An Energy Efficient D2D Model with Guaranteed Quality of Service for Cloud Radio Access Networks
Isuru Janith Ranawaka, Kasun T. Hemachandra, Tharaka Samarasinghe, Theshani Nuradha
aa r X i v : . [ ee ss . SP ] N ov An Energy Efficient D2D Model with Guaranteed Quality ofService for Cloud Radio Access Networks
Isuru Janith Ranawaka ∗ , Kasun T. Hemachandra ∗ , Tharaka Samarasinghe ∗† , Theshani Nuradha ∗∗ Department of Electronic and Telecommunication Engineering, University of Moratuwa, Moratuwa, Sri Lanka † Department of Electrical and Electronic Engineering, University of Melbourne, Victoria, AustraliaEmail: [email protected], [email protected], [email protected], [email protected]
Abstract —This paper proposes a spectrum selection schemeand a transmit power minimization scheme for a device-to-device(D2D) network cross-laid with a cloud radio access network(CRAN). The D2D communications are allowed as an overlayto the CRAN as well as in the unlicensed industrial, scientificand medical radio (ISM) band. A link distance based scheme isproposed and closed-form approximations are derived for thelink distance thresholds to select the operating band of theD2D users. Furthermore, analytical expressions are derived tocalculate the minimum required transmit power to achieve aguaranteed level of quality of service in each operating band.The results demonstrate that the proposed scheme achieves nearly50% power saving compared to a monolithic (purely overlay orpurely ISM band) D2D network.
I. I
NTRODUCTION
Cloud radio access network (CRAN) architecture has beenintroduced to mobile wireless networks to enable large-scaledeployment and to reduce capital and operating expenditure ofthe network operators. However, large traffic flow in backhauland fronthaul links can severely affect the throughput andlatency performance of CRANs. To reduce the backhaul trafficin CRANs, cache enabled edge CRANs (E-CRANs) are pro-posed [1], [2], while traffic offloading techniques [3]–[5] areproposed to reduce the fronthaul traffic. Both these approachesrequire separate access points (APs) for operation, whichresults in additional costs for network operators. To cater thedemands of increasing user densities, cache enabled device-to-device (D2D) communication has emerged a promisingtechnology to assist the CRAN infrastructure, as a means toimprove quality-of-service (QoS), throughput and energy effi-ciency [6]–[11]. However, energy limitations of user devicesaffects the QoS of D2D networks, which motivates researchon power efficient and QoS guaranteed D2D communicationprotocols and user association schemes.To account for the limited energy availability at user de-vices, power controlling strategies have been employed tomitigate interference and provide energy efficient communica-tion systems. In [12], a distance based power control schemehas been proposed for a D2D underlaid cellular system. Ascheme to mitigate the interference generated by the D2D userequipment (UE) to the cellular UE with the help of powercontrol of D2D UE, and also by selecting proper mode ofoperation based on the channel gain threshold is proposed in[13].The operating spectrum band is another crucial parame-ter for D2D communications. Overlay, underlay and unli-censed industrial, scientific and medical radio (ISM) band
This work is supported by the Senate Research Council, University ofMoratuwa, Sri Lanka, under grant SRC/LT/2018/2.
D2D communications have been investigated extensively inthe literature. Proper selection of spectrum band for D2Dcommunications based on the network dynamics may furtherimprove the QoS and energy efficiency of D2D networks.This paper proposes a spectrum selection scheme for aD2D network cross laid with an E-CRAN. The proposedscheme provides guaranteed QoS while minimizing powerconsumption. In contrast to a monolithic D2D network, ahybrid D2D network is proposed where D2D communicationsare allowed in the ISM band as well as an overlay to the E-CRAN. The contributions of this paper can be summarized asfollows. • Link distance based spectrum selection scheme is pro-posed for identified D2D user pairs. • Link length thresholds for spectrum selection are obtainedanalytically. • The minimum transmit power required to provide aguaranteed QoS level in each band is derived analytically.The remainder of this paper is organized as follows. SectionII presents the system model under consideration and sum-marizes the proposed D2D communication model. Section IIIpresents the link length threshold computations for each bandand Section IV gives the minimum transmit power calculationscheme for each D2D link. Numerical results obtained usingthe proposed scheme are shown in Section V, while SectionVIconcludes the paper.II. S
YSTEM M ODEL
ULDL
D2D
RRH Data ProducerEdge Cloud F r on t h a u l L i n k B a c k h a u l L i n k Cache BBUContent Cloud External User Data Consumer
Fig. 1. Communication modes and system model
We consider an E-CRAN cross laid with a D2D network,which comprises of remote radio heads (RRHs), a contentcache and a baseband unit (BBU) pool. The RRHs are spatiallydistributed according to a homogeneous Poisson point process(PPP) Φ bs of intensity λ bs . Each RRH uses a fixed transmitpower P bs . Three types of users, namely, data consumers(DCs), data producers (DPs), and external users (EUs) areonsidered in our model. The DCs are connected to theirnearest RRH, and they request content from their connectedRRH. The DPs cache the most popular content files from theedge cloud cache, such that the cache hit probability (CHP)for a given file is p . Moreover, we assume that a typical DCis at the origin and hereafter, we refer to it as the DC. Thespatial distributions of the DCs and the DPs are modeled usinghomogeneous PPPs Φ dc and Φ dp with intensities of λ dc and λ dp , respectively. A PPP Φ ext of intensity λ ext is used tomodel the spatial distribution of the EUs which operate in theISM band, with a fixed power P ext .An interference limited network is assumed where theadditive noise is negligible compared to interference. For alllinks, Rayleigh fading is assumed where the channel powercoefficients are independently and identically distributed ex-ponential random variables (RVs) of unit mean. A distancedependent path loss model with exponent α > is also usedto model large-scale fading, while the effects of shadowingare neglected due to the short lengths of D2D links.We assume that all DCs will make their requests simulta-neously. A request of a DC will generally be served by theRRH. However, if there is a DP in the vicinity who has therequested file in its cache, the DC may get served by this DP.Content delivery via an RRH is referred to as the cellularmode, while the delivery from a DP is referred to as theD2D mode. The D2D mode will be chosen only if it canprovide equal or better QoS than the cellular mode. Since weare interested in delay sensitive content such as high definitionvideo, the transmission delay violation probability (DVP) withrespect to a given delay threshold D max , i . e . , for link delay D , Pr { D > D max } , is used to measure the QoS. Intuitively,lower the DVP, higher the QoS experienced by the user.In D2D mode, the distance between the DC and the servingDP is used to determine whether the communication occur inthe ISM band or as an overlay to the cellular spectrum. Thesetwo schemes are referred to as outband mode and overlaymode, respectively. In similar environments, outband DPs, whoare assumed to operate at a higher carrier frequency, have asmall coverage area compared to overlay DPs, who operate at alower carrier frequency. Intuitively, the DC and DP pairs withshort links are allocated to the outband mode, pairs havingmoderately long links are allocated to the overlay mode, andpairs with long links may not use the D2D mode as they fail tosatisfy the QoS requirements. The content delivery procedurefor our system model is summarized in Algorithm 1, where d ⋆ ou and d ⋆ ol are the distance thresholds for outband and overlaymodes, respectively.Obtaining analytical expressions for the optimal values of d ⋆ ou and d ⋆ ol , and the minimum required transmit powers of theDPs are the main contributions of this paper. The notationsused in this paper are tabulated in Table I.III. S PECTRUM S ELECTION S CHEME
The computation of distance thresholds requires several in-termediate results, namely, the DVPs for each communicationmode and the spatial intensities of the DPs in each D2D mode.
Algorithm 1
Spectrum Selection and Transmit Power Control for each request d ← calculate the distance between DC and DP if ( d ≤ d ⋆ ou ) then P ← calculate the outband power if ( P ≤ P max ) then transmit in outband network using power P else transmit using cellular communication else if ( d ⋆ ou ≤ d ≤ d ⋆ ol ) then P ← calculate the overlay power if ( P ≤ P max ) then transmit in overlay network using power P else transmit using cellular communication else transmit using cellular communication do TABLE I. Notation Description
Description Notation
Bandwidth of a cellular channel B bs Bandwidth of an outband channel B ou Bandwidth of an overlay channel B ol application level processing delay c Distance from the DC to the nearest RRH d bs , Distance from the DC to the k th DP operating in outband d ou ,k Distance from the DC to the k th DP in overlay d ol ,k SIR of channel between DC to RRH γ bs SIR of channel between DC to k th DP in outband γ ou ,k SIR of channel between DC to k th DP in overlay γ ol ,k Delay of the channel between DC and RRH D bs , Delay of the channel between DC to the k th DP in outband D ou ,k Delay of the channel between DC to the k th DP in overlay D ol ,k Fading coefficient of the channel between DC and RRH h bs , Fading coefficient of the channel between DC to the k th DP in outband h ou ,k Fading coefficient of the channel between DC to the k th DP in overlay h ol ,k A. DVP Calculation
We begin by considering that the DC requests a file of size M from the edge cloud. The edge cloud may deliver the filedirectly through the RRH or via a DP. The DVPs of each modeare used to make this decision. The DVP of a link betweenthe DC and its nearest RRH is given by the following lemma. Lemma 1:
The DVP of the link between the DC and thenearest RRH is given by T bs ( D max ) = ( γ ⋆ bs ) α ( γ ⋆ bs ) α + sinc (cid:0) α (cid:1) , (1)where γ ⋆ bs = 2 MB bs( D max − c ) − . Proof:
Letting D to be the sum of the transmit duration,propagation and processing delays, the DVP conditioned on d bs , , the distance between the DC and the RRH, is given by Pr { D > D max | d bs , } = Pr (cid:26) MB bs log(1 + γ bs ) + c > D max | d bs , (cid:27) , = Pr { γ bs < γ ⋆ bs | d bs , } . (2)The signal-to-interference-ratio (SIR) at the receiver for thelink of interest is given by γ bs = P bs h bs , d − α bs , P j ∈ Φ ′ bs P bs h bs ,j d − α bs ,j , (3)here Φ ′ bs represents the point process governing the locationsof the interfering RRHs. Evaluating (2) is well studied in theliterature [14], and the DVP conditioned on d bs , is given by Pr { D > D max | d bs , } = 1 − exp − πλ bs ( γ ⋆ bs ) α d , sinc (cid:0) α (cid:1) ! . (4)Averaging (4) using probability density function (PDF) of d bs , given by f d bs , ( r ) = 2 πλ bs r exp (cid:0) − πλ bs r (cid:1) , completesthe proof.Next, T bs ( D max ) is compared with the DVP valuesachieved in the two D2D modes (outband and overlay). Toaccount for worst case DVP in D2D mode, we assume thatthe DP containing the requested content is located at a distanceequal to the threshold distance for each D2D mode. Note that(4) can be used to make this comparison. However, this leadsto decision thresholds which are functions of d bs , as well.Physically, this means each DC has its own decision threshold,that depends on its distance from the RRH. This makes itprohibitively hard for us to obtain the spatial intensities of theoverlay and outband DPs, λ ou and λ ol , respectively, whichare required to calculate the DVP values for each D2D mode.Therefore, we have averaged out the effect of d bs , to obtaina universal distance threshold, valid for the entire network.With the idea of this common threshold, next we derive λ ou and λ ol .To this end, we thin PPP Φ dc into three point processesto represent DCs served by RRHs, by a DP as outband andby a DP as an overlay. Moreover, we assume that outbandDCs and the overlay DCs form homogeneous PPPs Φ ou and Φ ol , respectively. Since the separation of the DCs into outbandand overlay depends on the distance between DCs and DPs,the thinning of Φ dc will not result in homogeneous PPPs.However, similar approximations are used in [15]–[18] withsufficient accuracy. In Section V, we relax this assumption insimulation results, which are used to validate the analyticalresults. The approximate values for λ ou and λ ol are given inthe following lemma. Lemma 2:
The intensities of the two point processes Φ ou and Φ ol are given by λ ou = λ dc h − e − pπλ dp ( d ⋆ ou ) i and λ ol = λ dc h e − pπλ dp ( d ⋆ ou ) − e − pπλ dp ( d ⋆ ol ) i , respectively. Proof:
Using the null probability of Φ dp , the probabilityof existence of a DP containing the requested file within thedistance of d ⋆ ou from the DC is given by h − e − pπλ dp ( d ⋆ ou ) i ,where we have assumed the intensity of the DPs containing therequested file is pλ dp . The edge cloud randomly selects a DPwithin the distance of d ⋆ ou from the DC, which will transmitin outband. Hence, multiplying the probability by λ dc givesthe intensity of DPs, who are eligible to transmit in outband.Assuming a one to one mapping of DCs to DPs, this intensityis equal to λ ou .Similarly, the probability of existence of a DP having therequested content between the distance of d ⋆ ou and d ⋆ ol is givenby h − e − pπλ dp ( d ⋆ ol ) i − h − e − pπλ dp ( d ⋆ ou ) i . The randomlyselected DP will transmit to the DC in the overlay band.Therefore, multiplying this probability by λ dc gives λ ol . Using the approximate intensities λ ou and λ ol , Lemma 3gives the conditional DVPs (conditional on D2D link lengths)of typical D2D links in outband and overlay modes. Lemma 3:
The DVPs of a typical outband D2Dlink ( k th ), and a typical overlay D2D link are givenby Pr { D ou ,k > D max | d ou ,k } = T ou ,k ( D max , d ou ,k ) and Pr { D ol ,k > D max | d ol ,k } = T ol ,k ( D max , d ol ,k ) , respectively,where T ou ,k ( D max , d ou ,k )= 1 − exp − π h λ ou E (cid:16) P α ou ,j (cid:17) + P α ext λ ext i ( γ ⋆ ou ) α d ,k sinc (cid:0) α (cid:1) P α ou ,k (5) T ol ,k ( D max , d ol ,k ) = 1 − exp − πλ ol E (cid:16) P α ol ,j (cid:17) ( γ ⋆ ol ) α d ,k sinc (cid:0) α (cid:1) P α ol ,k . (6) Proof:
Following the proof of Lemma 1, we have T ou ,k ( D max , d ou ,k ) = Pr { γ ou ,k < γ ⋆ ou | d ou ,k } , (7) T ol ,k ( D max , d ol ,k ) = Pr { γ ol ,k < γ ⋆ ol | d ol ,k } , (8)where γ ⋆ ou = 2 MB ou ,k ( D max − c ) − and γ ⋆ ol = 2 MB ol ,k ( D max − c ) − .The SIRs of D2D links in each mode can be given as γ ou ,k = P ou ,k h ou ,k d − α ou ,k P j ∈ Φ ′ ou P ou ,j h ou ,j d − α ou ,j + P j ∈ Φ ext P ext ,j h ext ,j d − α ext ,j , (9) γ ol ,k = P ol ,k h ol ,k d − α ol ,k P j ∈ Φ ′ ol P ol ,j h ol ,j d − α ol ,j , (10)where Φ ′ ou and Φ ′ ol are the PPPs governing the locations ofthe interfering DPs in Φ ou and Φ ol , respectively. Evaluating(7) and (8) using (9) and (10) as in the proof of Lemma 1concludes the proof. B. Link Length Threshold Calculation
Using the DP intensities and DVPs of each D2D mode,expressions for the link length thresholds d ⋆ ou and d ⋆ ol can befound as shown in Lemma 4. Lemma 4:
The outband and overlay distance thresholds aregiven by d ⋆ ou = (cid:16) √ B +4 AC − B A (cid:17) , d ⋆ ol = (cid:16) √ E +4 DC − E D (cid:17) , where A = π p ( γ ⋆ ou ) α λ dp λ dc E (cid:18) P α ou ,j (cid:19) sinc ( α ) P α max , B = π ( γ ⋆ ou ) α P α ext λ ext sinc ( α ) P α max , C = | ln (1 − T bs ( D max )) | , D = π pλ dc λ dp E (cid:18) P α ol ,j (cid:19) ( γ ⋆ ol ) α sinc ( α ) P α max and E = πpλ dc E (cid:18) P α ol ,j (cid:19) ( γ ⋆ ol ) α (cid:20) e − πλ dp ( d⋆ ou ) − (cid:21) sinc ( α ) P α max . Proof:
We assume that the selected DP is at the distancethreshold d ⋆ ou from the DC. To be eligible for a viable outbandD2D link while using the maximum available transmit power P max , this DP should be able to satisfy the QoS requirement T ou ,k ( D max , d ⋆ ou ) ≤ T bs ( D max ) . (11)y substituting the results of Lemma 2 and 3, and by applyingthe first order Taylor series approximation e − ax = 1 − ax , (11)can be simplified as π h πpλ dp λ dc ( d ⋆ ou ) E (cid:16) P α ou ,j (cid:17) + P α ext λ ext i ( γ ⋆ ou ) α ( d ⋆ ou ) sinc (cid:0) α (cid:1) P α max ≤| ln (1 − T bs ( D max )) | . (12)Solving (12), gives us d ⋆ ou . Same procedure can be used toobtain an expression for d ⋆ ol .Clearly, d ⋆ ou and d ⋆ ol depend on E (cid:16) P α ou ,j (cid:17) and E (cid:16) P α ol ,j (cid:17) ,which depend on the transmit powers of the other DPs in eachband. Obtaining analytical expressions for these expectationsappears to be intractable since the PDF of the transmit powersof the DPs is not known. Therefore, assuming worst case con-ditions, the interferes are allowed to transmit at their maximumpower, making E (cid:16) P α ou ,j (cid:17) = P α max and E (cid:16) P α ol ,j (cid:17) = P α max .This simplifies d ⋆ ou and d ⋆ ol such that A = π p ( γ ⋆ ou ) α λ dp λ dc sinc ( α ) , D = π p ( γ ⋆ ol ) α λ dp λ dc sinc ( α ) , and E = πpλ dc ( γ ⋆ ol ) α (cid:20) e − πλ dp ( d⋆ ou ) − (cid:21) sinc ( α ) ,which result in lower bounds for d ⋆ ou and d ⋆ ol .The thresholds can be further refined in a system setting byusing an iterative computation scheme. Initially, the distancethresholds and the transmit power of each DP are calcu-lated under the worst case conditions. In the next iteration, E (cid:16) P α ou ,j (cid:17) and E (cid:16) P α ol ,j (cid:17) are evaluated using the transmitpowers of the previous iteration, and the distance thresholdsand the transmit power of each DP are recalculated. Thisprocedure is repeated until the distance thresholds convergeto a fixed value. We refer to this approach as “iterativeoptimization” in our numerical results.From the distance threshold expressions, one can deducethat when d ⋆ ou → , all DPs will be allocated to overlay band.Since reducing the outband threshold will allocate more DPsinto the overlay network, the interference in the overlay bandwill increase. Therefore, when d ⋆ ou → , d ⋆ ol also decays expo-nentially. Furthermore, when d ⋆ ou increases, d ⋆ ol also increases.When the outband region expands, more users are allocatedto the outband. Hence, the interference in the overlay regionwill be reduced, providing more communication opportunitiesin the overlay band.IV. T RANSMIT P OWER C OMPUTATION
Next, we calculate the parameter P in Algorithm 1, whichis the required minimum transmit power of each DP to satisfythe QoS requirement. Assume that the k th DP containing therequested file is selected to serve the DC. We first decide onthe operating band of the DP by comparing the link length withthe distance thresholds. Next, the required minimum power ofeach DP is computed such that the DVP with a D2D link is atmost equal to the DVP of delivering content through an RRH.The following lemma formally states the required minimumpower for a selected DP in each band to achieve a DVP equalto the cellular mode.
Lemma 5:
The minimum transmit power of the k th DPallocated to the outband network or the overlay network canbe given as P ′ ou ,k = λ ou E (cid:16) P α ou ,j (cid:17) + P α ext λ ext λ bs α (cid:18) γ ⋆ ou γ ⋆ bs (cid:19) (cid:18) d ou ,k d bs , (cid:19) α (13a) P ′ ol ,k = λ ol E (cid:16) P α ol ,j (cid:17) λ bs α (cid:18) γ ⋆ ol γ ⋆ bs (cid:19) (cid:18) d ol ,k d bs , (cid:19) α . (13b) Proof:
We first consider an outband DP. To achieve equalor better QoS compared to the cellular mode, we need T ou ,k ( D max , d ou ,k ) ≤ T bs ( D max , d bs , ) . By substituting the DVP values, we have exp − π h λ ou E (cid:16) P α ou ,j (cid:17) + P α ext λ ext i ( γ ⋆ ou ) α d ,k sinc (cid:0) α (cid:1) P α ou ,k ≥ exp − πλ bs ( γ ⋆ bs ) α d , sinc (cid:0) α (cid:1) ! . (14)Solving (14) for P ou ,k yields (13a) as the minimum requiredtransmit power for the DP. A similar approach can be used toobtain (13b).One can observe that P ou ,k and P ol ,k depend on the ratio d ou ,k d bs , and the mean transmit power of the DPs in the operating band.The distance thresholds identify the feasible set of outbandDPs and the overlay DPs. However, since the threshold valuesare based on the average DVP of the cellular mode (averagedover the distance to the nearest RRH), all DPs in the feasibleset may not be able to satisfy the maximum transmit powerconstraint for individual links. Therefore, the DPs in feasibleset are individually checked for maximum power constraintviolation. The DCs with selected DPs who are not capableof satisfying the power constraint will be re-allocated to thecellular mode. This refines the DP intensities in each band. Therefined DP intensities in each band are given in the followinglemma. Lemma 6:
Refined intensities of the outband and the overlayband are given by λ th ou = " λ ou π λ ( d ⋆ ou ) P max β (cid:19) α , (15) λ th ol = λ ol (cid:16) ( d ⋆ ol ) − ( d ⋆ ou ) (cid:17) " π λ (cid:18) P max β (cid:19) α − ( d ⋆ ou ) , (16)where β = (cid:18) λ ou P α max + P α ext λ ext (cid:19) λ bs α (cid:16) γ ⋆ ou γ ⋆ bs (cid:17) and η = (cid:20) λ ol P α max λ bs (cid:21) α (cid:16) γ ⋆ ol γ ⋆ bs (cid:17) . ig. 2. Validation of the independent thinning approximation Proof:
The refined intensity of the outband DPs can befound as, λ th ou = Z ∞ λ ou Pr { P ou ,k ≤ P max | r } f d bs , ( r ) dr = Z ∞ λ ou Pr ( d ou ,k ≤ (cid:18) P max β (cid:19) α r ) f d bs , ( r ) dr ( a ) = Z ∞ λ ou (cid:16) P max β (cid:17) α r ( d ⋆ ou ) πλ bs re − πλ bs r dr. (17)where ( a ) follows from Pr { P ou ,k ≤ x } = x ( d ⋆ ou ) . Evaluating(17), yields (15). By following a similar approach and byusing Pr { d ol ,k ≤ r } = r − ( d ⋆ ou ) ( d ⋆ ol ) − ( d ⋆ ou ) , one can obtain (16). Wehave assumed the maximum interference in each band whencalculating the refined intensities.The refined intensities can be used to evaluate other perfor-mance metrics such as coverage probability, average achiev-able rate and transmission capacity of the network. However,due to page length restrictions, we do not include those resultsin this version. V. N UMERICAL R ESULTS
In this section, we provide numerical and simulation resultsto validate our assumptions and to identify the benefits ofthe proposed algorithm. Note that the assumptions made foranalysis are relaxed in simulation results. The parameters usedin the simulations are tabulated in Table II.
TABLE II. Simulation Parameters
Parameter ValueRRH power ( P bs ) 100 mW Maximum power of an end device ( P max ) 2 . mW Power of an external user ( P ext ) 2 mW Radius of the simulated area ( R ) 3000 m DP intensity ( λ dp ) 10 − DC intensity ( λ dc ) 10 − EU intensity ( λ ext ) 10 − . RRH intensity ( λ bs ) 10 − . Path loss exponent ( α ) 3 . File size ( M ) 80 kB Channel bandwith ( B bs , B ou , B ol ) 5 MHz
Application level delay threshold ( D max ) 0 . ms Processing delay ( c ) 0 . ms Fig. 3. Intensity of each D2D network against the external user intensityFig. 4. Intensity of each D2D network against the DP intensity
Firstly, we validate the assumption of Φ ou and Φ ol beinghomogeneous PPPs. For this, we use DPs and DCs that arespatially distributed according to homogeneous PPPs. Then,the DPs and DCs are randomly paired based on their linklengths. We split them into outband and overlay using athreshold distance d . The coverage probability of a typicalDC in each band is evaluated using simulations and comparedwith the theoretical coverage probability obtained by assumingthat Φ ou and Φ ol are homogeneous PPPs. Fig. 2 demonstratesthat the simulation results closely match our theoretical results,validating the approximation.Figure 3 illustrates the variation of the D2D link intensityin each band with λ ext . The subscripts ou and ol are used todenote outband and overlay, respectively. The superscripts s,th, al, and f are used to denote simulation results, theoreticalresults, iterative optimization and monolithic (fully overlay orunderlay) schemes, respectively. Increasing λ ext results in areduction in D2D links in both outband and overlay networks.The rate of reduction is faster in the outband network. As λ ext increases, the threshold distance d ⋆ ou is reduced to decreasethe user intensity in the outband, such that they do not violatethe QoS requirements. Moreover, this allocates more users tothe overlay mode, resulting in higher interference. Therefore, d ⋆ ol is also reduced with at a slower rate compared to d ⋆ ou , tomaintain QoS. Furthermore, one can observe that the iterativeoptimization provides more D2D communication opportunitiescompared to our approximate solution. However, it requireshigher computational time. Therefore, based on the resource ig. 5. Power consumption of the D2D network against the DP intensity and delay constraints of the system, one can choose betweenthe approximate technique and iterative optimization. Thetheoretical D2D intensities closely follow the results obtainedthrough simulation. Also, it can be seen that D2D opportunitieshave increased 4-5 times with the hybrid model compared topure overlay or outband D2D networks, which may result insignificant power savings at the infrastructure nodes.Fig. 4 presents the user intensities in each band with varyingDP intensities. At first, increasing λ dp results in a linearincrease in user intensities in each band. As λ dp is furtherincreased, the user intensities begin to saturate. The saturationoccurs mainly because additional DC-DP pairs cannot beadmitted since they will not satisfy the QoS requirementsusing the D2D mode due to increased interference in eachband. Initially, overlay intensity is higher than the outbandintensity since the sparse network in low λ dp regime resultsin a low probability of finding DP-DC pairs with small linklengths to be allocated to outband. Therefore, more D2D linksare eligible for the overlay mode. However, as the networkbecomes more dense, the probability of finding DC-DP pairswith shorter link lengths increases. Therefore, the number oflinks satisfying the outband threshold will be higher than thenumber of links satisfying the overlay threshold.Fig. 5 compares the average power consumption of a D2Dlink in the hybrid network, fully overlay network and the fullyoutband network, under three different λ ext values, namely λ e, = 10 − , λ e, = 1 . × − , and λ e, = 2 × − . Asexpected, increasing λ ext increases the power consumption ofthe outband networks since higher transmit power is requiredto maintain the QoS. Also, the power consumption of the fullyoverlay network is unaffected by λ ext . One can see that thehybrid network saves nearly of the power compared tothe monolithic networks, indicating the energy efficiency ofour proposed model. Again, it can be seen that the iterativeoptimization results in lower power consumption at the de-vices. However, it may result in higher power consumption atthe infrastructure nodes due to the increased complexity.VI. C ONCLUSION
A spectrum selection and transmit power minimizationscheme was proposed for a D2D network cross-laid witha CRAN, where D2D communications are allowed as both overlay to the CRAN and in the ISM band. Analytical approxi-mations were derived for the spectrum selection thresholds andthe required minimum transmit power to achieve a guaranteedQoS level. Theoretical approximations were derived for theD2D user intensity in each band, which can be used to evaluateimportant performance metrics such as coverage probabilityand transmission capacity. The proposed scheme achievesnearly 50% power savings compared to a monolithic D2Dnetwork, where D2D communications occur only as overlayor in the ISM band. R
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