Supporting More Active Users for Massive Access via Data-assisted Activity Detection
aa r X i v : . [ ee ss . SP ] F e b Supporting More Active Users for Massive Accessvia Data-assisted Activity Detection
Xinyu Bian, Yuyi Mao, and Jun Zhang
Department of Electronic and Information EngineeringThe Hong Kong Polytechnic University, Hong KongEmails: [email protected], [email protected], [email protected]
Abstract —Massive machine-type communication (mMTC) hasbeen regarded as one of the most important use scenarios inthe fifth generation (5G) and beyond wireless networks, whichdemands scalable access for a large number of devices. Whilegrant-free random access has emerged as a promising mechanismfor massive access, its potential has not been fully unleashed.Particularly, the two key tasks in massive access systems, namely,user activity detection and data detection, were handled sep-arately in most existing studies, which ignored the commonsparsity pattern in the received pilot and data signal. Moreover,error detection and correction in the payload data provideadditional mechanisms for performance improvement. In thispaper, we propose a data-assisted activity detection framework,which aims at supporting more active users by reducing theactivity detection error, consisting of false alarm and misseddetection errors. Specifically, after an initial activity detectionstep based on the pilot symbols, the false alarm users are filteredby applying energy detection for the data symbols; once datasymbols of some active users have been successfully decoded,their effect in activity detection will be resolved via successivepilot interference cancellation , which reduces the missed detectionerror. Simulation results show that the proposed algorithmeffectively increases the activity detection accuracy, and it is ableto support ∼ more active users compared to a conventionalmethod in some sample scenarios. Index Terms —Internet-of-Things (IoT), massive connectivity,grant-free massive access, data-assisted user activity detection,approximate message passing (AMP).
I. I
NTRODUCTION
The proliferation of the Internet of Things (IoT), such asconnected health, smart home, and intelligent manufacturing,is prompting a rapid revolution of wireless communications.In order to support a massive number of connected devices,massive machine-type communications (mMTC) has becomeone of the three generic services offered by the fifth generation(5G) wireless networks [1]. A unique feature of mMTC isthat, while a huge amount of devices are connected, only aproportion of them sporadically become active, normally witha small amount of data to transmit [2].Nevertheless, uplink access in legacy wireless networks isgenerally controlled by grant-based access schemes, whereeach user first transmits a scheduling request to the basestation (BS) and cannot start its data transmission until agrant is received. Although the grant-based access schemesreserve dedicated resources for each user that avoids potential
This work was supported by the General Research Fund (Project No.15207220) from the Hong Kong Research Grants Council. collisions, long latency and significant signalling overhead willbe incurred with a large number of devices [3], [4].Grant-free random access, where users can transmit datawithout waiting for approval from the BS [5], provides apromising solution for mMTC. In its protocols, the BS needsto detect the set of active users and estimate their channelconditions based on the received pilot signal, before per-forming data reception operations. Due to the vast amountof devices, users can only be assigned with non-orthogonalpilots, which makes it highly challenging for accurate activeuser identification and channel estimation at the BS. As aresult, accommodating the maximum number of active deviceswith minimum degradation of communication performance iswidely acknowledged as one of the most fundamental designconsiderations for grant-free massive access [3], [6], [7].Because of the sporadic traffic pattern of the connecteddevices, detecting the set of active users turns out to bea compressive sensing problem, for which, many efficientalgorithms were developed [8]. In [9], a joint user activitydetection and data detection algorithm was proposed for grant-free non-orthogonal multiple access (NOMA) by exploitingthe temporal correlations of user activities. A similar problemwas later revisited using approximate message passing (AMP)and expectation maximization (EM) in [10]. However, theseworks assume full channel state information (CSI) availableat the BSs, which is practicallly infeasible since most of theusers are inactive without transmitting their pilots to the BS.Therefore, joint activity detection and channel estimation hasattracted significant attentions most recently [11], [12]. In [11],a joint design of activity detection and channel estimation wasproposed based on AMP for massive multi-input multi-output(MIMO) systems, and it was shown that the activity detectionerror can be arbitrarily small in the asymptotic regime. Inaddition, a user activity detection and channel estimationapproach was developed in [12] by leveraging the joint sparsityfrom both the spatial and frequency domains. This approachobviates the need of knowing the number of devices.However, prior works on grant-free massive access mostlyfollow a separate design approach, i.e., the activity patternand CSI are estimated without incorporating any informationencoded in the received data symbols. In this way, it onlyutilizes the sparse activity pattern from the received pilotsignal, which limits the activity detection accuracy and thedata transmission reliability. An important but easily neglectedbservation in grant-free random access is that the same useractivity pattern replicates in the received data symbols, whichcan be exploited to improve the activity detection accuracyfor accommodating more connected devices. This inspires thedesign of a data-assisted activity detection framework in thispaper, where the false alarm and missed detection error canboth be suppressed. It is worthwhile to note that this idea wasinitially proposed for a single-antenna NOMA-based massiveaccess system [13], which, however, cannot be easily extendedfor multi-antenna receptions.In this paper, we endeavor to reduce the activity detectionerror by leveraging valuable information obtained in data sym-bols. The proposed data-aided activity detection frameworkcontains three basic modules, namely, an initial estimator, afalse alarm corrector and a missed detection corrector. On onehand, to minimize the false alarm error, energy detection is ap-plied in the false alarm corrector to filter inactive users that areincorrectly determined as active. On the other hand, inspiredby the successive interference cancellation (SIC) detection, themissed detection corrector progressively increases the sparsitylevel of the received pilot signal to reduce the probability ofmissed detection. Simulation results shows that the proposedframework is able to achieve noticeable improvements in termsof both user activity detection accuracy and data detectionerror. Moreover, about 20% more active users can be supportedby the proposed framework in sample scenarios, compared tothat achieved by the separate design.The rest of this paper is organized as follows. We introducethe system model and two basic tasks of grant-free access inSection II. A data-assisted user activity detection frameworkis developed in Section III. Simulation results are presentedin Section IV, and we conclude this paper in Section V.
Notations:
We use lower-case letters, bold-face lower-caseletters, bold-face upper-case letters, and math calligraphy let-ters to denote scalars, vectors, matrices, and sets, respectively.Besides, the conjugate transpose of a matrix M is denoted as M H and the complex Gaussian distribution with mean µ andcovariance matrix Σ is denoted by CN ( µ , Σ ) . In addition,the indicator function and the Kronecker product are denotedas ( · ) and ⊗ , respectively. We use vec ( · ) to denote thevectorization operator and let vec − ( · ) denote its inverse.II. S YSTEM M ODEL
A. Signal Model
We consider an uplink cellular system as shown in Fig.1, where a large number of mobile users are simultaneouslyserved by a BS. The scenarios where the mobile users havesporadic uplink data traffic (e.g., the IoT and mMTC) areof particular interests, where only a small fraction of theusers have data to transmit and become active at each timeinstant. The active probabilities of different users are assumedto be identical, and they are denoted as p . We denote the setof mobile users as N , { , · · · , N } , and use the activityindicator u n ∈ { , } to represent whether a user is activefor transmission, i.e., u n = 1 indicates the user is active and u n = 0 if it is inactive. The set of active users is represented by Ξ , { j ∈ N | u j = 1 } with its cardinality denoted as K ( K ≤ N ). For simplicity, the BS is assumed to have M receiveantennas while each user transmits with a single antenna.We adopt the quasi-static block fading channel model,where the channel condition remains unchanged within atransmission block spanning T symbol intervals, and changesindependently across different coherence blocks. The uplinkchannel vector from user n to the BS, denoted as h n , ismodeled as f n = √ β n α n , ∀ n , where α n and β n stand for thesmall-scale and large-scale fading coefficients, respectively.Besides, the users are assumed to be static and thus β n isknown at the BS. Fig. 1. System model and the adopted grant-free random access scheme.
A grant-free random access scheme as shown in Fig. 1, isadopted for uplink transmissions, where a transmission blockis divided into two phases: The first phase contains L symbolsthat are reserved for pilot transmission and the remaining L d , T − L symbols are used for payload data delivery in the secondphase. We consider the massive random access scenarios, i.e., L < N , in which, assigning orthogonal pilot sequences toall the users is infeasible. To overcome this issue, each useris instead assigned with a unique pilot sequence √ L a n with a n , [ a n, , · · · , a n,L ] T and a n,l ∼ CN (cid:0) , L (cid:1) [7]. It can beverified that { a n } Nn =1 achieves asymptotic orthogonality when L is sufficiently large. By defining A p as [ a , · · · , a N ] , thereceived pilot signal Y p ∈ C L × M at the BS in the first phasecan be expressed as follows: Y p = p Lρ A p H + N p , (1)where ρ is the user transmit power, H , [ h , ..., h N ] T denotes the effective channel matrix with h n , u n f n , and N p = [ n p, , ..., n p,L ] T is the Gaussian noise with zero meanand variance σ for each element.In the data transmission phase, each active user transmits s ( s < L d ) coded symbols, which is denoted as s n ∈ X s × .Here, X is the set of constellation points with the normalizedaverage power. For the set of inactive users, s n is set to bea zero vector for notation consistency. Since the number ofactive users in the system may far exceed the number ofreceive antennas at the BS, in order to avoid the system frombeing overloaded [14], we multiply the coded symbols by aprecoding matrix for each user [15] as follows c n = P n s n , (2)here c n is the precoded symbols and P n ∈ C L d × s is theprecoding matrix with full column-rank. Thus, the receiveddata signal at the BS, denoted as Y d ∈ C M × L d , can beexpressed as follows: Y d = √ ρ N X n =1 h n c Tn + N d = √ ρ X j ∈ Ξ h j s Tj P Tj + N d , (3)where N d = [ n d, , ..., n d,L d ] is the Gaussian noise with thesame distribution as N p . We denote y d = vec ( Y d ) , and let B n , P n ⊗ h n . As a result, the received data signal in (3)can be rewritten as the following expression: y d = √ ρ B a x a + N d , (4)where B a , [ { B j } j ∈ Ξ ] and x a , (cid:2) { s Tj } j ∈ Ξ (cid:3) . B. User Activity and Data DetectionUser activity detection and data detection are the two mostcritical tasks in grant-free massive access. Prior studies onmassive connectivity typically adopted a two-stage separatedesign as shown in Fig. 2(a) [10], [16], [17]. Specifically,in the first stage, activity detection and channel estimationare performed based on the received pilot signal, which canbe accomplished by exploiting the sparsity of the effectivechannel matrix using compressive sensing techniques [3]. Theestimated user activity pattern and CSI are then used for datadetection in the second stage.With limited resources available for pilot transmissions, it ischallenging to obtain accurate knowledge of the user activitypattern at the BS. In fact, missed detection, i.e., an active useris not detected at all, and false alarm, i.e., an inactive useris determined as active, are two major sources that contributeto the user activity detection error. On one hand, data of themiss-detected users is not decoded, leading to a one-hundredpercent data error for these users; On the other hand, falsealarm shall degrade the data detection accuracy, since the datadetector also attempts to decode data for the false alarm users,which is equivalent to introducing interference to the activeusers. Therefore, improving the activity detection accuracy isof the utmost importance to the communication performancein massive access systems.A key observation of the grant-free access scheme is that,both the transmitted pilots and data symbols are distorted bythe same wireless fading channel. In other words, the receivedpilot and data signals share the same sparsity pattern, whichcould be exploited to improve the activity detection accuracy.Nevertheless, this aspect was largely overlooked by existingstudies, which motivates our investigation on data-assistedactivity detection approaches. In the next section, we willcustomize dedicated methods to handle the two kinds of errors,in order to reduce the overall user activity detection error forreliable communications.III. T HE P ROPOSED F RAMEWORK
In this section, we propose a data-assisted activity detectionframework to improve the activity detection accuracy. A flow (a) Separate design of user activity and data detection.(b) The data-assisted activity detection framework.Fig. 2. The separate design and data-assisted design for massive access. chart of the proposed framework is shown in Fig. 2(b), whichcontains an initial estimator, a false alarm corrector, and amissed detection corrector. For each transmission block, theinitial estimator performs preliminary estimation on the CSIand the user activity pattern for subsequent data detection.This is essentially the separate design as shown in Fig. 2(a).Based on the initial data symbol estimates, the false alarmcorrector performs energy detection to filter part of the falsealarm users. This step is inspired by the intuition that theaverage magnitudes of the detected data symbols of the falsealarm users shall be much smaller than those of the activeusers. Then, with the updated user activity pattern, the channelmatrices and data symbols are re-estimated for processing inthe missed detection corrector. In particular, the design ofthe missed detection corrector leverages the SIC techniquesto further refine the activity detection result. In contrast toconventional SIC algorithms that remove interference from thereceived data signal, interference in the received pilot signalis eliminated by identifying a subset of users whose payloaddata can be successfully decoded in each iteration.We will elaborate different modules of the proposed frame-work in the following subsections. For better expositions, weuse the superscript “ ( i ) ” to denote the iteration number, andrefer the operations of the initial estimator as the -th iteration.Besides, the intermediate variables N (0) , K (0) , Y (0) p , y (0) d and N (0) are initialized as N , K , Y p , y d and N , respectively. A. The Initial Estimator
The initial estimator applies the AMP-based algorithm pro-posed in [10] to jointly estimate the CSI and user activity pat-tern, based on which, data symbol detection is performed. Inarticular, with Y ( i ) p as the input , the AMP-based algorithmobtains the channel estimates for the users in N ( i ) , denoted as ˆ H ( i ) = h { ˆ h ( i ) j } j ∈N ( i ) i , and the user activity pattern is derivedby thresholding, i.e., the set of active users is determined as ˆ K ( i ) a , n j ∈ N ( i ) | φ (ˆ h ( i ) j ) ≥ θ ( i ) j o , where φ ( · ) is a knownfunction and θ ( i ) j is the decision threshold for user j .We define ˆ H ( i ) a , h { ˆ h ( i ) j } j ∈ ˆ K ( i ) a i and ˆ B ( i ) a in a way similarto B a in (4). By using the MMSE equalizer, the estimated datasymbols for the users in ˆ K ( i ) a , are obtained via the followingexpression: ˆ D ( i ) a = vec − "(cid:18) ˆ B ( i ) Ha ˆ B ( i ) a + σ ρ I (cid:19) − ˆ B ( i ) Ha y ( i ) d , (5)where ˆ D ( i ) a , h { ˆ d ( i ) a,j } j ∈ ˆ K ( i ) a i with ˆ d ( i ) a,j , h { ˆ d ( i ) a, ( j,m ) } sm =1 i and ˆ d ( i ) a, ( j,m ) is the m -th estimated data symbol of user j . B. The False Alarm Corrector
In the i -th iteration, the false alarm corrector filters theinactive users from ˆ K ( i − a , which is obtained from the initialestimator if i = 1 and the missed detection corrector in theprevious iteration if i ≥ . We borrow the idea of energydetection for spectrum sensing in cognitive radio networks[18] to design the false alarm corrector. This is because ifthe estimated data symbols of a user have small averagemagnitudes, this user is likely to be a false alarm user.Specifically, in the false alarm corrector, a user that wasdetected as active in the previous iteration is determined as afalse alarm user if the following criteria is satisfied: s X m =1 (cid:16) | ˆ d ( i − a, ( j,m ) | ∈ (0 , θ F ) ∪ ( θ F , + ∞ ) (cid:17) ≥ θ F , ∀ j ∈ ˆ K ( i − a . (6)In (6), θ F , θ F and θ F are empirical threshold values, where θ F is to ensure the average estimated data symbol energyof an active user is sufficiently large, while θ F is designedfor reducing the sensitivity of the false alarm corrector to thechannel estimation error. Therefore, the updated estimate ofthe user activity pattern is given by ˆ Q ( i ) a , ˆ K ( i − a \ (cid:8) j ∈ ˆ K ( i − a | P sm =1 (cid:16) | ˆ d ( i − a, ( j,m ) | ∈ (0 , θ F ) ∪ ( θ F , + ∞ ) (cid:17) ≥ θ F (cid:9) . C. The Missed Detection Corrector1)
Overview : While the false alarm corrector is able toreduce the chances of including inactive users in ˆ K ( i − a , itcannot effectively handle the missed detection users. In thissubsection, we design a missed detection corrector to minimizethe number of active users that cannot be found in previoussteps. Our design is motivated by the SIC techniques formulti-user detection [19], where data from different usersare detected sequentially, and interference in the received In this subsection, we retain the superscript “ ( i ) ” as the key steps in theinitial estimator that are reused in the missed detection corrector as will bediscussed in Section III-D, in which the iteration number is greater than zero. data signal is iteratively removed for decoding data of theremaining users. However, as our objective is to reduce themissed detection error, we propose to perform SIC for thereceived pilot signal instead in the missed detection corrector.By identifying some users that are determined as active withhigh confidence and remove their pilot data from the receivedpilot signal in each iteration, we shall be able to increase thesparsity level of the received pilot signal, which is beneficialfor accurate user activity detection and channel estimation innext iterations. Fig. 3. The structure of the missed detection corrector.
In particular, the missed detection corrector performs threetasks as shown in Fig. 3, including i) Channel estimation, datasymbol detection and channel decoding ; ii) Pilot interferencecancellation ; and iii) User activity/symbol re-estimation . Thesetasks will be elaborated in the sequel. Channel estimation, symbol detection, and channeldecoding : With the updated estimate of the active user set ˆ Q ( i ) a from the false alarm corrector, the missed detectioncorrector first re-estimates the channel vectors and performsdata symbol detection accordingly, both of which apply theMMSE estimators. The estimated channel vectors of user j is denoted as ˇ h ( i ) j , and the detected symbol sequence on theconstellation, i.e., which constellation points are transmittedin the symbol sequence, is denoted as ˇ s ( i ) a,j for user j . Thedetected symbol sequence is then passed to a channel decoder,which outputs the parity check result in addition to the decodeddata. We denote the set of users that pass the parity check as ˆ P ( i ) a , whose channel-decoded data is denoted as ˇ x ( i ) a,j , j ∈ ˆ P ( i ) a . Pilot interference cancellation and activity/symbol re-estimation : After channel decoding, the missed detectioncorrector selects a number of users from ˆ Q ( i ) a based ontheir parity check results. The pilots of the selected set ofusers are then subtracted from the received pilot signal. Ourheuristics originate from a key theorem in compressive sensing(See Theorem 1.3 in [20]). This theorem implies that for anidealized user activity detection problem where the BS hasa single receive antenna and without the receive noise, if t ( t ≤ K ) of the active users can be identified by an oracle, theremaining K − t active users can also be accurately identifiedfrom the interference-cancelled pilot signal as long as thetriplet ( N, K, L ) satisfies the following inequality: L ≥ C ( K − t ) ln (cid:18) N − tK − t (cid:19) , t = 0 , , , · · · , K, (7)where C > is a constant. Since the right-hand side of (7)decreases with t , it means that if more active users can beccurately found by an oracle, the perfect active user recoverycondition can be met more easily for the remaining users. Inother words, increasing the sparsity level in the received pilotsignal is useful to improve the activity detection performance.Unfortunately, this conclusion is drawn by imposing strictassumptions, which is rarely the case in practice.To resolve this issue, the missed detection corrector selects min { S a , | ˆ P ( i ) a |} users from ˆ Q ( i ) a based on the channel decod-ing results, and the set of selected users for pilot interferencecancellation in the i -th iteration, is denoted as ˆ M ( i ) a . Here, S a is a preset parameter in the proposed framework. In casethat | ˆ P ( i ) a | > S a , the S a users with the minimum Euclideandistances between ˇ x ( i ) a,j and ˇ s ( i ) a,j are selected. Thereafter, thepilot data of the selected set of users is subtracted from thereceived pilot signal Y ( i − p for the next iteration: Y ( i ) p = Y ( i − p − p Lρ X j ∈ ˆ M ( i ) a ˇ h ( i ) j a Tj , (8)and Y ( i ) d is updated accordingly as follows: Y ( i ) d = Y ( i − d − √ ρ X j ∈ ˆ M ( i ) a ˇ x ( i ) a,j ˇ h ( i ) j . (9)If ˆ P ( i ) a = ∅ , the proposed algorithm will be terminated andthe data decoding results of all users from ˆ Q ( i ) a are deemedas incorrect. Otherwise, the AMP-based algorithm adopted bythe initial estimator will be invoked again with Y ( i ) p , Y ( i ) d , N ( i ) = N ( i − − | ˆ M ( i ) a | and K ( i ) = K ( i − − | ˆ M ( i ) a | as inputfor re-estimating the user activity pattern and data symbolsbefore calling the false alarm corrector in the next iteration.IV. S IMULATION R ESULTS
A. Simulation Settings and Baseline Schemes
We simulate a single-cell uplink cellular network with N = 500 users to corroborate the effectiveness of the proposeddata-assisted user activity detection algorithm, where the usersare located on a circle with a radius of 500 m to the BS.Each element of the precoding matrix P n is sampled fromthe complex Gaussian distribution with zero mean and unitvariance. In addition, we apply an idealized channel codingscheme, where perfect data recovery is assumed to be feasibleif the symbol error in each block is below 20%. It is worthymentioning that the proposed algorithm is readily applicablefor practical channel coding schemes, such as the low-densityparity-check codes (LDPC) [21]. The simulation results areaveraged over independent realizations. Other criticalparameters used in simulations are summarized in TABLE I.We adopt three baseline schemes for comparisons: • Separate design:
This scheme was proposed in [10],where channel estimation and user activity detection arefirst performed using the AMP-based algorithm as statedin Section III-A. After that, data symbols are detectedusing an MMSE estimator. • The proposed algorithm with false alarm correctiononly:
The main purpose of comparing this scheme is to
TABLE IS
IMULATION PARAMETERS
Parameters Values Parameters Values M L L d s β n − . dB α n CN ( , I M ) θ F θ F θ F S a reveal the impacts of the false alarm users on the systemperformance, including the activity detection error anddata error. Specifically, we execute the proposed frame-work without invoking the missed detection corrector inthis baseline scheme. • Perfect knowledge of the user activity pattern:
Thisscheme assumes perfect knowledge of the user activitypattern and consequently, channel estimation and datadetection can be performed for the active users as thosein conventional uplink cellular networks. However, asthe user activity pattern cannot be known as prior, thisscheme is unachievable in practice but can serve as avaluable performance upper bound.
B. Results
We first evaluate the user activity detection error rate,including the false alarm and missed detection probabilities,depicted in Fig. 4. As seen from this figure, both the falsealarm and missed detection probabilities increase with thenumber of active users. This is owing to the limited pilotresources available for user activity detection. Besides, forboth the proposed framework and the separate design, it isobserved that the false alarm probabilities dominate, whichconfirms the significance of the false alarm users to theoverall activity detection accuracy. In addition, comparedto the separate design, the proposed framework drasticallyreduces both types of activity detection error, which verifies itseffectiveness in improving the activity detection performanceby fully utilizing the sparsity pattern encoded in the receivedpilot and data signals. Moreover, we see that the performanceimprovement achieved by the proposed framework comparedto the separate design is much more remarkable when K isbelow 100, indicating that it is most effective when the trafficload in the systems ranges from light to medium.Next, we investigate the data error performance achievedby different algorithms and show the relationship between theblock error rates (BLERs) and the number of active users inFig. 5. Similar to the user activity detection error, the BLERsincrease with the number of active users in the system. It isalso noticed that the false alarm users have a significant impacton the BLER performance. For instance, when K = 100 ,the proposed framework is able to reduce the BLER from × − to × − by invoking the false alarm correctiononly, while further applying the missed detection correctoronly secures an extra 14.3% BLER reduction. This matches K -4 -3 -2 A c t i v i t y D e t e c t i on E rr o r P r obab ili t y Seperate Design (False alarm)Seperate Design (Missed detection)Proposed (False alarm)Proposed (Missed detection)
Fig. 4. Activity detection error probability vs. the number of active users. the results in Fig. 4, where false alarm dominates the activitydetection error. In addition, our proposed framework is able tosupport a substantially larger amount of active users comparedto the baselines. For instance, if the BLER requirement is setto be − , the proposed data-assisted user activity detectionalgorithm is capable of supporting fifteen additional users,which is a more than 20%-improvement compared to theseparate design. This again validates the superiority of thedata-assisted design by fully exploiting the signal sparsity.
60 70 80 90 100 110 120 130 140 K -5 -4 -3 -2 -1 B L E R Separate DesignProposed Algorithm with False Alarm Correction OnlyProposed AlgorithmPerfect Knowledge of User Activity
15 active users
Fig. 5. BLER vs. the number of active users.
V. C
ONCLUSIONS
In this paper, we proposed a data-assisted user activity de-tection framework for massive random access. This frameworkeffectively exploits the common sparsity pattern in both thereceived pilot and data signal, and thus boosts the performanceof massive access for mMTC applications. Simulation resultsdemonstrated that with the proposed framework, more than20% of active users can access the network with sufficientreliability. Based on this promising result, we advocate fora holistic approach on designing massive random access systems, by integrating the tasks of activity detection, channelestimation, and data detection and fully exploiting the availableprior structure information. This calls for further investigationson efficient algorithms and theoretical analysis.R
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