Enhanced Spatial Group Based Random Access for

Enhanced Spatial Group Based Random Access for Cellular M2M Communications Han Seung Jang† , Su Min Kim‡ , Hong-Shik Park† , and Dan Keun Sung† † School

of Electrical Engineering, KAIST, Daejeon, Korea of Electronics Engineering, Korea Polytechnic University, Siheung, Korea Email: [email protected], [email protected], {park1507, dksung}@kaist.ac.kr

‡ Department

Abstract—We have proposed a spatial group based random access (SGRA) scheme which is a novel RA scheme to effectively increase the number of available preambles for future cellular M2M communications. In the SGRA scheme, a machine node in the cell should determine its own spatial group (SG) by estimating the distance between the eNodeB and itself through any distance estimation methods. At the moment, the distance estimation error may inevitably occur in the distance estimation and may cause a group-mismatch problem, which affects the performance of the SGRA scheme in terms of RA collision probability and delay. Therefore, in this paper, we propose a group-reselection solution and a shared distance solution in order to resolve the group-mismatch problem in the SGRA scheme. Through numerical results, it is shown that the combination of the proposed solutions provides a significant robustness against the distance estimation errors, which leads to accommodating a significantly larger number of machine nodes with very lower collision probabilities and shorter average RA delay in more practical M2M deployment environments.

I. I NTRODUCTION Machine-to-machine (M2M) communications in cellular networks have recently received big attention for a wide range of M2M applications such as e-health, public safety, surveillance, remote maintenance and control, and smart metering, which are very important components in future smart cities [1]. Various M2M applications will newly emerge and the number of M2M devices will rapidly increase in the near future. In case of smart metering, we can expect that 35,670 smart meters are deployed in a single cell of urban London with a radius of 2 km [2]. In cellular M2M networks, a random access (RA) protocol is significantly important since a huge population of M2M devices may attempt RAs for initiating communications with a single eNodeB. Moreover, they release the connections after the communications for energy and resource savings, and access the eNodeB again when the communications are required. There have been several studies on the efficient RA schemes for cellular M2M communications [3]–[5]. In the aspect of radio resource, more efficient resource management schemes have been studied in order to accommodate a massive number of M2M devices [6], [7]. In our previous work [8], we proposed a spatial group based random access (SGRA) scheme to effectively increase the number of available preambles in future cellular M2M communications. Our proposed SGRA scheme provides additional preambles through spatially

partitioning a single cell coverage into multiple spatial group (SG) regions and reducing cyclic shift size in Zadoff-Chu (ZC) sequence-based RA preambles. As a result, the SGRA scheme can accommodate a significantly larger number of machine nodes with much lower collision probabilities and shorter RA delay than the conventional RA scheme. However, in the SGRA scheme, a machine node in the cell should determine its own SG based on the estimated distance between the eNodeB and itself through any distance estimation methods. In realistic environments, the distance estimation errors may inevitably occur in the distance estimation and cause a group-mismatch problem, which increases RA collision probability and delay. In this paper, we enhance our previous SGRA scheme through a group-reselection and a shared distance solutions which can resolve the group-mismatch problem. We analyze the performance of the enhanced SGRA scheme in terms of collision probability and access delay. Through numerical results, it is shown that the enhanced SGRA scheme is robust against the distance estimation error, which leads to accommodating a significantly larger number of machine nodes with very lower collision probabilities and shorter average RA delay even in more practical M2M deployment environments. The rest of this paper is organized as follows. In Section II, we describe the overview of our previously proposed SGRA scheme. In Section III, we describe a group-mismatch problem encountered in the SGRA scheme. We propose an enhanced SGRA scheme to solve the group-mismatch problem in Section IV. In Section V, we show the performance results. Finally, we draw conclusive remarks in Section VI. II. A N OVERVIEW OF SPATIAL GROUP BASED RANDOM ACCESS (SGRA) A. Background and system model In LTE system, ZC sequences are used to generate RA preambles defined as zr [n] , exp [−jπ · r · n · (n + 1)/NZC ] for n = 0, . . . , NZC −1, where NZC is the sequence length and r ∈ {1, . . . , NZC − 1} is the root index [9]. In principle, multiple RA preambles can be generated from the ZC sequences shifted by multiple of cyclic shift size, NCS . The number of available preambles per root index, ⌊NZC /NCS ⌋, depends on NCS , which highly relies on the cell radius. NCS should be appropriately set to be greater than both of the maximum roundtrip delay between the eNodeB and a cell edge node, and

Case 1

Case 2 Ͻ D=1.2 km d1=1.3 km

GK Root rK

žžž

G2

Root r2

G1

Root r1

d1 km

d2 km

žžž

dK km

d km Gk: k-th group

Fig. 1.

A cell model for the spatial group based random access.

d=2 km

Case 1 NCS(d1) = 17 With zr1 [n+ƐB1]

ž 1sample = 0.9535 țs

Case 2 NCS(d2) = 13 With zr2 [n+ƐB2]

the maximum delay spread since the received preambles from any non-synchronized machine nodes should be detected on correct preamble detection zones. Hence, the lower bound of NCS is obtained by NCS ≥ ⌈((20/3)d + τds ) NZC /TSEQ ⌉+ng [10], where d is the cell radius (km), τds is the maximum delay spread (µs), NZC and TSEQ denote the length and duration (µs) of ZC sequences, respectively, and ng is the number of additional guard samples. Let us define the cyclic shift as a function of d by NCS (d) , ⌈{(20/3)d + τds } NZC /TSEQ ⌉ + ng . Note that NCS (d) increases as the cell radius d increases and, thus, the number of available preambles per root inroot dex, NPA (d) , ⌊NZC /NCS (d)⌋, decreases as d increases. conv Conventionally, the eNodeB serves UEs with fixed NPA conv preambles in a single cell, e.g., NPA = 64 in the LTE root conv system. If NPA (d) < NPA , the cell needs to use more conv than two root indices in order to provide NPA preambles. We conv root define K , ⌈NPA /NPA (d)⌉ as the required number of root conv indices for generating NPA preambles of the conventional RA scheme when the cell radius is d. B. Spatial group based random access (SGRA) The SGRA scheme consists of a spatial grouping method and a modified preamble detection mechanism in the first step of the RA procedure [8]. Fig. 1 illustrates a cell model for the SGRA scheme. In this model, the entire cell area with radius d is spatially partitioned into multiple K SG regions and the cell uses total K root indices, {r1 , . . . , rK }. Here, K is the required number of root indices of the conventional RA scheme and it also corresponds to the total number of SGs in the cell coverage area of the SGRA scheme. For example, the k-th SG has its own group coverage distance (CD) dk and its own group root index rk . Instead of using the cell radius d to decide the cyclic shift size, the k-th SG uses its own group CD dk less than the cell radius d and, thus, it has the reduced size of group cyclic shift size, NCS (dk ). The key idea to obtain additional preambles comes from the fact root root that NPA (dk ) ≥ NPA (d) since NCS (dk ) ≤ NCS (d) for k = 1, . . . , K. After the eNodeB configures the K SGs, it broadcasts the SG parameters such as a set of group root indices, {r1 , . . . , rK }, and a set of group CDs, {d1 , . . . , dK }. After receiving the parameters, each machine node determines its own SG based on its estimated distance between the eNodeB and itself, which can be estimated by various distance estimation methods [11], [12]. Then, each machine node chooses its group root index and calculates its group cyclic shift size according to its group CD. Thereafter, a machine node in the k-th root SG randomly selects a preamble among NPA (dk ) preambles

Correct detection!

γ Preamble 0

γ

x (12)

Incorrect detection!

Preamble 0

Ͻ D=1.31 km d2=0.7 km

D=1.2 km d1=1.3 km

D=1.31 km d2=0.7 km

NCS(d1) Shifted by ƐB2 (9)

d=2 km

t,x (26)

ž ž ž

Preamble 1

2×NCS(d1)

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Prea

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t (21) ž ž ž

Preamble 1

NCS(d2)

Preamble 2

2×NCS(d2)

Preamble 3

3×NCS(d2)

4×NCS(d2)

Prea

Fig. 2. An example of two group-mismatch events and their preamble detections.

and transmits it on a physical RA channel (PRACH). In order to detect the preambles correctly with the reduced group cyclic shift sizes, a modified preamble detection mechanism based on the shifted reference ZC sequences is required. There exist K shifted reference ZC sequences, Z = {zr1 [n + τB1 ], zr2 [n + τB2 ], . . . , zrK [n + τBK ]}, and they are used to calculate cyclic correlation values among the received preambles. τBk denotes the round-trip delay in the number of samples between the eNodeB and the inner boundary of the k-th SG region, i.e., τB1 = 0 and ⌈ ⌉ ∑k−1 20 × i=1 di NZC τBk = × − 0.5 , k = 2, . . . , K. 3 TSEQ Among all shifted reference ZC sequences in the set Z, only zrk [n + τBk ] has an auto-correlation property with the preambles transmitted from the k-th SG using root index rk . If the correlation value is greater than or equal to the detection threshold γ, the received preamble is detected in one of preamble detection zones. The reason that we use the shifted reference ZC sequence, zr [n + τBk ], instead of zr [n] is for compensation of the round-trip delay between the eNodeB and the inner boundary of the k-th SG. The more details on the SGRA scheme can be found in [8]. III. G ROUP - MISMATCH PROBLEM IN THE SGRA

SCHEME

In realistic environments, there may be obstacles like buildings between the eNodeB and machine nodes, which cause multipath and shadowing effects. Any distance estimation methods may yield some distance estimation errors. To consider such errors, the estimated distance can be modeled as ˆ = D + De , D where D is the actual distance and the estimation error De follows a Gaussian distribution, i.e., De ∼ N (0, σe2 ). If we consider a single cell with 2 km radius (d = 2) and two SGs (K = 2) in the cell, a certain node in the cell suffers from a group-mismatch due to the estimation error with the following two events: ˆ ≤ d1 and d1 < D ≤ d1 + d2 ], E1 = [0 < D ˆ ≤ d1 + d2 and 0 < D ≤ d1 ], E2 = [d1 < D

where d1 and d2 denote the CDs of the first SG and the second SG, respectively, and d = d1 + d2 . Fig. 2 shows an example of two group-mismatch events and their preamble detections with a cell radius of 2 km and the two SGs. The group-mismatch event E1 occurs when a node is located in the second SG but its estimated distance is in the range of the first SG coverage (case 1 in Fig. 2). However, it is not crucial since preambles can be correctly detected due to some guard samples in the cyclic shift size. Although some errors can still occur due to exceeding the error tolerance from the guard samples, they are negligible in practice since the guard sample size is determined by considering this effect in the LTE standard. On the other hand, the group-mismatch event E2 occurs when a node is located in the first SG, however, its estimated distance is in the range of the second SG coverage (case 2 in Fig. 2). In this event, the machine node in the first SG attempts an RA using a preamble of the second SG and, thus, it fails to receive an RA response (RAR) message due to the incorrect preamble detection. Such incorrect preamble detection increases the collision probability of the second SG. In the preamble detection example of Fig. 2, a machine node transmits Preamble 1 and the first path of preamble signal among possible multipaths is only considered for simplicity. Here, t and x denote the received time instant and the detection time instant of the received preamble, respectively. In the first case, since τB1 = 0, t and x are the same whereas t and x in the second case are different from each other because τB2 = 9. The Preamble 1 transmitted from the machine node is correctly detected in the detection zone of the first preamble due to the guard samples as in the first case. However, the Preamble 1 transmitted from the machine node in the second case is incorrectly detected in the detection zone of Preamble 0 since the received preamble is shifted by τB2 = 9 according to the modified detection mechanism for correct detection in the SGRA scheme with the perfect distance estimation. Let us define the estimated group probabilities by Pr[0 < ˆ ≤ d1 ] = Pr[G = 1] and Pr[d1 < D ˆ ≤ d] = Pr[G = 2], D where G denotes the estimated SG index. In addition, the conditional probabilities for given D are given by Pr[G = 1|D] = Φ ((d1 − D)/σe ) and Pr[G = 2|D] = 1 − Φ ((d1 − D)/σe ), where Φ(·) denotes the cumulative distribution of the standard normal distribution and D is the distance from the eNodeB to the machine node in km. As a result, the group-mismatch probabilities of the events E1 and E2 are obtained as follows: (

) d1 − t P (t)dt, σe d1 ( )} ∫ d1 { d1 − t Pr[G = 2, 0 < D ≤ d1 ] = 1−Φ P (t)dt, σe 0 ∫

Pr[G = 1, d1 < D ≤ d] =

d

Φ

where P (t) = 2t/d2 is the probability density of the location of a machine node t km apart from the eNodeB.

GK Root rK

G2

žžž

d2 km d km

d1 km

G1

Root r2

Root r1

Gk: k-th group

žžž

ds km

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ds km ds km

Fig. 3. A cell model for the enhanced SGRA scheme with the shared distance ds . Case 1

Case 2 Ͻ D=1.2 km d1=1.3 km

Ͻ D=1.31 km

D=1.2 km d1=1.3 km

D=1.31 km ds=0.1 km

ds=0.1 km

d2=0.8 km

d2=0.8 km

d=2 km

Case 1 NCS(d1) = 17 With zr1 [n+ƐB1]

Correct detection!

γ Preamble 0

ž 1sample = 0.9535 țs Case 2 NCS(d2) = 14 With zr2 [n+ƐB2]

γ

NCS(d1)

x

Preamble 1

(14) Shifted by ƐB2 (8) Correct detection!

Preamble 0

ž ž ž 2×NCS(d1)

Preamble 2

Prea

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t (22) ž ž ž

Preamble 1

NCS(d2)

d=2 km

t,x (26)

Preamble 2

2×NCS(d2)

Preamble 3

3×NCS(d2)

Pr

4×NCS(d2)

Fig. 4. A preamble detection example in the enhanced SGRA scheme with the shared distance ds .

IV. G ROUP -R ESELECTION AND S HARED D ISTANCE S OLUTIONS FOR THE GROUP - MISMATCH A. Group-reselection solution for the group-mismatch In the group-reselection solution, a machine node reselects its group by the nearest neighbor group after N consecutive failures in receiving RAR messages in order to avoid continuous failures for the machine node with a group-mismatch due to distance estimation errors. This group-reselection solution enables the machine node to have an RA at the end. If the machine node belongs to the mismatched group, it requires to spend additional time in the RA procedure, which leads to the increased RA collisions and delay. B. Shared distance solution for the group-mismatch In the shared distance solution, in order to improve robustness against the distance estimation error, we set the shared CD between the neighboring SGs, as shown in Fig. 3, where ds denotes the shared distance between two neighboring SGs. For example, the first group CD d1 and the second group CD d2 are overlapped by the shared distance ds . Accordingly, the machine nodes located in d1 − ds < D ≤ d1 can select ˆ ≤ d1 and the second SG when the first SG when 0 < D ˆ d1 < D ≤ d2 . The latter case can only cause a groupmismatch but it is negligible due to the guard samples as described in the previous section. To use the shared distance ds , it is required to consider different round-trip delay between the eNodeB and inner boundary of a SG region for the set of shifted reference ZC sequences Z, i.e., τB1 = 0 and ⌉ ⌈ ∑k−1 20 × { i=1 di − (k − 1)ds } NZC × − 0.5 τBk = 3 TSEQ for k = 2, . . . , K.

Fig. 4 shows a preamble detection example in the enhanced SGRA scheme with the shared distance ds . In this example, we consider d = 2 km, K = 2, and ds = 0.1 km. Unlike the example without the shared distance ds in Fig. 2, the eNodeB can correctly detect the received preambles for both of cases. The second group CD is ds km longer than that of the SGRA scheme without the shared distance. The increased group distances may decrease the number of available preambles in the SG since it is inversely proportional to the group CD. Therefore, an appropriate setting of d1 , d2 , and ds is required for performance fairness among different SGs, while ds sufficiently covers the distance estimation error. As a result, the group-mismatch probability of the second SG is changed as Pr[G = 2, 0 < D ≤ d1 − ds ]. C. Collision Probability If more than two machine nodes use the same preamble in the same SG, a collision occurs since the eNodeB gives an uplink resource grant in an RAR message to the machine nodes, which access the eNodeB using the same uplink resource. According to the LTE RA procedure, in the fourth step, the eNodeB does not send a response to the machine nodes if there is a collision. After a timeout, the machine nodes can recognize the collision and defer the subsequent RA [13]. Let pk denote the collision probability of the k-th SG. The total RA arrival rate in the i-th PRACH slot is given by [8], [14]: λT [i] = λ · Mk · TRACH + η · pk · λT [i − 1], where λ denotes the RA arrival rate per machine node (sec−1 ), Mk denotes the number of machine nodes attempting RAs in the k-th SG, TRACH denotes the PRACH time slot duration, and η ·pk ·λT [i−1] represents the arrival rate of deferred RAs from the previous slot due to collisions. ∑Qthe proportion of ∑Q−1η denotes retried RAs defined as η = ( i=1 pik )/( i=1 pik ), where Q is the maximum number of RA trials. In general, M1 and M2 for K = 2 are determined by M1 = M (ps,1 + αpe ) and M2 = M (ps,2 +βpe ), respectively. Here, M is the number of machine nodes in the overall cell coverage, α is an indicator function that examines whether the number of consecutive failures in RAR message reception is less than or equal to the maximum RA retrial limit, i.e., α = IN ≤Q = 1 if N ≤ Q, 0 otherwise, and β is a coefficient of group-mismatch that is proportional to the maximum number of consecutive failures N in RAR message reception, i.e., β ≈ 2N . Moreover, ps,1 , ps,2 , and pe are obtained by ) ∫ d ( d1 − t ps,1 = Φ P (t)dt, σe 0 { ( )} ∫ d d1 − t ps,2 = 1−Φ P (t)dt, σe d1 −ds ( )} ∫ d1 −ds { d1 − t pe = 1−Φ P (t)dt, σe 0 In steady state, we can drop the slot index i, and then λT is expressed as λT = (λ · Mk · TRACH )/(1 − η · pk ). As a root root result, pk = 1 − {1 − 1/NPA (dk )}λT where NPA (dk ) is

TABLE I S IMULATION PARAMETERS AND VALUES Parameters Values Number of machine nodes, M Mean inter-arrival time of a node, 1/λ Period of PRACH time slot, TRACH Cell radius, d The number of spatial groups, K Group CDs, d1 and d2 Shared distance, ds root (d ), N root (d ) NPA 1 2 PA Maximum # of RA trials, Q Maximum # of failures in RAR reception, N RA response window size, TRAR Backoff indicator, TBO Mac-ContentionResolutionTimer, TMAC NZC , TSEQ , τds , ng

30,000 5 min 10 ms 2 km 2 1.3 km, 0.7 km 0 km ∼ 0.2 km 49, 64 10 3∼5 5 ms 20 ms 48 ms 839, 800µs, 5.25µs, 2

the number of available preambles in the k-th SG. Assuming η ≈ 1, pk can be obtained by [ ( ( ) )] 1 pk = 1 − exp W ln 1 − root λ · Mk · TRACH , NPA (dk ) where W (x) is the Lambert W function. V. P ERFORMANCE E VALUATION In this section, we evaluate the performance of the enhanced SGRA scheme and show the effect of distance estimation error in terms of collision probability and average RA delay. Table I lists a set of simulation parameters. In order to consider only M2M communications in the cellular network, we assume that 26 and 32 preambles are exclusively allocated to the first SG and the second SG, respectively, for humanto-human (H2H) communications. Therefore, the first and the root root second SGs provide NPA (d1 ) − 26 and NPA (d2 + ds ) − 32 preambles for M2M communications. If we set 0 ≤ ds ≤ 0.08, root root NPA (d2 + ds ) is equal to 64, while NPA (d2 + ds ) is equal to 59 if we set 0.08 < ds ≤ 0.22. Fig. 5 shows the effect of distance estimation errors on the collision probability only with the group-reselection solution for various N values. The collision probability of the second SG without any solution (i.e., the conventional SGRA, N = Q + 1 = 11 and ds = 0) linearly increases as the estimation error increases since the mismatched nodes in the second SG increase and then successive RAs are attempted until the number of RA trials reaches Q. These mismatched nodes end up with RA failures in the second SG. However, the groupreselection solution of the enhanced SGRA prevents these mismatched nodes from RA failures although their collision probabilities are slightly increased. Fig. 6 shows the effect of distance estimation error on the collision probability only with the shared distance solution for various shared distances. The shared distance ds can cover the half of the estimation error, σe . In other words, the collision probability of ds = 0.08 km is constant until σe reaches 0.04 km and linearly increases after σe = 0.04 km.

4

N = 11, N = 05, N = 04, N = 03, Group 1 Group 2

3.5

SIM, Conventional SGRA SIM, Enhanced SGRA SIM, Enhanced SGRA SIM, Ehhanced SGRA Analysis Analysis

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km, km, km, km,

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= 11, = 03, = 11, = 03,

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2, 2, 2, 2,

Conventional SGRA Enhanced SGRA Enhanced SGRA Enhanced SGRA

3

2.5

2

1.5

0

0.02

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0.1

Fig. 7. Effect of distance estimation error on collision probability for various N and ds . TABLE II ACCEPTABLE NUMBER OF SMART METERS WITH DIFFERENT TARGET COLLISION PROBABILITIES AND GROUP - MISMATCH SOLUTIONS WHEN σe = 0.1 km.

4 Conventional SGRA Enhanced SGRA Enhanced SGRA Enhanced SGRA

3.5

= 0.00 = 0.00 = 0.08 = 0.08

Standard deviation of estimation error, σe [km]

Fig. 5. Effect of distance estimation error on collision probability only with the group-reselection solutions.

ds = 0.00 km, SIM, ds = 0.02 km, SIM, ds = 0.04 km, SIM, ds = 0.08 km, SIM, Group 1, Analysis Group 2, Analysis

ds ds ds ds

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3

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0.1 %

1%

3%

The conventional SGRA ds = 0.00 km, N = 03 ds = 0.08 km, N = 11 ds = 0.08 km, N = 03

900 1,400 1,400 1,600

8,600 13,500 13,100 15,500

25,600 40,000 38,700 45,800

2

1.5

0

0.02

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Standard deviation of estimation error, σe [km]

Fig. 6. Effect of distance estimation error on collision probability only with the shared distance solutions.

The combination of both the group-reselection and the shared distance solutions of the enhanced SGRA makes the conventional SGRA scheme more robust against the distance estimation error. Fig. 7 shows the collision probability when both solutions are employed. In the figure, a parameter set of N = 3 and ds = 0.08 km yields very low collision probability. This implies that the combined solution should be used to make the enhanced SGRA scheme more robust against the distance estimation error. In Fig. 8, the average RA delay of the first SG only with the group-reselection solution linearly increases as the estimation error increases since the mismatched nodes in the second SG increase and these increased mismatched nodes spend longer time during the first and the second RA procedures and then return back to the first own SG after N consecutive failures in RAR message reception. Thus, a larger N means spending more time in the mismatched SG. With fixed N = 3, Fig. 9 shows the effect of the shared distance ds on the average RA delay. The parameter set of N = 3 and ds = 0.08 km also yields very low average RA delay, which is almost constant until σe = 0.04 km. In Fig. 10, we fix N = 3 and σe = 0.1 km and vary the

shared distance ds from 0 km to 0.2 km in order to show the effect of shared distance on the performance. Until ds = 0.08 km, the performance improves but it is slightly degraded after ds = 0.08 km due to the fact that the number of available root preambles in the second SG NPA (d2 + ds ) is reduced with a longer group CD as d2 + ds . Note that it is very effective to choose the largest shared distance such that the number of preambles is not changed. Lastly, Table II shows the acceptable number of smart meters with different target collision probabilities and groupmismatch solutions when the period of metering report, 1/λ = 5 min [2]. For 3% collision probability, the enhanced SGRA scheme with ds = 0.08 km and N = 3 can accommodate 45,800 smart meters within a single cell with 2 km radius, while the conventional SGRA scheme without any solutions can accommodate 25,600 smart meters. Thus, our enhanced SGRA scheme has quite big improvement in terms of the number of accommodated machine nodes. This result implies that the enhanced SGRA scheme with group-mismatch solutions is enough to accommodate a large number of smart meters (e.g., 35,670) required in the urban London scenario [2] under even more realistic situations with imperfect distance estimation. VI. C ONCLUSION In this paper, we enhanced our previous SGRA scheme for future M2M communications based on two group-mismatch solutions. The proposed group-reselection and shared distance solutions make the SGRA scheme more robust against distance estimation errors and the combination of two proposed

48

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1, 1, 1, 2, 2, 2,

Enhanced Enhanced Enhanced Enhanced Enhanced Enhanced

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= 05, = 04, = 03, = 05, = 04, = 03,

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50 N N N N N N

47

20 0.2

Shared distance, ds [km]

Fig. 8. Effect of distance estimation error on average RA delay of the enhanced SGRA only with the group-reselection solutions.

Fig. 10. Effect of shared distance ds on collision probability and average RA delay of the enhanced SGRA for N = 3 and σe = 0.1 km.

43 ds ds ds ds ds ds ds ds

42.5

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42 41.5 41

= 0.00 = 0.02 = 0.04 = 0.08 = 0.00 = 0.02 = 0.04 = 0.08

km, km, km, km, km, km, km, km,

N N N N N N N N

= 03, = 03, = 03, = 03, = 03, = 03, = 03, = 03,

Group Group Group Group Group Group Group Group

1 1 1 1 2 2 2 2

Group 1

40.5 40 39.5 39 38.5 38

0

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Standard deviation of estimation error, σe [km]

Fig. 9. Effect of distance estimation error on average RA delay of the enhanced SGRA for various ds and N = 3.

solutions provides a significant robustness. As a result, the enhanced SGRA scheme can accommodate a significantly larger number of machine nodes with very lower collision probabilities and shorter average RA delay in more practical M2M deployment environments. VII. ACKNOWLEDGMENT This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005192). R EFERENCES [1] P. Vlacheas, R. Giaffreda, V. Stavroulaki, D. Kelaidonis, V. Foteinos, G. Poulios, P. Demestichas, A. Somov, A. Biswas, and K. Moessner, “Enabling smart cities through a cognitive management framework for the internet of things,” IEEE Commun. Mag., vol. 51, no. 6, pp. 102–111, June 2013. [2] Study on RAN improvements for machine-type communications, 3GPP TR 37.868 V11.0.0, Sept. 2011. [3] K. S. Ko, M. J. Kim, K. Y. Bae, D. K. Sung, J. H. Kim, and J. Y. Ahn, “A novel random access for fixed-location machine-to-machine communications in OFDMA based systems,” IEEE Commun. Lett., vol. 16, no. 9, pp. 1428–1431, Sept. 2012.

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