1 Variational Bayesian Inference Clustering Based Joint User Activity and Data Detection for

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Variational Bayesian Inference Clustering Based

Joint User Activity and Data Detection for

Grant-Free Random Access in mMTC

Zhaoji Zhang, Member, IEEE, Qinghua Guo, Senior Member, IEEE, Ying Li, Member, IEEE,

Ming Jin, Member, IEEE, and Chongwen Huang, Member, IEEE

Abstract—Tailor-made for massive connectivity and sporadic

access, grant-free random access has become a promising candi-

date access protocol for massive machine-type communications

(mMTC). Compared with conventional grant-based protocols,

grant-free random access skips the exchange of scheduling infor-

mation to reduce the signaling overhead, and facilitates sharing

of access resources to enhance access efﬁciency. However, some

challenges remain to be addressed in the receiver design, such

as unknown identity of active users and multi-user interference

(MUI) on shared access resources. In this work, we deal with

the problem of joint user activity and data detection for grant-

free random access. Speciﬁcally, the approximate message passing

(AMP) algorithm is ﬁrst employed to mitigate MUI and decouple

the signals of different users. Then, we extend the data symbol

alphabet to incorporate the null symbols from inactive users. In

this way, the joint user activity and data detection problem is

formulated as a clustering problem under the Gaussian mixture

model. Furthermore, in conjunction with the AMP algorithm, a

variational Bayesian inference based clustering (VBIC) algorithm

is developed to solve this clustering problem. Simulation results

show that, compared with state-of-art solutions, the proposed

AMP-combined VBIC (AMP-VBIC) algorithm achieves a signif-

icant performance gain in detection accuracy.

Index Terms—Massive machine-type communications, grant-

free, joint user activity and data detection, variational Bayesian

inference, clustering, approximate message passing.

I. INTRODUCTION

INternet of Things (IoT) facilitates information exchange

among objects in the physical world, and motivates the

development for a diversity of novel applications, such as

the smart city, smart grid, factory automation, etc. As an

important constituent scenario in 5G, massive machine-type

communications (mMTC) has been proposed to accommodate

Zhaoji Zhang and Ying Li are with the School of Telecommunica-

tions Engineering, Xidian University, Xi’an 710071, China (email: zhao-

jizhang@xidian.edu.cn; yli@mail.xidian.edu.cn).

Qinghua Guo is with the School of Electrical, Computer and Telecommu-

nications Engineering, University of Wollongong, Wollongong, NSW 2522,

Australia (e-mail: qguo@uow.edu.au)

Ming Jin is with the Faculty of Electrical Engineering and Com-

puter Science, Ningbo University, Ningbo 315211, China (e-mail: jin-

ming@nbu.edu.cn).

Chongwen Huang is with the College of Information Science and Electronic

Engineering, Zhejiang University, Hangzhou 310027, China, also with the

International Joint Innovation Center, Zhejiang University, Haining 314400,

China, and also with the Zhejiang Provincial Key Laboratory of Information

Processing, Communication and Networking (IPCAN), Hangzhou 310027,

China (e-mail: chongwenhuang@zju.edu.cn).

(Corresponding Author: Ying Li)

diversiﬁed IoT services [1]. Compared with conventional sce-

narios, mMTC is characterized by (i) the massiveness and low

activation probability of user equipments (UEs), (ii) short data

packets from activated UEs, and (iii) demand for low power

consumption by low-cost UEs. Furthermore, these features will

become more prominent with the evolution of B5G and 6G.

In medium access control (MAC) protocols, the random

access mechanism conﬁgures connection setup for uplink

transmission, i.e., the random access procedure allocates trans-

mission resources to randomly activated UEs. However, the

massiveness of UEs and shortage of uplink resources in

mMTC have made random access a bottleneck problem for

MAC designs [2], [3]. Existing random access schemes can

be roughly divided into two categories, i.e. grant-based and

grant-free schemes. In grant-based random access schemes,

a handshaking procedure is needed to exchange the control

signaling between the base station (BS) and active UEs.

However, this handshaking procedure may incur prohibitively

high signaling overhead for mMTC, which undermines the

transmission efﬁciency of the small-sized data packets.

As an alternative to grant-based schemes, grant-free random

access has emerged in recent years. In grant-free schemes, the

handshaking procedure is skipped, while active UEs can share

the uplink access resources, and directly transmit their data

packets without the grant from the BS. To ensure successful

data recovery under grant-free random access, several critical

problems need to be addressed at the BS. For example, the

BS needs to solve the user-activity detection (UAD) problem

to identify the active UEs, as well as the channel estimation

(CE) problem to obtain the channel state information (CSI) for

these active UEs. After that, the BS needs to solve the multi-

user detection (MUD) problem to detect the data from active

UEs. Considering different enabling techniques for grant-free

random access, the state-of-art solutions to above-mentioned

problems are reviewed as follows.

A. Grant-Free Random Access Enabled by MIMO and OFDM

As important enabling techniques for mMTC, the multi-

ple input multiple output (MIMO) technique and orthogo-

nal frequency division multiplexing (OFDM) technique can

exploit spatial diversity and frequency diversity respectively

to support the massive connectivity. On the other hand, the

mobile trafﬁc report [4] shows that only a small fraction of

UEs will be activated in typical IoT applications. To exploit

arXiv:2210.13773v1 [eess.SP] 25 Oct 2022

this sparseness of active UEs, the framework of compressed

sensing (CS) [5], [6] has received extensive studies. Under

this CS framework, each UE is allocated with a unique pilot

sequence, which will be transmitted with its data packet if

this UE is activated. In this way, MIMO-enabled and OFDM-

enabled grant-free random access share similar formulation

of the detection problem, and the entire detection procedure

is typically divided into two steps. Firstly, the joint UAD

and CE problem is formulated as a sparse-signal recovery

problem. Different CS algorithms have been proposed for this

problem, such as the modiﬁed Bayesian CS algorithm [7], the

block orthogonal matching pursuit (BOMP) algorithm [8], the

approximate message passing (AMP) algorithm [9]–[11], the

deep neural network-aided sparse Bayesian learning algorithm

[12]. In the second step, the MUD problem can be readily

addressed according to the UAD and CE results.

B. Grant-Free Random Access Enabled by Spreading

The spreading technique serves as another enabling tech-

nique for mMTC with intriguing implementation feasibility.

In spreading-enabled grant-free access mechanisms [13]–[17],

each data symbol is spread with a UE-speciﬁc spreading

sequence, while all the spread symbols of each UE experience

the same scalar channel gain during transmission. In this way,

the CE problem is signiﬁcantly simpliﬁed, and spreading-

enabled grant-free random access enjoys a much simpler prob-

lem formulation for receiver design. Then, different solutions

have been proposed for the joint UAD and MUD problem.

For example, an iterative order recursive least square (IORLS)

algorithm [13] was proposed to exploit the joint sparsity of

the data matrix to improve the detection accuracy. A joint

expectation maximization and AMP (EM-AMP) algorithm was

proposed in [14], where the data matrix is detected from the

received signal by the AMP algorithm [18], while the activity

detection is addressed by the EM algorithm [19]. In addition,

a structured iterative support detection (SISD) algorithm is

proposed in [15]. In [16], a block sparsity adaptive subspace

pursuit (BSASP) algorithm is proposed for the joint UAD

and MUD problem, while the CE problem is addressed with

a reference symbol. Recently, a joint UAD, CE, and signal

detection (JUICESD) algorithm was proposed in [17], where

the AMP algorithm is employed for signal detection and the

detected signals are also used to reﬁne the CE result.

These above-mentioned solutions [13]–[17] involve some

infeasible assumptions or deﬁciencies. For example, the spar-

sity level, i.e. the exact number of active UEs is assumed

known to the BS in [13], while the schemes in [14], [15]

require perfect knowledge on CSI at receiver (CSIR) even for

inactive UEs. Such information is commonly unavailable in

mMTC scenarios due to the massiveness and random activity

of UEs. In addition, the subspace pursuit principle in [16] fails

to address the inherent modulation constraint of data symbols,

which undermines the data-detection accuracy. The UAD in

[17] relies on a non-deterministic detection threshold, while

ﬁne-tuning this threshold may incur tedious work under com-

plicated mMTC scenarios. Recently, some advances on MUD

techniques have inspired new ideas to tackle these deﬁciencies,

and the details are explained in the next subsection.

C. Clustering and Variational Bayesian Inference for MUD

It is noted that modulated data symbols are discrete, while

the received signals corrupted by fading and noise approxi-

mately follow the Gaussian distribution. Inspired by this fact,

an unsupervised clustering approach is proposed in [20] for

the joint CE and MUD problem. Speciﬁcally, the Gaussian-

mixture model (GMM) is used to model the noise-corrupted

received signals, where each cluster in the GMM is associated

with one data symbol. Then, the EM algorithm is adopted for

this clustering problem. However, the successive interference

cancellation (SIC) principle is adopted for MUD in [20], which

requires sufﬁciently large power difference among different

users. For mMTC scenarios with densely deployed UEs, the

received power of different UEs can be strongly correlated,

which undermines the detection accuracy of SIC-based MUD.

In addition, the variational Bayesian inference (VBI) method

was employed for CE and MUD in one-bit quantized MIMO

system [21]. With its powerful inference capability for in-

tractable distributions, the VBI could effectively infer the

distributions of the CSI and the data symbols from the received

signals, which are heavily distorted after one-bit quantization.

D. Motivations and Contributions

Intrigued by the implementation feasibility, we consider

the spreading technique to enable grant-free random access

for mMTC in this paper. In order to address the deﬁciencies

of existing solutions and improve the detection accuracy, an

AMP-combined variational Bayesian inference-based cluster-

ing (AMP-VBIC) algorithm is proposed for joint user activity

and data detection. Speciﬁcally, the decoupling operations

in the AMP framework are adopted to mitigate multi-user

interference (MUI) and decouple the signals of different UEs.

Given the decoupled signals, we ﬁrst extend the data symbol

alphabet to incorporate the null symbols from inactive UEs,

and then formulate the joint user activity and data detection

as a novel clustering problem under the GMM. Then, we

develop a variational Bayesian inference based clustering

(VBIC) algorithm for this clustering problem, where the CE

result is also reﬁned during the clustering procedure. The

major contributions of this paper are summarized as follows.

(i) With the extended symbol alphabet, the joint user activity

and data detection is formulated as a clustering problem under

GMM. Then, we derive the VBIC algorithm for this clustering

problem, which iteratively works in conjunction with the AMP

decoupling module to reﬁne the detection accuracy.

(ii) In the VBIC algorithm, the CE result is iteratively

updated with the clustering result of all the data symbols,

which in return improves the UAD and MUD accuracy.

(iii) Analyses are provided to demonstrate the favorable

linear complexity of the proposed AMP-VBIC algorithm,

while simulation results show its superior detection accuracy

over the state-of-art solutions.

The remainder of this paper is organized as follows. Section

II describes the system model, and the AMP-VBIC algorithm

is proposed in Section III for the joint user activity and data

detection problem. Simulation results are provided in Section

IV, and Section V concludes this paper.

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1VariationalBayesianInferenceClusteringBasedJointUserActivityandDataDetectionforGrant-FreeRandomAccessinmMTCZhaojiZhang,Member,IEEE,QinghuaGuo,SeniorMember,IEEE,YingLi,Member,IEEE,MingJin,Member,IEEE,andChongwenHuang,Member,IEEEAbstractTailor-madeformassiveconnectivityandsporadicaccess,grant-freera...

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