Bayesian Inference Algorithms for Multiuser
Detection in M2M Communications
Invited Paper
Xiaoxu Zhang
†
, Student Member, IEEE, Ying-Chang Liang
†∗
, Fellow, IEEE and
Jun Fang
†
, Member, IEEE
†
National Key Laboratory of Science and Technology on Communications
University of Electronic Science and Technology of China (UESTC)
∗
Institute for Infocomm Research, A*STAR, Singapore
Email: liangyc@ieee.org
Abstract—Machine-to-Machine (M2M) communications will
be playing an important role in the development of 5th gen-
eration (5G) and future wireless communication systems. Due
to the sporadic nature of massive access, Low-Activity Code
Division Multiple Access (LA-CDMA) is one of possible multiple
access schemes for M2M communications. In the literature,
maximum a posterior (MAP) detector has been proposed to
detect the active users when the user activity factor is known
and small. However, the user activity factor is usually unknown
and could be large in practice, which makes the multiuser
detection (MUD) a challenging task for LA-CDMA. In this paper,
we first introduce sparse Bayesian learning (SBL) method to
recover the transmitted signals for LA-CDMA uplink access.
The proposed method exploits the sparsity of the transmitted
signals and does not require the knowledge of user activity.
Furthermore, we add on the known finite-alphabet constraints
and introduce Gaussian mixture model (GMM) method to obtain
the transmitted signals. Simulation results have shown that the
proposed methods outperform the conventional algorithms.
I. INTRODUCTION
The 5th generation (5G) communication systems are ex-
pected to support four typical application scenarios, including
gigabit wireless connectivity, Internet of Thing (IoT), tactile
Internet and heterogeneous networking [1], [2]. Among these
applications, IoT, which is supported by Machine-to-Machine
(M2M) communications [3], [4], is promising technology to
transform the conventional sectors such as agriculture, trans-
portation, healthcare, industrial automation, etc. With the focus
shift from traditional human-to-human (H2H) to M2M, several
important issues related to communication system designs
have to be re-considered, including multiple access schemes,
resource allocations, and networking aspects.
In M2M, the number of devices is typically large, but,
at any given time interval, only part of the devices will be
active. Thus Low-Activity Code Division Multiple Access
(LA-CDMA) is a promising multiple access scheme to sup-
port such massive and sporadic communications. In the past
decades, a number of multiuser detection (MUD) algorithms
have been proposed for conventional CDMA in literature,
each with different complexity and performance tradeoff. For
LA-CDMA, when the user activity factor p
a
is known and
small (p
a
< 0.5), it has been shown that the joint detector
based on maximum a posterior (MAP) criterion achieves the
optimal detection performance [5]. Due to the NP-hard nature
of the MAP detector, the authors have proposed algorithms
by relaxing the combinatorial constraint so that optimization
tools can be applied directly to obtain the solutions.
When the user activity factor is low enough, the transmitted
signal vector is sparse, thus the reconstruction of the transmit-
ted signals becomes a compressive sensing (CS) problem. The
methods for recovering such sparse signals include orthogonal
matching pursuit (OMP) [6], basis pursuit (BP) [7], the FOcal
Underdetermined System Solver (FOCUSS) [8], and sparse
Bayesian learning (SBL) [9]. In this paper, we first apply
SBL method to recover the transmitted signals for LA-CDMA
uplink access by exploiting the sparsity of the transmitted
signals. This method does not require the knowledge of the
user activity factor. Furthermore, using Bayesian inference,
we propose a novel approach called Gaussian mixture model
(GMM) method [10] by exploiting the possible signal formats
of both inactive and active devices, i.e., the zero transmissions
of the inactive devices, and the known finite-alphabet of the
active devices. The algorithms for recovering the transmitted
signals of both active and inactive devices are proposed.
This paper is organized as follows. Section II presents the
system model for LA-CDMA uplink access, and reviews the
conventional MAP algorithms. In Section III, we introduce
the SBL algorithm for MUD for the formed problem. The
proposed GMM algorithm is derived in Section IV in details.
The simulations results are presented in Section V. Finally, we
conclude the paper in Section VI.
II. LA-CDMA
A. System Model
We focus on the uplink access in M2M communications,
in which there are massive devices transmitting data to a
central BS, as depicted in Fig.1. In such transmissions, in
an given time interval, some devices are active while others
are inactive, which makes the communications sporadic. LA-
CDMA is used to support such communication scenario, in