Random Access for Cellular M2M Communications. Han Seung ... scheme. Index TermsâM2M, random access, spatial group, preamble, .... in LTE system. If Nr.
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A Non-Orthogonal Resource Allocation Scheme in Spatial Group Based Random Access for Cellular M2M Communications Han Seung Jang, Student Member, IEEE, Hong-Shik Park, Member, IEEE, and Dan Keun Sung, Fellow, IEEE
Abstract—Cellular machine-to-machine (M2M) communication can be one of major candidate technologies to develop an Internet of Things (IoT) platform. A massive number of machine nodes access the cellular networks and typically send/receive small-sized data. In this situation, severe random access (RA) overload and radio resource shortage problems may occur if there is no evolution in the conventional cellular system. Focusing on RA, we need a larger number of preambles as well as a more efficient resource allocation scheme in order to accommodate a significantly large number of RA requests from machine nodes. In this paper, we propose a non-orthogonal resource allocation (NORA) scheme combined with our spatial group based RA (SGRA) mechanism in order to provide a sufficiently large number of preambles at the first step of RA procedure and nonorthogonally allocate physical uplink shared channel (PUSCH) resources at the second step of RA procedure. As a result, the proposed SGRA-NORA scheme can significantly increase the RA success probability, compared with that of the conventional RA scheme. Index Terms—M2M, random access, spatial group, preamble, non-orthogonal resource allocation.
I. I NTRODUCTION ELLULAR machine-to-machine (M2M) communication has attracted great attention as one of major candidate technologies to develop an Internet of Things (IoT) platform, in which a massive number of machine (sensor/device) nodes communicate with the network or each other for a wide range of IoT or M2M applications such as e-health, public safety, surveillance, remote maintenance and control, and smart metering [1]. A network connection of each machine node is initiated through a random access (RA) procedure [2]. At the first step of RA procedure, a number of machine nodes access the eNodeB based on contention using given limited RA preambles on physical RA channels (PRACH), which may result in a significant preamble (PA) collision problem. Then, at the second step of RA procedure, the eNodeB should allocate physical uplink shared channel (PUSCH) resource blocks (RBs) to each of machine nodes for its RA-step 3 data transmission. Since PUSCH resources are mainly utilized for uplink user data transmission, in general, a small amount of PUSCH resources are reserved for the RA procedure. At this time, some of machine nodes may fail to receive the RB allocation due to lack of PUSCH resources, and if so, they reattempt RAs and spend extra time in the RA procedure, which causes much severer RA congestion. Therefore, both of an efficient RA overload control scheme [3]–[7] and an
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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).
efficient resource allocation scheme [8], [9] are required for the cellular M2M communications. We previously proposed a spatial group based RA (SGRA) scheme to effectively increase the number of available PAs [6]. Even though the SGRA scheme is very effective to reduce the PA collision probability at the first step of RA procedure, it cannot resolve a resource allocation problem at the second step of RA procedure when the available PUSCH resources are limited. Wiriaatmadja and Choi [10] proposed a joint adaptive resource allocation and access barring scheme to maximize RA throughput and resolve RA congestion problem with a detailed mathematical analysis for all four steps in the RA procedure. According to [10], even though a large number of nodes successfully transmit their PAs at the first step of RA procedure, a much severer bottleneck of RA may occur at the second step of RA procedure due to lack of PUSCH resources for RA procedure. Hence, a more efficient resource allocation scheme is required in the RA procedure. In this paper, we propose a non-orthogonal resource allocation (NORA) scheme combined with our previously proposed SGRA mechanism to resolve both a PA shortage problem at the first step of RA procedure and a PUSCH shortage problem at the second step of RA procedure together for a large number of RA-attempting nodes. The main idea is to allocate the same PUSCH RBs for RA-step 3 data transmission to a subgroup of machine nodes belonging to distinct spatial groups, and then to decode multiple received RA-step 3 data by using a successive interference cancelation (SIC) scheme. As a result, the proposed SGRA-NORA scheme effectively utilizes both PRACH and PUSCH and achieves significantly higher RA success probabilities even with a small number of RBs reserved for M2M communications, compared with those of the conventional RA scheme. II. BACKGROUND AND S YSTEM MODEL A. Spatial Group Based Random Access (SGRA) At the first step of RA procedure, machine nodes transmit PAs as their signatures since they are not connected with the network [11]. To generate these PAs, Zadoff-Chu (ZC) sequences are used, and they are expressed as zr [n] , exp[−jπrn(n + 1)/NZC ] for n = 0, . . . , NZC − 1, where NZC is the sequence length and r ∈ {1, . . . , NZC − 1} is the root index [12]. In principle, multiple PAs can be generated from a single ZC sequence by cyclically shifting the sequence by a factor of cyclic shift size, NCS [11]. NCS is specified as a function of cell radius d (km), NCS (d) , d(20d/3 + τds ) × (NZC /TSEQ )e + ng , where τds , TSEQ , and ng denote the maximum delay spread (µs), the duration (µs)
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Fig. 1.
A cell model of the spatial group based random access.
of ZC sequence, and the number of additional guard samples. The number of available PAs per root index r is specified as r NPA (d) , bNZC /NCS (d)c. Conventionally, an eNodeB serves conv conv UEs with fixed NPA PAs in a single cell, e.g., NPA = 64 r conv in LTE system. If NPA (d) < NPA , the cell needs to use conv multiple root indices in order to provide NPA PAs. We define conv r K , dNPA /NPA (d)e as the required number of root indices conv for generating fixed NPA PAs when the cell radius is d. K also corresponds to the total number of spatial groups (SGs) in the cell. Fig. 1 illustrates a cell model of the SGRA. In this model, the entire cell area with radius d is spatially partitioned into multiple K SG regions since the cell uses total K root indices, {r1 , . . . , rK }. The k-th SG has its own group root index rk and its own group coverage distance (CD) dk determining the reduced size of group cyclic shift NCS (dk ) in rk order to exclusively generate NPA (dk ) = bNZC /NCS (dk )c PAs. The key idea to obtain additional PAs compared to PK rk conv conv , i.e., , comes from the fact NPA N (d ) ≥ N PA k=1 PA k rk rk that NPA (dk ) ≥ NPA (d) since NCS (dk ) ≤ NCS (d) for k = 1, . . . , K. When the eNodeB configures K SGs, it broadcasts the group parameters such as a set of group root indices, {r1 , . . . , rK }, and a set of group CDs, {d1 , . . . , dK }. Upon reception of 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. Then, a machine node in the k-th SG rk randomly selects a PA among NPA (dk ) PAs and transmits it on PRACH. In order to correctly detect the PAs with the reduced group cyclic shift sizes, we can utilize the shifted reference ZC sequences. There exist K shifted reference ZC sequences, Z = {zr1 [n + τB1 ], . . . , zrK [n + τBK ]}, and they are used to calculate the cyclic correlation values among the received PAs on the basis of each SG. τBk denotes the round-trip delay between the eNodeB and the inner boundary Pk−1 of the k-th SG region, i.e., τB1 = 0 and τBk = d(20× i=1 di /3)×(NZC /TSEQ )−0.5e, k = 2, . . . , K. Among all shifted reference ZC sequences in the set Z, only zrk [n + τBk ] has an auto-correlation property with the PAs transmitted from the k-th SG using the group root index rk . If the correlation value is greater than or equal to the PA detection threshold within the j-th PA detection zone, the j-th PA is detected. The more details on the SGRA scheme can be found in [6]. B. System model Based on the SGRA, the eNodeB can independently detect PAs utilized by the k-th spatial group SGk for k = 1, . . . , K. Let mk denote the number of detected PAs in SGk , and the total number of detected PAs in the cell is expressed as
PK M = k=1 mk . In addition, let tk,i denote the PA detection time instant of the i-th node in SGk . It indicates the roundtrip delay between the eNodeB and the i-th node, and is used to determine the timing alignment (TA) value [11]. From the results of PA detections, random access response (RAR) messages are delivered to the corresponding nodes at the second step of RA procedure. Here, the RAR message includes a PA identifier (PI), TA value, and uplink resource grant (URG) for the third step of RA procedure, at which nodes convey the RA-step 3 data including radio resource control (RRC) connection request, tracking area update, or scheduling request on the allocated PUSCH resource informed by the URG. Ωk,i = {PIk,i , TAk,i , URGk,i } represents the RAR message and its contents for the i-th node in SGk for k = 1, . . . , K and i = 1, . . . , mk . The i-th machine node in SGk transmits the RA-step 3 data with transmission power Pk,i on the allocated uplink RBs informed by URGk,i . The signal-to-noise ratio (SNR) of RA-step 3 data transmitted by the i-th node in −α SGk is calculated as SNRk,i = Hk,i Pk,i rk,i /N0 , where Hk,i , rk,i , α, and N0 are the channel coefficient, the distance from the eNodeB, the path loss coefficient, and the noise power, respectively. We assume that total Q RBs on PUSCH are reserved for M2M communications, and they are divided into U RBs and V RBs for PRACHs and the RA-step 3 channels (RA-S3CHs), respectively, i.e., Q = U + V . Since one PRACH requires 6 RBs and one RA-S3CH requires 2 RBs with QPSK modulation [11], the number of available PRACHs u and the number of available RA-S3CHs v are expressed as u = U/6 and v = V /2, respectively. III. T HE P ROPOSED N ON -O RTHOGONAL R ESOURCE A LLOCATION (NORA) S CHEME In the conventional RA scheme, the eNodeB orthogonally allocates RA-S3CHs to nodes, and then they transmit the RAstep 3 data on their exclusive RA-S3CHs. However, in the proposed SGRA-NORA scheme, the eNodeB allocates the same RA-S3CHs to multiple nodes based on a new node subgrouping method, and data decoding is performed by a SIC scheme. It is well known that the SIC scheme performs well under the condition when multiple received data on the same RB have different SNR conditions [13]. In this sense, multiple spatial groups in the SGRA are very attractive conditions for the NORA and the SIC scheme in terms of distinct SNR conditions. In this section, we describe the proposed SGRANORA scheme and analyze the RA success probability, which consists of the successful PA transmission probability and the successful RA-S3CH allocation probability. A. Proposed Non-orthogonal Resource Allocation (NORA) Scheme in the SGRA After the eNodeB detects PAs utilized by SGk , it sorts the TA values (unit: samples) of SGk in ascending order as TAk = {TAk,1 , . . . , TAk,mk } for k = 1, . . . , K. Fig. 2 shows an example of ordered TA sets for three SGs when m1 = 3, m2 = 4, and m3 = 5, where mk denotes the number of detected PAs utilized by SGk . According to the
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Fig. 2. An example of ordered TA sets for three (K) SGs when m1 = 3, m2 = 4, and m3 = 5.
ordered TA values of each SG, the eNodeB forms multiple subgroups which contain nodes belonging to distinct SGs. The subgrouping method for the proposed SGRA-NORA scheme is as follows. The subgrouping starts from the first SG, and, thus, the first node of SG1 searches for a node in SG2 such that |TA1,1 −TA2,i | ≥ δ1 , i = 1, . . . , m2 , where δ1 is the minimum TA threshold (unit: samples) for a sufficient SNR difference with respect to the SG1 . If a satisfactory node j is found in the SG2 , the first node of SG1 and the j-th node of SG2 forms a subgroup, and then the j-th node of the SG2 searches for a new node in SG3 such that |TA2,j − TA3,i | ≥ δ2 , i = 1, . . . , m3 , otherwise the first node of the SG1 searches for a node in SG3 such that |TA1,1 − TA3,i | ≥ δ1 , i = 1, . . . , m3 . This searching procedure is repeated until the last SGK . After all nodes in the SG1 belong to their own subgroup, unorganized nodes in the SG2 do the same procedure. This subgrouping procedure is repeated until all nodes in the last SGK belong to their own subgroup. The maximum number of members in a subgroup is K, which is the total number of SGs, and there may exist some nodes configuring a subgroup by itself since there are no such nodes that the above conditions hold. The minimum TA threshold of the SGk , δk , is calculated under the assumption that the transmission power of RA-step 3 data is set to Pref only when the nodes share the RA-S3CHs, and the edge node of the SGk is used for the threshold calculation. If we set the minimum SNR difference to x (dB) between the edge node of the SGk with channel coefficient Hk and another node with channel coefficient Hk0 , the minimum distance Pk gap is expressed as ηk = ( j=1 dj )(Hk0 /Hk )1/α 10x/(10α) − Pk Pk Pk ( j=1 dj ) ≈ ( j=1 dj )10x/(10α) − ( j=1 dj ). Here, we have an approximation of (Hk0 /Hk )1/α ≈ 1 in order to obtain an average value without consideration of the specific channel conditions. Consequently, the minimum TA threshold of the k-th SG is derived as δk = d(20ηk /3) × (NZC /TSEQ ) − 0.5e. For example, if we set x to 3 dB, δ1 and δ2 are calculated as 3 and 4 samples, respectively, with d1 = 2.02 km and d2 = 1.07 km, and five subgroups are configured as {TA1,1 , TA2,1 , TA3,1 }, {TA1,2 , TA2,2 , TA3,2 }, {TA1,3 , TA2,3 , TA3,3 }, {TA2,4 , TA3,4 }, and {TA3,5 } in the above example of Fig. 2. According to the configured subgroups, the eNodeB inserts the same URG for an RA-S3CH in each of RAR messages
for the nodes in the same subgroup. Upon reception of RAR messages, each node checks its own RAR message based on the corresponding PI and TA information, and also checks other RAR messages whether they include the same URG as its own. If there are any other RAR messages including the same URG, the node transmits its RA-step 3 data with the fixed transmission power Pref 1 at the third step of RA procedure. As a result, the nodes belonging to the same subgroup transmit their own RA-step 3 data on the same allocated RA-S3CH. Since the eNodeB exactly knows the number of simultaneous RA-step 3 data transmissions on each RA-S3CH, it can successfully decode multiple received RAstep 3 data through the SIC scheme2 . We can summarize the required additional functions for the actual implementation of the proposed SGRA-NORA scheme as (1) configuring subgroups for resource sharing, (2) the allocation of the same resource in RAR messages, and (3) SIC decoding. B. Performance Analysis We assume that the number of RA arrivals per PRACH follows a Poisson distribution. Let λk denote PK the average RA arrivals per PRACH in SGk and λtotal = k=1 λk denote the total average RA arrivals per PRACH in the cell. For the SGk , the successful PA transmission probability is derived as [6] rk ppa (k) = (1 − 1/NPA )
λk
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(1)
rk NPA
where represents the number of available PAs in the SGk . Let Ak denote the random variable for the number of RA arrivals in the SGk . The probability of n RA arrivals in the SGk is obtained as Pr[Ak = n] = (λk )n exp(−λk )/n!. In addition, the detection probability of a single PA when each of n nodes randomly selects one PA among NPA PAs is derived n as P (n, NPA ) = 1 − (1 − 1/NPA ) . The conventional SGRA-orthogonal resource allocation (ORA) scheme is to orthogonally allocate the maximum v RAS3CHs among all detected PAs in the cell. Thus, the successful RA-S3CH allocation probability in the conventional SGRAORA scheme is written as P∞ P∞ n QK pORA = · · · step3 nK =0 n1 =0 k=1 Pr[Ak = nk ] o . (2) × min 1, PK N rkvP (n ,N rk ) k=1
PA
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However, since multiple nodes from distinct SGs in the same subgroup can share the same RA-S3CH in the proposed SGRA-NORA scheme, the successful RA-S3CH allocation probability of the SGk is written as P∞ v (k) = Pr[A = n ] min 1, . pNORA r r k k k k step3 nk =0 N P (n ,N ) PA
k
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(3) 1 By exploiting TA values of the nodes in the same subgroup, the nodes may further control their transmission power. However, in this paper, we consider the simple case of fixed transmission power. In addition, by setting Pref to guarantee the sufficient SNR for cell edge nodes, we can resolve the unfairness problem in the proposed SGRA-NORA scheme. 2 A potential drawback of the proposed SGRA-NORA scheme may occur when the SNR differences among the multiple RA-step 3 data on the same uplink resource are insufficient or marginal. If the first RA-step 3 data may fail to be decoded due to insufficient SNR differences, the remaining data successively may fail to be decoded.
Parameters
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Total RA arrival rate per PRACH, λtotal Number of spatial groups, K Number of RBs on PUSCH for M2M, Q Group CDs, d1 , d2 , and d3 r1 r2 r3 NPA (d1 ), NPA (d2 ), and NPA (d3 ) conv M2M NPA and NPA in the conventional RA Minimum TA thresholds, δ1 and δ2
10 ∼ 30 3 (d = 4 km) 6 ∼ 74 2.02, 1.07, and 0.91 km 38, 52, and 59 64 and 20 3 and 4 samples
The RA success probability consists of both the successful PA transmission and RA-S3CH allocation probabilities. As a result, the RA success probability of the SGk in the SGRAORA scheme is expressed as follows: ORA pORA success (k) = ppa (k) × pstep3 .
(4)
The RA success probability of SGk in the proposed SGRANORA scheme is expressed as follows: NORA pNORA success (k) = ppa (k) × pstep3 (k).
(5)
The conventional RA scheme does not configure spatial groups and performs orthogonal resource allocations [11]. Accordingly, the RA success probability of the conventional conv λtotal × RA scheme is expressed as pCONV success = (1 − 1/NPA ) CONV pstep3 . Here, the successful RA-S3CH allocation probability in the conventional RA scheme is derived as P∞ v pCONV Pr[B = n] min 1, conv conv step3 = n=1 NPA ×P (n,NPA ) , (6) conv represent the random variable for the where B and NPA number of RA arrivals and the number of available PAs, respectively, in the conventional RA scheme. IV. P ERFORMANCE E VALUATION We evaluate the performance of the proposed SGRA-NORA scheme in terms of the successful PA transmission probability, the successful RA-S3CH allocation probability, and the RA success probability, compared with the SGRA-ORA scheme, the enhanced RA scheme proposed by Kim et.al [7], and the conventional RA scheme. Table I lists a set of simulation parameters. We assume that the set of all available PAs is separated into two subsets, where one for M2M communications and the other for human-to-human (H2H) communications, in order to avoid interference between both groups. In the M2M conventional RA scheme, M2M utilizes NPA PAs and H2H H2H conv M2M utilizes NPA = (NPA − NPA ) PAs. On the other hand, in PK rk (dk ) the proposed SGRA-NORA scheme, among k=1 NPA H2H PAs, NPA PAs are allocated to H2H and the remainders are allocated to M2M. Fig. 3 shows the successful PA transmission probabilities of the SGRA scheme, Kim’s RA scheme, and the conventional RA scheme. Here, the total RA arrival rate3 λtotal (RA arrivals/PRACH) varies, and Q is fixed to 20, which gives 3 Assuming 50,000 nodes in a cell with RA attempt rates of 1, 2, and 3 (attempts/minute/node), the corresponding λtotal values become approximately 9, 17, and 25, respectively, with 10 ms PRACH period.
100 90 80 70 60 50 40 SGRA (Sim.) SGRA (Anal.) Kim’s (Sim.) Kim’s (Anal.) Conventional (Sim.) Conventional (Anal.)
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Fig. 3. Successful preamble transmission probabilities with varying λtotal and the fixed Q = 20 (u = 1 and v = 7). Successful S3CH allocation propbability [%]
TABLE I S IMULATION PARAMETERS AND VALUES
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Fig. 4. Successful RA-S3CH allocation probabilities with varying λtotal and the fixed Q = 20 (u = 1 and v = 7).
1 (= u) PRACH and 7 (= v) RA-S3CHs. It represents a very scarce uplink resource environment. Since the SGRA scheme can utilize more PAs at the first step of RA procedure, the successful PA transmission probabilities of the SGRA-NORA and SGRA-ORA schemes are significantly higher than those of the conventional RA scheme. Kim’s RA scheme is based on a PA reuse method so that the number of available PAs logically increases. In a 4 km cell, four spatial groups are configured with distances 2.0 km, 0.83 km, 0.64 km, and 0.53 km, and each spatial group can logically utilize 21 PAs. Thus, Kim’s RA scheme shows a slightly lower result than that of the SGRA scheme. Fig. 4 shows the successful RA-S3CH allocation probabilities. As λtotal increases, the successful RA-S3CH allocation probability of the conventional RA scheme decreases to 45% for λtotal = 30, while the successful RA-S3CH allocation probability of the proposed SGRA-NORA scheme slightly decreases to 80% due to the proposed non-orthogonal RAS3CH allocation scheme at the second step of RA procedure. However, the SGRA-ORA scheme and Kim’s RA scheme show the lowest successful RA-S3CH allocation probability since they utilize a larger number of PAs, and, thus, the number of detected PAs to require RA-S3CHs is significantly larger. Fig. 5 shows the RA success probabilities. Since the number of available RA-S3CHs is very small, the RA success probabilities of the SGRA-ORA, Kim’s, and the conventional RA schemes decrease to 20%, 20%, and 10%, respectively, for λtotal = 30 mainly due to severe RA-S3CH contentions, while
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V. C ONCLUSION
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Fig. 5. RA success probabilities with varying λtotal and the fixed Q = 20 (u = 1 and v = 7).
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In this paper, we proposed a non-orthogonal resource allocation (NORA) scheme combined with the spatial group based RA (SGRA) mechanism in order to solve a PUSCH shortage problem in the RA procedure. Since the proposed SGRA-NORA scheme can provide a sufficiently large number of preambles at the first step of RA procedure and can effectively allocate the same RBs to a subgroup of machine nodes belonging to distinct spatial groups at the second step of RA procedure, it significantly increases both the successful PA transmission and RA-step 3 channel allocation probabilities, which results in the significantly high RA success probability. The simulation result shows that in case of a massive number of RA attempts (50,000 machine nodes, 2 RA attempts/minute/node), the proposed SGRA-NORA scheme can achieve an RA success probability of approximately 90% with 30 RBs, which is significantly higher than 30% of the conventional RA scheme. As a result, the proposed SGRANORA scheme can accommodate a significantly large number of RA requests even with a small number of PUSCH resources reserved for cellular M2M communications.
40 Prop. Prop. Prop. Conv. Conv. Conv.
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Fig. 6. RA success probabilities with varying Q and the fixed λtotal = 20.
the proposed SGRA-NORA scheme shows an RA success probability of 60% for λtotal = 30 due to the combined result from more successful PA transmissions at the first step of RA procedure and non-orthogonal RA-S3CH allocations at the second step of RA procedure. Fig. 6 shows the RA success probabilities of the proposed SGRA-NORA and the conventional RA schemes as Q varies and λtotal is fixed to 20. Here, we consider three cases to differently allocate Q RBs to PRACHs (u) and RA-S3CHs (v). As Q increases, the optimal allocation of Q changes, i.e., until Q = 24, allocation of one PRACH can achieve the maximum RA success probability, and thereafter, allocation of two PRACHs can achieve the maximum value until Q = 40 in the proposed SGRA-NORA scheme. It indicates that depending on a given number of RBs for M2M communications, the eNodeB can optimally allocate RBs to u and v in order to achieve the maximum RA success probability based on the proposed SGRA-NORA. However, in the conventional RA scheme, it requires a larger number of PRACHs (u = 4) and RA-S3CHs (v = 16), which requires total 56 RBs, in order to achieve a RA success probability over 70%. To achieve an RA success probability of approximately 80%, 22 and 66 RBs are required in the proposed SGRA-NORA scheme and the conventional RA scheme, respectively, which implies that the proposed SGRA-NORA scheme utilizes approximately onethird of radio resources to achieve the same performance, compared with that of the conventional RA scheme.
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