Self-Organized Scheduling Request for Uplink 5G Networks: A D2D Clustering Approach
Mohammad Gharbieh, Ahmed Bader, Hesham ElSawy, Hong-Chuan Yang, Mohamed-Slim Alouini, Abdulkareem Adinoyi
aa r X i v : . [ c s . I T ] O c t Self-Organized Scheduling Request for Uplink 5GNetworks: A D2D Clustering Approach
Mohammad Gharbieh, Ahmed Bader, Hesham ElSawy, Hong-Chuan Yang,Mohamed-Slim Alouini, and Abdulkareem Adinoyi
Abstract —In one of the several manifestations, the futurecellular networks are required to accommodate a massive numberof devices; several orders of magnitude compared to today’snetworks. At the same time, the future cellular networks will haveto fulfill stringent latency constraints. To that end, one problemthat is posed as a potential showstopper is extreme congestionfor requesting uplink scheduling over the physical randomaccess channel (PRACH). Indeed, such congestion drags alongscheduling delay problems. In this paper, the use of self-organizeddevice-to-device (D2D) clustering is advocated for mitigatingPRACH congestion. To this end, the paper proposes two D2Dclustering schemes, namely; Random-Based Clustering (RBC)and Channel-Gain-Based Clustering (CGBC). Accordingly, thispaper sheds light on random access within the proposed D2Dclustering schemes and presents a case study based on a stochasticgeometry framework. For the sake of objective evaluation, theD2D clustering is benchmarked by the conventional schedulingrequest procedure. Accordingly, the paper offers insights intouseful scenarios that minimize the scheduling delay for eachclustering scheme. Finally, the paper discusses the implemen-tation algorithm and some potential implementation issues andremedies.
Index Terms —LTE cellular networks, self-organized networks,D2D clustering, random access, stochastic geometry.
I. I
NTRODUCTION T HE next generation of cellular networks is expected toinvolve a massive number of connected devices vary-ing from sensors, smart objects, machines, all the way tosmartphones and vehicles [1]. For future networks to en-able a broad spectrum of new usage and applications, thecellular infrastructure must support a mixture of human-typeand machine-type communications with ever-increasing trafficlevels. In fact, 5G networks are expected to handle a 1000-fold increase in capacity [2], an appreciable portion of whichis uplink traffic [3]. Within this context, a primary challenge
M. Gharbieh and H.-C. Yang are with the Department of Electrical andComputer Engineering, University of Victoria, Victoria, BC V8P 5C2, Canada;e-mail: { mohammadgharbieh, hy } @uvic.ca.A. Bader is with Insyab Wireless Limited, 1961 Dubai- UAE; e-mail:[email protected]. ElSawy was with the Computer, Electrical, and Mathematical Sciencesand Engineering (CEMSE) Division, King Abdullah University of Science andTechnology (KAUST), Thuwal 23955, Saudi Arabia. He is now with the Elec-trical Engineering Department, King Fahd University of Petroleum and Min-erals, Dhahran 31261, Saudi Arabia; e-mail: [email protected]. Alouini is with the Computer, Electrical, and Mathematical Sci-ences and Engineering (CEMSE) Division, King Abdullah University ofScience and Technology (KAUST), Thuwal 23955, Saudi Arabia; e-mail:[email protected]. Adinoyi is with Saudi Telecom Company (STC); e-mail: [email protected] work of the KAUST team was supported in part by STC under grantRGC/3/2374-01-01. Fig. 1: At low to moderate device counts, minimal to negligiblelevels of collisions occur on the RA radio resources. However,mobile networks are already past this phase, i.e. the numberof devices in a small cell is rapidly growing beyond 1000 [3].pertains to the uplink scheduling request that is performedvia random access (RA) procedure over the physical RAchannel (PRACH). Particularly, devices with uplink trafficneed to go through RA procedures over the PRACH to requestresource allocation from the base station (BS) [4]. As thenumber of devices grows, contention over scarce PRACHresources escalates substantially thus leading to a large numberof devices dropping off the RA process, and high volume ofunserved traffic demand as discussed in [3] and illustratedthrough the experimental data shown in Fig. 1. The figureshows that while there are enough resources to schedule moreuplink traffic, such resources are wasted because the devicesfail to pass their scheduling request to the BS through thePRACH. Hence, it is clear that RA scheduling requests leadto congestion that needs to be alleviated to fulfill the foreseen5G performance.The most straightforward proposition to alleviate RA con-gestion is to simply allocate additional radio resources forPRACH. This option obviously reduces the available re-sources for scheduling uplink data traffic. Moreover, allocatingspectrally adjacent blocks for RA increases computationalcomplexity at the BS side due to parallelized processing [4].As such, it is not an appealing solution for the vendors.Another obvious proposition is to densify BS deployments asa mean to reduce congestion. Nonetheless, densification makessense to mobile network operators only up to a certain limit.Beyond that, it ceases to offer either economic benefit [5] orperformance improvement [6]. From the economic perspective,1ig. 2: Network realization for the system model for Devices-to-BS ratio α = 16 and cluster head selection probability δ =0 . . The BSs are denoted by black squares, CHs are denotedby the red circles, and the CMs are denoted by blue circles.The Voronoi cell of the BSs are denoted by the solid blacklines while the Voronoi cell of the CHs are denoted by thedotted red lines. The black dashed lines denote the associationsof the CHs to the BSs while the red dashed line denote theassociations of the CMs to the CHs. In this model, uplink anddownlink interfaces can be decoupled, i.e., downlink trafficand signaling can be transmitted directly by the BS to theCMs.right-of-way and site acquisition costs may become majorchallenges. From the performance perspective, there is acritical density after which the coverage probability and ratedegrade with BS density due to the overwhelming inter-cellinterference. Another drawback for network densification isthe increased handover rate for mobile users which consumesphysical resources and incurs a delay [7], [8].To this end, a distributed self-organized RA procedureis better positioned to accommodate this tremendous uplinkdemand in the future cellular networks. Indeed, standards forLong Term Evolution (LTE) have identified self-organizationas a vital requirement for future networks [9]. The self-organized random access can response to actual network varia-tions in near-real-time. Moreover, the self-organization randomaccess is less costly since it entails the use of significantly lessresource allocation complexity and administrative overhead. A. Prior Work
Device-to-device (D2D) relaying has been classically ex-ploited within LTE networks, i.e., in-band D2D, mainly as acoverage improvement solution [10]. A corollary to coverageenhancements is indeed a boost in throughput or the spectrumefficiency through traffic offloading from cellular networks.In the stochastic geometry literature, different network ar- chitectures and systems were proposed to study and assessthe spectrum sharing of in-band D2D communication [11]–[16]. The authors in [17] analyze out-band D2D for uniformand k-closest content availability in terms of the coverageprobability and the area spectral efficiency. Moreover, [18]studies the economic aspect of downlink traffic offloading viaD2D for in-band and out-band operating modes. Furthermore,[19] develops an approach to model single- and multi-clusterwireless networks and study the coverage probability forclosest-selection and uniform-selection strategies. It is worthto highlight that the model in [19] is suitable for downlinkcellular networks or ad hoc networks. However, the idea ofaggregating the uplink generated traffic within a cluster usingout-band D2D communication in the presence of the cellularnetworks was investigated in [20]–[22]. The authors of [20]provide analytical expressions for the throughput and powerconsumption for a point-to-point scenario. In [21] the authorsstudied the latency-power trade-off of aggregating traffic onD2D links, where they showed that the transmit power canbe reduced but at the expense of higher latency. Furthermore,[22] defines a protocol stack for the D2D communication incellular networks, and uses system-level simulation to showthe throughput improvement. However, none of the proposedprotocols state the criterion and/or the effective scenarios toactivate the D2D communication [10]. Most notably, D2Drelaying literature rarely touches upon its advents relayingscheduling request to relieve RA congestion over the PRACH.While it may be quite intuitive, but a proper quantification ofsuch an advantage is still missing out from literature.
B. Contributions
This paper presents an out-band D2D relaying setup (e.g.,WiFi Direct [22]) that can be exploited to boost the RAperformance and LTE network capacity as well in densenetworks. Within the context of this paper, the D2D paradigmrefers to the situation where a number of devices clusterthemselves together through an out-band link and assign acluster head (CH) as depicted in Fig. 2. Uplink schedulingrequests from cluster members (CM)s are forwarded to theassigned CH over unlicensed spectrum. The CH aggregatesthe requests from the CMs into larger ensembles and transmitsone RA request per ensemble over the LTE interface. TheBS process the RA request from the CHs and sends theuplink resources scheduling to the CMs directly through thedownlink signaling. Without any doubt, such clustering relaxesthe congestion over the LTE RA resources since the numberof LTE RA requests is reduced, and hence, reduces the latencyfor resource allocation over the LTE interface. The problemis not trivial though. One has to consider whether the averageaccess delay perceived by a device is actually enhanced byvirtue of D2D clustering or not. This has to be evaluated inlight of intra- and inter-cell interference. Indeed, this is thecrux of the study carried out in this paper. The contributionof this work can be summarized as follows:1) The paper proposes a self-organized D2D clustering inwhich each CH acts as a virtual Access Point (AP) overan LTE connection to boost the RA performance. This work is presented in part in [23].
2) The paper considers two CH assignment mechanisms: • Random-Based Clustering (RBC) in which eachdevice is assigned randomly with probability ( δ ) tobe a CH. • Channel-Gain-Based Clustering (CGBC) in whichonly the devices with channel gain greater than athreshold ( τ ) are assigned to be CHs.3) We present analytical expressions, based on stochasticgeometry which takes into account the spatial intraand inter-cell/cluster interference sources to assess thetransmissions success probabilities. Consequently, wequantify the average uplink scheduling delay for theD2D clustering.4) The proposed self-organized D2D clustering scheme isbenchmarked by the conventional RA procedure whereall the devices have to send RA request to the BS overthe LTE interface.5) We quantify the critical device density beyond whichthe self-organized D2D clustering, for relaying uplinkscheduling requests, offers performance gains (i.e., re-duction in channel access delay).6) For the range of device densities where D2D is feasi-ble we answer the following crucial question: How toactivate the D2D relaying and how should the CH beassigned? i.e., what are the suitable design parametersfor these setups?The results show that for the RBC and low device intensityis actually better to follow the conventional RA procedure.However, the self-organized D2D relaying scheme starts to payoff as the intensity grows. On the other hand, when the channelgains are considered in the CGBC scheme, D2D clusteringprovides higher delay reduction. Moreover, there is an optimalCH selection probability ( δ ) or a channel gain threshold ( τ )that minimizes the average delay for every device intensity. C. Notation & Organization
Throughout the paper, we use the math italic font for scalars,e.g., x . We use the calligraphic font, e.g., X to represent arandom variable (RV) while the math typewriter font, e.g., x is used to represent its instantiation. Moreover, E X {·} , F X ( · ) , ¯ F X ( · ) , and L X ( · ) denote, respectively, the expectation, thecumulative distribution function (CDF), the complementarycumulative distribution function (CCDF), and the LaplaceTransform (LT) of the PDF of the random variable X . We use P {·} to denote the probability. {·} is the indicator functionwhich has value of one if the statement {·} is true and zerootherwise. Γ( · ) indicates the Gamma function and F ( . ) isthe Gaussian hypergeometric function. The imaginary unit isdenoted by j = √− and imaginary component of a complexnumber is denoted as Im { . } . Lastly, y ∗ denotes the optimalvalue of y .The rest of the paper is organized as follows. Section IIpoints out a high-level protocol description for the D2D clus-tering scheme. Section III models the physical layer attributesof the communication system and highlights the performancemetrics. Section IV characterizes the D2D clustering protocols,while Section V provides the numerical results and insights.Section VI sheds light on some implementation obstacles and pertinent remedies and recommendations. Finally, Section VIIsummarizes and concludes the paper.II. O VERIEW OF THE P ROTOCOL
The goal of this section is not to define an exhaustiveprotocol stack for self-organized D2D clustering within LTEnetworks as in [22]. Rather, the aim is to point out a high-level description that helps to digest the presented scheme. Theself-organized D2D clustering process can be summarized asfollows:1)
D2D Clustering Initiation Order : the BS broadcastingthis order along with the chosen value of the CHselection probability ( δ ) over the downlink signaling.2) CH Selection : for a given target fraction (i.e., δ ) ofdevices that are required to act as CHs, the clusteringfor each scheme is performed as follows: • for the RBC scheme, each device has a probability δ to be a CH. The selection can be done in adistributed manner, i.e., without the control of theBS. This can be done via a generating a randomnumber v ∈ [0 , , and hence, the device becomes aCH if v ≤ δ . • for the CGBC scheme, each device has to estimateits channel over the LTE interface and the devicebecomes a CH if the channel gain is greater than τ , where τ is identified such that the fraction δ ofdevices are selected as CHs. Let h be the channelgain, then τ is identified through the inverse of theCCDF of h as τ = ¯ F − h ( δ ) = − ln( δ ) . Therefore,the selection can be done in a distributed manner aswell.3) CH Announcement : Once the CHs are identified eachCH selects a frequency channel in the D2D spectrum andbroadcasts its D2D-Identification (D2D-ID) to declareitself as a CH.4)
Cluster Formation : each CM scans the D2D channelssearching for CHs broadcast messages. The CMs asso-ciate themselves to their nearest CH, by measuring thereceived signal strength (RSS) and selecting CH with thehighest RSS. Through the association phase, the CMssend their D2D-ID along with their LTE-ID, e.g., SAE-Temporary Mobile Subscriber Identity (S-TMSI).5)
Cluster Registration at BS : each CH sends the D2D-LTE-ID association table to its serving BS via uplinkLTE channel. Such a table is vital for the uplink re-sources scheduling so that the BS transmits the downlinksignaling directly to the CMs.Upon the D2D cluster formation, the CMs relay their uplinkscheduling requests via the CH. The CH in turn, stamps therequests by the D2D-ID of the CMs, then aggregates all theRA requests from the CMs with its own request into a largerensemble, and transmits one scheduling request via RA on theshared LTE PRACH for each ensemble.III. S
YSTEM M ODELING & A
SSUMPTIONS
After describing the clustering process from a protocol pointof view, this section portrays the modeling attributes of theproposed self-organized clustering schemes from a physicallayer point of view.3 . Spatial & Physical Layer Parameters
A two-tier cellular network is considered, namely the out-band D2D and LTE networks. Due to the disjoint spectrumallocation, the interference interactions on each network aredecoupled. Since the cellular networks topologies from onelocation to another tend to be random, stochastic geometry isutilized to model the spatial distribution of the BSs as a pointprocesses [24]–[26]. In this regards, the Poisson point process(PPP) is widely accepted and utilized due to its simplicityand practical relevance [25]–[28]. Therefore, we assume thatthe BSs and the devices are spatially distributed according totwo independent homogeneous PPPs with densities λ and µ ,respectively. A power-law path-loss model is considered wherethe signal power decays at a rate of r − η with the propagationdistance r , where η > is the path-loss exponent. In additionto the path-loss attenuation, Rayleigh block fading is assumedwithin a multi-path environment, in which all the channelpower gains ( h ) are assumed to be independent of each otherand are identically and exponentially distributed with unitypower gain. B. Random Access over the LTE Network
Each CH should go through the RA process over thePRACH to request uplink channel access from the BS [4].The RA process is uncoordinated and all devices can mutu-ally interfere with one another, which may lead to intra-cellinterference in addition to the inter-cell interference. Only theCHs are eligible to request uplink resources over the LTEinterface (i.e., PRACH) from the nearest BS. To request anuplink channel access, each CH randomly and independentlytransmits its RA request on one of the available prime-length orthogonal Zadoff-Chu (ZC) codes defined by the LTEPRACH preamble [4].During the RA, each CH uses full path-loss inversion powercontrol with target power level ρ L [4]. Therefore, the RAtransmit power is expressed by P RA = ρ L R η L , where R L isthe distance between the CH and its geographically closestBS. That is, the CH controls its transmit power such that theaverage signal power received at its serving BS is equal to ρ L . The target power level ρ L is assumed to be conveyed ondownlink signaling channels by the BS. It is assumed thatthe BSs are dense enough such that each of the CHs caninvert its path-loss towards the closest BS almost surely, andhence the maximum transmit power of the IoT devices isnot a binding constraint for packet transmission. Extensionto fractional power control and/or adding a maximum powerconstraint can be done by following the methodologies in [29]and [30]. An RA transmission is assumed to be decodable ifthe signal to interference and noise ratio (SINR), denoted by Υ RA , is greater than a certain threshold θ RA . C. D2D Clustering Over an Unlicensed Spectrum
The clustering process is initiated by the BS where theclustering criterion, i.e., RBC or CGBC, is dictated by the Note that logical clustering does not change the physical locations ofthe devices. Hence, the PPP distribution of the devices is preserved. Note that in the case of physically clustered devices, fading is correlated.
BS. Each CM associates with its nearest CH through a single-hop link and relays the uplink scheduling requests via thatlink as shown in Fig. 2. CMs are assumed to employ fullpath-loss power control with target power level ρ C . Therefore,the transmit power is given by P D = ρ C R η C , where R C is thedistance between the CM and its geographically closest CH.The target power level ρ c is assumed to be conveyed alongwith the D2D-ID of the CH in step 3 in Section II.Each CH randomly and independently selects one of the k available channels dedicated for D2D communications withinthe unlicensed spectrum. Moreover, transmission from CMsover the D2D interface is assumed to be managed by the CHvia a time division multiple access (TDMA) schedule. Hence,intra-cluster interference is prohibited and only inter-clusterinterference exists. Obviously, this comes at the expense ofaccess delay that grows with the size of the cluster. For acorrect transmission at the D2D link, an SINR capture model isadopted such that a transmission can be decoded if the SINR,denoted by Υ C , is greater than a certain threshold θ C .IV. P ERFORMANCE A NALYSIS
Latency, or channel access delay to be more precise, is veryimportant for several 5G application (e.g., tactile internet [31],[32]). It also has been a key aspect in the design objectives ofcellular systems. Therefore, the channel access (i.e., resourceallocation) delay is the primary metric used in this study toevaluate the gain of the self-organized D2D clustering schemein reducing congestion over RA resources. Before delving intothe analysis, we state the following important approximationsthat will be utilized in this paper.
Approximation 1.
The spatial correlations between proximatedevices, in terms of transmission power, can be ignored.
Remark 1.
It is well known that the sizes of adjacent Voronoicells are correlated. Such correlation affects the numberof devices, as well as, the service distance realizations inadjacent Voronoi cells. Consequently, the transmission powersat adjacent cells are correlated. Accounting for such spatialcorrelation would impede the model tractability. Hence, wefollow the common approach in the literature and ignoresuch spatial correlations when characterizing the aggregateinterference [29], [30], [33]–[38]. However, all spatial cor-relations are intrinsically accounted for in the Monte Carlosimulations that are used to validate our model in Section V.
Approximation 2.
For the D2D transmission, the point pro-cesses of inter-cluster interfering CMs seen at the test CH ismodeled by a non-homogenous PPP.
Remark 2.
Despite that a PPP is used to model the completeset of CMs, the subset of scheduled CMs for the TDMAtransmission is not a PPP. The constraint of scheduling oneCM per Voronoi cell of the cluster leads to a Voronoi-perturbed point process for the set of mutually interferingCMs. Approximation 2 is commonly used in the literature tomaintain tractability [29], [30], [34]–[38].
Approximation 3.
The transmission success probabilities ofall devices in the network are assumed to have a negligibletemporal correlation. otation Description µ ; λ ; α device density; BS density; devices-to-BS ratio δ ; τ CH selection probability; channel gain threshold forCGBC θ RA Detection threshold for successful RA θ C Detection threshold for successful D2D transmission ρ L ; ρ c Power control parameter for RA; Power control parame-ter for D2D P RA ; P C RA success probability; D2D transmission success prob-ability n Z number of ZC codes dectitated for random access k number of frequencies available for D2D transmission η ; σ path-loss exponent; noise power TABLE I: Summary of Notation
Remark 3.
The full path loss inversion makes the receivedsignal power at the serving BSs/CHs independent from theservice distance (i.e., the distance between the device andthe serving BS/CH). Hence, the different realizations of theservice distance across the devices do not affect the SINR.Furthermore, the random channel selection randomizes theset of interfering devices over different time slots, whichdecorrelate the interference across time. Hence, all devices inthe network tend to have a negligible temporal correlation forthe transmission success probabilities as shown in [33]–[35].
It is worth mentioning that Approximations 1-3 are manda-tory for tractability, regularly used in the literature, and are val-idated in Section V via independent Monte-Carlo simulations.Based on these approximations, the D2D cluster size, the RAsuccess probability, D2D success probability, and the channelaccess delay are presented in, respectively, Section IV-A,Section IV-B, Section IV-C, and Section IV-D. For a quickreference, the notation used in this paper is summarized inTable I.
A. D2D Cluster Size
Since the adopted clustering mechanisms are independentamong all the devices, and by exploiting the independentthinning property of the PPP [39], the CHs constitute a PPPwith intensity δµ [39]. Similarly, the CMs constitute a PPPwith intensity (1 − δ ) µ . Moreover, due to the nearest CHassociation, the footprint of each CH can be expressed by aVoronoi cell with size and shape depending on the locationsof its neighboring CHs as depicted in Fig. 2. Therefore, thenumber of CMs associated to each CH is random. Let N denote the number of CMs served by a generic CH, following[40], the probability mass function of N is given by: P {N = n } ≈ Γ( n + c )Γ( n + 1)Γ( c ) ((1 − δ ) µ ) n ( δ µc ) c ((1 − δ ) µ + δ µc ) n + c , (1)where c = 3 . is a constant related to approximate the PDFof the PPP Voronoi cell area in R . Let ˜ δ = (1 − δ ) /δ , then(1) can be rewritten as: P {N = n } ≈ Γ( n + c )Γ( n + 1)Γ( c ) ˜ δ ˜ δ + c ! n (cid:18) c ˜ δ + c (cid:19) c . (2)It is worth noting that the D2D cluster size depends only on theCH selection probability ( δ ) and is independent of the intensity of the devices µ . As such, δ is a key performance factor thatthe protocol designers can use to optimize the delay. From (2),it can be shown that average cluster size E [ N ] = ˜ δ . B. RA Success Probability
Let P RA = P { Υ RA > θ RA } denote the probability that theCH’s RA attempt over the LTE interference is successful. Assuch, the SINR for the RA ( Υ RA ) can be computed as follows: Υ RA = ρ L h ◦ σ + P m ∈ ˜Φ P RA m h m R m − η , (3)where h ◦ represents the LTE channel gain between the testCH and its associated BS. σ denotes the noise power and η denotes the path-loss exponent. The set ˜Φ contains all theinterfering CHs that are simultaneously performing RA overthe same ZC code, which may contain intra-cell and inter-cell interferes due to the uncoordinated nature of the RA. P RA m , h m , and R m represent, respectively, the transmit power,the channel gain, and the distance between the interfering CHsand the associated BS of the test CH. Due to the uncoor-dinated nature of the RA, there are two possible sources ofinterferences, namely the intra-cell interference and the inter-cell interference. Using stochastic geometry, we characterizethe intra-cell and inter-cell interference on a test device viathe LT of their probability density functions (PDFs). Then, theobtained LTs are used to derive the RA success probability,which is characterized in terms of CH selection probability ( δ )and the device-to-BS ratio ( α ), i.e., α = µ/λ .From the independent thinning property of the PPP [39],the CHs interfering on the same ZC code constitute a PPPwith intensity δ µn Z , where n Z is the number of available ZCcodes. Consequently, the average number of CHs that mayuse the same ZC code per BS is given by ˜ α = δ µλ n Z . Bythe PPP assumption, the number and locations of the pointsin disjoint areas are independent. Consequently, the intra-celland inter-cell interference are independent. Exploiting this fact,the success probability for each of the clustering schemes isgiven in the sequel.
1) RBC Scheme:
The RA success probability for the RBCcan be expressed as P RA = P (cid:26) ρ L h ◦ σ + I In + I Out > θ RA (cid:27) ( a ) = exp (cid:26) − σ θ RA ρ L (cid:27) L I In (cid:18) θ RA ρ L (cid:19) L I Out (cid:18) θ RA ρ L (cid:19) , (4)where I In is the intra-cell interference and I Out is the inter-cellinterference. Note that ( a ) in (4) follows from the exponentialdistribution of h ◦ [41]. The RA access success probability in(4) is characterized with the following theorem. Theorem 1.
The RA access success probability in a PPP net-work and Random-Based Clustering where each CH employsfull path-loss inversion power control is given by: P RA ≈ exp n − σ θ RA ρ L − δ α θ RA n Z ( η −
2) 2 F (cid:16) , − η , − η , − θ RA (cid:17)o(cid:16) δ α θ RA n Z (1+ θ RA ) c (cid:17) c , (5) here c = 3 . is a constant related to the approximate PDFof the PPP Voronoi cell area in R .Proof. Similar to [35, Lemma 1], where 5 is not exact dueto ignoring the spatial correlations among the transmissionpowers of the CHs as mentioned earlier in Approximation 1.For the special case of η = 4 , which is a typical path lossexponent for urban outdoor environment, (5) reduces to: P RA ≈ exp n − σ θ RA ρ L − δαn Z √ θ RA arctan (cid:0) √ θ RA (cid:1)o(cid:16) δαθ RA n Z (1+ θ RA ) c (cid:17) c . (6)The expression in (6) gives the RA success probability in termsof the elementary arctan function instead of the computation-ally complex Gaussian hypergeometric function.
2) CGBC Scheme:
The RA success probability for theCGBC scheme can be expressed as: P RA = P (cid:26) ρ L h ◦ σ + I In | h >τ + I Out | h >τ > θ RA | h > τ (cid:27) ( b ) = exp n − σ θ RA ρ L + τ o L I In | h >τ (cid:16) θ RA ρ L (cid:17) × L I Out | h >τ (cid:16) θ RA ρ L (cid:17) , θ RA ( σ + I ) ρ L > τ , otherwise, (7) where I In | h >τ is the intra-cell interference given that theinterfering CHs have channel gain greater than τ , I Out | h >τ isthe inter-cell interference given that the interfering CHs havechannel gain greater than τ , and I is the total interference.Note that ( b ) in (7) follows from the exponential distributionof h ◦ [41]. The RA access success probability in (7) ischaracterized by the following theorem. Theorem 2.
The RA access success probability in a PPPnetwork and Channel-Gain-Based Clustering where each CH employs full path-loss inversion power control is given by P RA ≈ exp − σ θ RA ρ L + τ − δ α θ /η RA ∞ R θ − η RA (cid:16) − exp {− τy − η } y − η +1 (cid:17) y dy (cid:16) δ α ((1+ θ RA ) − exp {− τθ RA } )(1+ θ RA ) c (cid:17) c × ¯ F I (cid:18) τ ρ L θ RA − σ (cid:19) + F I (cid:18) τ ρ L θ RA − σ (cid:19) , (8) where c = 3 . is a constant related to the approximate PDFof the PPP Voronoi cell area in R and F I ( x ) is the CDF ofthe aggregated interference which has the form of (9) in thebottom of this page. Proof. See Appendix A, where 2 is not exact due to ignoringthe spatial correlations among the transmission powers of theCHs as mentioned earlier in Approximation 1.
C. D2D Transmission Success Probability
On the D2D links, each CH aggregates the uplink schedul-ing requests originated from its associated CMs TDMAscheduling. Hence, inter-cluster interference and noise are theonly two channel impairment for D2D transmission. There-fore, the transmission SINR for the D2D relaying can becomputed as follows: Υ C = ρ C h ∗ σ + P i ∈ Φ P D i h i R i − η , (10)where h ∗ represents the D2D channel gain between the testCM and its associated CH. The set Φ contains all the interfer-ing CMs that transmit simultaneously over the same frequency,which are one CM per cluster due to the TDMA scheduling. P D i , h i , and R i represent the transmit power, the channelgain, and the distance between the interfering CMs and theassociated CH of the test CM. To characterize Υ C , we followa similar methodology described for Υ RA , while accountingfor the fact that each CH has a single active CM to serveat a given time instant. Hence, the intensity of interferingCMs on each channel is equal to the intensity of the CHsthat selected the same frequency, i.e., intensity of interferingCMs is δ µk , where k is the number of frequencies available forD2D transmission. Consequently, the D2D success probability P C = P { Υ C > θ C } is characterized by the following theorem. Theorem 3.
The probability of successful uplink schedulingrequest over a PPP D2D link where each CM employs fullpath-loss inversion power control, can be expressed as P C ≈ exp (cid:26) − σ θ C ρ C − θ C k ( η − F (cid:18) , − η , − η , − θ C (cid:19)(cid:27) . (11) Proof.
Similar to [36, Theorem 1], where (11) is not exactdue to ignoring the spatial correlations among the transmissionpowers of the CMs as mentioned earlier in Approximation 1and due to approximating the inter-cluster interfering CMswith a PPP as mentioned in Approximation 2.For the special case of η = 4 , (11) reduces to: P C ≈ exp (cid:26) − σ θ C ρ C − √ θ C k arctan (cid:16)p θ C (cid:17)(cid:27) . (12)It is worthwhile to mention that the approximations in (5),(8), and (11) are mandatory for tractability and are commonin stochastic geometry analysis for uplink systems [29], [30],[37]. F I ( x ) = 12 − π ∞ Z t Im exp {− j t x } exp − δ α ρ /η L ∞ Z ρ − η L (cid:18) − exp { j τ t z − η }− j t z − η + 1 (cid:19) z dz (cid:18) δ α ((1 − j t ρ L ) − exp { jτ t ρ L } )(1 − j t ρ L ) c (cid:19) − c dt. (9) . Channel Access Delay ( D ) The channel access delay ( D ) is defined as the averagenumber of time slots required by a device before the uplinktransmission is successfully scheduled. In the depicted com-munication system, where the CMs sends their requests to theCH via a TDMA schedule, D is given by D ≈ P RA + E [ N ] P C , (13)which is derived by modeling the trials for both of the RAand the D2D transmissions by geometric random variables. Inaddition, the mean number of CMs associated to a CH ( E [ N ] )is introduced here to take into account the TDMA scheduling.It is worth to highlight that (13) is not exact due to ignoringthe negligible temporal correlation of the transmission successprobabilities as mentioned in Approximation 3.V. N UMERICAL R ESULTS
This section first validates the developed model via indepen-dent Monte Carlo simulations. Then, selected numerical resultsare presented to assess and compare the performance of theRBC and CGBC schemes. In each simulation run, the BSs andthe devices are realized over a 100 km area via independentPPPs and the collected statistics are taken for devices locatedwithin 1 km from the origin to avoid the edge effects. First, weexamine the D2D cluster size in (2). Fig. 3 shows the PDF ofthe associated CMs for each CH for µ = 160 and UE/km for different values of CH selection probability δ = 0 . and . . Fig. 3 supports the remark given in Section IV-A aboutthe independence of the PDF of N from the devices intensity.This can be explained as follows: The cluster’s geographicalfootprint is represented by a Voronoi cell whose average areais ¯ d = δµ . The average geographical footprint ¯ d of the clustershrinks as more devices are elected as CHs. However, theintensity of CMs also increases such that the cluster size interms of number of CMs stays constant. Fig. 3 also showsthat as δ increases, the D2D cluster size becomes smaller, andhence, the PDF of N is pushed to have a smaller mean.Fig. 4 depicts the RA transmission success probabilities forRBC and CGBC schemes along with the D2D transmissionsuccess probability. The simulation parameters are as follows; µ = 160 and device/km , λ = 10 BS/km , and equiv-alently, α = 16 and device/BS. CH selection probability δ = 0 . , n z = 64 code per BS, ρ C = − dBm, ρ RA = − dBm, noise power σ = − dBm, number of frequenciesavailable for D2D transmission k = 3 , and path-loss exponent η = 4 . It is important to note the close match between theanalysis and simulation results which validates the developedmathematical framework and Approximations 1-2.At this point of the discussion, we look into the channelaccess delay as a key performance metric. The conventionalRA procedure is used as a benchmark to evaluate the perfor-mance of the proposed D2D clustering procedure. It is worthmentioning that the conventional RA procedure is a specialcase of the RBC D2D clustering by setting δ = 1 , also it isa special case of the CGBC D2D clustering by setting τ = 0 .The parameters used in this section are summarized in Table II. (a) µ = 160 , δ = . (b) µ = 640 , δ = . (c) µ = 160 , δ = . (d) µ = 640 , δ = . Fig. 3: The PDF of the number of CMs associated to a CHfor for µ = 160 and UE/km for different values of CHprobability δ = . and . .7
10 -9 -8 -7 -6 -5 -4 -3 -2 -1 000.10.20.30.40.50.60.70.80.91 (a) α = 16 device/BS. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 000.10.20.30.40.50.60.70.80.91 (b) α = 64 device/BS. Fig. 4: The RA and D2D transmission success probability as afunction of θ RA and θ C for CH selection probability δ = 0 . . Notation Description Value µ device densities and devices/km λ BS density BS/km n Z number of ZC codes dectitatedfor random access code per BS δ CH probability [ . , θ C Detection threshold forsuccessful D2D transmission − dB θ RA Detection threshold forsuccessful RA − dB ρ c Power control parameter forD2D − dBm ρ L Power control parameter forRA − dBm σ noise power − dBm k number of frequenciesavailable for D2D transmission η path-loss exponent TABLE II: Numerical Evaluation ParametersFig. 5 and Fig. 6 show respectively the RA success probabil-ity and the delay as a function of δ . As expected, Fig. 5 showsthat the RA success probability for both the D2D clusteringand the conventional cases decreases as α grows. And in turn, (a) α = 16 device/BS. (b) α = 64 device/BS. Fig. 5: The RA success probability as a function of CHselection probability δ .the delay increases as α increases. Also, Fig. 5 shows thatas the CH selection probability δ increases the RA successprobability for D2D clustering decreases. This is due to thefact that as δ increases, more CHs are eligible to performan RA procedure over the LTE interface. Therefore, both ofthe inter-cell and intra-cell interference increases leading tolower RA success probability ( P RA ). Furthermore, the resultsshow that CGBC D2D clustering offers the highest RA successprobability.For insightful conclusions, Fig. 5 and Fig. 6 should beconsidered jointly. While one case may be favorable from theRA success probability perspective, it may be invoking toomuch delay and an adverse impact on the average waitingtime for a successful RA. Fig. 6 gives an interesting insightby comparing performance at two device densities. For RBCD2D clustering, the RA performance will not gain any benefitat low device densities. Regardless how aggressive δ is, theconventional case always offers lower channel access delay.From a mere RA perspective, it is simply just not worth it touse D2D clustering. However, the RBC D2D clustering startsto pay off at high intensities as shown in Fig.6. On the otherhand, the CGBC offers an improvement over the conventionalRA even for low device intensities as shown Fig. 6.8 .1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 14681012141618 (a) α = 16 device/BS. (b) α = 64 device/BS. Fig. 6: The average delay needed for successful RA as afunction of CH selection probability δ .It is straightforward to notice the trade-off between thedelay and the CH selection probability δ or equivalently τ .Specifically, δ has a two-fold effect on the delay as can beinferred from Eq. (13). First, the larger the δ the more deviceare eligible to be CHs, and hence, the smaller cluster sizein terms of the number of the associated CMs. Therefore,smaller number of CMs results in a shorter delay in the TDMAscheduled transmission. As such, the right-hand term of Eq.(13) decreases because the numerator ( N ) decreases while thedenominator ( P C ) is not intact with the change of δ . Second,it is worthy recalling however that larger δ means a largernumber of CHs, which leads to degraded success probabilityof the RA over the LTE PRACH interface. In more preciseterms, the first term of Eq. (13) increases as δ increases. Tosum up, the first term of Eq. (13) is a negative monotonein δ while the second is positive monotone. Consequently, δ can be optimized to achieve a minimum delay. For example,employing RBC D2D clustering and at α = 64 device/BS witha value of δ ∗ = 0 . minimizes the delay with a rate of when compared to the conventional RA case. On the otherhand, for CGBC D2D clustering and at α = 16 device/BSwith a value of τ ∗ = − . dB and a corresponding valueof δ ∗ = 0 . would minimize the delay at a reduction rate of Fig. 7: Optimum delay and the corresponding values of δ ∗ asa function of the devices-to-BS ratio ( α ). Fig. 8: Protocol efficiency for optimum delay reduction rateas a function of the devices-to-BS ratio ( α ). when compared to the conventional RA case. While at α = 64 device/BS, τ ∗ = 0 . dB with a corresponding valueof δ ∗ = 0 . would minimize the delay at a reduction rate of .Fig. 7 depicts the optimum delay and the correspondingvalue of the CM selection probability ( δ ) for both RBC andCBGC clustering schemes. The result shows that the RBCstarts to offer a reduction in the RA access delay whendevices-to-BS ratio becomes larger than 50. However, theCBGC always offers an enhancement over the conventionalRA. Another insightful observation from Fig. 7 is that as α increases, δ decreases. This behavior is mainly due to thefact that the RA congestion over the LTE interface is morecritical when the devices intensity increases compared withthe delay that stems from the TDMA transmission within theD2D cluster.It should be mentioned, however, that the improved per-formance of the CGBC scheme comes at the cost of higherprotocol overhead. That can be justified by the lower optimalCH selection probability, which leads to higher cluster pop-ulation for the CGBC scheme, and in turn, larger signaling9n the cluster formation process. As such, there is a needto quantify the protocol efficiency which can be definedby the delay reduction rate over the protocol overhead. Weconsider the average cluster size E [ N ] as a measure for theprotocol overhead. Therefore the protocol efficiency ( ζ ) canbe calculated as follows: ζ = D ( δ = δ ∗ ) − D ( δ = 1) D ( δ = 1) E [ N ] × , (14)where D ( δ ) is the delay in (13) as a function of the CHselection probability ( δ ) .Fig. 8 shows the protocol efficiency for the optimal delay inFig. 7. The figure shows that even though the CGBC provides alower delay, the protocol efficiency is lower when the devicesintensity scales. Specifically, it is more rewarding in termsof protocol efficiency to follow the RBC scheme when thedevices intensity goes beyond devices/BS.VI. I MPLEMENTATION , I
SSUES , & REMEDIES
The foreseen gain that Fig. 7 depicts can be best achievedthrough an automated self-optimization algorithm. Such analgorithm can be implemented through a back-end script atthe network core whose goal is to estimate network parametersand calculate the optimum value of CHs selection probability( δ ) for RBC and CGBC schemes. The analytical results inSection IV show that the performance of the proposed D2Dclustering schemes depends on three estimated parameters,namely, the intensity of BSs, the devices intensity, and thepath-loss exponent. The intensity of BSs may be the easiestparameter to estimate as the number of BSs in a geographicarea is available to the operators, then the intensity of BSs canbe estimated accordingly. The devices intensity, on the otherhand, can be estimated through event-triggered reporting forthe association table. As such, the CH reports to the BS anychange occurred to its associated CMs, then the BS, in turn,reports this change to the core network. The core networkcan estimate the current device intensity and then broadcastthe optimum value of δ in a reclustering order. Moreover,for the CGBC scheme, the CHs are required to report to theBS if the estimated channel gain goes below the threshold τ . In this case, the BS can broadcast a reclustering order tomaintain the performance edge. Lastly, the path-loss exponentestimation can be done by a self-estimator that only requirescollecting multiple Received Signal Strength (RSS) as in [42]which can be executed easily due to its independence. Thepseudo code for the back-end self-optimization script is shownin Algorithm 1 , where the optimization problems in (16) and(17) can be solved via a one-dimensional line search with aninitial uncertainty range of I ◦ ∈ (0 , . One of the algorithmsthat can be used to solve (16) and (17) is the golden-sectionsearch. The number of golden-section search iterations ( n ) thatachieves an accuracy of ( ǫ ) for the can be estimated by [43] n ≥ log K I ◦ ǫ , (15)where K = (1 + √ / is the golden ratio constant. Forexample, the golden-section search achieves an accuracy of ǫ = 10 − with n = 29 iterations and only function eval-uations. The brute-force method, on the other hand, requires function evaluations to find a δ ∗ with the same accuracy. Algorithm 1 : Pseudo code for the back-end self-optimizationscript. Estimate λ, µ, η . Solve the optimization problem of D in (13) for RBCscheme as: minimize δ D RBC = 1 P RA + ˜ δP C . subject to < δ ≤ (16)where P RA can be evaluated by (5). Solve the optimization problem of D in (13) for CGBCscheme as: minimize δ D CGBC = 1 P RA + ˜ δP C . subject to < δ ≤ (17)where P RA can be evaluated by (8), and τ = − ln( δ ) . Compare D RBC and D CGBC and select the scheme thatresults in lower D . Return the optimum δ and the selected scheme.However, incentivizing and commercializing D2D cluster-ing have been dwelling in a slightly stagnant state for sometime due to some practical concerns. First, one of the majorimplementation challenges of the proposed scheme is thatthe CM may fall in a BS footprint different than the CH isassociated to. Since the uplink resources are better granted tothe devices by the closest BS, the core network is in the bestposition to process the uplink resource scheduling such thateach device is granted uplink resources from the nearest BS.Second, the use of D2D clustering network to reroute uplinkscheduling requests entails fairness issues regarding batterydepletion rates of the CHs. Furthermore, the proposed D2Dclustering entails low-layer modifications to the protocol stacksomething that needs to be taken into standardization meetings.VII. C ONCLUSIONS
This paper introduces a self-organized D2D clusteringscheme to relieve the congestion on the RA resources inmassively loaded networks. Two D2D clustering schemes arestudied, namely, RBC and CGBC. The results show that theRBC scheme offers no delay reduction at low device densitiesand hence it is preferable to follow the conventional accessmodel. As the device intensity grows, the RBC starts tooffer reduced delay and there is an optimal value of CHsselection probability ( δ ) that minimizes the delay. To maintainthe performance edge of the RBC, the BS has to revisitthe clustering relationships whenever the intensity changes.On the other hand, the CGBC offers significant performancegains when compared to both the conventional and RBCschemes even for low device intensities. However, the gainedge comes at the cost of higher overhead due to the largercluster size, and hence, larger signaling in the clusteringprocess. As such the two schemes offer a trade-off betweencomplexity and performance. To this end, a self-optimizationalgorithm to execute the D2D clustering is presented. We alsohighlight a few remedies and recommendations for practicalimplementation.10 PPENDIX
A. Proof of Theorem 2.
Note that the nearest BS association and the employedpower control enforce the following two conditions; (i) theintra-cell interference from an interfering device is equal to ρ L ,and (ii) the inter-cell interference from any interfering deviceis strictly less than ρ L . The aggregated inter-cell interferencereceived at the BS is obtained as: I out | h >τ = X m ∈ ˜Φ { P RA m R m − η <ρ L } P RA m h m R m − η . (18)Approximating the set of interfering devices by a PPP withindependent transmit powers, the Laplace Transform of (18)can be approximated as (19). L I out | h >τ ( s ) ≈ exp ( − π δ αλ E P RA (cid:20) P η RA (cid:21) × ∞ Z ( ρ L ) − η (cid:18) − exp {− τ s y − η } s y − η + 1 (cid:19) y dy ) . (19)The LT is obtained by using the probability generating function(PGFL) of the PPP [39] and following [36], where the LTis obtained by substituting the value of E P RA (cid:20) P η RA (cid:21) from[Lemma 1, [36]]. The Intra-cell interference conditioned onthe number of neighbors is given by: I in | h >τ, n = n X i =1 ρ L h i . (20)The Laplace Transform of (20) is obtained as: L I in | h >τ, n ( s ) = E [ e − s I in | h >τ, n ] = exp {− n τ sρ L } (1 + sρ L ) n . (21)The probability mass function of the number of neighbors N which is found in [40] as: P {N = n } ≈ Γ( n + c )Γ( n + 1)Γ( c ) (cid:16) δ µn Z (cid:17) n ( λc ) c (cid:16) δ µn Z + λc (cid:17) n + c . (22)Considering that there is only Inter-cell interference when thenumber of neighbors in the cell is 0, and both of inter-cell andintra-cell interference otherwise we can write equation (7) as(23). P RA = exp (cid:26) − σ θ RA ρ L + τ (cid:27) L I out | h >τ (cid:18) θ RA ρ L (cid:19) × " P {N = 0 } + ∞ X n =1 P {N = n } × L I in | h >τ, n (cid:18) θ RA ρ L (cid:19) . (23)To take into account the boundaries in (7), we use Gil-Pelaez theorem [44]. Therefore, the CDF of the aggregatedinterference F I ( x ) can be calculated by: F I ( x ) = 12 − π ∞ Z t Im { exp {− j t x } L I ( − j t ) } dt, (24) where L I is the Laplace Transform of the aggregated inter-ference which has the form of: L I ( s ) = L I out | h >τ ( s ) × " P {N = 0 } + ∞ X n =1 P {N = n } × L I in | h >τ, n ( s ) . (25) After Applying the total probability theorem (8) is obtained.R
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