Chenmin Sha，Shidong Zhou

Department of Electronic Engineering，Tsinghua University，Beijing 100084，China

*The corresponding author，email: zhousd@tsinghua.edu.cn

Abstract: We try to extend the current configuredgrant (CG) uplink scheme in 5G New Radio (NR)to support massive potential users and study activity detection under this scenario.Characteristics of the continuously varying channel and the multiple repetition scheme are utilized to improve the detection accuracy，which can be an enhancement to existing activity detection algorithms.Numerical results under 3GPP TDL (Tapped Delay Line) fading channel show the superiority of our algorithm.And system-level simulation reveals that enhancements on activity detection can improve reliability and reduce latency.

Keywords:configured-grant;massive access;activity detection

I.INTRODUCTION

As an important application context of B5G (beyond 5G)，the Industrial Internet of Things (IIoT) raises great demands of massive sporadic access，which，however，also requires ultra reliability and low latency communications (URLLC) [1].Although traditional grant-based (GB) transmission is capable of supporting reliable access by avoiding collision through wellorganized resources，the procedure of the handshaking before data transmission introduces significant access delay and resource overhead especially for sporadic short packet data access，which is typical in IIoT[2，3].In recent years，grant-free (GF) transmission has gained much attention in the literature，reducing uplink access delay and overhead of handshaking by allowing access without permission，e.g.，[4，5，4].In 5G NR by 3GPP，GF is adopted in the configure-grant mode，where shared radio resources are preserved for a set of potential users to transmit sporadic short packets without request for each packet[6].In this mode，the newly arrived packet is coded and transmitted in a single short TTI(transmit time interval)with multiple repetitions in subsequent TTIs for reliability enhancement.Orthogonal pilot (reference signal) sequences are assigned to the potential users sharing the same resources，in order to distinguish which user is active[7，8].Although CG has its advantages on low latency and high reliability，it is mainly designed for URLLC with few users [9] by now.To support URLLC requirements for massive users，enhancements on the current CG mode are needed.

There have been many researches on design and performance evaluation of CG (e.g.，[10-12]).Some of these assume that at most one user is able to be resolved[12，13].Others have taken multiuser decoding into consideration but they assume the procedure of activity detection(AD)to be perfect[10].

However，neither of these two assumptions are practical in massive access scenario.As the number of potential users increases，there will be collisions in almost every TTI and more sophisticated multi-user decoding schemes are needed，e.g.，sparse code multiple access (SCMA) [14]，interleave division multiple access(IDMA)[15]，etc.

Although many progresses on capacity approaching multi-user coding schemes have been achieved in recent years，the successful decoding for grant-free multiple access relies heavily on accurate activity detection.Since the number of resource elements(REs)for pilots is very limited in a TTI，orthogonal pilot design is not capable for cases with massive potential users[16].Therefore，non-orthogonal pilot and corresponding AD should be taken into account in the application of CG for future IIoT，where the assumption of ideal AD is inappropriate.Yet there are still no reports on the design and performance evaluation of such cases，which will be the main target of this paper.

In recent years，there are many researches on AD of massive sporadic access in flat block fading channel[16-19]，however，these methods and their performance evaluation could not be applied directly to CG for the following reasons:

1.Correlated frequency selective fading(FSF)channel should be considered since the wider band is needed to support shorter TTI for low latency.

2.The opportunity for AD enhancement from multiple repetitions in CG are not dealt with in these literature.

Although there are several literatures providing AD methods in multiple bands with independent fading[20]，such assumption cannot take advantage of the correlation among adjacent sub-channels，which will introduce performance loss in practical channel.Some researches have taken the time-varying characteristics of user activity into consideration[21，22]using probabilistic models，but they can hardly cover the scene of multiple repetitions with ACK feedback and they require the information about the active probability of users.

In this paper，we try to explore the capability of CG in 5G NR for massive sporadic access with heavy traffic，focusing on enhanced AD and system-level evaluation.The main contributions are as follows:

· To improve activity detection under correlated FSF channel，we extend the maximum likelihood(ML) method [19] to adapt to fading channels with arbitrary covariance.

· Under the multiple repetition scheme，in order to identify the current active users together with their current redundancy version，we propose a way to utilize several TTIs for combined detection.

· Simulation under the standard TDL-C channel verifies the effectiveness of the proposed methods.

The rest of this paper is organized as follows: Section II depicts the system model and Section III introduces the performance metrics.Section IV presents how we exploit the characteristic of the FSF channel and K-repetition scheme.Then Section V shows the simulation results and analysis.Finally，the discussion and conclusion of this work are in Section VI.

II.SYSTEM MODEL

2.1 Configured-grant Access Model

Consider an uplink single-cell system consisting of one base station(BS)withMantennas andNsingleantenna users.At the beginning of each TTI，a data packet of each user arrives independently with probabilitypa，and the arrived packet is coded and transmitted together with pilots immediately in this TTI and the same packet is repeatedly transmitted in following TTIs until an ACK is received orKrepetitions are transmitted (as shown in Figure 1).In this paper，where massive sporadic access is considered，it is assumed thatpa ?1，so that the queuing at the user is negligible.System parameters such as uplink resource，modulation and coding scheme (MCS)are configured by BS before GF transmission.In this paper，it is assumed that the user will immediately know when it is decoded successfully，that is to say，there won’t be any unnecessary repetitions.Besides，HARQ retransmission is not included here-a packet is dropped when it could not be decoded successfully after K repetitions.

2.2 Pilots Configuration

In order for BS to be able to identify which repetition an active user is sending，we consider each device uses a different pilot sequence for each repetition，which means that the pilot sequence can tell which user is sending which repetition.The total number of pilot sequences isNK，and the sequence carried inkthrepetition of usernis denoted as skn.

2.3 Channel Model

A typical MIMO-OFDM system is considered here.The channels betweenMantennas at BS and each user are independent.And channel gains vary continuously on different subcarriers.Pilot symbols are allocated uniformly across all the subcarriers.Suppose that one TTI occupiesTOFDM symbols in the time domain andRadjacent RBs in the frequency domain(each RB consists of 12 subcarriers).However，in this article we only care about the small scale fading of the channel，assuming that the path-loss is fully compensated by power control.

2.4 Received Signal

Since channels between users of each receive antenna are supposed to be independent identically distributed，we can only pay attention to signals received on one antenna.The length of the pilot sequence in one repetition isL- there areLREs in one TTI used for pilots.AtithBS antenna，the received pilot symbols in current TTI，forming a vector yi ∈CL，can be expressed as:

where Skn=diag(skn)，and wiis the additive gaussian white noise，wi ～CN(0，σ2wI)，hni ∈CLrepresents the channel all pilot symbols of userngo through atithantenna，hni ～CN(0，Σhi)，Σhi= E(hnihTni).More precisely，hnionly indicates the small scale fading brought by multipath effect.γkn=akngnis the multiplication of activity indicatorakn ∈{0，1}which indicates whether usernis sending thekthrepetition and large scale fadinggn.By assuming perfect power control，we havegn= 1.What’s more，a user at most sends one repetition at a time so.And we denote γ = (γT1，...，γTn，...，γTN)Tand γn=(γ1n，...，γKn)T.

III.PERFORMANCE METRIC

3.1 Detection Latency and Decoding Latency

Considering the K-repetition scheme，the state of the system at the current time is influenced by states in history and will impact the system behavior in the following TTIs.Therefore，we consider the cumulative distribution of latency as a performance metric of the grant-free system even，which is different from other works on activity detection and can better describe the temporal behavior of the system.

The system latency includes detection latencyτdetectionand decoding latencyτdata.τdetectionis defined as the number of TTIs between packet arrival and this packet is detected by BS for the first time，andτdatais the number of TTIs between packet arrival and the packet is decoded successfully.For instance，in Figure 1，the latency for User A isτdetection= 2 andτdata= 3.But user B is not discovered by BS and henceτdetection=τdata=∞.As a matter of fact，under our assumptions，the delay means the actual number of repetitions that have been sent before detection or decoding and obviouslyτdetection ≤τdata.

Figure 1. Illustration of timing relationship in the system.

Then definition of the CDF of detection latency Pr{τdetection ≤k}and decoding latency Pr{τdata ≤k}are given as below.Suppose the system has worked forTTTIs，and during this period，a total ofNppackets are generated，among which there arendetkpackets that satisfyτdetection=kandndatkthat satisfyτdata=k，andk ∈{1，2，...，K}if at mostKrepetitions is allowed，then

3.2 Reliability and Average Latency

Based on the CDF of decoding latency，we can define the system reliability and average latency (measured in TTIs).The system reliability means the probability a packet is decoded successfully withinKrepetitions:

And the average latency is defined as the average delay of the successfully decoded packets:

3.3 Detection Error Probability

WhenK=1，we can use a more explicit way to compare performances of different detection algorithm，that is detection error probability Pe.Peis defined as

where PMand PFAmean miss detection probability and false alarm probability respectively and they are defined as follow:

whereAcis the set of actual active users andis the set of active users estimated at the BS side.

IV.ACTIVITY DETECTION ENHANCEMENT

Our first scheme is to identify the active users and their redundancy version in the current TTI according to the pilot signals received in this TTI under correlated FSF channel.The second method gives a way to combine the observation in history TTIs based on the relevance of users’ redundancy versions in time for further enhancements on detection accuracy.

4.1 Activity Detection under Correlated FSF Channel

4.1.1 Maximum likelihood estimation

Similar to[19]and[23]-we get activity information through the maximum likelihood estimation of the γ.The greatest difference is that in our model pilot symbols of one user can have different channel gains while the original method only considers block fading channel.According to Equation (1)，the distribution conditioned on γ of the signal at theithBS antenna is as follows:

Algorithm 1. SGD to estimate γ.Require: covariance matrix ?Σy = 1 M YYH Ensure: estimated result ?γ 1: Initialize: ?γ=0，Σ=σ2wI 2: while The number of iteration has not been reached do 3: Select an index(n，k)randomly or according to a specific schedule.4: Set d* =max{-tr(Σ-1Ckn-Σ-1CknΣ-1 ?Σy)tr(Σ-1CknΣ-1Ckn)，-?γkn}5: Update ?γkn ←?γkn+d*6: Update Σ ←Σ+d*Ckn 7: end while

and the constraint (12) is just another expression of

4.1.2 Optimization method

The objective function (11) is non-convex，and the constraint is hard to tackle directly.To solve the problem，we first relax the constraint(12)and find the unconstrained optimal solution(possibly infeasible)and then project it to the feasible set.

For the unconstrained problem (11)，since it is still non-convex，we handle it using stochastic gradient descent(SGD)method.The gradient on each dimension is easy to give as follows:

The step sizeηknin each update of SGD is set to be adaptive-we setBesides，to meet the non-negativity of γ，the update step needs to be modified toThe algorithm to estimate γ is listed in algorithm1.

Remark 1.The optimization procedure is similar to that in[23].And under this set of step size，the procedure of parameter updating is the same as[23]whenthe channel covariance matrixΣh is all one matrix.The similarity in the mathematical form will ensure the good convergence of our SGD process.

4.1.3 Activity detection

4.1.4 Channel covariance matrix

When the accurate covariance of channel gains cannot be attained，we propose to adopt the following empirical covariance matrix:

where 1lmeans all-one matrix with the size ofl×l，andlrepresents the number of pilot symbols that are located within a coherent bandwidth andρrepresents the coefficient of association between adjacent coherent bandwidths.It is assumed that pilot symbols are uniformly allocated on different subcarriers and this is the common case.As a reminder，when Σhis written as above，the pilot vector sknshould be formed in the shape that adapts to the covariance matrix.

4.2 Combined Detection under K-repetition Scheme

In the previous subsection，we have investigated how to improve activity detection under correlated FSF channels.However，the ?γ obtained from Algorithm 1 for activity estimation is merely based on signals received in current single TTI，and this will lose the prior information of multiple repetition scheme.More straightforward，when a user hasn’t received ACK，it will keep active in consecutive TTIs.For example，suppose we haveakn= 1 in one TTI，but the usernisn’t decoded successfully by this repetition，then it is sure to haveakn+1= 1 t he next TTI.But current estimation method may cause contradicts to this characteristic.

Algorithm 2. Sequential update rule of π during each TTI.Require: Old π from last TTI，?γ estimated at this TTIs Ensure: The new π 1: Define a temporary variable μ=π 2: for n=1，...，N do 3: if User n is decoded successfully then 4:πn =0 5: else 6:π1n =0 7:for k =2，··· ，K do 8:πkn =μk-1n +?γkn 9:end for 10: end if 11: end for

To cope with this problem，we put forward a heuristic method.The estimation of γ obtained from Algorithm 1 can be treated as the belief indicator of the corresponding state.For a given user，as more repetitions are sent，we hope that the BS will have more belief in its activity.That is to say，the belief indicator should be able to increase when more repetitions are sent.So we introduce the concept of ”accumulative belief indicator”，whose meaning is explained as after.It has to be mentioned that in [20] the sparsity ratio of different sub-bands is averaged to obtain the gain of diversity transmission，but this cannot adapt to the asynchronous access considered here.

Let’s denote π as the accumulative belief indicator of activity where π = (πT1，...，πTN)Tand πn=(π1n，...，πKn)T.π represents the belief indicator of the current state of each user in the system.The renewal procedure of π is shown in Algorithm 2.The idea of combining indicators can be seen through Figure 2 explicitly-The accumulative indicator π stores the activity information of past.Each time we estimate new ?γ from the received signal in current TTI we update π and using it for activity judgement.

The estimated activity of each user is then accom-plished through π as shown in Equation(16).

V.SIMULATION RESULTS

In the simulation results part，we will prove the effectiveness of the proposed scheme.We first present the improvements in system latency and reliability brought by them.Then we show respectively the gains from the two proposed methods.We test activity detection under correlated FSF channels and show its superiority against baseline methods.We also test its performance under different levels of delay spread.Then，we verify the necessity of the combined detection method under the K-rep scenario by comparing it with only lowing down the decision thresholdlth.Finally，we explore how the system capacity scales with the increase of receive antennas based on our simulation environment.

5.1 Simulation Settings

5.1.1 Basic System Settings In subsequent simulations a TTI is 2 OFDM symbols with 20 RBs(one RB has 240 REs).A total of 120 pilot symbols are uniformly allocated in the first OFDM symbol and 360 REs are left for data.The frame structure is illustrated in Figure 3.Before we explore the relationship between system capacity with the antenna number，we all set antenna numberM= 4.3GPP standard TDL-C channel model is used.Channel covariance matrix(15)is adopted here and it is supposed that channels are invariant within a RB hencel=6 in(15).The arrival rate of packets is set aspa= 0.01.Basic system settings that remain unchanged through simulations are summarized in Table 1.

Table 1. Basic system settings.

Figure 2. Illustration of the idea of combining estimation results.

Figure 3. Description of the frame structure.

5.1.2 Physical Layer Abstraction

When considering the multiple repetition scheme，activity detection and data decoding are integrated into the system-level simulation.The activity detection procedure is entirely simulated，but the decoding procedure is simplified through physical layer abstraction to reduce simulation time.It is assumed that each repetition is transmitted using the same redundancy version and they are combined via chasing combing(CC).After activity detection，channel estimation is obtained through a minimum-mean square error(MMSE)estimator and the channel gain in each RB is still thought to be constant.To reduce computational complexity，pilots in adjacent 4 RBs are used for activity detection in system-level simulation and others are used for channel estimation only.The MMSE decoder is assumed.The success or not of the decoding of a packet depends on the post-processing SINR after the decoder combining.The block error probability is acquired according to link-to-system mapping based on exponential effective SNR mapping (EESM) as depicted in [24] and model parameters also come from[24].The parameters of system-level simulation are listed in Table 2.

Table 2. Parameters of system-level simulation.

5.1.3 Baseline Methods

The GMMV-AMP method in[20]and the maximumlikelihood(ML)algorithm in[19]are chosen as baselines.GMMV-AMP method treats channels in different coherence blocks as independent and the ML algorithm considers channels as invariant through all blocks.For GMMV-AMP，the parameters of the algorithm are set according to[20] and belief-indicator based activity detection is used.Noting that our Algorithm 1 is also based on ML and is an extension of[19].Actually，the ML method of [19] corresponds to the special case of our method whenρ= 1 in the covariance matrix(15).

5.2 Performance of Proposed Schemes

5.2.1 Improvements in Latency and Reliability In our system-level simulation，there are a total ofN= 250 users and a user is allowed to sendK= 6 repetitions of a packet at most.The delay spread of the TDL channel is DSdesired= 300ns.The threshold used for activity judgment is set aslth= 0.15 for our proposed methods.The CDF of the overall latency(computed according to(3))and reliability is shown in Figure 4 and Table 3.

Table 3. Quantitative comparisons of different methods.

5.2.2 Activity Detection Under Correlated FSF Channel

We then show the detection error probability of different detection methods.Here we don’t consider multiple repetitions.The comparison is taken under the delay spread of DSdesired=300ns.We compare their performance by changing the number of total users in the system.The result is shown in Figure 5.It is obvious that our scheme obtains the best performance with the most accurate assumption on the channel.

Figure 4. Comparison of different detection algorithms in system level.

Figure 5. Error probability of different detection algorithms.

Figure 6. Compare of performance under different delay spread.

We further explore how our detection algorithm performs under different delay spreads.Notice that the larger the delay spread means the faster change of channel between coherence blocks.The desired delay spread DSdesiredof 100nsand 300nsare tested and in our algorithm we setρ= 0.9 andρ= 0.6 respectively for the two situations.The total user number is set to beN=500.And we change the number of RBs used for activity detection(which is reflected as pilot length) since we are interested in how the correlation of sub-channels affects the detection performance.

From Figure 6 we can first see that when the correlation between adjacent blocks is weaker，the detection algorithm performs worse.Besides，we can observe the difference in descending rate of the error probability against pilot length.When the channel changes more slowly among frequencies，the detection performance improves more quickly as pilots increase.

5.2.3 Combined Detection Using Multiple Repetitions

Next，we show the effect of belief indicator combining.We change the threshold of activity decision but without combination and compare the performance through system-level simulation.The result is shown in Figure 7.It can be seen that although we seem to get a shorter detection delay by a smaller threshold，the reliability can hardly achieve the effect of indicator combining.This is because a lower threshold brings more false alarms，which harms the quality of channel estimation and decoding as well.In other words，the combining method decreases the total missed users without increasing false alarms.

Figure 7. Comparison of detection with and without indicator combining.

5.3 Scaling Law of System Capacity with Number of Antennas

At the end of the simulation part，we are interested in the relationship between the ability of CG to support massive access and the number of antennas.We increase the number of antennasMat the BS side and change the number of usersNto find the most users the system can support under certain reliability constraints.Our proposed schemes are used for activity detection.Other system parameters stay the same as Table 1 and 2.We first show the outage reliability of the system under different numbers of users with different numbers of users in Figure 8.

Figure 8. Outage probability under different parameters.

Then we plot the maximum users the system can support with different antenna numbers under given reliability constraint，which is observed from the above figure.The curves are shown in Figure 9.It can be seen that the user number increases with the antenna numbers approximately linearly.

Figure 9. Maximum users the system can support under reliability constraint.

VI.CONCLUSION

In this paper，the CG scheme for massive potential users is studied and we propose two algorithms for enhancements of activity detection.The performance of detection is improved utilizing the characteristics of the dispersive channel and K-repetition scheme.To our best known，our work is the first to take frequency selectivity into activity detection.Although the use of the SGD method in our solution to the non-convex optimization problem is heuristic，it shows great convergence in practice.The combined detection method to exploit multi-segment pilots is useful but also has low complexity.However，the correlation of channels on consecutive TTIs is not considered here and how to utilize this characteristic is still worth further study.In addition，the evaluations of activity detection are taken under the practical channel.Since we focus on activity detection，we do not pursue the practicality of the decoding part.But the conclusions in this paper are still valuable.

ACKNOWLEDGEMENT

This work was supported in part by the Key Research and Development Program of China under Grant 2018YFB1801102; in part by the National Natural Science Foundation of China under Grant 61631013;in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 61621091; in part by the Civil Aerospace Technology Project under Grant D040202;in part by the Tsinghua-Qualcomm Joint Project; and in part by the Tsinghua University Initiative Scientific Research Program under Grant 20193080005.