performance analysis of grant-free multiple access for

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Performance Analysis of Grant-FreeMultiple Access for Supporting SporadicTraffic in Massive IoT NetworksTAEHOON KIM1, (Member, IEEE), and BANG CHUL JUNG2, (Senior Member, IEEE)1Agency for Defense Development, Daejeon 34186, South Korea (e-mail: [email protected])2Department of Electronics Engineering, Chungnam National University, Daejeon 34134, South Korea (e-mail: [email protected])

Corresponding author: Bang Chul Jung (e-mail: [email protected]).

This research was supported in part by the NRF through the Basic Science Research Program funded in part by the Ministry of Science andICT under Grant NRF2019R1A2B5B01070697, in part by the MSIT(Ministry of Science and ICT), Korea, under the ITRC(InformationTechnology Research Center) support program(IITP-2019-2017-0-01635) supervised by the IITP(Institute for Information &communications Technology Promotion, and in part by Institute of Information and Communications Technology Planning and Evaluationgrant funded by the Korea Government (MSIP, Research on Near-Zero Latency Network for 5G Immersive Service) under Grant2015-0-00278.

ABSTRACT Grant-free multiple access (GFMA) protocol has been regarded as a key element to supportsporadic traffic generated from massive internet-of-things (IoT) networks. In GFMA protocol, each IoTdevice transmits data packets without grant from a base station (BS) via pre-reserved uplink resources.Packet collisions inherently occur when multiple IoT devices transmit packets by using the same radioresource, but the collision effect can be alleviated with multi-packet reception (MPR) capability of the BS.Since a number of studies have focused on improving the physical layer performance such as bit error rate,they may be hard to provide intuitions from the MAC layer perspective when a number of IoT devicessporadically generate uplink packets and attempt the GFMA. In this paper, we thoroughly investigate theGFMA from the MAC layer perspective. We provide an analytical framework based on a Markov chainto capture the performance of the GFMA in terms of packet transmission success probability, ergodicthroughput, and access delay. Through simulations, we validate our analytical framework and verify thenecessity of adopting MPR technique for supporting a massive number of IoT devices generating sporadictraffic.

INDEX TERMS Cellular IoT networks, grant-free multiple access, sporadic traffic, massive connectivity,multi-packet reception.

I. INTRODUCTION

INTERNET-OF-THINGS (IoT), which connects a massivenumber of IoT devices with a wide range of applications

through IP-based networks, has been considered as a keyenabler for Industry 4.0 [1]. Due to the advantage of cellularnetworks such as coverage and security, the cellular networkshave attracted great attention as one of candidates for im-plementing IoT. Accordingly, there have been a number ofstudies for implementing IoT in practical cellular networkssuch as LTE/5G new radio (NR) [2], [3].

A number of IoT devices are expected to sporadicallytransmit small-sized packets in uplink direction for reportingpurpose [4]. In this case, each IoT device may transit toa sleep mode after completion of packet transmissions forsaving energy consumption and release its connection with

the base station (BS) [5]. This implies that each IoT deviceshould perform a random access (RA) procedure to (re-)establish the connection with the BS when it has a newpacket to be sent to the IoT server.

The RA procedure consists of 4-steps of handshaking [6],which takes several tens of millisecond (ms) [7]. From theperspective of data packet transmission, the RA procedurecan be regarded as additional signaling procedure requiredin advance. In particular, it has been considered as a criticalsignaling overhead for supporting sporadic traffic generatedfrom IoT devices. As the size of packet becomes smaller,this signaling procedure becomes more inefficient. Withoutconsidering significant modifications of the legacy proto-col, minimizing the RA delay spent before the actual datatransmission as small as possible can be the straightforward

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T. Kim, B. C. Jung: Performance Analysis of Grant-Free Multiple Access for Supporting Sporadic Traffic in Massive IoT Networks

approach to improve the latency performance. For the lastfew years, a number of studies have focused on reducing theRA delay by mitigating collision problem [7]–[9], however,the latency cannot be reduced below a certain value due tothe inherent handshaking procedure.

One of the solutions introduced in [10] is contention-based uplink transmissions. Andreev et al. [11] proposed acontention-based access, where each IoT device sends datapackets over the shared resources without spending time onthe RA procedure, i.e., without grant acquisition procedure.This may reduce the latency, however, a collision problemmay still occur when multiple IoT devices utilize the sameresource.

To address the collision problem, non-orthogonal trans-mission mechanisms [12], such as a sparse code multiple ac-cess (SCMA) [13], a multi user shared access (MUSA) [14],a pattern division multiple access (PDMA) [15], and a re-source spread multiple access (RSMA) [16], are expected tobe applied on top of the contention-based framework [17].The MPR capability provided by such non-orthogonal trans-mission mechanisms can mitigate the occurrence of packetcollisions. In line with those of approaches, enormous effortshave been made to improve the grant-free protocol. Wang etal. [18] proposed a compressive sensing based access mech-anism using the sparsity of sporadic traffic. Similarly, Zhanget al. [19] studied the joint user activity and data detectionproblem in an uplink grant-free non-orthogonal multiple ac-cess (NOMA) system based on compressive sensing. Doganet al. [20] proposed NOMA with index modulation for grant-free access. Moreover, Berardinelli et al. [21] analyzed thereliability of the contention-based access protocol.

To the authors’ best knowledge, most of previous studieshave still focused on the physical layer performance, but didnot provide any insightful intuitions from the MAC layerperspective. In this paper, we thoroughly investigate grant-free multiple access (GFMA) from the MAC layer perspec-tive under the IoT scenario with sporadic traffic. The maincontributions of this paper can be summarized as follows:• We propose an analytical framework based on a Markov

chain to capture the MAC layer performance of theGFMA such as packet transmission success probability,ergodic throughput, and access delay, and validate ouranalytical framework through extensive system-levelsimulations.

• We investigate the effect of resource configuration onthe MAC layer performance, and verify that resource-spreading approach is much beneficial than multi-channel approach to support the IoT scenario with spo-radic traffic.

• We investigate the effect of sporadic traffic from a largenumber of IoT devices on the system, and find that eventhough the IoT scenario with sporadic traffic imposescritical burden on the system, a few more resources aresufficient enough to support it.

The rest of this paper is organized as follows. In Section II,we describe the GFMA protocol in more detail. In Section III,

we analyze the GFMA with a Markov chain model from theMAC layer perspective. In Section IV, we provide numericalresults. Finally, we draw conclusions in Section V.

II. GRANT-FREE MULTIPLE ACCESSIn this section, we explain the system model and introducethe GFMA protocol in more detail.

A. SYSTEM MODELIn this subsection, we first explain the system model weconsidered in this paper. Fig. 1 describes the system model.We consider a single cell, and the BS is assumed to adoptthe MPR-capable receiver. We consider a general IoT sce-nario [7]–[9], where each IoT device sporadically generatesits data packet. Accordingly, we use a Poisson process as atraffic model [4].1 In other words, each IoT device generatesa new packet following a Poisson distribution with arrivalrate of λ [22], and its probability mass function (pmf) canbe expressed as

Pr {K = k} = pk =e−λTP (λTP)

k

k!, (1)

where K represents the number of newly arrived packetswithin a given time interval TP. It is worth noting thatthe packet arrival rate λ is assumed to have an arbitrarysmall value due to the sporadic characteristic of the trafficgenerated from the IoT devices [8]. We assume that thegenerated packet is sufficiently small and thus it can besuccessfully transmitted through each transmission attempt ifthere is no packet collision. If there exists at least a packet tobe sent in each IoT device’s queue (or, equivalently, buffer),it attempts uplink transmissions with a probability of pt onthe next available GFMA resource, which is periodicallyreserved for the GFMA protocol only. Note that the transmitprobability pt plays an important role to control the overalltraffic load in the system. Here, the period of the GFMAresource is denoted as Tp. Let NR denote the amount of pre-reserved GFMA resources per period, which can be definedasNR = NC×NM, whereNC andNM represent the numberof channels and the MPR capability of the BS, respectively.NC and NM can be arbitrary values.

B. OVERALL PROCEDUREIn this subsection, we introduce the overall procedure of theGFMA protocol, which consists of 2-steps of handshakingprocedure. Key idea of the GFMA is that whenever each IoTdevice has packets, it attempts uplink transmissions with aprobability of pt at the next available GFMA resource. Fig. 2visualizes the handshaking procedure of the GFMA protocol,where delay-incurring components are also specified. It isworth noting that the time duration of each component takes

1The IoT scenario can be categorized into twofolds [4]: One is theoverload scenario due to the event-driven situation such as a simultaneouspower-on event after a disaster situation, which can be modeled by eitherbeta distribution or uniform distribution. The other is the general scenariowithout traffic overload, which can be modeled by Poisson distribution.

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...

...

...

...

...

Total number of

IoT devices :

MPR-capable

base station

...

NU

pt

pt

pt

pt

pt

Frequency

MPR capability

Time

NM

NC

Tp

GFMA resource

FIGURE 1: System model where active IoT devices among NU IoT devices attempt its uplink packet transmissions with a probability of ptat the next-available GFMA resource. TP represents the period of the GFMA resource, and NC and NM represent the number of channelsand the MPR capability of the BS, respectively, which satisfy NR = NC ×NM.

IoT device BS

Queuing

Delay Step1. Data

transmission

Step2. ACKProcessing time

Packet arrival

Propagation delay

Propagation delay

FIGURE 2: Overall procedure of the GFMA protocol

an integer multiple of the transmission time interval (TTI)value (e.g., 1ms in LTE/LTE-A systems [23]). The details ofeach step are as follows:• (Step 1) Packet transmissions : Each IoT device ran-

domly selects a channel among NC channels within theGFMA resource, and transmits its data packet with aprobability of pt. For contention resolution, whenevereach IoT device transmits the packet, it starts a con-tention resolution (CR) timer.

• (Step 2) Acknowledgement : The BS attempts to de-code the packets received through the GMFA resource.The BS transmits the acknowledgement (ACK) mes-sages to the IoT devices, whose transmitted packetsare successfully decoded. If each IoT device receivesthe ACK message before the CR timer expires, then itregards the packet transmission as a success. Otherwise,it regards the packet transmission as a failure and re-peats Step 1 and Step 2 for reattempting uplink packettransmission.

C. DISCUSSIONSFrom Fig. 2, we can conjecture the overall delay when thepacket is successfully transmitted at once without any packet

collision, which can be calculated as the summation of thequeuing delay, the propagation delays, and the processingtime. When the packet experiences the collision, both Step 1and Step 2 should be repeated until the packet is successfullytransmitted. In this case, the time duration spent during thereattempts should be considered for the overall delay. Thedetailed explanation on the success of packet transmissionand the overall delay will be followed in the next section.

III. PERFORMANCE ANALYSISIn this section, we propose a Markov chain to capture theperformance of the GFMA protocol in terms of packet trans-mission success probability, ergodic throughput, and accessdelay. Moreover, we mathematically analyze those of perfor-mance metrics in detail.

A. MARKOV CHAIN MODELFig. 3 shows the state transition diagram of the proposedMarkov chain. Our approach is proposed based on a wellknown literature [24] and we tailor it for our system model.Thus, each state represents the queue length of each IoTdevice, where the queue length implies the number of packetsin the queue. It is noteworthy that since our proposed Markovchain model considers the queue length of each IoT device asstate, it has primary benefit that it can be applied to any trafficmodel not restricted to Poisson based traffic model. The statespace S can be defined as

S = {0, 1, · · · , i, · · · , I} , (2)

where I represents the maximum queue size. πi(n) repre-sents the state probability that the queue length equals to iat time n and thus the distribution of the state probability attime n, π(n), can be denoted as

π(n) = {π0(n), π1(n), · · · , πI(n)} . (3)

A state transition occurs whenever each IoT device at-tempts to perform an uplink transmission, and the state tran-

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0 1 2 i I-1 I......

p0,0

p1,1

p2,2

p2,1

p1,2

p0,1

p1,0

pi,i

pI-1,I-1

pI,I

pI,I-1

pI-1,I

p0,I

p0,2

p0,i

p1,i

p0,I-1

p1,I-1

p1,I

pi,I

pi,I-1

FIGURE 3: A state transition diagram of the proposed Markovchain, where pj,k represents the state transition probability fromstate j to state k

sition probability from state j to state k, pj,k, is given in (4),shown at the next page, where ps represents the transmissionsuccess probability. Even though each IoT device does notperform actual transmissions due to pt value, the state updateoccurs. Note that our proposed Markov chain model canalso describe a drastic packet generation (e.g., pj,k wherek ≥ j), but this hardly occurs in the general IoT scenariowith sporadic traffic.

B. PACKET TRANSMISSION SUCCESS PROBABILITYPacket transmission success probability, ps, is defined as theprobability that a packet is successfully transmitted wheneach IoT device performs an uplink transmission. In orderto mathematically derive the packet transmission successprobability, we should obtain the probability of existing atleast a packet in the queue, τ , which implies the probabilitythat attempts to perform the uplink transmissions. In order toderive τ , we should obtain a stationary distribution, π.

The steady-state probabilities can be expressed as

π0 = π0p0,0 + π1p1,0, (5)

πi =i+1∑j=0

πjpj,i, i ∈ [1, I − 1], (6)

and

πI =

I−1∑j=0

πjpj,I + πI (1− pI−1,I) . (7)

With above equations, it is hard to express the stationarydistribution in a closed-form. Hence, we obtain the stationarydistribution by using the fact that it converges to a certaindistribution regardless of the initial state probabilities.

Let P denote the one-step state transition matrix, whichhas pj,k as an element of the j-th row and the k-th column.The steady-state probability of the state i, πi, can be obtainedby πi = lim

n→∞πi(n). Finally, the stationary distribution, π,

which is denoted as π = {πi} for i ∈ [0, I], can be derivedby:

π = limn→∞

π(n) = limn→∞

Pnπ(0) , (8)

where π(0) represents the distribution of the initial stateprobabilities.

Now, we haveτ = 1− π0, (9)

which is a function of ps, since π and P are also functionsof ps (see (4) and (8)). From the viewpoint of system, ps canbe derived as

ps =NM−1∑k=0

(NU − 1

k

)(τptNC

)k (1− τpt

NC

)NU−1−k

,

(10)

which is a function of τ . Finally, (9) and (10) comprisea non-linear equation and thus τ and ps can be found bynumerical methods. Our numerical approach is summarizedas Algorithm 1.

Fig. 4 shows the convergence of the solutions based onAlgorithm 1. As the iteration round proceeds, both τ andps interact with each other and consequently converge tothe final values within a few iteration rounds. Since we setthe γmax value as 20 in this example, we can find thatthe algorithm is terminated when 20 samples of pprev

s - psmaintain arbitrary small value (see Fig. 4(a) and Fig. 4(b)).Finally, Fig. 4(c) shows the stationary distribution of theMarkov chain, in which the IoT device can maintain thequeue length less than 4 with a probability of 0.9.

Especially for extremely sporadic traffic, it is reasonableto assume that pk = 0, for k ≥ 2, and, thus, p1 can beexpressed as 1−p0. In this case, we can express the stationarydistribution in a closed-form. The steady-state probabilitiescan be expressed as

π0 = π0p0,0 + π1p1,0, (11)

πi = πi−1pi−1,i + πipi,i + πi+1pi+1,i, i ∈ [1, I − 1], (12)

andπI = πI−1pI−1,I + πI (1− pI, I−1) (13)

With above equations, we have

πi =

π0 , i = 0

π0

i−1∏j=0

(pj,j+1

pj+1,j

), i ∈ [1, I] .

(14)

By using the normalization condition for the stationary dis-tribution, we have

1 =I∑i=0

πi = π0

1 +I∑i=1

i−1∏j=0

(pj,j+1

pj+1,j

) . (15)

Therefore, by using (15), π0 can be expressed as

π0 =

1 +I∑i=1

i−1∏j=0

(pj,j+1

pj+1,j

)−1

. (16)

Similarly, after substituting (16) in (9), we can also find τ andps by using numerical methods (see also Algorithm 1).

4 VOLUME 4, 2019




pj,k =

pk, j = 0, 0 ≤ k ≤ Ipk−jpt(1− ps) + pk−j(1− pt) + pk−j+1ptps, 1 ≤ j ≤ I − 1, j < k ≤ Ip0ptps, 1 ≤ j ≤ I, k = j − 1p0pt(1− ps) + p0(1− pt) + p1ptps, 1 ≤ j ≤ I − 1, k = j1− p0ptps, j = I, k = j

(4)

Algorithm 1 : Finding ps and τInput : NU, λ, pt, TP, NC, NM, I , γmax and εOutput : ps, τ

1 : γ← 02 : while (1) do3 : if extremely sporadic traffic then4 : Calculate π05 : else6 : Generate a one-step transition matrix, P7 : Find a stationary distribution, π = {π0, ..., πI}8 : end if9 : Calculate τ = 1− π0 // from (9)

10 : Calculate ps // from (10)11 : if abs (pprevs - ps) < ε then12 : γ← γ + 113 : if γ == γmax then14 : break15 : else16 : γ← 017 : end if18 : end if19 : pprevs ← ps20 : end while

C. ERGODIC THROUGHPUTErgodic throughput, T , is defined as the total number of IoTdevices which successfully transmit their packet during asingle period of the GFMA resource, which can be derivedas

T = min( NU × λ︸︷︷︸offered load

, NU ×function of pt︷︸︸︷

ptps︸︷︷︸system capacity

), (17)

where the system capacity implies the maximum throughputthat the system can achieve using the given amount of theGFMA resources. Note that even though the amount of theGFMA resources is given, how to set pt can vary the systemcapacity. Therefore, for a given pt, the system may operatein a saturated condition or a unsaturated condition. Whenoffered load exceeds the system capacity, the system operatesin a saturated condition, which implies that all IoT deviceshave at least a packet to transmit. On the contrary, offeredload is less than the system capacity, the system operates in aunsaturated condition, which implies that some IoT deviceshave at least a packet to transmit. Using (17), we can derivethe maximum packet arrival rate that the system can support,λmax, as follows:

λmax = maxpt

ptps . (18)

D. ACCESS DELAYAccess delay, D, is defined as the time duration from a newpacket arrival to the successful completion of transmitting the

0 2 4 6 8 10 12 14 16 18 20

Iteration round

0.6

0.7

0.8

0.9

1

(a) Convergence of τ according to the iteration round

0 2 4 6 8 10 12 14 16 18 20

Iteration round

0.5

0.6

0.7

0.8

0.9

1

(b) Convergence of ps according to the iteration round

0 2 4 6 8 10 12 14 16 18 20

Queue length

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

pm

f

analysis

simulation

(c) Stationary distribution of the Markov chain

FIGURE 4: Finding τ , ps, and π when NU = 15, λ = 0.3, pt =0.52, TP=10ms, NC = 1, NM = 8, I = 20, γmax = 20, and,ε = 0.001.

corresponding packet, which can be expressed as

D = DQ +DT, (19)

where DQ and DT represent the queuing delay and thetransmission delay, respectively.

Queuing delay is defined as the time duration between thenew packet arrival and the first attempt of uplink transmis-sion, which can be derived as

DQ =I∑i=0

πiDQ,i, (20)

where DQ,i represents the queuing delay of a new packetwhich is arrived to the queue with the length of i, which can

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be expressed as

DQ,i =Tp2

+ i · Tp · EX [X], i ∈ [0, I] (21)

where X represents the number of transmission opportunitiesuntil the packet is successfully transmitted, which follows ageometric distribution with parameter ptps [22], and its pmfcan be expressed as

fX (x) = (1− ptps)x−1(ptps) forx ∈ {1, 2, 3, ...} . (22)

Transmission delay is defined as the time duration fromthe first attempt of uplink transmission to the time when thecorresponding ACK message is successfully received, whichcan be expressed as

DT = EX [(X − 1)Tp + TS1−S2], (23)

where TS1−S2 represents the time duration from Step 1 toStep 2, which can be expressed as TS1−S2 = 2 × Tprop +Tproc as shown in Fig. 2. Here, Tprop and Tproc represent thepropagation delay via air-interface and the processing time atthe BS, respectively.

It is noteworthy that when the system operates in a sat-urated condition, the queuing delay may infinitely increase.Even though the system can minimize the transmission delayby adjusting pt, however, the access delay may also infinitelyincrease due to the large impact of the queuing delay. As aresult, in order to achieve meaningful latency performanceduring the packet transmissions, the system should be op-erated in a unsaturated condition. Furthermore, in order tosupport low-latency featured data transmissions (e.g., ∼9msin our system model), pt should be 1. This will be furtherdiscussed in Table 2. The system should utilize sufficientenough GFMA resources, and carefully select the optimaltransmit probability, pt∗, which can minimize the accessdelay. We can formulate an optimization problem as

pt∗ = argminD (pt)

subject to pt ∈ [0, 1].(24)

Using any optimization algorithms, we can obtain pt∗.

IV. NUMERICAL RESULTSWe perform system-level simulations using a process-oriented discrete-event simulation package, CSIM, and spe-cific simulation parameters are listed in Table 1. We assumethat there is no frame error due to the channel condition,and also assume that the BS successfully decodes packetswhenever less than NM devices utilize the same resource,where NM represents the MPR capability of the BS. Inall figures, markers and lines indicate the simulation andanalytical results, respectively.

From Fig. 5 to Fig. 9, we first investigate the effect ofresource configuration on the performance. Moreover, inTable 2, we then investigate the effect of sporadic trafficgenerated from a massive number of IoT devices on theperformance. The delay performance is evaluated under theassumption that the transmission time interval (TTI) value

TABLE 1: Simulation parameters and values [6], [25]

Parameters Values

Physical layer related parameters and values

Transmission time interval (TTI) 1msPropagation delay (Tprop) 1msProcessing time at the BS (Tproc) 1msTime duration for handshaking (TS1−S2) 4ms

MAC layer related parameters and values

Period of GFMA resource (TP) 10msAmount of radio resources per TP (NR) 8, 24Number of IoT devices (NU) 15,000, 1,500, 150, 15Packet arrival rate per TP (λ) 0.0003, 0.003, 0.03, 0.3Transmit probability (pt) 0 ∼ 1Contention resolution (CR) timer 8ms

Algorithm related parameters and values

Queue length (I) 20Required number of comparisons (γmax) 20Termination condition (ε) 0.001

is 1ms and thus the point what we should note is that theminimally achievable access delay is 9ms2.

Fig. 5 shows the transmission success probability forvarying the transmit probability, pt. The success probabilitytends to decrease as pt increases for all combinations of NC

and NM due to packet collisions. Especially when the MPRcapability is sufficient enough, the higher value of successprobability can be achieved when pt is carefully adjusted,e.g., pt < 0.53 in case that NC = 1 and NM = 8, comparedto other combinations. The resource configuration ofNC = 1and NM = 8 implies that it cannot support more than 8devices at the same time. This results in a steep decrease ofps as the traffic load increases, which can be observed whenpt > 0.53.

Fig. 6 shows the ergodic throughput for varying the trans-mit probability, pt. The ergodic throughput decreases as ptdecreases, since each IoT device hardly transmits its packetdue to low pt. It also decreases as pt increases, since eachIoT device hardly succeeds in its transmissions due to lowps (or, equivalently, due to high packet collision probabil-ity). Accordingly, there exists an optimal p∗t , which variesaccording to the combinations of NC and NM. With theoptimal p∗t , the case that NC = 1 and NM = 8 achievesthe highest throughput. It is noteworthy that the throughputof the case that NC = 1 and NM = 8 becomes unchangedwhen 0.31 < pt < 0.53 since all input traffic is transferredto the BS in this range, which is also called unsaturated case.pt should be carefully adjusted for the optimal throughputperformance.

Fig. 7 shows both the transmission delay and the queuingdelay for varying values of pt. The transmission delay in-creases as pt decreases, since each IoT device hardly attemptsits uplink transmissions due to low pt and thus each IoT

2Queuing delay (DQ) and the transmission delay (DT) are 5ms and 4ms,respectively. In near future, we expect that the advances in hardware andair-interface can further contribute to improve the delay performance.

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

FIGURE 5: Comparison of success probability for varying valuesof pt in various combinations of NC and NM when NU = 15 andλ = 0.3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

FIGURE 6: Comparison of ergodic throughput for varying valuesof pt in various combinations of NC and NM when NU = 15 andλ = 0.3

device spends time to reattempt uplink transmissions. As ptincreases, the transmission delay also increases, since eachIoT device hardly succeeds in its transmissions due to low ps(see Fig. 5). Thus, each combination has an optimal p∗t thatminimizes the transmission delay as in ergodic throughputcase. With p∗t , the case thatNC = 1 andNM = 8 achieves thebest transmission delay. Basically, queuing delay is infiniteif service rate is lower than the arrival rate. In our case, theservice rate depends on the ergodic throughput. In Fig. 7,only the case that NC = 1 and NM = 8 operates in aunsaturated condition in which the queuing delay is finite.As shown in Fig. 7, the queuing delay drastically changesaccording to pt and thus pt should be carefully chosen byconsidering both the transmission and queuing delay. Thecase that NC = 1 and NM = 8 can provide meaningfullatency performance by adjusting pt value, but it cannotprovide low-latency performance, i.e., ∼9ms. To achieve thelowest latency performance, the system should be operated

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

20

40

60

80

100

120

FIGURE 7: Comparison of transmission and queuing delay forvarying values of pt when NU = 15 and λ = 0.3.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

1

2

3

4

5

6

0

10

20

30

40

50

60

70

80

FIGURE 8: Ergodic throughput, queuing delay, and transmissiondelay of the GFMA with p∗t for varying values of λ whenNU = 15,NC = 1, and NM = 8

with pt = 1, which implies the more radio resources arerequired. With more radio resources, the delay monotonicallydecreases as pt increases. This issue will be discussed indetail in Table 2.

Fig. 8 shows the relationship among the ergodic through-put, queuing delay, and transmission delay of the GFMAwith optimal transmission probability in (24) for varying thepacket arrival rate, λ, whenNU = 15,NC = 1, andNM = 8.The ergodic throughput becomes saturated beyond a certainpoint, i.e., λ = 0.32, which is the maximum load that thesystem can support. In other words, the system operates ina unsaturated condition whenever λ ≤ 0.32, and it operatesin a saturated condition whenever λ > 0.32. Interestingly,the transmission delay has also similar trend with the ergodicthroughput. On the contrary, the queuing delay exponentiallyincreases until the system is saturated. It is worth noting thatthe access delay increases to infinity because of the queuingdelay when the system is saturated.

Fig. 9 shows the access delay for varying values of λ when

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TABLE 2: Summary of performance of the GFMA in various scenarios when Tp = 10ms and TS1−S2 = 4ms

Scenario NU λ NR NC NM p∗t

Successprob-ability(%)

Ergodicthrough-put

Queueingdelay (ms)

Transmissiondelay (ms)

Accessdelay (ms)

Scenario 1

150 0.03

8 8 1 0.05 39.29 2.95 ∞ 502 ∞8 4 2 0.043 52.13 3.38 ∞ 437 ∞8 2 4 0.040 66.30 3.91 ∞ 373 ∞8 1 8 0.043 80.02 4.50* 2,598 284 2,882

1,500 0.003

8 8 1 0.0053 37.03 2.94 ∞ 5088 ∞8 4 2 0.0043 52.16 3.36 ∞ 4,452 ∞8 2 4 0.0040 65.49 3.89 ∞ 3,811 ∞8 1 8 0.0042 76.39 4.50* 44,880 3,111 47,991

Scenario 2

15 0.3 24 8 3 1.0 97.92 4.50* 5.21 4.22 9.433 8 1.0 99.99 4.50* 5.20 4.00 9.20

150 0.03 24 8 3 1.0 97.84 4.50* 5.17 4.22 9.393 8 1.0 99.98 4.50* 5.16 4.00 9.16

1,500 0.003 24 8 3 1.0 97.76 4.50* 5.02 4.23 9.253 8 1.0 99.98 4.50* 5.02 4.00 9.02

15,000 0.0003 24 8 3 1.0 97.75 4.50* 5.00 4.23 9.233 8 1.0 99.98 4.50* 5.00 4.00 9.00

(*) denotes that the system operates in a unsaturated condition

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

20

40

60

80

100

120

FIGURE 9: Comparison of access delay of the GFMA with p∗t forvarying values of λ in various combinations of NC and NM whenNU = 15

NU = 15. For each λ, optimal transmit probability pt∗ is

applied. The access delay gradually increases for low trafficload, but it drastically increases as the traffic load approachesto the saturated condition. When the required access delay isset to 20ms, the supportable traffic load in the case thatNR =16 is equal to 0.7, while the supportable traffic load the casethat NR = 8 is equal to 0.2. It is noteworthy that nearly 3.5times more traffic can be supported by increasing resources2 times, which comes from the statistical multiplex effect.From the observation, in order to support much higher loadin a unsaturated condition, the system should utilize moreresources. Furthermore, if the amount of GFMA resources isthe same, increasing NM is much effective than increasingNC to support higher load.

Finally, Table 2 summarizes the performance of the GFMAin various scenarios. In Scenario 1, we investigate the effectof NU on the performance, when the offered load on average

is equally set, i.e., NU × λ = 4.5. It is noteworthy that eventhough the average offered load is the same, sporadicallygenerated packets from a large number of IoT devices givemuch burden on the system. Scenario 2 shows that a fewmore resources are sufficient enough to support low-latencytransmissions of sporadic traffic generated from a massivenumber of IoT devices. Furthermore, it is worth noting thatthe access delay cannot be reduced under a certain value, i.e.,9 ms, even though the system utilizes more resources, sincethis is an inherent signaling overhead which comes from thehandshaking procedure itself as shown in Fig. 2.

V. CONCLUSIONSIn this paper, we investigated the grant-free multiple ac-cess (GFMA) from the MAC layer perspective under theIoT scenario with sporadic traffic. We proposed an analyticalframework based on a Markov chain, and mathematicallyanalyzed the MAC layer performance of the GFMA in termsof packet transmission success probability, ergodic through-put, and access delay. Moreover, we thoroughly investigatedthe effect of MPR capability on the performance, and foundthe optimal transmit probability which minimizes the delayperformance. Through simulations, we validated our analyt-ical framework and verified that the GFMA can support thelow-latency transmissions of sporadic traffic generated froma massive number of IoT devices when the MPR capability issufficient enough.

REFERENCES[1] M. R. Palattella, M. Dohler, A. Grieco, G. Rizzo, J. Torsner, T. Engel,

and L. Ladid, “Internet of things in the 5G era: Enablers, architecture, andbusiness models,” IEEE J. Sel. Areas Commun., vol. 34, no. 3, pp. 510–527, March 2016.

[2] Service requirements for machine-type communications, 3GPP TS 22.368V13.1.0, Dec. 2014.

[3] RAN Improvements for machine-type ommunications, 3GPP TR 37.868V11.0.0, Oct. 2011.

8 VOLUME 4, 2019




[4] E. Soltanmohammadi, K. Ghavami, and M. Naraghi-Pour, “A survey oftraffic issues in machine-to-machine communications over LTE,” IEEEInternet Things J., vol. 3, no. 6, pp. 865–884, Dec 2016.

[5] T. Kim and I. Bang, “An enhanced random access with preamble-assistedshort-packet transmissions for cellular IoT communications,” IEEE Com-mun. Lett., vol. 23, no. 6, pp. 1081–1084, June 2019.

[6] Evolved universal terrestrial radio access network(E-UTRAN); mediumaccess control (MAC) protocol specification, 3GPP TS 36.321 V12.7.0,Sept. 2015.

[7] T. Kim, H. S. Jang, and D. K. Sung, “An enhanced random access schemewith spatial group based reusable preamble allocation in cellular M2Mnetworks,” IEEE Commun. Lett., vol. 19, no. 10, pp. 1714–1717, Oct.2015.

[8] K. S. Ko, M. J. Kim, K. Y. Bae, D. K. Sung, J. H. Kim, and J. Y. Ahn, “Anovel random access for fixed-location machine-to-machine communica-tions in OFDMA based systems,” IEEE Commun. Lett., vol. 16, no. 9, pp.1428–1431, Sept. 2012.

[9] E. Park, T. Kim, and Y. Han, “An efficient time-shifted random accessscheme for cellular-based IoT networks,” IEEE Commun. Lett., vol. 23,no. 3, pp. 522–525, March 2019.

[10] Study on latency reduction techqniues for LTE (Release 13), 3GPP TR36.881 V0.5.0, Nov. 2015.

[11] S. Andreev, A. Larmo, M. Gerasimenko, V. Petrov, O. Galinina, T. Tir-ronen, J. Torsner, and Y. Koucheryavy, “Efficient small data access formachine-type communications in LTE,” Proc. IEEE International Confer-ence on Communications (ICC), pp. 3569–3574, June 2013.

[12] L. Dai, B. Wang, Z. Ding, Z. Wang, S. Chen, and L. Hanzo, “A surveyof non-orthogonal multiple access for 5G,” IEEE Commun. Surveys Tuts.,vol. 20, no. 3, pp. 2294–2323, thirdquarter 2018.

[13] K. Au, L. Zhang, H. Nikopour, E. Yi, A. Bayesteh, U. Vilaipornsawai,J. Ma, and P. Zhu, “Uplink contention based SCMA for 5G radio access,”Proc. IEEE Globecom Workshops, pp. 900–905, Dec 2014.

[14] Z. Yuan, G. Yu, W. Li, Y. Yuan, X. Wang, and J. Xu, “Multi-user sharedaccess for internet of things,” Proc. IEEE 83rd Vehicular TechnologyConference (VTC Spring), pp. 1–5, May 2016.

[15] S. Chen, B. Ren, Q. Gao, S. Kang, S. Sun, and K. Niu, “Pattern divi-sion multiple access: A novel nonorthogonal multiple access for fifth-generation radio networks,” IEEE Trans. Veh. Technol., vol. 66, no. 4, pp.3185–3196, April 2017.

[16] Y. Cao, H. Sun, J. Soriaga, and T. Ji, “Resource spread multiple access -a novel transmission scheme for 5G uplink,” Proc. IEEE 86th VehicularTechnology Conference (VTC-Fall), pp. 1–5, Sept 2017.

[17] B. Singh, O. Tirkkonen, Z. Li, and M. A. Uusitalo, “Contention-basedaccess for ultra-reliable low latency uplink transmissions,” IEEE WirelessCommun. Lett., vol. 7, no. 2, pp. 182–185, April 2018.

[18] B. Wang, L. Dai, Y. Zhang, T. Mir, and J. Li, “Dynamic compressivesensing-based multi-user detection for uplink grant-free NOMA,” IEEECommun. Lett., vol. 20, no. 11, pp. 2320–2323, Nov 2016.

[19] J. Zhang, Y. Pan, and J. Xu, “Compressive sensing for joint user activityand data detection in grant-free NOMA,” IEEE Wireless Commun. Lett.,vol. 8, no. 3, pp. 857–860, June 2019.

[20] S. Dogan, A. Tusha, and H. Arslan, “NOMA with index modulation foruplink URLLC through grant-free access,” IEEE J. Sel. Topics SignalProcess, vol. 13, no. 6, pp. 1249–1257, Oct 2019.

[21] G. Berardinelli, N. H. Mahmood, R. Abreu, T. Jacobsen, K. Pedersen,I. Z. Kovács, and P. Mogensen, “Reliability analysis of uplink grant-freetransmission over shared resources,” IEEE Access, vol. 6, pp. 23 602–23 611, April 2018.

[22] A. Papoulis and S. U. Pillai, Probability, Random Variables and StochasticProcesses. New York, McGraw-Hill, 2002.

[23] S. Sesia, I. Toufik, and M. Baker, LTE-the UMTS long term evolution:From theory to practice, Second Edition. WILEY, 2011.

[24] G. Bianchi, “Performance analysis of the IEEE 802.11 distributed coordi-nation function,” IEEE J. Sel. Areas Commun., vol. 18, no. 3, pp. 535–547,March 2000.

[25] Evolved universal terrestrial radio access(E-UTRA); Physical layer proce-dures, 3GPP TS 36.213 V12.7.0, Sept. 2015.

TAEHOON KIM (S’13–M’17) received the B.Sdegree in Media Communications Engineeringfrom Hanyang University, Seoul, Rep. of Korea, in2011, and the M.S. and Ph.D. degrees in ElectricalEngineering from Korea Advanced Institute forScience and Technology (KAIST), Daejeon, Rep.of Korea, in 2013 and 2017, respectively. He hasbeen with the Agency for Defense Development(ADD), Rep. of Korea, as a Senior Researchersince September 2017. His research interests in-

clude wireless communications, 5G, machine-type communications (MTC),internet-of-things (IoT), military communications, physical-layer security,wireless avionics intra-communications (WAIC), and laser detection andranging (LADAR).

BANG CHUL JUNG (S’02-M’08-SM’14) re-ceived the BS degree in electronics engineeringfrom Ajou University, Suwon, Korea, in 2002, andthe MS and PhD degrees in electrical & computerengineering from KAIST, Daejeon, Korea, in 2004and 2008, respectively.

He was a senior researcher/research professorwith the KAIST Institute for Information Technol-ogy Convergence, Daejeon, Korea, from January2009 to February 2010. From March 2010 to Au-

gust 2015, he was a faculty of Gyeongsang National University, Tongyeong,Korea. He is currently a Professor in the Department of Electronics En-gineering, Chungnam National University, Daejeon, Korea. He has servedas Associate Editor of IEICE Transactions on Fundamentals of Electronics,Communications, and Computer Sciences since 2018.

Dr. Jung was the recipient of the 5th IEEE Communication SocietyAsia–Pacific Outstanding Young Researcher Award in 2011, KICS HaedongYoung Scholar Award in 2015, and the 29th KOFST Science and TechnologyBest Paper Award in 2019. His research interests include wireless com-munications, statistical signal processing, information theory, interferencemanagement, radar signal processing, spectrum sharing, multiple antennas,multiple access techniques, radio resource management, machine learning,and deep learning.

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