device-to-device discovery for proximity-based service in

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 1, JANUARY 2015 55

Device-to-Device Discovery for Proximity-BasedService in LTE-Advanced System

Kae Won Choi, Member, IEEE, and Zhu Han, Fellow, IEEE

Abstract—In this paper, we propose a device-to-device (D2D)discovery scheme as a key enabler for a proximity-based ser-vice in the Long-Term Evolution Advanced (LTE-A) system.The proximity-based service includes a variety of services exploit-ing the location information of user equipment (UE), for example,the mobile social network and the mobile marketing. To realizethe proximity-based service in the LTE-A system, it is necessaryto design a D2D discovery scheme by which UE can discoveranother UE in its proximity. We design a D2D discovery schemebased on the random access procedure in the LTE-A system. Theproposed random-access-based D2D discovery scheme is advan-tageous in that 1) the proposed scheme can be readily appliedto the current LTE-A system without significant modification;2) the proposed scheme discovers pairs of UE in a centralizedmanner, which enables the access or core network to centrallycontrol the formation of D2D communication networks; and3) the proposed scheme adaptively allocates resource blocks for theD2D discovery to prevent underutilization of radio resources. Weanalyze the performance of the proposed D2D discovery scheme.A closed-form formula for the performance is derived by meansof the stochastic geometry-based approach. We show that theanalysis results accurately match the simulation results.

Index Terms—Proximity-based service, device-to-device com-munication, device-to-device discovery, random access, Long-Term Evolution.

I. INTRODUCTION

R ECENTLY, the device-to-device (D2D) communicationas an underlay over the cellular network (e.g., Long-Term

Evolution (LTE) [1], [2]) has received great attention becauseof its advantages such as i) the proximity gain, ii) the hopgain, iii) the spatial reuse gain, and iv) the introduction ofnew proximity-based services [3], [4]. To reap such gains, theresearch community should address the challenges posed byunderlaying the D2D communication over the cellular infras-tructure. A number of recent works on the D2D communicationhave focused on the issue of radio resource management [5], forexample, the mode selection [6], the joint power control andmode selection [7], the joint scheduling and resource allocation[8], and the distributed power control [9]. However, relatively

Manuscript received October 6, 2013; revised November 16, 2013; acceptedAugust 5, 2014. Date of publication November 11, 2014; date of current versionJanuary 30, 2015. This work was supported in part by the National ResearchFoundation of Korea under Grant 2014R1A5A1011478 funded by the KoreanGovernment (MSIP) and in part by NSF under Grants CNS-1443917, ECCS-1405121, CNS-1265268, and CNS-0953377.

K. W. Choi is with the Department of Computer Science and Engineering,Seoul National University of Science and Technology, Seoul 139-743, Korea(e-mail: [email protected]).

Z. Han is with the Department of Electrical and Computer Engineering,University of Houston, Houston, TX 77004 USA (e-mail: [email protected]).

Digital Object Identifier 10.1109/JSAC.2014.2369591

less attention has been given to D2D discovery, which is akey enabler for the new proximity-based services for the D2Dcommunication.

The proximity-based service includes a variety of servicesexploiting the location information of user equipments (UEs),for example, mobile social network [10], mobile marketing,proximal multi-player gaming, and media swap [11]. As aneffort to integrate these proximity-based services in the LTE-Advanced (LTE-A) system, the standardization body of LTE(i.e., third-generation partnership project (3GPP)) published adocument [12] which defines the new proximity-based servicesand their requirements. According to [12], to realize the mobilesocial network, two or more UEs should be able to detect eachother if they come to each other’s proximity. For the mobilemarketing application in [12], a UE in a store should be able todiscover a customer as the customer approaches the store andto send an advertisement.

To realize the above-mentioned proximity-based servicesin the LTE-A system, it is essential to design a D2D dis-covery scheme optimized for the LTE-A system. For theD2D discovery, we can use wireless localization methods [13]such as angle-of-arrival (AOA), time-of-arrival (TOA), time-difference-of-arrival (TDOA), and global positioning system(GPS) to track the location of each UE. However, the AOA,TOA, and TDOA cannot guarantee the accuracy required forthe proximity-based services. In the GPS-based localization,which is currently used by mobile applications such as GoogleLatitude and Foursquare, UEs have to frequently report thecurrent location to the base station (BS) to maintain their up-to-date location. To do this, the UE should remain connectedto the BS or should alternate between the idle and connectedmode very frequently, which leads to inefficient use of radioresources and severe battery consumption. Moreover, the GPS-based D2D discovery scheme can neither be used by the UEswithout the GPS device nor by the UEs in the location wherethe GPS signal does not reach (e.g., indoor environment).

To overcome these difficulties of the localization-based D2Ddiscovery, we can use a beacon-based D2D discovery schemein which each device sends a beacon to nearby devices. Forthe D2D discovery in a wireless local area network (WLAN), adevice can periodically send a beacon message to be discoveredby other devices (e.g., [14]). The D2D discovery protocols(e.g., [15], [16]) have been proposed for FlashLinQ [17]. Theauthors of [15] propose a D2D discovery protocol for Flash-LinQ, in which each device transmits a discovery signal. In[16], a joint iterative decoding solution for multi-user detectionof the identifier sent by each device is proposed for the pos-sible application to FlashLinQ. However, these beacon-based

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56 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 1, JANUARY 2015

schemes for WLAN and FlashLinQ are not compatible with theLTE-A system in its current form.

For the LTE-A system, the authors of [18] proposed abeacon-based D2D discovery scheme. The beacon consists ofprimary and secondary synchronization signals followed byinformation bits. However, the use of such a beacon for the D2Ddiscovery can lead to underutilization of resource blocks (RBs)and a high collision probability. A number of RBs dedicated forbeacon transmission should be allocated by the BS, but some ofthese allocated RBs can be wasted due to low utilization. In thecase that UEs are very densely placed, it frequently happensthat two or more nearby UEs send beacons via the same RB,which causes the beacons to collide at a receiving UE.

In this paper, we propose a D2D discovery scheme thatdiscovers pairs of UEs in a centralized manner. In the proposedscheme, a discovery entity residing in the network side gathersinformation relevant to the proximity between UEs in order todiscover pairs of UEs. The proposed scheme adaptively allo-cates RBs based on the random access procedure to minimizethe radio resource required for gathering the information. In theLTE-A system, the random access procedure is used for a UEin an idle mode to establish a connection to the network. Inthe random access procedure, each UE transmits a preamblevia a physical random access channel (PRACH) to the BS.Upon receiving the preambles, the BS allocates uplink RBs toeach respective preamble so that a UE can send a connectionsetup request message. Since this random access procedurewas originally introduced to prevent underutilization of RBs inconnection establishment, we can apply this procedure to theD2D discovery for the same purpose.

The proposed scheme modifies this random access procedurein such a way that each UE sends a preamble to the nearbyUEs via a newly introduced physical channel, called a D2D-PRACH. The UE, which receives a preamble, sends a reportingmessage to the BS by means of a normal random accessprocedure to report the received preambles to the discoveryentity. Then, the BS allocates an uplink RB for each reportedpreamble so that the UEs initially sent a preamble via the D2D-PRACH can send a reporting message to the BS. Finally, a pairof UEs, which are in each other’s proximity, are identified bythe discovery entity by comparing the reported preambles.

The advantage of the proposed D2D discovery scheme isthreefold. First, the proposed scheme can readily be appliedto the current LTE-A system without significant modificationsince the proposed scheme is designed based on the existingrandom access procedure. Second, the proposed scheme dis-covers pairs of UEs in a centralized manner, which enablesthe access or core network to centrally control the formationof D2D communication networks. Third, the proposed schemecan effectively prevent underutilization of RBs by making useof the random access procedure.

The contribution of the proposed paper is summarized asfollows:

• We propose a practical and efficient D2D discoveryscheme that discovers pair of nearby UEs in a centralizedmanner, based on the random access procedure, as anenabler for the proximity-based service. As far as weknow, the centralized D2D discovery scheme based on

the random access has not been proposed in any previousliterature.

• We analyze the performance of the proposed D2D discov-ery scheme in terms of the average number of allocatedRBs, the collision probability, and the D2D link discov-ery ratio. A closed-form formula for the performance isderived by means of the stochastic geometry-based ap-proach. We show that the analysis results accurately matchthe simulation results.

The rest of the paper is organized as follows. In Section II,we explain some preliminaries and motivations for designinga D2D discovery scheme. Section III elaborates the proposedrandom access-based D2D discovery scheme in detail. InSection IV we analyze the performance of the proposed D2Ddiscovery scheme. Section V presents numerical results, andthe paper is concluded in Section VI.

II. PRELIMINARIES AND MOTIVATION

A. Proximity-Based Service

In the 3GPP document [12] on the proximity-based service,the mobile social networking and the mobile marketing are sug-gested as important examples of the proximity-based service.In the use case of the mobile social networking, this documentsupposes that there are three social networking users, Mary,Peter, and John. In this scenario, Mary and John are friends;John and Peter are friends; but Mary and Peter are not friends.As Mary’s UE comes into the proximity of John’s UE, Mary’sUE detects that John’s UE is in its proximity and Mary’s socialnetworking application learns that John is in her proximity,and vice versa. However, Mary’s UE and Peter’s UE do notdetect each other since their owners are not friends. As anotherexample, the mobile marketing is suggested in [12]. In thisexample, Mary and the owner of a store are subscribed to anoperator service pertaining to the mobile marketing. As Marywalks into the neighborhood where the store is located, Mary’sUE is notified of the proximity of the store.

To realize these proximity-based services, an appropriateD2D discovery scheme should be designed for the LTE-Asystem. Actually, it is not necessary for the LTE-A system tobe equipped with the functionality of the direct communicationin order to realize the proximity-based service. Once two UEsdiscover each other, they can either use a direct communicationpath or use an indirect communication path involving the BS,for data communication. This paper focuses on designing theD2D discovery scheme, rather than the direct communication,since the D2D discovery is a necessary and sufficient conditionfor realizing the proximity-based service.

In the proposed D2D discovery scheme, the discovery entityin the network side (i.e., in an access network or in a corenetwork) is in charge of centrally discovering all pairs of nearbyUEs within a given area (e.g., a single cell). Once the discoveryentity discovers pairs of nearby UEs, the discovery entity caninitiate the connection between the discovered pair of UEs orcan form a multi-hop D2D network in which multiple UEs areinvolved. The proposed centralized discovery scheme allowsthe discovery entity to have full knowledge about the proximityrelationships between all UEs in a given area. On the other


CHOI AND HAN: DEVICE-TO-DEVICE DISCOVERY FOR PROXIMITY-BASED SERVICE IN LTE-ADVANCED SYSTEM 57

Fig. 1. Power delay profile on a PRACH.

hand, in the distributed discovery scheme (e.g., the beacon-based scheme), each UE only knows the existence of UEs in itsproximity. Due to the full knowledge of the proximity relation-ships in the system, the proposed scheme has advantages overthe distributed discovery scheme in establishing and managingthe multi-hop D2D communication networks.

B. Random Access Procedure in LTE-A System

In this subsection, we provide a brief introduction to therandom access procedure of the LTE-A system [2]. When aUE intends to establish a connection to the BS, the UE initiatesa random access procedure by sending a preamble to the BSvia a physical random access channel (PRACH). A PRACHis a time-frequency radio resource, which is multiplexed to-gether with a physical uplink shared channel (PUSCH) and aphysical uplink control channel (PUCCH). On a PRACH, aUE can transmit a preamble, which is a Zadoff-Chu sequence.The Zadoff-Chu sequence satisfies a constant amplitude zeroautocorrelation (CAZAC) property [19]. The CAZAC propertyallows multiple orthogonal sequences to be generated fromthe same Zadoff-Chu sequence. In a PRACH in the LTE-Asystem, a UE can choose and send a preamble out of 64 or-thogonal preambles, which are made from the same Zadoff-Chusequence. Upon receiving preambles via a PRACH, the BS cal-culates a power delay profile to detect which preambles are sent.

In Fig. 1, we present an example power delay profile cal-culated by the BS. In this example, four UEs send preamblesto the BS in a PRACH. UE 1 sends preamble 4, UE 2 sendspreamble 16, UE 3 sends preamble 2, and UE 4 sends preamble4. Note that multiple peaks are observed for each transmittedpreamble due to delay spread. To find out a certain preamble issent or not by using a power delay profile, the BS estimates thetotal energy during the interval corresponding to the preamble,and decides that the preamble is sent if the estimated energyis higher than a threshold. In this example, the BS detects thatpreambles 2, 4, and 16 are sent. However, the BS does not knowhow many UEs have sent each preamble.

The random access procedure is completed by the followingfour steps [2], [20].

• Preamble transmission (step 1): A UE randomly selects apreamble out of all available preambles with equal proba-bility and transmits a preamble to the BS via a PRACH.

• Random access response (step 2): Upon detecting pream-bles, the BS sends a random access response (RAR) foreach detected preamble via a physical downlink sharedchannel (PDSCH). An RAR conveys the identity of thedetected preamble and an initial uplink resource grant forthe transmission of a connection setup request messagein step 3.

• Connection setup request message (step 3): When a UEreceives an RAR corresponding to the selected preamble,the UE can send the connection setup request message byusing the initial uplink resource grant in the received RAR.

• Connection setup response message (step 4): If the BS suc-ceeds in receiving the connection setup request messagein step 3, the BS sends the connection setup response mes-sage to the UE. The random access procedure is completedif the UE receives the connection setup response message.Finally, the UE moves from the idle mode to the connectedmode.

If two or more UEs select the same preamble in step 1(i.e., a collision happens), these UEs send the connection setuprequest messages in step 3 through the same uplink RBs. Inthis case, the BS cannot decode the messages and the randomaccess procedure is failed because of a collision. In the above-mentioned example (i.e., the example in the second paragraphof this subsection), three RBs are allocated in step 2, which arefor preambles 2, 4, and 16, respectively, under the assumptionthat one RB is needed for sending a connection setup requestmessage. While UE 2 and UE 3 can successfully send theconnection setup request messages to the BS, both UE 1 andUE 4 attempt to transmit the connection setup request messagesvia the same RB corresponding to preamble 4, which results ina collision.

This random access procedure can minimize the under-utilization of RBs while prevent collisions, compared to theslotted ALOHA (S-ALOHA). To achieve the same collisionprobability as the random access in the LTE-A system does,the S-ALOHA-based scheme should allocate 64 RBs in a fixedway so that each UE can select one RB out of 64 RBs fortransmitting a message. We can see that a large portion of theseallocated RBs can be wasted. If we apply the above-mentionedexample scenario to the S-ALOHA-based scheme, only 3 RBsare used and the remaining 61 RBs are not used by any UE.Compared to the S-ALOHA requiring 64 RBs to be fixedlyallocated, the random access in the LTE-A system only requiresa few RBs for the PRACH (i.e., 12 RBs for 64 preambles[2, p. 428]) and 3 RBs for sending connection setup requestmessages (in the example), adding up to only 15 RBs.

In this paper, we modify the random access procedure in theLTE-A system to design the D2D discovery scheme. By doingso, we not only benefit from the above-mentioned advantagesof the random access procedure in the LTE-A system but alsomake the proposed D2D discovery scheme more compliant tothe current LTE-A system.

III. DEVICE-TO-DEVICE DISCOVERY SCHEME

A. System Model

We consider a single cell centered by a BS. Let us denoteby U the set of the indices of all UEs involved in the D2Ddiscovery in the cell. A UE is indexed by u ∈ U . The two-dimensional coordinate of UE u is denoted by cu. UE u isinterested in discovering only a part of all UEs, which are calledtarget UEs of UE u. Let Su denote the set of all target UEs ofUE u.



Fig. 2. Example network.

A UE wants to discover target UEs within the discoverydistance D. A unidirectional link from UE i to UE j representsthat UE i wants to discover UE j in proximity. That is, thereexists link (i, j) if and only if UE j is in proximity of UE i (i.e.,|ci − cj | ≤ D) and UE j is a target UE of UE i (i.e., j ∈ Si).Let L denote the set of all links.

In Fig. 2, we present an example network in which there are12 UEs. In this example, we have U={1, 2, . . . , 12}. The targetUEs of each UE is S1 = {5, 7}, S2 = {3, 4, 6}, S3 = {1, 5, 7},S4 = {2, 3, 6}, S5 = {2, 3, 4, 6}, S6 = {2, 3, 4, 6}, S7 = {2,3, 4, 6}, S8 = {9, 10, 11, 12}, S9 = {8, 10, 11, 12}, S10 ={8, 9, 11, 12}, S11 = {8, 9, 10, 12}, and S12 = {8, 9, 10, 11}.There are 11 links such that L = {(3, 1), (5, 4), (7, 6), (8, 9),(8, 10), (8, 11), (9, 8), (9, 10), (10, 8), (10, 9), (11, 8)}.

For coarse filtering of UEs during the discovery procedure,we divide UEs into G discovery groups. Let qu denote the indexof the discovery group to which UE u belongs. In addition, wedenote by Qu the set of the indices of all discovery groupsthat UE u is interested in. The proposed discovery scheme isdesigned in such a way that link (i, j) can be discovered only ifUE i is interested in the discovery group to which UE j belongsto, that is, if qj ∈ Qi. Therefore, if UE j is one of the targetUEs of UE i (i.e., j ∈ Si), it should be satisfied that qj ∈ Qi sothat UE j is discoverable to UE i when they are in each other’sproximity.

A discovery entity is defined as a central coordinator of theD2D discovery scheme, which resides in a network side. Thegoal of the proposed discovery scheme is to make the discoveryentity discover all links in L in a centralized manner. We assumethat the discovery entity is aware of all UEs involved in the D2Ddiscovery (i.e., U ) and the set of the target UEs of each UE (i.e.,Su). Based on this information, the discovery entity assigns adiscovery group to each UE (i.e., qu) and decides the set ofdiscovery groups in which each UE is interested (i.e., Qu) sothat all target UEs are discoverable (i.e., if j ∈ Si, it should besatisfied that qj ∈ Qi).

As an example, let us suppose that there are three discoverygroups in Fig. 2. The discovery groups to which each UE be-longs are q1 = 1, q2 = 2, q3 = 2, q4 = 2, q5 = 1, q6 = 2, q7 =1, q8 = 3, q9 = 3, q10 = 3, q11 = 3, and q12 = 3. The sets ofdiscovery groups in which each UE is interested are Q1={1},Q2={2}, Q3={1}, Q4={2}, Q5={2}, Q6={2}, Q7={2},Q8={3}, Q9={3}, Q10={3}, Q11={3}, and Q12={3}.

TABLE ITABLE OF SYMBOLS FOR D2D DISCOVERY SCHEME

A list of key mathematical symbols used in this paper issummarized in Table I.

B. Proposed Device-to-Device Discovery Scheme

In this subsection, we introduce the proposed D2D discoveryscheme in detail. In Fig. 3, we present a flow chart of theoperation of a UE and the BS, and a message sequence chart forthe proposed scheme. As seen in Fig. 3, a cycle of the proposedscheme consists of three phases, namely, a D2D-PRACH accessphase, an Rx-UE reporting phase, and a Tx-UE reporting phase.Note that it can take several cycles of the proposed scheme todiscover all the links in the system.

For each cycle, a UE randomly selects either a transmit stateor a receive state. A UE selects the transmit state with proba-bility ρ and selects the receive state with probability (1− ρ).Henceforth, a Tx-UE (resp., Rx-UE) refers to a UE that selectsthe transmit (resp., receive) state. Let UTx and URx denote theset of the indices of Tx-UEs and Rx-UEs, respectively.

Each cycle of the proposed scheme begins from the D2D-PRACH access phase. A newly introduced physical channel,called a D2D-PRACH, is placed at the start of a cycle. Weassume that a D2D-PRACH is in the uplink band, taking up oneor more RBs. A UE can send a preamble on a D2D-PRACH. LetATx denote the set of the indices of available preambles in aD2D-PRACH. We assign a set of preambles in a D2D-PRACHto each discovery group. Let ATx(g) denote the set of pream-bles assigned to discovery group g. Each preamble is assigned



Fig. 3. Flowchart of the operation of a UE and the BS, and message sequence chart.

to one discovery group, that is, ATx(i) ∩ ATx(j) = ∅ for alli �= j and

⋃Gg=1 ATx(g) = ATx. For example, if there are

15 preambles (i.e., ATx = {1, 2, . . . , 15}) and 3 discov-ery groups, we can assign 5 preambles to each discoverygroup in such a way that ATx(1) = {1, 2, . . . , 5}, ATx(2) ={6, 7, . . . , 10}, and ATx(3) = {11, 12, . . . , 15}.

Each Tx-UE selects a preamble out of the set of the pream-bles assigned to the discovery group that the Tx-UE belongs to.Let aTx

u denote the preamble index that is selected by Tx-UEu. Tx-UE u selects a preamble aTx

u out of ATx(qu), and sendsthe selected preamble on the D2D-PRACH. The transmissionpower of the preamble from a Tx-UE is set so that the Rx-UEswithin the discovery distance D can receive but the other Rx-UEs cannot. Therefore, the preamble from UE u can be heardby all Rx-UE i’s for which |cu − ci| ≤ D.

An Rx-UE listens to the D2D-PRACH for hearing a pream-ble from a nearby Tx-UE. Rx-UE u tries to receive preamblesassigned to the discovery groups that Rx-UE u is interestedin. That is, Rx-UE u monitors preambles in ATx(g) for allg ∈ G(u). We define ATx,Rcvd

u as the set of the indices of thepreambles that Rx-UE u receives. Then, we have

ATx,Rcvdu =

{aTxi

∣∣aTxi ∈ ATx(g) for any g ∈ G(u),

|ci − cu| ≤ D, i ∈ UTx}, (1)

for u ∈ URx. Note that if there are more than one nearbyTx-UEs that send the same preamble, the Rx-UE cannot tellhow many Tx-UEs send the preamble but only knows thereis at least one nearby Tx-UE which sends the preamble.An Rx-UE is activated only when it receives at least one

preamble. Let URx,Act denote the set of the indices of theactivated Rx-UEs, which is given as

URx,Act ={u ∈ URx|ATx,Rcvd

u �= ∅}. (2)

Next, we explain the second phase of the proposed scheme,which is the Rx-UE reporting phase. In this phase, all theactivated Rx-UEs try to report the received preambles by usinga method similar to the standard random access procedureexplained in Section II-B. We consider a PRACH for which theset of the indices of all available preambles is denoted by ARx.An activated Rx-UE u selects one preamble out of ARx. LetaRxu denote the preamble index selected by activated Rx-UE u.

The BS receives the preambles transmitted by all the activatedRx-UEs.

The BS allocates φ uplink RBs for each preamble which ischosen by at least one activated Rx-UE, where φ is the numberof uplink RBs required for transmitting a reporting message.Therefore, the set of the preambles each of which has thecorresponding uplink RBs is

ARx,RB ={i ∈ ARx| there exists u ∈ URx,Act

such that aRxu = i

}. (3)

The BS sends an RAR message for each preamble in ARx,RB.An RAR message contains a uplink RB grant which maps apreamble in ARx,RB to the corresponding uplink RBs. Uponreceiving the RAR message, activated Rx-UE u finds the RBscorresponding to the preamble aRx

u and sends a reporting mes-sage on those RBs. The reporting message contains the indicesof all preambles received by the activated Rx-UE.



If more than one activated Rx-UEs select the same preamblein the PRACH, a collision happens since more than one Rx-UEssend a reporting message on the same RBs. Therefore, the setof the preambles with a collision is

ARx,Col={i∈ARx,RB| there exists j∈URx,Act, k ∈ URx,Act

such that j �= k, aRxj = aRx

k = i}. (4)

The BS can decode the reporting messages transmitted onRBs without collision. We define a successful Rx-UE as a UEthat succeeds in transmitting the reporting message to the BS,among the activated Rx-UEs. Let URx,Succ denote the set of theindices of all successful Rx-UEs. Then, we have

URx,Succ={u∈URx,Act|aRx

u ∈ARx,RB, aRxu �∈ARx,Col

}. (5)

The reporting message transmitted by an activated Rx-UEu contains a report of all received preambles on the D2D-PRACH (i.e., ATx,Rcvd

u ). The BS can receive these reportsin the reporting messages from all successful Rx-UEs. Then,the BS becomes aware of all the preambles received by allsuccessful Rx-UEs. The set of the indices of these preambles is

ATx,RB =⋃

u∈URx,Succ

ATx,Rcvdu . (6)

Finally, we explain the third phase, which is the Tx-UEreporting phase. The BS allocates φ uplink RBs for eachpreamble in ATx,RB so that Tx-UEs can send reporting mes-sages. The BS notifies the uplink RB grants to all the Tx-UEsby sending D2D-RAR messages. Tx-UE u decodes the D2D-RAR messages to see if there are allocated RBs correspondingto the preamble that the Tx-UE u has sent in the D2D-PRACH(i.e., aTx

u ). If Tx-UE u finds out RBs corresponding to aTxu , the

Tx-UE sends a reporting message on the allocated RBs. If twoor more Tx-UEs select the same preamble, a collision happensin that preamble. Therefore, the set of the preambles in which acollision happens is

ATx,Col ={i ∈ ATx,RB| there exists j ∈ UTx, k ∈ UTx

such that j �= k, aTxj = aTx

k = i}. (7)

Only when Tx-UE u selects a preamble in ATx,RB withoutcollision, the reporting message from the Tx-UE u can besuccessfully received by the BS. Then, the set of the indicesof all successful Tx-UEs is given as

UTx,Succ={u ∈ UTx|aTx

u ∈ ATx,RB, aTxu �∈ ATx,Col

}. (8)

Now, the discovery entity in the BS receives reportingmessages from all the successful Tx-UEs and the successfulRx-UEs. The discovery entity knows the preamble in the D2D-PRACH, selected by successful Tx-UE j (i.e., aTx

j ) as well asthe set of the indices of the preambles in the D2D-PRACH,received by successful Rx-UE i (i.e., ATx,Rcvd

i ). If aTxj ∈

ATx,Rcvdi for j ∈ UTx,Succ and i ∈ URx,Succ, it means that UE

i and UE j are close to each other. The discovery entity includeslink (i, j) such that aTx

j ∈ ATx,Rcvdi into the discovered links if

UE j is a target UE of UE i (i.e., j ∈ Si). Therefore, the set ofall links that are discovered by the discovery entity is given as

LDiscov ={(i, j)|aTx

i ∈ ATx,Rcvdj , j ∈ Si,

i ∈ UTx,Succ, j ∈ URx,Succ}. (9)

The following lemma states that the proposed scheme cor-rectly discovers a subset of all links.

Lemma 1: The discovered links are included in the set of alllinks, i.e., LDiscov ⊂ L.

Proof: A preamble chosen by a successful Tx-UE (i.e.,aTxi for Tx-UE i such that i ∈ UTx,Succ) is not chosen by any

other Tx-UE, since any collision should not happen for a Tx-UEto successfully send the reporting message. In other words,if i ∈ UTx,Succ, then aTx

i �= aTxj for all j �= i, j ∈ UTx. This

means that a preamble chosen by a successful Tx-UE is notincluded in the received preambles of successful Rx-UEs whichis not close to that successful Tx-UE. That is, if i ∈ UTx,Succ,then aTx

i �∈ ATx,Rcvdj for all j such that |ci − cj | > D. Hence,

if aTxi ∈ ATx,Rcvd

j for i ∈ UTx,Succ and j ∈ URx,Succ, then|ci−cj |≤D. Therefore, we can conclude that LDiscov⊂L. �

C. Illustrative Example

To help understanding of the proposed D2D discoveryscheme, we give an illustrative example of the operation of theproposed scheme in Fig. 4. In this example, the sets of UEs (i.e.,U ), the set of links (i.e., L), target UEs (i.e., Su), discoverygroups (i.e, G, qu, and Qu), and preambles assigned to eachdiscovery group (i.e, ATx(g)) are as given in the examples inSection III-A and B.

In the D2D-PRACH access phase, each UE randomly de-cides its state between the transmit state and the receive state.We can see in Fig. 4(a) that 7 UEs select the transmit state and5 UEs select the receive state, i.e., UTx = {1, 4, 5, 6, 9, 10, 11}and URx = {2, 3, 7, 8, 12}. There are 15 available preamblesin the D2D-PRACH and each preamble is assigned to threediscovery groups such that ATx(1) = {1, 2, . . . , 5}, ATx(2) ={6, 7, . . . , 10}, and ATx(3) = {11, 12, . . . , 15}. Each Tx-UE uselects one preamble out of ATx(qu) and sends the selectedpreamble to the nearby Rx-UEs via the D2D-PRACH. In thisexample, considering that q1 = 1, q4 = 2, q5 = 1, q6 = 2, q9 =3, q10 = 3, and q11 = 3, we have aTx

1 = 1, aTx4 = 6, aTx

5 = 3,aTx6 = 6, aTx

9 = 11, aTx10 = 13, and aTx

11 = 14. Considering thatQ2={2}, Q3={1}, Q7={2}, Q8={3}, and Q12={3}, theset of preambles received by each Rx-UE is ATx,Rcvd

2 = ∅,ATx,Rcvd

3 = {1}, ATx,Rcvd7 = {6}, ATx,Rcvd

8 = {11, 13, 14},and ATx,Rcvd

12 = ∅. Since only Rx-UEs receiving at least onepreamble are activated, the set of the activated Rx-UEs isURx,Act = {3, 7, 8}.

In Fig. 4(b), we illustrate the Rx-UE reporting phase. Inthis phase, the activated Rx-UEs attempt to establish a con-nection to the BS by sending a preamble on the PRACH. Weassume that there are 15 available preambles in the PRACH,i.e., ARx = {1, 2, . . . , 15}. Each activated Rx-UE selects onepreamble out of ARx. In this example, we have aRx

3 = 7, aRx7 =

4, and aRx8 = 2. Then, the set of the preambles, for which



Fig. 4. Illustrative example of the proposed D2D discovery scheme.(a) D2D-PRACH access phase. (b) Rx-UE connection setup phase. (c) Tx-UEconnection setup phase.

uplink RBs are allocated by the BS, is ARx,RB = {2, 4, 7}.Since each activated Rx-UE selects a different preamble, thereis no preamble with a collision, i.e., ARx,Col = ∅. Therefore,all activated Rx-UEs succeed in sending the reporting mes-sage to the BS. Hence, the set of all successful Rx-UEs isURx,Succ = {3, 7, 8}. Each successful Rx-UE reports to theBS the received preambles in the D2D-PRACH. That is, thesuccessful Rx-UEs report ATx,Rcvd

3 = {1}, ATx,Rcvd7 = {6},

and ATx,Rcvd8 = {11, 13, 14}. The set of all preambles reported

to the BS is ATx,RB = {1, 6, 11, 13, 14}.

In the Tx-UE reporting phase described in Fig. 4(c), theBS allocates uplink RBs for each preamble in ATx,RB andsends D2D-RAR messages mapping each preamble to uplinkRBs. Tx-UE u sends the reporting message on the RBs corre-sponding to preamble aTx

u . Therefore, the RBs for preamble 1are used by Tx-UE 1, the RBs for preamble 6 are used byTx-UEs 4 and 6, the RBs for preamble 11 are used by Tx-UE 9,the RBs for preamble 13 are used by Tx-UE 10, and theRBs for preamble 14 are used by Tx-UE 11. Since the RBsfor preamble 6 are used by two Tx-UEs, a collision happensin preamble 6, that is, ATx,Col = {6}. Besides the Tx-UEsselecting preamble 6 (i.e., Tx-UEs 4 and 6), all other Tx-UEssuccessfully sending the reporting messages. Therefore, wehave UTx,Succ = {1, 9, 10, 11}.

To discover links, the BS tests if aTxi ∈ ATx,Rcvd

j for eachconnected Tx-UE i and each connected Rx-UE j. The BS findsthat aTx

1 ∈ ATx,Rcvd3 , aTx

9 ∈ ATx,Rcvd8 , aTx

10 ∈ ATx,Rcvd8 , and

aTx11 ∈ ATx,Rcvd

8 . Therefore, the set of the discovered links isLDiscov = {(3, 1), (8, 9), (8, 10), (8, 11)}.

IV. PERFORMANCE ANALYSIS OF PROPOSED SCHEME

A. Performance Measure

In this subsection, we introduce several performance mea-sures for evaluating the proposed D2D discovery scheme. Thenumbers of RBs allocated for Tx-UEs and Rx-UEs to sendthe reporting messages are important performance measures.The expected number of uplink RBs allocated for Tx-UEs canbe calculated as

φE[|ATx,RB|

], (10)

where | · | is the number of elements in a set. Similarly, theexpected number of uplink RBs allocated for Rx-UEs is

φE[|ARx,RB|

]. (11)

A small expected number of allocated RBs implies that theradio resource is efficiently used.

The collision probability of Tx-UEs (resp., Rx-UEs) is de-fined as the expected number of the preambles, in which acollision happens, in the D2D-PRACH (resp., PRACH) over thenumber of all preambles in the D2D-PRACH (resp., PRACH).Thus, the collision probability of Tx-UEs is

E[|ATx,Col|

]|ATx| , (12)

and the collision probability of Rx-UEs is

E[|ARx,Col|

]|ARx| . (13)

The most important performance measure is the link dis-covery probability. The link discovery probability is defined asthe expected number of the discovered links over the expectednumber of all links. Therefore, the link discovery probability isgiven by

E[|LDiscov|

]E [|L|] . (14)



B. System Model for Analysis

To analyze the performance of the proposed D2D discoveryscheme, we introduce a system model which assumes that thecoordinates of UEs follow the Poisson point process [21]. Weconsider a circular cell area of radius R, which is centered bythe origin in the two-dimensional space. Let Φ(x, Y ) denotethe disk of radius Y centered by the coordinate x. Then, thecell area is represented by Φ(0, R).

From now on, we will refer to a UE by the coordinate of theUE rather than by the index of the UE. Then, UE x representsa UE located at the coordinate x. In addition, U denote the setof the coordinates of all UEs involved in the D2D discovery.We assume that U follows the Poisson point process. Thedensity of U is λ within the cell area (i.e., Φ(0, R)), and iszero outside the cell area. We define δ(U ,X ) as the numberof points of the point process U in the area X . If Φ(x, Y ) ⊂Φ(0, R), then δ(U ,Φ(x, Y )) follows the Poisson distributionwith mean λπY 2 since the area of Φ(x, Y ) is πY 2. Note thatthe probability mass function (pmf) of the Poisson distributionwith mean μ is

f(i) =μi exp(−μ)

i!. (15)

With a slight abuse of notation, Sx, qx, Qx, aTxx , aRx

x , andATx,Rcvd

x are respectively the set of all target UEs of UE x, thediscovery group to which UE x belongs, the set of discoverygroups in which UE x is interested, the preamble index selectedby Tx-UE x, the preamble index selected by Rx-UE x, andthe set of the indices of the preambles that Rx-UE x receives.Furthermore, UTx, URx, URx,Act, UTx,Succ, and URx,Succ arethe sets of the coordinates of UEs, not the indices of UEs.

The discovery group of each UE is randomly selected out ofG available discovery groups. That is, the probability that qx =g for given discovery group g is 1/G. Each UE is interestedin only one discovery group which is also randomly selectedout of G discovery groups. In other words, the probability thatQx = {g} for given discovery group g is 1/G. We assume that,if UE x is interested in the discovery group that UE y belongsto (i.e., qy ∈ Qx), then UE y is a target UE of UE x.

C. Performance Analysis

In the D2D-PRACH, a UE selects either the transmit stateor the receive state. Recall that ρ is the probability that a UEselects the transmit state. Then, the set of the coordinates of allTx-UEs (resp., Rx-UEs), denoted by UTx (resp., URx), followsthe Poisson point process with density ρλ (resp., (1− ρ)λ) inthe cell area.

Let us focus on one Rx-UE x. The disk of radius D aroundRx-UE x is included in the cell area (i.e., Φ(x, D) ⊂ Φ(0, R)).We consider the set of Tx-UEs that are within the discoverydistance D from Rx-UE x and belong to the discovery group inwhich Rx-UE x is interested. This set is given as

W(x) ={y∣∣|y − x| ≤ D, qy ∈ Qx,y ∈ UTx

}. (16)

The number of Tx-UEs within the discovery distance D fromRx-UE x (i.e., δ(UTx,Φ(x, D))) follows the Poisson distri-bution with mean ρλπD2. In addition, the probability that aTx-UE belongs to a given discovery group is 1/G. Therefore,the number of Tx-UEs in W(x) in (16) follows the Poissondistribution with mean ρλπD2/G.

Rx-UE x becomes an activated Rx-UE if and only if W(x)is not an empty set. From (15), the probability that W(x) isnot an empty set is given by 1− exp(−ρλπD2/G). Therefore,we have

Pr[x ∈ URx,Act

∣∣x ∈ URx]= Pr

[|W(x)| ≥ 1

∣∣x ∈ URx]

=1− exp(−ρλπD2/G). (17)

Let us assume that the discovery distance is much smallerthan the cell radius, i.e., D R. Under this assumption, theprobability that an Rx-UE becomes an activated Rx-UE is asgiven in (17) for all Rx-UEs in the cell area. Since the numberof Rx-UEs in the cell area follows the Poisson distributionwith mean E[|URx|] = (1− ρ)λπR2, the expected number ofactivated Rx-UEs is calculated as

E[|URx,Act|

]=E

[|URx|

]Pr

[x ∈ URx,Act

∣∣x ∈ URx]

=(1−ρ)λπR2(1− exp(−ρλπD2/G)

). (18)

The number of activated Rx-UEs approximately follows thePoisson distribution. Then, the distribution of activated Rx-UEsselecting a given preamble also follows a Poisson distribution.Let us define CRx

i as the set of activated Rx-UEs selectingpreamble i, that is

CRxi =

{x∣∣aRx

x = i,x ∈ URx,Act}. (19)

Then, the expected number of activated Rx-UEs in CRxi is

E[∣∣CRx

i

∣∣]=E[|URx,Act|

]/|ARx|

=(1−ρ)λπR2(1−exp(−ρλπD2/G)

)/|ARx|. (20)

In addition, |CRxi | follows the Poisson distribution with mean

E[|CRxi |], and |CRx

i | is independent of |CRxj | for j �= i.

The probability that preamble i is received by the BS isequal to the probability that |CRx

i | ≥ 1, which is calculated from(15) as

Pr[∣∣CRx

i

∣∣ ≥ 1]= 1− exp

(−(1− ρ)λπR2

×(1− exp(−ρλπD2/G)

)/|ARx|

). (21)

Since there are |ARx| preambles in the PRACH, the expectednumber of uplink RBs allocated for Rx-UEs is

φE[|ARx,RB|

]=φ|ARx|Pr

[∣∣CRxi

∣∣ ≥ 1]

=φ|ARx|{1− exp

(−(1− ρ)λπR2

×(1−exp(−ρλπD2/G)

)/|ARx|

)}. (22)



Similarly, the collision probability of Rx-UEs is calculated as

E[|ARx,Col|

]|ARx| = Pr

[∣∣CRxi

∣∣ ≥ 2]

= 1− Pr[∣∣CRx

i

∣∣ = 0]− Pr

[∣∣CRxi

∣∣ = 1]

= 1−(1 + (1− ρ)λπR2

(1− exp(−ρλπD2/G)

)/|ARx|

)

× exp(−(1− ρ)λπR2

(1− exp(−ρλπD2/G)

)/|ARx|

).

(23)

Now, we calculate the expected number of uplink RBs allo-cated for Tx-UEs. Let Bi(x) denote the set of Tx-UEs, whichselect preamble i in the D2D-PRACH, within the discoverydistance D from Rx-UE x. That is,

Bi(x) ={y∣∣aTx

y = i, |y − x| ≤ D,y ∈ UTx}. (24)

For Rx-UE x such that Φ(x, D) ⊂ Φ(0, R), the number ofTx-UEs in Bi(x) follows the Poisson distribution with meanρλπD2/|ATx|. Therefore, the probability that Rx-UE x re-ceives preamble i via the D2D-PRACH is

Pr[i ∈ ATx,Rcvd

x

∣∣x ∈ ΠRx]

= Pr[|Bi(x)| ≥ 1, i ∈ ATx(g) for g ∈ Qx|x ∈ ΠRx

]

=(1− exp

(−ρλπD2/|ATx|

))/G. (25)

Since the expected number of all Rx-UEs is (1− ρ)λπR2, theexpected number of Rx-UEs receiving preamble i is

E[∣∣{x|i ∈ ATx,Rcvd

x

}∣∣]

= E[|ARx|

]Pr

[i ∈ ATx,Rcvd

x |x ∈ ΠRx]

= (1− ρ)λπR2(1− exp

(−ρλπD2/|ATx|

))/G. (26)

Let us assume that the number of Rx-UEs receiving preamble ifollows the Poisson distribution with mean in (26). In addi-tion, the number of all activated Rx-UEs follows the Poissondistribution with mean in (18). Therefore, the probability thatpreamble j in the PRACH is selected by only one Rx-UEreceiving preamble i in the D2D-PRACH is

Ξ =Pr[∣∣CRx

j

∣∣ = 1, i ∈ ATx,Rcvdx for x ∈ CRx

j

]

=Pr[∣∣CRx

j

∣∣ = 1] E [∣∣{x|i ∈ ATx,Rcvd

x

}∣∣] /|ARx|E [|URx,Act|] /|ARx|

=(1− ρ)λπR2(1− exp(−ρλπD2/|ATx|)

)/(G|ARx|

)

× exp(−(1− ρ)λπR2(1− exp(−ρλπD2/G))/|ARx|

).

(27)

The probability Ξ in (27) is actually the probability that anRx-UE receiving preamble i in the D2D-PRACH becomes asuccessful preamble through preamble j in the PRACH. Theprobability that preamble i is included in ATx,RB is equal tothe probability that at least one Rx-UE receiving preamble ibecomes a successful Rx-UE. Since we have |ARx| preamblesin the PRACH, we have

Pr[i ∈ ATx,RB] = 1− (1− Ξ)|ARx|. (28)

Finally, the expected number of uplink RBs allocated forTx-UEs is

φE[|ATx,RB|

]=φ|ATx|Pr[i ∈ ATx,RB]

=φ|ATx|(1− (1− Ξ)|A

Rx|), (29)

where Ξ is given in (27).We can calculate the collision probability of Tx-UEs as

E[|ATx,Col|

]|ATx| =

E[|ATx,RB|

]− E

[|ATx,Succ|

]|ATx| , (30)

where ATx,Succ is the set of preambles without collision amongATx,RB in the D2D-PRACH. That is,

ATx,Succ ={i∣∣∣∣CTx

i

∣∣ = 1, i ∈ ATx,RB}, (31)

where CTxi denotes the set of Tx-UEs selecting preamble i in

the D2D-PRACH, that is, CTxi = {x|aTx

x = i}. For a preambleto be included in ATx,Succ, there should be only one Tx-UEselecting the preamble. The number of Tx-UEs select-ing preamble i follows the Poisson distribution with meanρλπR2/|ATx|. Therefore, the probability that only one Tx-UEselects preamble i is

Pr[∣∣CTx

i

∣∣=1]=(ρλπR2/|ATx|

)exp

(−ρλπR2/|ATx|

). (32)

Suppose that Tx-UE x is the only Tx-UE selecting preamble i(i.e., CTx

i = {x}). The set of activated Rx-UEs receivingpreamble i from Tx-UE x is given as

Hi(x)={y∣∣|y−x|≤D, i ∈ ATx (g) for g ∈ Qy,y∈URx

}.

(33)

The number of Rx-UEs in Hi(x) follows the Poisson distri-bution with mean (1− ρ)λπD2/G. In addition, the expectednumber of all activated Rx-UEs, under the condition thatTx-UE x is the only Tx-UE selecting preamble i, is given as

Λ =E[|URx,Act|

∣∣CTxi = {x}

]

= Pr[y ∈ URx,Act

∣∣y ∈ URx , |y − x| ≤ D, CTxi = {x}

]

× E[y∣∣y ∈ URx , |y − x| ≤ D]

+ Pr[y∈URx,Act

∣∣y∈URx , |y−x|>D, CTxi ={x}

]

× E[y∣∣y ∈ URx , |y − x| > D

]

=((1− ρ)λπR2(G− 1)/G

) (1− exp(−ρλπD2/G)

)

+((1− ρ)λπ(R2 −D2)/G

)

×(1− exp

(−ρλπD2

(G−1 − |ATx|−1

)))

+ (1− ρ)λπD2/G. (34)

Then, the probability that preamble j in the PRACH is selectedby only one Rx-UE receiving preamble i in the D2D-PRACH,



given that there is only one Tx-UE selecting preamble i, is

Γ = Pr[∣∣CRx

j


j

∣∣ ∣∣CTxi

∣∣ = 1]

=(1− ρ)λπD2/(G|ARx|

)exp

(−Λ/|ARx|

). (35)

The probability that preamble i is included in ATx,RB, giventhat there is only one Tx-UE selecting preamble i, is

Pr[i ∈ ATx,RB

∣∣ ∣∣CTxi

∣∣ = 1]= 1− (1− Γ)|A

Rx|. (36)

Therefore, we have

E[|ATx,Succ|

]= |ATx|Pr

[i∈ATx,RB

∣∣ ∣∣CTxi

∣∣=1]Pr

[∣∣CTxi

∣∣=1]

= ρλπR2 exp(−ρλπR2/|ATx|

) (1− (1− Γ)|A

Rx|). (37)

Finally, the collision probability of Tx-UEs is

E[|ATx,Col|

]|ATx| = 1− (1− Ξ)|A

Rx|

−(ρλπR2/|ATx|

)exp

(−ρλπR2/|ATx|

) (1−(1−Γ)|A

Rx|).

(38)

We now derive the link discovery probability. The probabilitythat a link from an Rx-UE, selecting preamble j in the PRACH,to a Tx-UE, selecting preamble i in the D2D-PRACH, isdiscovered is

Pr[∣∣CTx

i

∣∣ = 1,∣∣CRx

j


j

]

= ΓPr[|CTx

i | = 1]

= ρλπR2(1− ρ)λπD2/(G|ATx||ARx|

)

× exp(−ρλπR2/|ATx|

)exp

(−Λ/|ARx|

). (39)

By multiplying |ATx||ARx| to the equation in (39), the ex-pected number of the discovered links is calculated as

E[|LDiscov|

]=

(ρλπR2(1− ρ)λπD2/G

)

× exp(−ρλπR2/|ATx|

)exp

(−Λ/|ARx|

). (40)

We can calculate the expected number of all links as E[|L|] =λπR2λπD2/G. Therefore, the link discovery probability is

E[|LDiscov|

]E [|L|] = ρ(1− ρ) exp

(−ρλπR2/|ATx|

)

× exp(−Λ/|ARx|

). (41)

V. NUMERICAL RESULTS

In this section, we present numerical results for the proposedD2D discovery scheme by using simulation and analysis. Inboth simulation and analysis, the number of UEs follows thePoisson point process with density λ. The density is given inthe unit of the number of UEs per square meter. The radius of acell is R = 500 m. We assume that four uplink RBs are neededfor transmitting a reporting message of Tx-UEs and Rx-UEs,

Fig. 5. The expected number of uplink RBs allocated for Tx-UEs and Rx-UEsas a function of the number of UEs.

i.e., φ = 4. Unless noted otherwise, the probability of selectingthe transmit state is ρ = 0.5 and the number of discovery groupsis G = 400. The number of preambles in the PRACH is fixedto |ARx| = 64. The PRACH uses 12 RBs (i.e., 6 subchannelsduring 2 slots) to provide 64 preambles, which is preambleformat 0 for small-medium cells (up to 14 km in radius) in theLTE-A system [2].

In our simulation, the D2D-PRACH also uses 6 · τ RBs(i.e., 6 subchannels during τ slots), where τ is the number ofslots for the D2D-PRACH. While the PRACH is configuredfor a maximum round-trip distance of 14 km, we design theD2D-PRACH under the condition that a maximum round-tripdistance is 100 m between a Tx-UE and an Rx-UE. In [2],the number of available preambles, made by a cyclic shift ofa single root Zadoff-Chu sequence, is less than the duration ofa preamble sequence divided by the maximum round-trip time.The duration of a preamble sequence is the length of one slot,i.e., 0.5 ms, and the maximum round-trip time correspondingto 100 m is 0.66 μs. Therefore, it is possible to have more than700 preambles in one slot of the D2D-PRACH. Considering theguard time and the cyclic prefix, we assume that 400 preamblesare available in one slot of the D2D-PRACH. Therefore, thenumber of available preambles in the D2D-PRACH is |ATx| =400 · τ .

In Figs. 5 and 6, we present the simulation and the analysisresults in terms of the expected number of allocated uplinkRBs and the collision probability, respectively. In these figures,the number of slots for the D2D-PRACH is fixed to τ = 2.These results are plotted as a function of the density of UE,i.e., λ, and we also vary the discovery distance (i.e., D).From these figures, we can observe that the analysis resultsaccurately match the simulation results. Therefore, by meansof the analysis, we can easily evaluate the performance of theproposed scheme without simulation.

In Fig. 5, we can see that the number of allocated uplink RBsincreases as the density increases. In this figure, we plot thesum of the numbers of uplink RBs for Tx-UEs and Rx-UEs. We



Fig. 6. The collision probability of Tx-UEs and Rx-UEs as a function of thenumber of UEs.

Fig. 7. The link discovery probability and the collision probability as afunction of the number of preambles.

can see that more uplink RBs are allocated when the discoverydistance is high. This result shows that the proposed scheme isable to adaptively allocate uplink RBs in response to the numberof links. Fig. 6 shows the collision probability increases as moreUEs attempt to transmit a preamble.

Fig. 7 shows the link discovery probability and the collisionprobability as a function of the number of slots for the D2D-PRACH (i.e., τ ). The collision probability in this figure is thecollision probability of Tx-UEs in the D2D-PRACH.In thisfigure, we can see that the collision probability can be decreasedby increasing the number of preambles in the D2D-PRACH.Therefore, we can achieve a target link discovery probabilityby adjusting the number of preambles. For example, to achievethe link discovery probability of 0.2 given that the density isλ = 0.01, there should be at least 5 slots for the D2D-PRACH,which means we need 2000 available preambles for theD2D-PRACH.

In Fig. 8, we present the link discovery probability accordingto the probability of selecting the transmit state (i.e., ρ). For this

Fig. 8. The link discovery probability as a function of the probability ofselecting the transmit state, ρ.

Fig. 9. Expected number of cycles until a link is discovered.

figure, two slots are used for the D2D-PRACH. In this figure, itis seen that the optimal value of ρ, which maximizes the linkdiscovery probability, is close to 0.5 in the parameter rangein which the collision probability is low. On the other hand,the optimal value of ρ is lower than 0.5 when the collisionprobability is high. This is because more collisions tend tohappen in the D2D-PRACH than in the PRACH, which can berelieved by reducing the number of UEs selecting the transmitstate.

In Fig. 9, we present the simulation result that shows theexpected number of cycles taken for a link to be discovered.To obtain this result, we run the simulation for multiple cyclesand count the number of cycles until each link is discovered. Inthis figure, we can see that, when the link discovery probabilitybecomes lower due to a small number of available preambles ora high density of UEs, more cycles are required for discoveringa link. This figure can be used to decide the required number ofslots for the D2D-PRACH. For example, suppose that the den-sity of UEs is λ = 0.0005, each cycle is placed every 100 ms,



and the D2D application demands that the discovery is donewithin 500 ms in average. In Fig. 10, we can see that the numberof slots required for the D2D-PRACH is 3 to achieve less then5 cycles for discovery when λ = 0.0005.

VI. CONCLUSION

In this paper, we have proposed a D2D discovery schemeto realize the proximity-based service. The proposed scheme isdesigned based on the random access procedure in the LTE-Asystem. The proposed random access-based D2D discoveryscheme is advantageous in that i) the proposed scheme canreadily be applied to the current LTE-A system without sig-nificant modification; ii) the proposed scheme discovers pairsof UEs in a centralized manner, which enables the accessor core network to centrally control the formation of D2Dcommunication networks; and iii) the proposed scheme adap-tively allocates resource blocks (RBs) for the D2D discovery toprevent underutilization of radio resources.

We have derived a closed-form analytic expression for theperformance of the proposed scheme in terms of the expectednumber of allocated uplink RBs, the collision probability, andthe link discovery probability. We have verified that the analysisresults accurately match the simulation results. The closed-form analysis can be used to calculate the required number ofavailable preambles in the D2D-PRACH and the PRACH toachieve a target link discovery probability.

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Kae Won Choi (M’08) received the B.S. degreein civil, urban, and geosystem engineering and theM.S. and Ph.D. degrees in electrical engineering andcomputer science from Seoul National University,Seoul, Korea, in 2001, 2003, and 2007, respectively.From 2008 to 2009, he was in the telecommunica-tion business with Samsung Electronics CompanyLtd., Korea. From 2009 to 2010, he was a Postdoc-toral Researcher with the Department of Electricaland Computer Engineering, University of Manitoba,Winnipeg, MB, Canada. In 2010, he joined the fac-

ulty at Seoul National University of Science and Technology, Seoul, where heis currently an Assistant Professor in the Department of Computer Scienceand Engineering. His research interests include machine-to-machine com-munication, device-to-device communication, cognitive radio, radio resourcemanagement, and wireless network optimization.

Zhu Han (S’01–M’04–SM’09–F’14) received theB.S. degree in electronic engineering from TsinghuaUniversity, Beijing, China, in 1997 and the M.S.and Ph.D. degrees in electrical engineering fromthe University of Maryland, College Park, MD,USA, in 1999 and 2003, respectively. From 2000 to2002, he was a Research and Development Engineerwith JDSU, Germantown, MD. From 2003 to 2006,he was a Research Associate at the University ofMaryland. From 2006 to 2008, he was an AssistantProfessor with Boise State University, Boise, ID,

USA. He is currently an Associate Professor with the Department of Electri-cal and Computer Engineering, University of Houston, Houston, TX, USA.His research interests include wireless resource allocation and management,wireless communications and networking, game theory, wireless multimedia,security, and smart grid communication. He has been an Associate Editor ofthe IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS since 2010. Hewas a recipient of an NSF CAREER award in 2010 and the IEEE Fred W.Ellersick Prize in 2011.


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