dean of the GlasgowCollege, UESTC, and the Program Director of theElectrical and Electronics with Communications.

He is also an Adjunct Associate Professor with the University of Oklahoma,Tulsa, OK, USA. He also led the new physical layer work area for 5G Inno-vation Center. He has a global collaborative research network spanning bothacademia and key industrial players in the field of wireless communications.He has supervised 21 successful Ph.D. graduates. He has published over200 peer-reviewed research papers including over 20 IEEE TRANSACTIONS

papers. He has given an invited TEDx talk in 2015 and over ten plenarytalks, several tutorials, and seminars in international conferences and otherinstitutions. He has taught international short courses in USA and China.He is a Senior Fellow of the Higher Education Academy, U.K. He was aChair for several tracks/workshops of international conferences. He was arecipient of the IEEE Comsoc’s Fred Ellersick Award 2014, the Sentinelof Science Award 2016, and the FEPS Learning and Teaching Award 2014.He was nominated twice for the Tony Jean’s Inspirational Teaching Award.He was a Shortlisted Finalist for the Wharton-QS Stars Awards in 2014,the Reimagine Education Award for Innovative Teaching, and the VC’sLearning and Teaching Award at the University of Surrey. He received theAward of Excellence in recognition of his academic achievements, conferredby the President of Pakistan. He is the co-founder of the IEEE WorkshopBackNets 2015. He is an Associate Editor for the IEEE COMMUNICATIONS

LETTERS, the IEEE OPEN ACCESS, and IET Communications Journal.

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S. A. R. Naqvi et al.: Energy-Aware Radio Resource Management in D2D-Enabled Multi-Tier HetNets

XIAOHU GE (M’09–SM’11) received thePh.D. degree in communication and informationengineering from the Huazhong University ofScience and Technology (HUST), China, in 2003.From 2004 to 2005, he was a Researcher with AjouUniversity, South Korea, and the Politecnico DiTorino, Italy. He is currently a Full Professor withthe School of Electronic Information and Com-munications, HUST. He is an Adjunct Professorwith the Faculty of Engineering and Information

Technology, University of Technology Sydney, Australia. Since 2005, hehas been with HUST. He has published about 160 papers in refereed journalsand conference proceedings and has been granted about 15 patents in China.His research interests are in the areas of mobile communications, trafficmodeling in wireless networks, green communications, and interferencemodeling in wireless communications. He is a Member of the NationalNatural Science Foundation of China and the Chinese Ministry of Scienceand Technology Peer Review College and a Senior Member of the ChinaInstitute of Communications. Since 2005, he has been actively involved inorganizing over ten international conferences. He served as the General Chairfor the 2015 IEEE International Conference on Green Computing and Com-munications. He serves as an Associate Editor for the IEEE TRANSACTIONS ON

VEHICULAR TECHNOLOGY and the IEEE WIRELESS COMMUNICATIONS, and so on.

RAHIM TAFAZOLLI (SM’07) is currently a Pro-fessor and the Director of the Institute for Com-munication Systems and 5G Innovation Centre,University of Surrey, U.K. He has published over500 research papers in refereed journals, interna-tional conferences, and as an invited speaker. He isthe editor of two books Technologies for WirelessFuture (Wiley, Volume1, in 2004 and Volume 2,2006). He holds over 20 patents in mobile com-munications. He was appointed as a Fellow of

Wireless World Research Forum in 2011, for the recognition of his personalcontribution to the wireless world. He is the Head of one of the Europe’sleading research groups. He is a Chair of the European Union Net! WorksTechnology Platform Expert Group.

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