Reed-Muller Sequences for 5G Grant-free Massive Access
aa r X i v : . [ c s . I T ] J a n Reed-Muller Sequences for 5G Grant-free MassiveAccess
Huazi Zhang ∗ , Rong Li ∗ , Jun Wang ∗ , Yan Chen ∗ and Zhaoyang Zhang †∗ Huawei Technologies Co. Ltd. † College of Information Science & Electronic Engineering, Zhejiang University, ChinaEmail: [email protected], ning [email protected]
Abstract —We propose to use second order Reed-Muller (RM)sequence for user identification in 5G grant-free access. Thebenefits of RM sequences mainly lie in two folds, (i) support ofmuch larger user space, hence lower collision probability and(ii) lower detection complexity. These two features are essentialto meet the massive connectivity ( links/km ), ultra-reliableand low-latency requirements in 5G, e.g., one-shot transmission( ≤ ms) with ≤ − packet error rate. However, the non-orthogonality introduced during sequence space expansion leadsto worse detection performance. In this paper, we propose anoise-resilient detection algorithm along with a layered sequenceconstruction to meet the harsh requirements. Link-level simu-lations in both narrow-band and OFDM-based scenarios showthat RM sequences are suitable for 5G. Index Terms —5G, Grant-free access, Reed-Muller Sequences,Internet of Things (IoT).
I. I
NTRODUCTION
A. Motivation
We are ushering in the fifth-generation (5G) wirelesscommunications [1]. The rich diversity of applications aredriving technologies towards not only higher bandwidth andthroughput, but a variety of metrics. This application-drivennetwork (ADN) vision will potentially revolutionize wirelessnetworking from all aspects, including the physical layer.The use cases will be very different from the incumbentlong term evolution (LTE). First, 5G should support massiveconnectivity with a much larger number of devices, e.g., links/km . Second, in mission-critical scenarios, suchas vehicular-to-vehicular networks, ultra-high reliability and low latency , e.g., ≤ − packet loss rate within ≤ msresponse time, should be supported [2] [3].Current wireless systems, such as 4G LTE and WiFi, arenot designed to support the above-mentioned features. InLTE, scheduling is required to establish a connection betweena user equipment (UE) and a base station (BS). In the contextof massive connectivity and ultra-low-latency communica-tions, scheduling has two weaknesses. First, short packettransmissions will be the dominant traffic pattern. In thesecases, scheduling will lead to high signaling-to-data ratio andlow spectrum efficiency. Second, the extra round-trip delaytime consumed by scheduling incurs unacceptable latency . Inthe IEEE 802.11 standards, scheduling-free transmissions areallowed with the help of carrier sense multiple access withcollision avoidance (CSMA/CA). However, it only supportlocal area networking with a small number of users. Seq. 7 Seq. 1Seq. 2Seq. 3 (cid:258)(cid:258)
Seq. N-1Seq. N
User Sequence Space (cid:256) setofavailablesequences (cid:257)
Seq. 2Seq. 7 Seq. 5Seq. 1 Seq. 9Seq. 3
Collision BS Fig. 1: Collision in grant-free massive access.TABLE I: Collision rate in contention-based access
Sequence Space Number of Active Users2 4 652 (LTE PRACH [5]) 0.0192 0.0566 0.092516000 (5G, proposed) × − . × − × − B. Grant-free multiple access
In order to fulfill the massive connectivity ( links/km ),ultra-high reliability ( ≤ − packet loss rate) and ultra-lowlatency ( ≤ ms response) promises in 5G IoT, a sparse codemultiple access (SCMA) based uplink grant-free design [4]is proposed to eliminate the scheduling procedure. In orderto support low latency, the basic radio resource for grant-freetransmission is a contention transmission unit (CTU), definedas a combination of time, frequency and pilot sequence. Auser is allowed to transmit data on the CTUs immediatelyafter packet arrival without waiting for a grant. During anuplink transmission, a UE transmits both a pilot sequence (orpreamble) and data in one shot , and the BS jointly decodesthe data of all users from the superimposed signal. Since thelength of the entire packet is usually very short, ultra-lowlatency can be achieved. The benefits of grant-free accessare two-fold, much shorter access delay and lower overheadratio.However, the performance bottleneck of grant-free accessturns out to be the “collisions” among users. As shown inFig. 1, each active user randomly chooses a sequence froma “sequence space”, and all users simultaneously transmit onthe same time-frequency resource block. There is a chancethat two users choose the same sequence to access, resultingin a collision-incurred packet loss. As shown in Table I, thecollision rate is determined only by the size of sequence space and the number of simultaneous accessing users. As seen, alarge sequence space is necessary for grant-free access.The pilot sequence is of paramount importance here be-cause it not only identifies a user but also enables channelestimation and indicates the SCMA codebook being used,all of which are necessary for a successful transmission.The current contention-based access scheme in LTE, suchas the Physical Random Access Channel (PRACH), may notsupport massive connectivity mainly due to the fact that theuser sequence being used (i.e. Zadoff-Chu (ZC) sequence).When the number of active users grows, picking from asmall and fixed-sized sequence pool will inevitably incurhigh collision rate between users. According to LTE [5], thenumber of ZC sequences for contention-based random accessis 52. As shown in Table I, the collision rate is close to 0.1when six users simultaneously access. One straightforwardway to alleviate this issue is expanding the sequence spacewith longer ZC sequences. In practice, this may not be a wiseoption for grant-free access due to (i) high overhead ratio and(ii) high detection complexity.We propose to use second-order Reed-Muller (RM) codes[6] for grant-free massive access in 5G, both as sequencesfor user detection and as demodulation reference signal forchannel estimation. RM sequences and its detection processhas the following attractive features: (i) it can create asequence space of orders of magnitudes larger than ZCwith same-length sequences, (ii) in both small- and large-sized sequence spaces, the detection algorithm can be muchfaster than that of ZC sequences. To our best knowledge,although RM sequences have wide applications in imageprocessing, its potential in wireless communications is yetto be exploited. In [7], full-duplex neighbor discovery isproposed in a fully distributed network, based on on-off RMsequences with erasures. In [8], RM sequences are used fordownlink modulation to achieve a higher sum rate. In thispaper, we focus on its application in 5G massive connectivityand ultra-low latency communications. Our contributions aresummarized as follows:1) It is the first to use Reed-Muller sequences for grant-free massive access. The huge RM sequence spacecan greatly reduce collisions between users duringcontention-based access. We illustrate a collision-detection tradeoff due to the non-orthogonality incurredduring sequence space expansion, and propose a lay-ered RM construction to reduce multi-user interference.2) To cope with the inherent noisy nature of wirelesschannels, we made a variety of improvements in thedetection algorithm. In particular, we shuffle over mul-tiple orders to recover the columns of P matrix whichcorresponds to the detected user, and propose twodecision metrics to pick the most reliable one froma set of candidates. The proposed algorithm is shownto have significant performance gain.3) We implemented Reed-Muller sequences in bothnarrow-band IoT and wideband OFDM-SCMA underrealistic parameter setting. Both the dramatically in-creased sequence space (20x to 50x) and our noise- resilient detection algorithm have contributed to thesignificant performance gain in terms of collision rate,detection rate and block error rate (BLER).II. R EED -M ULLER SEQUENCE FOR USER IDENTIFICATION
According to the contention-based grant-free access, anumber of users simultaneously transmit on a particularcontention region. When using RM sequences φ P l ,b l , thereceived aliased signal is y ( t ) = k X l =1 h l φ P l ,b l ( t ) + n ( t ) , (1)where k is the total number of active users, φ P l ,b l is the RMsequence of the l -th active user, h l is the channel betweenthe l -th user and the BS, and n ( t ) is white Gaussian noise.Our goal is to detect from the aliased signal all k activeusers, recover the transmitted signal ˆ φ and estimate thecorresponding channel ˆ h .Reed-Muller (RM) sequences of length m can create upto a m ( r +2) -sized sequence space, and is parameterized by ( m, r ) . Given a user ID in a C -sized user space, we proposeto construct RM sequences through the following steps:1) Choose a user space of size C ≤ m ( r +2) .2) Convert a user ID ∈ { , · · · , C − } to m ( r + 2) bitsin the binary form.3) Map the m ( r + 2) -bit user ID to an m × m -sized P matrix and an m -length b vector as follows: • Take the least significant m bits as the b vector. • Take the rest m ( r + 1) bits and evenly partitionthem into r + 1 groups. The group containingthe least significant m bits are mapped to a P matrix in the Kerdock set [9]; the groups con-taining the higher bits are mapped to matrices P t , t ∈ { , · · · , r } , each corresponding to a matrixin the Delsarte-Goethals ( m, t ) set [9]. Now wehave m + 1 matrices in total and sum them up in GF (2) , and obtained the P matrix.4) Construct the m -bit Reed-Muller sequence corre-sponding to the user ID as follows: φ P,b ( x ) = ( − weight ( b ) √ m i (2 b + P x ) T x , (2)where x is an m -length binary vector, which indicatesthe index of the RM sequence ranging from 1 to m .The above function is called the second-order Reed-Muller function (see [9] and the references therein).Reed-Muller sequences have the following properties:1) RM sequence has length m and all values are takenfrom { , i, − , − i } . The maximal value of r is ⌊ m − ⌋ ,thus the m -length sequence can create up to a m ( r +2) = 2 m ( m +3)2 -sized sequence space to supporta same-sized user space.2) RM sequences are well structured. If we pointwise-multiply any φ P,b with the conjugate of φ P, , the resultis a Walsh function determined by b . All m Walsh functions form the rows of Hadamard matrix H m ,which is constructed in the following recursive fashion: H m = (cid:20) H m − H m − H m − − H m − (cid:21) . (3)3) The m RM sequences generated from the same P areorthogonal. The two RM sequences generated from twodistinct matrices P and Q , P, Q ∈ DG ( m, r ) , havecoherence [9] µ P,Q = (cid:26) √ m − r , m − r times, , m − m − r times. (4)In the context of grant-free massive access [4], we haveboth good news and bad news. The first good news, thanksto the first property, is that we can create a user spaceof much larger and flexible size. This feature may solvethe user sequence resource scarcity problem under massiveconnectivity. At least, it offers huge flexibility to expand theuser space when needed.Another good news is a fast detection algorithm broughtby the second property. Owing to the recursive structureof Walsh functions, we can determine an unknown b byperforming a fast Walsh-Hadamard transform, which onlytakes O ( n log n ) multiplications as compared with O ( n ) forthe correlation method. Moreover, since RM sequences onlytake values from { +1 , − , + i, − i } , the multiplications onlyrequires flip of signs which is extremely simple. This featurealone provides tremendous complexity reduction than othersequences such as ZadoffChu (ZC) sequence in LTE. Forexample, for a 64-length sequence, RM requires only mul-tiplications of ZC, and the complexity of each multiplicationis negligible compared with ZC.The bad news is the non-orthogonality introduced duringspace expansion. The last property reveals to us the fun-damental tradeoff between user space size (collision prob-ability) and inter-user interference (detection performance).As we expand the user space, we have to compromise onthe orthogonality and thus inevitably loose some detectionperformance.III. C OLLISION - DETECTION TRADEOFF AND LAYEREDCONSTRUCTION OF RM SEQUENCES
As aforementioned, there exists a fundamental tradeoffbetween better orthogonality and larger sequence space. Ingrant-free massive access, the former implies lower multi-user interference and thus detection performance; the latteris associated to collision rate.Given the sequence size C and active user number k , thecollision rate drops as the sequence space expands p col ( k, C ) = Ck k X i =2 iC ik (cid:18) C (cid:19) i (cid:18) C − C (cid:19) k − i ! (5)The detection performance depends on the specific se-quences we use and the detection algorithm. The rule ofthumb is that the higher interference (i.e., coherence) betweensequences, the worse detection performance we may achieve. TABLE II: Partition of RM sequence space by coherence Space Space Corresponding RM Sequences MaxLevel Size Coherence1 N = 2 m Sequences generated by single P N Seqs. generated by Kerdock set √ N N Seqs. generated by DG ( m, set N − m · · · · · · · · · · · · l N l Seqs. gen. by DG ( m, l − set N − l − m Following this principle, we partition the entire RM sequencespace into multiple levels in Table II according to thecoherence of the corresponding RM sequence space.Our mapping from user ID to RM sequence in Section IIexactly follows Table II, where users with lower ID usesthe sequences from lower-level space with lower coherence.As we expand sequence space to achieve a lower collisionrate, we should first use the RM sequences from lower-level subspace and then higher-level space. With this layeredconstruction of RM sequences, if we want to use C -sizedsequence space, the optimal set of sequences are those withID ∈ { , · · · C − } as described in Section II. Through thislayer-by-layer expansion, multi-user interference is mitigatedto facilitate a better detection performance.IV. S UCCESSIVE INTERFERENCE CANCELLATION (SIC)
BASED SEQUENCE DETECTION
A. Level-1 space
The most elementary group of RM sequences are theRM sequences generated from a single P matrix, i.e., level-1 space. The detection problem is the same as (1) exceptthat P = · · · = P k = P . To detect from (1) the activeusers, we simply perform a fast Walsh-Hardamard transform(FWHT) on the received signal y to obtain the correlationvalues between y and all m possible transmitted signals φ P,b . The positions of the k highest peaks correspond tothe b vectors of the k active users. The above scenario issimilar to the uplink grant-free multiple access discussed in[4, Chap. III-B], in which three algorithms with complexity O ( N ) , O ( N ) , and O ( N ) are introduced, respectively.Here, leveraging the computationally efficient fast transform,the complexity is only O ( N log N ) . Since all sequencesin level-1 are orthogonal, they provide the best detectionperformance but have the minimal user space. B. Higher-level space
When a larger user space is required, we can expandthe user space by including the RM sequences generatedfrom multiple P matrices. In contrast to level-1 space, herethe sequences of different users are no longer orthogonal.To suppress the inter-user interference as low as possible,successive interference cancellation (SIC) is adopted in [6].The SIC-based method is outlined in Algorithm 1. The Note that the higher-level space includes lower-level subspace. objective of the SIC-based algorithm is to recover the P matrices of the k users without traversing over all possible P matrices. In each iteration, the algorithm extracts the P matrix and b vector associated with the highest-power user,and repeats this process until all users are detected. Algorithm 1
SIC-based sequence detection [6]Input: { y } ; Output: { h l , P l b l , ∀ l ∈ (1 , · · · , k ) } Initialization: t = 1 , y t = y while {k y t k > ǫ } or t ≤ t max do Extract from y t the ( ˆ P t , ˆ b t ) of the largest-power userChannel estimation for all the detected users: arg min −→ c k y − P tl =1 ˆ h l φ ˆ P l , ˆ b l k Cancel the detected sequence of the t users: y t +1 = y − P tl =1 ˆ h l φ ˆ P l , ˆ b l Increase t by 1 end while The key step in Algorithm 1 is extracting the P matrix ofthe largest-power user from the potentially huge user space.Once a P is recovered, the corresponding b vector can berecovered as in the level-1 space. According to Section II,each ( P, b ) pair uniquely determines a user ID.V. I MPROVED RM DETECTION FOR NOISE RESILIENCE
The original recovery algorithm in [6] works well innoiseless or high signal-to-noise ratio settings. However, itsperformance degrade quickly in wireless channels with bothnoise and fading. To combat the noisy channel in grant-free access, we modify the original algorithm and haveharvested significant performance gain. The improvementsare described as follows.
A. Shuffling over multiple orders
In Algorithm 1, only one { P t , b t } pair (one user) isextracted for interference cancellation in each iteration. Ifthe { P t , b t } pair is wrongly detected, canceling the signalassociated with { P t , b t } is equivalent to adding a fake user’ssequence c t φ P t ,b t to the received signal. This will not onlycause false alarm but also incur more interference to theexisting users. Therefore, we propose a two-fold strategy toavoid this situation. First, try to extract multiple P candidatesrather than only one P . Second, check the credibility of theextracted { P t , b t } pairs before canceling its associated signal.The algorithm is described in Algorithm 2.According to [6], each P matrix is detected based on thecorrelation between the received signal y ( x ) and the shiftedversion of itself y ( x + e ) y ( x + e ) y ( x ) = 12 m k X l =1 h l ( − b Tl e ( − e T P l x + chirps , (6)where e is a unit weight m -length binary vector where onlythe j -th bit is 1, and the chirps are multi-user interference andnoise. Since the chirps are of lower power, applying FHWTto (6) results in peaks at position P l e which corresponds to Algorithm 2
Shuffling based user detectionInput: { y } ; Output: { P, b } for p = 1 → p max do perm p = randperm ( m ) . for j = perm p ( j ) do Set unit weight m -length vector e j , where the j -thelement is 1, and all other elements are 0Obtain y ( x + e j ) as follows: take the y sequence,swap neighboring blocks of size j − (e.g., if j = 3 ,then swap the values indexed by → with → ,and → with → and so on)Pointwise multiply y ( x + e j ) with the conjugate of yY e j = fwht ( y ( x + e j ) . ∗ conj ( y )) The position of the highest peak of Y e j correspondsto ˆ P p ’s j -th column vector end for Pointwise-multiply y with the conjugate of φ P,b =0 :Take the fast Walsh-Hardamard transform: Y = fwht ( y. ∗ conj ( φ P, )) Find the highest peaks of Y , take the binary form of thepeak positions as ˆ b p end for Compute the error metric for all candidates ( ˆ P p , ˆ b p ) , p ∈{ · · · p max } .Pick the ( P, b ) pair with the lowest error metric as the nextuserthe j -th column of the P matrix. Repeating this m timesleads to the recovery of all m columns of a P matrix.To extract the P matrix in a more noise-resilient way, thefirst part of our strategy can be done by shuffling the ordersof column recovery in Algorithm 2. Instead of recovering thecolumns sequentially from the 1st to the m -th, we can trya different order each time. The orderings can be generatedfrom random permutations of [1 , · · · , m ] .We argue that different permutations may lead to extrac-tions of different P . We assume that two users with similarreceived power have P matrices as shown in Fig. 2. Giventhat the 2nd column/row of the highest-power user has beencorrectly recovered, if we recover the 1st column in the nextround (Permutation 1), we will not confuse with the 1stcolumn of the 2nd highest-power user. This is because thesearch of the highest peak is conducted only in the symmetry-constrained space , thus excluding the false peak. However,if we recover the 4-th column in the next round (Permutation2), we may wrongly recover the 4-th column of the 2ndhighest-power user. This time, the column vectors of boththe highest-power user and the 2nd highest-power user arewithin the search space. The real peak may not be easilydistinguished due to inter-user interference and noise.The second part of our strategy help us to decide which ofthe extracted { P, b } pairs is the most credible one. This canbe done by exploiting some side information of the extracted All P matrices are symmetric by definition.
0 1 1 0 0 1 1 1 0 0
1 1 1
0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1
1 0 1
1 0 1 0 0 0 1 0
Highest power P2 nd highest power P e = 01000, p(2)=1 (cid:284) Symmetry-constrained search space P e r m u t a t i on e = 10000, p(1)=2e = 00010, p(4)=3e = 01000, p(2)=1 P e r m . e = 00010, p(4)=3 Noise cause false peak × Fig. 2: Shuffling intuition: an example that two differentcolumn-recovery orders may lead to extractions of different P matrices. Permutation 1 is lucky to find the correct columnvector, but Permutation 2 is deceived by noise. In practice,we may shuffle the order to obtain multiple P candidates,and pick the most credible P according to certain decisionrule. { P, b } pair. In the following, we propose two methods tocompute the error score.
1) Distance based decision:
Given two m × m matrices P and Q , one way to tell which is more credible is the rankingof their column vectors in the Hadamard spectrum in termsof amplitude. If P belongs to one of the accessing users,each column vector of P should represents a peak equal orclose to the highest peak. We sort the Hadamard spectrum ofeach column according to the amplitude in descending order.The distance of P ’s j -th column vector p j is thus defined asthe ranking of its peak in the Hadamard spectrum. Our errormetric is the sum distance of all m columns: Dist ( P ) = m X j =1 ranking ( p j ) . (7)We pick the lowest-sum-distance ˆ P p and its associated ˆ b p from all candidates as the extracted ( P, b ) pair.
2) Residual energy based decision:
A more powerful butmore computationally complex method is selecting { P, b } pair according to the residual energy after signal cancellation.We perform channel estimation for all sequences generatedby the { P, b } candidates, and calculate their residual energyby canceling c t φ P t ,b t . Intuitively, if the { P, b } being tested isfrom a real user, then residual energy should decrease afterits signal is canceled. Therefore, we may use the residualenergy as the error metric, and pick the { P, b } pair with thelowest residual energy as the extracted P .Shuffling can also dramatically improve the detectionperformance in certain scenarios. For m = 8 , the detectionresults for “no shuffling, shuffle and pick from 4 { P, b } candidates, shuffle and pick from 8 { P, b } candidates” are C o rr e c t de t e c t i on p r obab ili t y Detection peformance of 256−length RM sequences No shuffling: only one candidateShuffle and pick from 4 candidatesShuffle and pick from 8 candidates
Fig. 3: Shuffling gain: significant improvement is observedwhen we shuffle 4 times. As more shuffling is added, theimprovement diminishes.shown in Fig. 3. We observe significant improvement inthe detection performance even if a few candidates aregenerated for decision. Note that the fast Hadamard transformof all m columns is computed only once at the beginning,therefore shuffling itself does not incur additional complexity.However, if we use the residual energy based decision rule,additional computation is incurred during additional channelestimation.The complexity of Algorithm 2 is O ( m ( m + 1)2 m ) ,where the main computation tasks are the H-transforms.Algorithm 1 iterate k times to detect all k users, the overallcomplexity is thus O ( k × m ( m + 1)2 m ) . Note that thiscomplexity is not dependent on the value of r , therefore alsoindependent of the user space size. In contrast, traversing allsequences yields complexity O (2 m ( r +2) × m ) . B. Double checking the detected P Sometimes the recovered P candidates may violate therank property, i.e., rank ( P ) ≥ m − r [9]. These candidatesare absolutely wrong and should be discarded. Thanks to theshuffling technique, we may re-permute the column recoveryorder until we obtain a valid P .Occasionally an already detected user can be re-detected insubsequent iterations. This will induce an endless loop if notproperly intervened. In this case, we may shuffle the columnrecovery order to extract a distinct { P, b } pair. In the worstcase, we keep shuffling until we find something new.VI. L INK - LEVEL SIMULATION RESULTS
To validate the proposed sequence design and the improveddetection algorithm, we conducted extensive experimentsusing our SCMA-based grant-free massive access simula-tor. Two potential configurations for 5G are examined, i.e.,narrow-band IoT for massive connectivity and widebandOFDM for ultra-reliable and low-latency communications.
A. Narrowband IoT
First, we examine the performance of RM sequences aspreamble in the narrow-band massive connectivity setting.The simulation parameters (e.g., bandwidth) follow the mostrecent 3GPP draft report [10] which describes the possiblefuture IoT configurations, and are listed in Table III.TABLE III: Narrow Band IoT Configuration
Channel EPA Urban Micro (3Km/h)
In the narrow-band setting, we restrict our attention onthe detection & collision performance under massive con-nectivity. We assume that each IoT device transmits onceper hour, which corresponds to an active probability of × − . To support massive connectivity in 5G IoT, abase station that covers 1 km should serve about links[3]. That means about 5 to 10 users will be active at thesame time. Therefore, we simulated two typical cases, 10users simultaneously access under medium SNR (7dB), andfive users simultaneously access under relatively low SNR(1dB). In our detection algorithm, we pick the k users withhighest energy using the proposed algorithm, where k equalsthe number of active users. In each grant-free access, eachuser randomly chooses an ID from [0 , · · · , C − , where C is the sequence space size, and uses the correspondingRM sequence as its preamble. When more than one userchooses the same sequence, we count them as collisions. Ifour algorithm fails to detect an active user, we count it asa miss detection. Both collisions and miss detection lead topacket losses. Therefore we also count the sum of collisionsand miss detection as total failures.The results of these three metrics are given in Fig. 4 andFig. 5, respectively. The observation is as follows. On theone hand, thanks to the huge sequence size provided by RM,the number of collisions between users drops quickly as thesequence space expands. On the other hand, facilitated byour detection algorithm, the miss detection rate only growsslightly with the space size even under low SNR, whichexhibits robustness under multi-user interference and noise.In summary, we conclude that it is worthwhile to dramaticallyexpand the user sequence space in 5G IoT scenarios withmassive connections. B. Wideband OFDM-SCMA
We use RM sequences as pilots for a OFDMA-based grant-free access system to realize ultra-reliable and low-latencycommunications (e.g., one-shot ( ≤ ms) transmission with Sequence space size P r ob a b ili t y
10 users grant−free access with 64−long RM sequences, SNR = 7
Miss detectionsCollisionsTotal failures
Fig. 4: The total access failures drops quickly thanks to thehuge sequence space provided by RM.
Sequence space size P r ob a b ili t y Miss detectionsCollisionsTotal failures
Fig. 5: Even in very adverse channel condition, the missdetection rate only slightly grows thanks to our robustalgorithm. ≤ − packet error rate). The simulation configuration iscompatible with the incumbent LTE system and is listedin Table IV. This time we not only examine the collision& detection performance, but also include data transmissionperformance. Based on OFDM, we also implement sparsecode multiple access (SCMA) to obtain a 3x spectrumefficiency (interested readers are referred to [11] for details.).Note that our pilot design is not restricted to SCMA, but alsoapplies to other modulation techniques. Apart from activeuser detection, the pilot sequences are also used for multi-path channel estimation. Here we use the SCME UrbanMacro channel model, which has relatively long delay spreadthan the EPA channel. In such a case, MMSE multi-userchannel estimation [12] is adopted to address the severemulti-path fading.We compare the performances between the RM-basedscheme and the ZC-based scheme used in the incumbentLTE system. The sequence design of the two schemes is TABLE IV: Wideband OFDM-SCMA Configuration
Channel SCME Urban Macro (3Km/h) . msContention-based access YesSCMA spreading factor 4Channel Code Turbo 1/3 (including CRC) as follows. The RM sequences have length 127 and theZC sequences have length 139. An uplink frame has 12OFDM symbols. For both sequences, we perform a 144-point discrete Fourier transform (DFT) and map them ontothe 144 subcarriers on the 4-th and the 11-th symbols. For ZCsequences, we use 12 roots and 12 cyclic shifts for each root;therefore we have 144 ZC pilots in total. For RM sequences,we set the sequence space C = 16000 and use the sequencesfrom ID 0 to 15999 according to Section II; therefore wehave 16000 RM pilots in total.As shown in Fig.6, we let six active users simultaneouslyaccess by randomly choosing a sequence, and examine (i)collision, (ii) detection and (iii) block error rate (BLER). Dueto the dramatically increased pilot space (from 144 for ZCto 16000 for RM), the collision rate reduces from 0.0342to − . Since the collision rate is independent from SNR,it will impose an error floor to the grant-free system. Thecollision-incurred performance bottleneck may be greatlyloosened by the huge space of RM sequences, while the errorfloor is high for the ZC-based scheme. With our detectionalgorithm, our miss detection rate can be as low as − in the high SNR regime. Finally, combining all aspects, theblock error rate (BLER) performance shows that RM-basedpilot design achieves a packet loss rate close to − without any scheduling and re-transmission. Since the packet length is12 OFDM symbols which last about . ms, the ultra-reliableand low-latency requirements are satisfied.VII. C ONCLUSION
In this work, we revealed the potential of RM sequencesfor user identification in grant-free massive access. Whilethe collision rate can be reduced by sequence space ex-pansion, the sequence construction and detection algorithmneed to be re-designed to address the noise and multi-user interference in wireless channel. As an initial study,we implemented our scheme in narrow-band and widebandgrant-free access systems. The former validates the massiveconnectivity scenario; the latter validates the ultra-reliableand low-latency communications scenario. In both cases, RMsequences helped to fulfill the harsh requirements of 5G. −2 0 2 4 6 8 10 12 1410 −4 −3 −2 −1 Eb/N0 B L E R Fig. 6: The proposed RM-based grant-free access scheme hassignificant gain over the traditional ZC-based scheme.R
EFERENCES[1] J. Andrews, S. Buzzi, W. Choi, S. Hanly, A. Lozano, A. Soong andJ. Zhang, “What will 5G be?”
IEEE Journal on Selected Areas inCommunications , vol. 32, no. 6, pp. 1065-1082, 2014.[2] 3GPP Technical Report 22.862: Feasibility Study on New Servicesand Markets Technology Enablers - Critical Communications, February,2016.[3] D. Giuseppe, T. Koch and P. Popovski. “Towards massive, ultra-reliable,and low-latency wireless: The art of sending short packets,” arXivpreprint :1504.06526, 2015.[4] A. Bayesteh, E. Yi, H. Nikopour and H. Baligh, “Blind detection ofSCMA for uplink grant-free multiple-access,” in
Proc. InternationalSymposium on Wireless Communications Systems (ISWCS)
Proc. IEEE Annual Conference on InformationSciences and Systems (CISS) , pp. 11-15, March, 2008.[7] L. Zhang, J. Luo and D. Guo, “Neighbor discovery for wireless networksvia compressed sensing,”
Performance Evaluation , vol. 70, no. 7, pp.457-471, 2013.[8] V. Aggarwal, L. Applebaum, A. Bennatan, A. Calderbank, S. Howardand S. Searle, “Enhanced CDMA communications using compressed-sensing reconstruction methods” in
Proc. IEEE Annual Allerton Con-ference on Communication, Control, and Computing , pp. 1211-1215,September, 2009.[9] A. Calderbank and S. Jafarpour, “Reed Muller sensing matrices andthe LASSO,” in
Proc. Sequences and Their Applications (SETA) , pp.442-463, Springer Berlin Heidelberg, 2010.[10] Draft Report of 3GPP TSG RAN WG1
Proc.IEEE International Symposium on Personal Indoor and Mobile RadioCommunications (PIMRC) , 2013.[12] F. Vook and T. Thomas. “MMSE multi-user channel estimation forbroadband wireless communications,” in