Message-Embedded Random Access for Cellular

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Message-Embedded Random Access for Cellular M2M Communications Han Seung Jang, Su Min Kim, Hong-Shik Park, and Dan Keun Sung

Abstract—In this letter, we propose a message-embedded random access (MERA) scheme to simultaneously transmit both preambles (PAs) and messages (MSGs) as MSG-embedded PAs based on auto- and cross-correlation properties of Zadoff-Chu sequences using distinct root numbers. The proposed MERA scheme enables machine nodes to transmit small-sized data during a PA transmission on control channel (i.e., PRACH) without using any scheduling mechanism and resources on data channel (i.e., PUSCH). The performance of the proposed MERA scheme is mathematically analyzed and evaluated through simulations in terms of PA detection probability, MSG decoding probability, and the throughput of MSG transmissions on PRACH. Index Terms—Message, random access, preamble, M2M, Zadoff-Chu sequence, LTE.

I. I NTRODUCTION

M

ACHINE-to-machine (M2M) communications in cellular networks have been actively studied for a future infrastructure of Internet of Things (IoT) and smart cities supporting a wide range of M2M applications such as ehealth care, public safety, surveillance, remote maintenance and control, and smart metering [1]. One of significant features of M2M communications is that a massive number of machine nodes may transmit small-sized data, for example, one byte information for status report and emergency alarm [2]. Another feature is that a large number of machine nodes generally stay out of connections to save energy consumption after data transmission, which makes the initial random access (RA) procedure more important in M2M communications. In general, the RA procedure [3] is used for an uplink synchronization, a hand-off, or a scheduling request. A few studies dealt with incorporating small-sized data transmissions into the RA procedure. Wiriaatmadja and Choi [4] proposed a hybrid RA and data transmission protocol, which allows machine nodes to transmit data on physical uplink shared channel (PUSCH) right after a preamble (PA) transmission on physical RA channel (PRACH) to reduce signaling overhead. Andreev et al. [5] proposed a contentionbased data transmission scheme, which sends small-sized data packets not on a control channel or PRACH but directly on PUSCH. However, both studies have a limitation which requires extra resources for data transmissions on PUSCHs.

Zhou et al. [6] proposed an implicit message (MSG) transmission scheme in IEEE 802.16d/e by utilizing a cyclic shift mechanism of Zadoff-Chu (ZC) sequence [7] where the shift size indicates the MSG information, similarly to our proposed scheme in this letter. However, this scheme exploits extra resources on a shared RACH reserved for data transmission in order to transmit an MSG ZC sequence. In this letter, we propose an MSG-embedded RA (MERA) scheme where nodes transmit MSG-embedded PAs on PRACH and then the eNodeB decodes MSG bits at the first step of RA procedure based on auto- and cross-correlation properties of ZC sequences using distinct root numbers. Since the proposed MERA scheme does not require any scheduling mechanism and extra resources on PUSCHs but only utilizes PRACH, it is significantly effective to reduce control and signalling overheads and to save radio resource on PUSCH. The proposed MERA scheme can achieve data throughput on PRACH which is typically used for control purpose, while the conventional RA schemes in [4]–[6] do not achieve any data throughput on PRACH. Therefore, the proposed MERA scheme can be utilized for connection-less short data transmission such as a low-latency report or alarm MSG at the first step of RA procedure for M2M applications. II. BACKGROUND AND SYSTEM MODEL A. Conventional preamble In LTE system, ZC sequences are used to generate PAs defined as zr [n] , exp[−jπrn(n + 1)/NZC ] for n = 0, . . . , NZC − 1, where NZC denotes the sequence length and r ∈ {1, . . . , (NZC − 1)} is the root number [7]. The ZC sequences have a cyclic auto-correlation property as √ |crr [τ ]| = NZC δ[τ ] for the sequence zr [n] at lag τ , and a cyclic cross-correlation property, where the magnitude of correlation between any two ZC sequences using different root numbers, r and k, is constant, i.e., |crk [τ ]| = 1. The sequence shifted by iNCS is the i-th PA expressed as zr,i [n] = zr [(n + iNCS ) mod NZC ], i ∈ {0, . . . , (bNZC /NCS c − 1)}, where NCS denotes the cyclic shift size. In the current LTE system, an eNodeB serves UEs with fixed 64 PAs, and the number of available root numbers is (NZC − 1) = 838 in a single cell. More details are found in [8]. B. Proposed message-embedded preamble

H. S. Jang, H.-S Park, and D. K. Sung are with the School of Electrical Engineering, KAIST, Daejeon, Korea (e-mail: {jhans, park1507, dksung}@kaist.ac.kr). S. M. Kim is with the Dept. of Electronics Engineering, Korea Polytechnic University, Siheung, Korea (e-mail: [email protected]).

Based on the cross-correlation property of the ZC sequences, we propose an MSG-embedded PA defined as Xr0 ,R [n] , β(pr0 ,i0 [n] + qR,I [n]),

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Preamble index

Blocks for message indices

0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 ... 0 1 1 0 0 0 1 1 1 log2NPA bits 1st log2NZC bits block for preamble index i0 for message index i1

J-th log2NZC bits block for message index iJ

Fig. 1. An example of bit-map for a message when blog2 NPA c = 6 bits and blog2 NZC c = 9 bits

where β denotes the signal strength of the MSG-embedded PA, and pr0 ,i0 [n] is a PA sequence given by pr0 ,i0 [n] = zr [(n + i0 NCS ) mod NZC ], n = 0, . . . , (NZC − 1), where r0 is the PA root number, i0 ∈ {0, . . . , (2blog2 NPA c − 1)} is the PA index, NPA is the number of available PAs, and qR,I [n] is an MSG PJ PJ sequence given by qR,I [n] = j=1 qrj ,ij [n] = j=1 zrj [(n+ i0 NCS + ij ) mod NZC ], n = 0, . . . , (NZC − 1) with the set of MSG root numbers R = {r1 , . . . , rJ } and the set of MSG indices I = {i1 , . . . , iJ }, where rj denotes the j-th MSG root number, ij ∈ {0, . . . , (2blog2 NZC c − 1)} denotes the j-th MSG index, and J denotes the total number of MSG indices. Here, rj is determined by the j-th MSG root function of the PA index i0 , i.e., rj = fj (i0 ). In other words, the PA index i0 is mapped to J MSG root numbers, which are exclusive of the PA root number r0 (i.e., rj 6= r0 , ∀j ∈ {1, . . . , J}), based on a set of MSG root functions, F(i0 ) = {f1 (i0 ) = r1 , . . . , fJ (i0 ) = rJ }. In addition, qrj ,ij [n] is cyclically shifted from zrj [n] by (i0 NCS + ij ), which is the sum of the PA shift i0 NCS and the MSG shift ij . Combinations of i0 and I can deliver blog2 NPA c + Jblog2 NZC c bits of information. Fig. 1 shows an example of MSG bit-map divided into two fields: the first blog2 NPA c bits determining i0 and J blocks of blog2 NZC c bits determining I = {i1 , . . . , iJ }. C. System model We assume that M nodes listed in a set of nodes M = {1, . . . , M } simultaneously transmit MSG-embedded PAs on the same PRACH. The m-th node in M has (blog2 NPA c + Jblog2 NZC c) bits data to transmit, which determines a PA m m index im = {im 0 and a set of MSG indices I 1 , . . . , iJ }. A common PA root number r0 is utilized for all nodes’ PA sequences, and a set of MSG root numbers Rm = {r1m , . . . , rJm } are exclusively utilized based on the F(im 0 ) for the m-th node’s MSG sequences. The MSG-embedded PA of the mth node is defined as
Xr0 ,Rm [n] , β m pr0 ,im [n] + qRm ,I m [n] . 0 For every m ∈ M, let us define a set of transmitted PA indices as I0 = {i10 , . . . , iM 0 }, a super set of transmitted MSG indices as I = {I 1 , . . . , I M }, and a super set of used MSG root numbers as R = {R1 , . . . , RM }. The received sequence at the eNodeB is expressed as Yr0 ,R [n] =

M X Lm X m=1 l=0

m hm l Xr0 ,Rm [(n + tl ) mod NZC ] + W [n],

m m where hm denote the channel coefficient, the l , tl , and L propagation delay of the l-th multipath, and the number of multipaths for the m-th node, and W [n] represents the complex Gaussian noise with zero mean and variance σ 2 , i.e., W [n] = WR [n] + jWI [n] ∼ CN (0, σ 2 ). Note that every superscript represents the node index and all 0 subscripts represent the PA related variables throughout this letter.

III. T HE PROPOSED MERA SCHEME A. Procedure of the proposed MERA scheme Fig. 2 shows the overall procedure of the proposed MERA scheme, which consists of three phases (circled numbers). • (Phase 1) The m-th node has (blog2 NPA c + Jblog2 NZC c) bits data to transmit, which determine im 0 , Rm , and I m . Then, the m-th node transmits the MSGembedded PA Xr0 ,Rm [n] on PRACH. Note that all nodes in M use the common PA root number r0 in order to transmit their PA sequences, while the m-th node uses an exclusive set of MSG root numbers Rm = F(im 0 ) m determined by its PA index i0 in order to transmit the MSG sequence qRm ,I m [n]. • (Phase 2) At the eNodeB, the transmitted PAs are detected. To detect each of PA indices in I0 , the eNodeB computes the correlation value |c{r0 ,R},r0 [τ ]| between the received sequence Yr0 ,R [n] and the PA reference sequence zr0 [n] and verifies each PA detection zone Di0 for i0 ∈ [0, (NPA − 1)]. If the correlation value exceeds the PA detection threshold γpa on Di0 , the eNodeB detects the i0 -th PA and stores the detected position as Ωi0 into a set of detected PA positions, Ωpa . After completing the PA detection procedure, we obtain a set 0 of detected PA indices I00 = {i10 , . . . , iM 0 } ⊂ I0 and a set 0 of detected PA positions, Ωpa = {Ω1i0 , . . . , ΩM i0 }, where M 0 (≤ M ) is the total number of detected PAs. Then, based on F(I00 ), the eNodeB decodes the super set of 0 MSG root numbers R 0 = {R1 , . . . , RM } ⊂ R, where m m m m Rm = F(im 0 ) = {r1 = f1 (i0 ), . . . , rJ = fJ (i0 )}. • (Phase 3) The eNodeB again calculates the correlation value |c{r0 ,R},rjm [τ ]| between Yr0 ,R [n] and the MSG reference sequence zrjm [n] generated by the j-th decoded MSG root number rjm in Rm in order to detect the jth MSG of the m-th node. If the peak correlation value exceeds the MSG detection threshold γmsg at one out of NZC samples, its position is stored as Ωm ij in the set of detected MSG positions for the m-th node, Ωm msg . After correlation calculation of all J MSGs for the m-th node, m m Ωm msg = {Ωi1 , . . . , ΩiJ } is completely obtained. Then, m m the MSG index ij is determined from Ωm ij ∈ Ωmsg and m Ωi0 ∈ Ωpa forj = 1, . . . , J, as follows: m m m if Ωm i j ≥ Ωi 0 im = Ωij − Ωi0 j

m m NZC − Ωm if Ωm i0 + Ω ij i j < Ωi 0 This MSG detection procedure is repeatedly performed for all M 0 nodes and their all J MSG indices. Throughout

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Correlation value i0-th PA

Message bits 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1

i0

i1 ䷵ Xr0,r1[n] 䢿 pr0,i0 [n]䢭 qr1,i1[n]

Fig. 2.

P R A C H

detection zone

r0

f1(i0) 䢿 r1 Root number

γpa

䢢䷶

䷷䢢

Ωi0

i1 Ωi1  Ωi0

Ω i1

PA sequence

γmsg

MSG sequence



Overall procedure of the proposed MERA scheme (e.g., J = 1).

JM 0 correlation calculations1 , the super set of detected 0 MSG indices I 0 = {I 1 , . . . , I M } is obtained and all MSG bits of M are decodable from I00 and I 0 . To notify the successful MSG receptions, the eNodeB includes acknowledgments in the RA response (RAR) MSG at the second step of RA procedure. When more than one node transmit an identical PA, a PA collision can be detected based on the MSG detection procedure. In this case, it is not necessary to transmit the corresponding RAR MSG in order to prevent resource waste at the third step of RA procedure. B. Analysis of PA detection and MSG decoding probabilities For simplicity, we assume that J = 1 and the MSGembedded PA of each node suffers from only a single path, m i.e., hm 0 = 1 at t0 . In addition, all nodes in M choose distinct PA indices. Hence, the received sequence is given by XM Yr0 ,R [n] = Xr0 ,r1m [(n + tm 0 ) mod NZC ] + W [n]. m=1

Firstly, each PA index in I0 = {i10 , . . . , iM 0 } is detectable by computing the correlation value |c{r0 ,R},r0 [τ ]| as PNZC −1 |c{r0 ,R},r0 [τ ]| = √N1 Yr0 ,R [n]zr∗0 [n + τ ] n=0 ZC PM = m=1 (cm r0 ,r0 [τ ] + cr1m ,r0 [τ ]) + W [τ ] , where cm r0 ,r0 [τ ] and cr1m ,r0 [τ ] are derived, respectively, as PNZC −1 m ∗ cm [τ ] = √N1 β pr0 ,im [n + tm r0 ,r0 0 ]zr0 [n + τ ] and n=0 0 ZC P NZC −1 m ∗ cr1m ,r0 [τ ] = √N1 β qr1m ,im [n + tm 0 ]zr0 [n + τ ], n=0 1 ZC and (·)∗ denotes the complex conjugate. Then, each of PA detection zones is verified. In the im consisting of NCS 0 -th PA detection zone Dim 0 m + 1)N samples (i.e., τ ∈ [im N , (i CS CS − 1]), we denote 0 0 the peak instant for the PA sequence of the m-th node, m m m τ = {(im 0 NCS + t0 ) mod NZC }, as Ωi0 . Then, at τ = Ωi0 , q c{r ,R},r [Ωm (θim0 cos α + WR )2 + (θim0 sin α + WI )2 i0 ] = 0 0 m becomes a Rician random variable (RV) Gm i0 ∼ Rice(θi0 , σ) [9] whose probability density function (PDF) is given by  2 m 2  gθm  g +(θ ) i0 g m I exp − 2σ2i0 , fGm (g; θ , σ) = i0 σ2 0 σ2 i 0

1 The additional number of computations of the proposed MERA scheme is JM 0 , compared with that of the conventional RA scheme. However, in practice, the additional computational complexity is not significant since M 0 , is relatively small (e.g., 1 ∼ 5) and the practical J would be 1 or 2.

√ PM m = where θim0 = | NZC β m + k=1 cr1k ,r0 [Ωi0 ]|, α √ P M −1 m m m cos {Re( NZC β + k=1 cr1k ,r0 [Ωi0 ])/θi0 }, and I0 (·) is the modified Bessel function of the first kind with the zerom th order. At any other instants τ 6= Ωi0 , c{r0 ,R},r0 [τ ] bem [τ ] ∼ Rice(ρm comes a Rician RV Vim i0 [τ ], σ) where ρi0 [τ ] = 0 PM | k=1 cr1k ,r0 [τ ]|. Let us define the maximum noise RV Zim0 , m m , whose cumulative max{Vim [τ ] | ∀τ = 6 Ω } in D i i 0 0 0 distribution function (CDF) is given by n  ρm [τ ] o Q i0 z Pr[Zim0 ≤ z; ρm , σ] = 1 − Q m 1 i0 τ 6=Ω σ , σ i0

ρm i0

[ρm i0 [τ ]

where = | ∀τ 6= Ωm i0 ] and Q1 (a, b) denotes the Marcum-Q function. When Gm i0 is greater than or equal to m m γpa and greater than Zi0 , i0 is correctly detected in Dim . 0 Hence, the PA detection probability for im 0 is defined as m m m m Pim (γpa , ρm i0 , θi0 ) , Pr[Gi0 ≥ γpa , Gi0 > Zi0 ] 0 R∞ m m = γpa Pr[Zim0 < g; ρm (1) i0 , σ]fGi0 (g; θi0 , σ)dg.  1  Employing a probability vector Pi0 = Pi0 , . . . , PiM , the 0 eNodeB can detect each PA index in I0 and decode each MSG root number in R = {r11 , . . . , r1M } based on f1 (I0 ). As 0 a result, the set of detected PA indices I00 = {i10 , . . . , iM 0 }, the super set of decoded MSG root numbers R 0 = {r11 = 0 0 f1 (i10 ), . . . , r1M = f1 (iM 0 )}, and the set of detected node 0 indices M0 = {m|im 0 ∈ I0 } are finally obtained. The eNodeB again calculates the correlation value between Yr0 ,R [n] and each of the MSG reference sequences {zr11 [n], . . . , zrM 0 [n]} generated from R 0 . The correlation 1 value |c{r0 ,R},r1k [τ ]| between Yr0 ,R [n] and zr1k [n] is given by PNZC −1 Yr0 ,R [n]zr∗k [n + τ ] |c{r0 ,R},r1k [τ ]| = √N1 n=0 ZC 1 PM = m=1 (cm [τ ] + c [τ m k k r1 ,r1 ]) + W [τ ] . r0 ,r 1

r1k

r1m ,

When = in the MSG detection zone consisting of NZC samples, the peak instant for the first MSG sequence m m of the m-th node, τ = {(im 0 NCS + i1 + t0 ) mod NZC }, is m m denoted as Ωi1 . Then, at τ = Ωi1 , |c{r0 ,R},r1m [Ωm i1 ]| becomes √ m m a Rician RV Gm ∼ Rice(θ , σ) where θ = | NZC β m + i1 i1 i1 PM u P M m m u m u=1 cr0 ,r1m [Ωi1 ] + u=1,r1u 6=r1m cr1 ,r1 [Ωi1 ]|. At any other m instants τ 6= Ωi1 , |c{r0 ,R},r1m [τ ]| becomes a Rician RV PM u m Vim [τ ] ∼ Rice(ρm i1 [τ ], σ) where ρi1 [τ ] = | u=1 cr0 ,r1m [τ ] + 1 PM u m u=1,r u 6=r m cr1 ,r1 [τ ]|. 1

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TABLE I S IMULATION PARAMETERS AND VALUES Parameters Values 64, 16 839 1, 2 −20, −16 −24, −20, −16 −20 ∼ −10 1, 2, 6, 10

, Let us define the maximum noise RV Zim1 m } whose CDF is given by [τ ] | ∀τ = 6 Ω max{Vim i1 1 n  ρm [τ ] o Q i1 z 1 − Q Pr[Zim1 ≤ z; ρm m 1 i1 , σ] = τ 6=Ω σ , σ i1

m m m where ρm i1 = [ρi1 [τ ] | ∀τ 6= Ωi1 ]. The MSG index i1 can be correctly detected based on the difference between the two m peak instants of PA and MSG sequences (i.e., |Ωm i1 − Ωi0 |) m when Gi1 is greater than or equal to γmsg and greater than Zim1 . The MSG detection probability for im 1 is defined as m m m m Pim (γmsg , ρm i1 , θi1 ) , Pr[Gi1 ≥ γmsg , Gi1 > Zi1 ] 1 R∞ m m = γmsg Pr[Zim1 < g; ρm i1 , σ]fGi (g; θi1 , σ)dg. (2) 1

0

Throughout M correlation calculations, we can detect each 0 of the first MSG indices in the super set I 0 = {im 1 |m ∈ M } 1 M m with probability vector Pi1 = [Pi1 , . . . , Pi1 ], where Pi1 = 0 for m 6∈ M0 . From I00 and I 0 , the set of the MSG bits sent by M can be decoded with the MSG decoding probabilities P = Pi0 ◦Pi1 , [Pi10 Pi11 , . . . , PiM PiM ], where a◦b represents 0 1 the element-wise product between two vectors. C. Throughput analysis We define the throughput as the number of transmitted MSG bits on a single PRACH. The probability that a single node selects an exclusive PA is derived by ps = (1 − 1/NPA )(M −1) where M and NPA denote the number of RA-attempting nodes per PRACH and the number of available PAs, respectively. Based on the average number of nodes transmitting exclusive PAs, M = dps M e, the throughput is derived
PM M m (M −m) as T = mNbits (J) where m=1 m (P ) (1 − P ) J P = Pi0 (Pi1 ) denotes the MSG decoding probability, J denotes the number of MSG indices per node, and Nbits (J) = blog2 NPA c + Jblog2 NZC c. IV. P ERFORMANCE E VALUATION We evaluate the performance of the proposed MERA scheme in terms of the PA detection and MSG decoding probabilities, and the MSG throughput on PRACH. The simulation parameters are listed in Table I. For M = 1, we set r0 = 1, i0 = 10, i1 = 10, and r1 = f1 (i0 ) = 100 + i0 = 110. Fig. 3 shows the PA detection and MSG decoding probabilities as the SNR increases. It is shown that both simulation and analysis results agree well. The MSG decoding probabilities are lower than the PA detection probabilities since the MSG decoding

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Probability [%]

Number of preambles, NPA Length of ZC sequence, NZC Number of message indices, J PA detection threshold, γpa (dB) MSG detection threshold, γmsg (dB) Signal-to-noise ratio (SNR), β (dB) Number of RA nodes per PRACH, M

100

70 60 50 40

◦ γpa = −16 ◦ γmsg,1 = −20 ◦ γmsg,2 = −16

◦ γpa = −20 ◦ γmsg,1 = −24 ◦ γmsg,2 = −20

PA detection (Sim) on γpa PA detection (Anal) on γpa MSG decoding (Sim) on γmsg,1 MSG decoding (Anal) on γmsg,1 MSG decoding (Sim) on γmsg,2 MSG decoding (Anal) on γmsg,2

30 20 10 0 -20

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SNR [dB]

Fig. 3. PA detection and MSG decoding probabilities with different PA and MSG detection thresholds.

probabilities depend on both the PA i0 and the MSG i1 . When γpa > γmsg , the similar performance is achieved between the PA detection and the MSG decoding at high SNR region. In case of multiple nodes2 (M > 1), different setups of M , I0 , and I may yield different results. For experiments, we randomly choose I0 and I 1000 times for varying M . Fig. 4 shows the average PA detection and MSG decoding probabilities of the first node for varying M values. In those setups, the average PA detection and MSG decoding probabilities show the similar values, respectively, as M increases. It implies that the different combinations of I0 and I with various M values do not significantly affect both probabilities, and the average PA detection probability of the proposed MERA scheme is similar to that of the conventional RA scheme, which proves the feasibility of the proposed MERA scheme. Fig. 5 shows the throughput of the proposed MERA scheme with the fixed MSG decoding probability of 0.96. The throughput increases until M increases to NPA , and then it decreases due to severe PA collisions, while the conventional RA schemes in [4]–[6] do not achieve any data throughput on PRACH. However, since the practical number of M 3 would be less than 20 due to the MSG decoding performance, the number of MSG transmissions achieved per minute would be approximately 120,000 for 10 ms of a PRACH period (100 PRACHs/sec). Since the proposed MERA scheme operates at the first and second steps of RA procedure and only uses a given PRACH 2 The additional MSG sequences may degrade the PA detection performance since the ZC sequences with distinct root numbers have a certain crosscorrelation value. This is an expense for sending additional MSG bits in the proposed MERA scheme. This negative effect is examined in Fig. 4. 3 Assuming 50,000 nodes with RA-attempting rates of 1 and 2 (attempts/min), the corresponding M values become approximately 9 and 17.

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on PRACHs without using any scheduling mechanism and resources on PUSCHs. The results show that the PA detection performance of the proposed scheme is similar to that of the conventional RA scheme, although the proposed scheme can send additional MSG bits. It can be further utilized for future connection-less data transmission in cellular M2M networks.

PA Detection [%]

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M M M M M

60 40 20 0 -20

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= 10, = 06, = 02, = 01, = 01,

MERA MERA MERA MERA CONV

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MERA MERA MERA MERA

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Fig. 4. Average PA detection and MSG decoding probabilities for varying M when γpa = −16 dB and γmsg = −20 dB.

Throughput per PRACH [bits]

600

500

NPA = 64 400

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Proposed MERA, J = 2 (Sim) Proposed MERA, J = 2 (Anal) Proposed MERA, J = 1 (Sim) Proposed MERA, J = 1 (Anal) Conventional schemes in [4]-[6]

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Fig. 5.

Throughput per PRACH for varying M , J, and NPA .

in order to transmit MSG bits, a single node can save at least 3 RBs (2 RBs for the third step and 1 RB for data transmission), compared with the conventional RA scheme. For example, assuming 5 RA-attempting nodes per PRACH (10 ms period) on average, 1500 RBs are saved per second. V. C ONCLUSION In this letter, we proposed an MSG-embedded RA scheme where nodes transmit MSG-embedded PAs, and then the eNodeB decodes MSG bits at the first step of RA procedure. It enables a small-sized data transmission within a very short time period (less than 5 ms) during a PA transmission

[1] Service Requirements for Machine-Type Communications, 3GPP TS 22.368 V13.1.0, Dec. 2014. [2] Study on RAN Improvements for Machine-type Communications, 3GPP TR 37.868 V11.0.0, Sept. 2011. [3] Medium access control (MAC) protocol specification, 3GPP TS 36.321 V11.3.0, June 2013. [4] D. T. Wiriaatmadja and K. Choi, “Hybrid random access and data transmission protocol for machine-to-machine communications in cellular networks,” IEEE Trans. Wirel. Commun., vol. 14, no. 1, pp. 33–46, Jan. 2015. [5] S. Andreev, A. Larmo, M. Gerasimenko, V. Petrov, O. Galinina, T. Tirronen, J. Torsner, and Y. Koucheryavy, “Efficient small data access for machine-type communications in LTE,” in Proc. ICC, June 2013. [6] P. Zhou, H. Hu, H. Wang, and H.-H Chen, “An efficient random access scheme for OFDMA systems with implicit message transmission,” IEEE Trans. Wirel. Commun., vol. 7, no. 7, pp. 2790 – 2797, July 2008. [7] D. Chu, “Polyphase codes with good periodic correlation properties,” IEEE Trans. Inf. Theory, vol. 18, no. 4, pp. 531 – 532, July 1972. [8] H. S. Jang, S. M. Kim, K. S. Ko, J. Cha and D. K. Sung, “Spatial group based random access for M2M communications,” IEEE Commun. Lett., vol. 18, no. 6, pp. 961–964, June 2014. [9] S. O. Rice, “Mathematical analysis of random noise,” The Bell System Technical Journal, vol. 24, no. 1, pp. 46–156, January 1945.