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54
AbstrAct
The anticipated 1000-fold increase in mobile
data traffic over the next decade and the explo-
sion of new services and applications pose great
challenges for the current orthogonal multiple
access (OMA)-based 4G systems. A promising
solution to address these challenges is to shift
from the currently predominant OMA to non-or-
thogonal multiple access (NOMA). This article first
introduces the principle of the complexity-con-
strained capacity-achieving NOMA design. Then
a non-orthogonal pattern division multiple access
(PDMA) scheme is proposed to meet the expo-
nentially growing demand of mobile users for
computing and information application services.
The key feature of the PDMA scheme is a joint
design of transmitter and receiver, which allows
low-complexity successive interference cancella-
tion (SIC)-based multi-user detection with substan-
tially improved performance over conventional
OMA schemes. More specifically, the patterns of
multiple users are judiciously designed so that the
data symbols of different users are of appropriate
diversity disparity at the symbol level and power
disparity at the resource element level. The appro-
priate disparity in diversity and power can be
effectively exploited by the low-complexity SIC-
based detector to realize the near-perfect cancel-
lation of multi-user interference. Moreover, the
PDMA system parameters can be flexibly adjusted
to provide different levels of overload, rendering it
suitable to meet the diverse traffic requirements in
future 5G systems. Link-level simulations illustrate
that PDMA is capable of accommodating a 300
percent overload, while it still enjoys transmission
reliability close to conventional OMA schemes.
The results demonstrated in this article indicate
that PDMA can be a promising multiple access
technology with low signaling overhead, low
latency, and massive connectivity support for 5G.
IntroductIon
The unprecedented increase of mobile data traf-
fic brought about by the wide proliferation of
smartphones and tablet computers is driving the
wireless communications industry to undergo an
unprecedented paradigm shift [1]. In addition, the
advent of the Internet of Things (IoT) will enable
new ways to monitor, assist, secure, and control
smart homes, smart factories, and so on, which
opens up a broad range of diverse applications
ranging from mission-critical services to massive
deployment of autonomous devices. These new
services may require the fifth generation (5G) net-
works to support massive connectivity of users
and/or devices to meet the demand for low laten-
cy, low-cost devices, and diverse service types.
Fast and efficient multiple access is the key tech-
nology to handle the massive number of sporad-
ic traffic-generating devices, such as the devices
which are inactive most of the time but regularly
access the network for minor updates without
human interaction.
The current wireless communication systems
have predominantly adopted orthogonal multiple
access (OMA) schemes, where users are allocat-
ed orthogonal physical resources in the time, fre-
quency, or space domain. Existing OMA schemes
efficiently eliminate multi-user interference and
thus allow relatively simple transceiver implemen-
tations. However, it is shown that OMA schemes
achieve strictly lower capacity than non-orthog-
onal multiple access (NOMA) schemes in the
downlink broadcast channel (BC) [2]. Such inef-
ficiency of OMA schemes is even exacerbated in
the uplink scenario [3]. Dimensioning the channel
access based on existing OMA paradigms may
lead to a severe waste of physical resources or
even fail to work in massive connectivity scenari-
os, such as the IoT applications.
To support the daunting task of massive spo-
radic connections, the wireless research commu-
nity is exploring different technical approaches,
such as novel cellular network architectures,
massive multiple-input multiple-output (MIMO)
techniques, spectrum utilizations at untapped mil-
limeter-wave frequency bands, new waveform
designs, and novel multiple access technologies.
Among these potential solutions, the NOMA
approach is especially suitable for meeting the
requirement of massive connectivity, and it is
also efficient in reducing transmission latency and
improving energy efficiency [4–8]. It has been
proven that NOMA is optimal in achieving the
entire capacity region of the BC [2] and exhibits
higher spectral and energy efficiency than OMA
for delay-sensitive applications in the multiple
access channel (MAC) [3].
However, the theoretically predicted gains of
NOMA over OMA rely on proper multi-user signal
separation at the receiver. To reap the full benefits
of NOMA, the maximum a posteriori probability
(MAP) multi-user detection (MUD) technique can
Xiaoming Dai, Zhenyu Zhang, Baoming Bai, Shanzhi Chen, and Shaohui Sun
P D M A:
A N M A T 5G
NON-ORTHOGONAL MULTIPLE ACCESS FOR 5G
Xiaoming Dai and Zhenyu Zhang are with the University of Science and Technology Beijing; Baoming Bai is with Xidian University;
Shanzhi Chen and Shaohui Sun are with the China Academy of Telecommunications Technology.
Digital Object Identifier:
10.1109/MWC.2018.1700084
IEEE Wireless Communications • April 2018 55
NON-ORTHOGONAL MULTIPLE ACCESS FOR 5G be utilized to achieve the desired performance.
The computational complexity of the MAP MUD
scales exponentially with the number of users and
imposes a formidable challenge to practical hard-
ware implementations. As an alternative to the
optimal MAP detector, the low-complexity succes-
sive interference cancellation (SIC)-based detec-
tor with single-user decoding is able to achieve
the Shannon capacity region boundaries in both
the BC and MAC scenarios [9, 10]. Nonetheless,
one main disadvantage of SIC-based detectors is
that errors occurring in detection of transmitted
symbols will propagate further into subsequent
symbols due to interference subtraction. Such
error propagation may severely degrade the sys-
tem performance, especially when the number of
users is large.
In this article, we first introduce the complex-
ity-constrained capacity-achieving NOMA design
principle, which was not addressed in [7, 8]. Then
we propose a non-orthogonal pattern division
multiple access (PDMA) scheme based on a joint
design of the transmitter and an SIC-based detec-
tor at the receiver for the uncorrelated and cor-
related channel scenarios. The latter is an extension
of [7, 8]. The patterns of different users are judi-
ciously designed to exhibit appropriate diversity
disparity at the symbol level and power disparity at
the physical resource element level. Such diversi-
ty disparity and power disparity among users can
be effectively exploited by the SIC-based detector
to achieve near-perfect cancellation of multi-us-
er interference. Furthermore, the PDMA system
parameters can be flexibly adjusted to support a
wide range of overload to accommodate diverse
applications. The analysis based on the constel-
lation-constrained (CC) capacity shows that the
PDMA scheme outperforms conventional OMA
schemes with affordable computational complexi-
ty. In addition, an iterative detection and decoding
(IDD)-based receiver [11] structure is elaborated to
improve the performance of the PDMA scheme.
Link-level simulations show that the PDMA scheme
is able to support up to 300 percent overload
and achieves significant performance gains over
conventional OMA schemes. The superior perfor-
mance on massive connectivity support is also veri-
fied by system-level simulations.
FundAmentAls oF
PAttern dIvIsIon multIPle Access
bAsIcs oF the sIc-bAsed detector
The SIC-based detector [2] iteratively decodes
symbols by subtracting the detected symbols of
strong users first to facilitate the following detec-
tion of weak users. The decoded data of the early
detected symbol is re-encoded, and by using
accurate channel knowledge, it can be recon-
structed to closely resemble the real transmitted
signal. However, the error propagation resulting
from low diversity of early SIC detection stages
may severely degrade the system performance. It
is generally accepted that, for a system equipped
with an SIC-based detector, the performance is
highly dependent on the first-step detection accu-
racy. The low-complexity belief propagation (BP)
algorithm and its variant SIC-BP [12] are shown
to be able to achieve a close approximation of
the MAP MUD. The SIC-BP algorithm solves
inference problems, exactly or approximately, via
probabilistic graphical models [12]. The SIC-BP
algorithm obtains a posteriori estimates of the sys-
tem unknowns by iteratively passing locally calcu-
lated conditional probabilities between variable
and function nodes [12]. Similar to SIC-based
detectors, the performance of the SIC-BP algo-
rithm is also determined by the initial inference
accuracy of the transmitted symbols involved with
the iterative detection process.
This observation suggests that enhancing the
first-step inference accuracy is of paramount
importance for improving the overall perfor-
mance of non-orthogonal systems employing an
SIC-based detector, such as the BP algorithm.
PAttern dIvIsIon multIPle Access
We first introduce some notations for the PDMA
scheme, where K users can non-orthogonally share
N(N < K) orthogonal radio resource elements, a
chip for the code-division multiple access (CDMA)
system, and a subcarrier for the orthogonal fre-
quency-division multiple access (OFDMA) system.
The overload factor, which is the ratio of the num-
ber of users to the total number of utilized physi-
cal resource elements, is defined as a = K/N. The
pattern matrix of the PDMA is defined as S = [s1,
s2, ,sK], where sk = [s1k, s2k, sNk]T denotes the
pattern for user k. The set of positions of non-zero
elements in the nth row of the pattern matrix S
denotes the set of users that contribute their data
at the physical resource element. In addition, the
pattern matrix S consists of groups of user pat-
terns with the same number of non-zero entries.
The design philosophy of the PDMA scheme is
that user signals are judiciously allocated in a spe-
cific physical resource space (frequency, code, or
spatial domain) at the transmitter, which can be
effectively exploited to enhance the performance
of SIC-based detectors at the receiver. More spe-
cifically, the data of different users should exhibit
appropriate diversity disparity at the symbol level
and power disparity at the physical resource ele-
ment level. Such disparities are expected to intro-
duce a convergence-amenable characteristic that
can be fully exploited by the SIC-based detector
in eliminating multi-user interference as well as
retrieving transmit diversity at the receiver.
Inspired by the properties of the SIC-based
detector discussed earlier, we present a non-or-
thogonal PDMA scheme where the correspond-
ing pattern matrix has the following three features:
1. The number of groups having different num-
bers of non-zero elements in the pattern matrix
is maximized.
2. The interference among the user patterns in the
same type group is minimized.
3. The size of each group is maximized to the
degree allowable by the computational com-
plexity constraints (further detailed earlier).
The maximum number of supported users K
for the PDMA scheme with N orthogonal physical
resource elements is given by K = C1
N + C2
N + … +
CN
N = 2N – 1, where Cn
N denotes the number of all
n-combinations of a set N.
Depending on whether the user’s data is sent
consecutively or in a distributed manner, we pro-
pose a distributed-mapping-based PDMA and a
localized-mapping-based PDMA, respectively, as
below.
e SIC-BP algorithm
obtains a posteriori
estimates of the system
unknowns by itera-
tively passing locally
calculated conditional
probabilities between
variable and function
nodes. Similar to SIC-
based detectors, the
performance of the
SIC-BP algorithm also
is determined by the
initial inference accu-
racy of the transmitted
symbols involved with
the iterative detection
process.
IEEE Wireless Communications • April 2018
56
Distributed-Mapping-Based PDMA: First
we design a distributed-mapping-based PDMA
scheme. We illustrate these three design features
of the PDMA as presented above using the fol-
lowing two PDMA matrices in the frequency
domain for N = 2 and N = 3 as follows:1
Sdm
(2×3) =
frequency
fi
fi+d
user1
1
1
group1 with size of 1(=C2
2)
!"#
user2 user3
2 0
0 2
group 2 with size of 2 =C2
1
( )
! "### $###
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
S
dm
(3×7) =
frequency
fi
fi+d
fi+2d
user1
1
1
1
group1 with size of 1(=C3
3)
!"#
user2 user3 user4
3/ 2 3/ 2 0
3/ 2 0 3/ 2
0 3/ 2 3/ 2
group 2 with size of 3=C3
2
( )
! "#### $####
user5 user6 user7
3 0 0
0 3 0
0 0 3
group 3 with size of 3=C3
1
( )
! "### $###
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
where fk represents the subcarrier k, and d is the
subcarrier spacing between subcarriers where
two PDMA encoded symbols are sent. When
d is a sufficiently large value, say d = 512 for
the 4G system with 15 kHz subcarrier spacing
over the extended pedestrian A (EPA) channel,
S
dm
(2
×
3) and S
dm
(3
×
7) correspond to the distribut-
ed-mapping-based design. When d = 1, S
dm
(2
×
3)
and S
dm
(3
×
7) degenerate into the localized-map-
ping-based design.
The PDMA scheme is designed so that each
group (which is composed of users patterns
with the same number of non-zero elements
in the pattern matrix S) has a different number
of non-zero entries (within each group); that is,
the diversity orders of users’ data in different
groups are different. Taking the pattern matrix
S
dm
(3
×
7) as an example, the users defined by the
pattern matrix S
dm
(3
×
7) can be categorized into
three groups, and the users belonging to different
groups, each having a different diversity order.
Specifically, group 1 consisting of user 1 has the
highest diversity order of 3, while group 2 with
users 2–4 has a 2-fold diversity, and users 4–7 in
group 3 all have the lowest diversity order of 1.
The overload factors for the PDMA schemes
with S
dm
(2
×
3) and S
dm
(3
×
7) are 150 and 233 percent,
respectively.
Localized-Mapping-Based PDMA: For the
localized mapping approach, we can exploit
the correlation between adjacent physical radio
resource elements and design the PDMA matrix
with quasi-orthogonal property to mitigate the
multi-user interference. Based on this observa-
tion, we design a localized-mapping-based PDMA
scheme with N = 3 as follows:
Slm
(3×7) =
frequency
fi
fi+1
fi+2
user1
1
1
1
group 1 with size of 1=C3
3
( )
!"#
user2 user3 user4
3/ 2 3 /2 0
−3/ 2 0 −3 / 2
0 −3/ 2 3/ 2
group 2 with size of 3=C3
2
( )
! "#### $####
user5 user6 user7
3 0 0
0 3 0
0 0 3
group 3 with size of 3=C3
1
( )
! "### $###
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
As can be seen from this example, user 1 is
orthogonal to users 2–4, and it also exhibits low
correlation with users 5–7. Users 2–4 have an
overall higher correlation than user 1. Users 5–7
experience the largest average interference level
among all users.
For the PDMA scheme with the distributed
mapping based pattern matrix S
dm
(3
×
7) , the sym-
bol x1 (xk denotes the symbol of user k) has the
highest diversity order of 3, so the preliminary
inference of x1 is the most reliable among all user
symbols. Then the accuracy of inference estima-
tion of x1 will propagate in the iterative SIC-based
detection process. As a result, the error propaga-
tion can be significantly alleviated in the iterative
detection of symbols of other users. The symbols
x2, x3, and x4 with a lower diversity order can
benefit from accurate inference of the previously
detected symbol x1 with a higher diversity order.
The resulting reliable estimates of the correctly
detected symbols can, in turn, aid in the detection
of previously detected symbols, thus leading to
more accurate detection performance and faster
convergence of the iterative algorithm.
Similar phenomena can also be observed for
the localized-mapping-based PDMA with pattern
matrix S
lm
(3
×
7)
.
Remark 1: The structural irregularity embodied
in an appropriate diversity disparity at the sym-
bol level and power disparity at the resource ele-
ment level can facilitate the convergence for the
low-complexity SIC-based receiver. The diversity
gains obtained in the iterative SIC process can
be leveraged to increase the transmission rate for
NOMA, so as to achieve higher spectral efficiency
than conventional OMA schemes.
receIver desIgn For PdmA
BP-Based MUD: In this section, we describe
the BP-based algorithm [12], which can effectively
exploit the SIC-amenable structure of the PDMA
scheme to obtain near-optimal MUD. BP is an
efficient iterative message passing algorithm for
computing the marginal a posteriori distributions,
which is designed on the factor graph (FG) of the
underlying Bayesian inference networks [12]. Fig-
ure 1 illustrates the FG of the PDMA scheme with
pattern matrix S
dm
(3
×
7) , where the FG is a bipar-
tite graph containing two types of nodes: variable
nodes (VNs) and function nodes (FNs). In Fig. 1,
each VN xk (representing a user) is denoted by
a circle, while each FN yn (representing a phys-
ical resource element) is illustrated by a square,
and dn
f denotes the number of connected VNs
for FN yn, e.g., dn
f = 4, ∀n of S
dm
(3
×
7) . The messag-
es are updated by iteratively exchanging them
between FNs and VNs along the respective edges
(representing the non-zero element of the PDMA
matrix). When the FG contains no loops, the BP
algorithm can be used to perform exact inference
for each symbol after a sufficient number of itera-
tions [12].
Operating on the FG of the PDMA scheme,
the BP algorithm iteratively approximates the glob-
al MAP detection by factorizing it into a prod-
uct of simpler local observations. When the FG
contains cycles, it may lead the BP algorithm to
converge to imprecise conditional distributions
or, more critically, to diverge. PDMA consists of
groups of users with different diversity orders at
the symbol level and different power levels at the
resource element level. The structural irregularity
of the PDMA pattern matrix is beneficial for initi-
ating the convergence of the iterative detection,
especially for the most difficult equi-powered case.
As shown in [12], the computational complex-
ity of the BP-based MUD is O(Xdf
max(S)), where
df
max (S)
=
max
1<n≤N
df
n(S)
1 The illustration of PDMA
with N = 2 and N =3 in the
manuscript is mainly due
to their easy adaptability
to one physical resource
block (PRB) occupying 12
subcarriers by 7 orthogonal
frequency domain multiplex-
ing (OFDM) symbols, which
is specified in the 4G system.
The extension of the PDMA
scheme for N larger than 3 is
straightforward.
e design philosophy
of the PDMA scheme
is that user signals are
judiciously allocated
in a specific physi-
cal resource space
(frequency, code, or
spatial domain) at the
transmitter, which can
be effectively exploit-
ed to enhance the
performance of SIC-
based detectors at the
receiver.
IEEE Wireless Communications • April 2018 57
denotes the maximum row weight of S and |X|
represents the size of the modulation order,
which is considerably lower than O(XK) of the
optimal MAP MUD.
Turbo BP for MUD Enhancement: We can fur-
ther enhance the performance of the BP-based
MUD by combing the BP detector with the chan-
nel decoder to form an outer-loop turbo BP receiv-
er structure. Figure 2 illustrates that two outer-loop
iterations (labeled Outer-it) can enhance the
link-level performance for a PDMA system with
300 percent overload by about 2.1 dB at block
error rate (BLER) of 10–2 over the BP-based MUD
without outer-loop iteration (i.e., Outer-it = 0).
constellAtIon-constrAIned cAPAcIty AnAlysIs For PdmA
We analyze the CC capacity to illustrate the
achievable sum-rate for PDMA in the MAC. For a
K-user MAC, the effective received symbol vector
y at the base station is given by y = H
⊙
Sx + n =
Hefx + n, where H = [h1, h2, …, hK]NK denotes
the channel matrix for all users, the entry hn,k, ∀n
{1, 2, …, N}, ∀k {1, 2, …, K} is assumed to
be independent and identically distributed (i.i.d.)
complex Gaussian random variable with zero
mean and unit variance, Hef = H
⊙
S denotes the
effective channel matrix for all K users, x = [x1, x2,
…, xK]T refers to the transmitted symbol vector of
all K users with normalized power E[xK2] = 1,
⊙
denotes the element-wise Hadamard product
of two matrices, and n ∼ CN (0, s2I) is the noise
vector. For illustrative purposes, we write the
received signal vector y for the PDMA scheme
with pattern matrix S
dm
(2
×
3) as follows:
y=h11 h12 h13
h21 h22 h23
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥⊙1 2 0
1 0 2
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
x1
x2
x3
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
+n1
n2
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥.
=h11x1+h12 2x2
h21x1+h23 2x3
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥+n1
n2
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥.
(1)
Utilizing the chain rule from the information
theory, we can express the sum of the CC capac-
ity as follows:
I (x, y) = I(x1 : y) + I(x2 : yx1) + I(x3 : yx1, x2), (2)
where I(x,y)
=
H(y)
−
H(yx
1
), H(y)
=−p(y)log2dy,
∫ p(y)=1
k=1
3Xk
∏p(y x)
x
∑,
and XK denotes the size of modulation order
of the kth user, which is assumed to be 4 (i.e.,
quadrature phase shift keying [QPSK] constella-
tion is considered) for all users in this article with-
out loss of generality. As an illustrative example,
we utilize two PDMA pattern matrices S
dm
(2
×
3) and
S
dm
(4
×
6) (shown below) with the same overload
ratio of 150 percent to explain the design of a
PDMA scheme.
Sdm
(4×6 ) =
user1 user2 user3
4 / 3 0 4 / 3
4 / 3 4 / 3 0
4 / 3 4 / 3 4 / 3
0 4 / 3 4 / 3
group1
! "### $###
user4 user5 user6
2 2 0
2 0 2
0 2 0
0 0 2
group1
! "### $###
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
We compute the CC sum-rates of pattern
matrices S
dm
(2
×
3) and S
dm
(4
×
6) as shown in Fig.
3, where the CC sum capacity of OMA is also
depicted for comparison. We can ascertain that
all PDMA matrices can achieve a maximum sum-
rate of 3 b/s/Hz in the high signal-to-noise ratio
(SNR) regime, indicating a 50 percent throughput
increase compared with the conventional OMA
scheme. The average CC sum-rate of the S
dm
(2
×
3)
is only 3 percent less than that of the S
dm
(4
×
6) in
the low- and intermediate-SNR range due to less
average diversity order of users.
For PDMA with pattern matrices S
dm
(2
×
3) and
S
dm
(4
×
6) , we have df = 2 and df = 4, respective-
ly. The computational complexity of PDMA with
S
dm
(2
×
3) is O(X2) compared with O(X4) of the
PDMA with S
dm
(4
×
6) . Although the PDMA with
S
dm
(4
×
6) achieves slightly higher CC sum-rate than
the PDMA with S
dm
(2
×
3) , its computational com-
plexity is about 16 times higher for MUD when
FIGURE 1. Factor graph representation of the PDMA scheme with pattern
matrix S
dm
(3×7) .
Variable nodes
Function nodes
x7
x6
x5
x4
x3
y3
y2
d1
f
y1
x2
x1
FIGURE 2. Turbo BP receiver structure for the PDMA and its performance.
SNR (dB)
4
10-1
BLER
10-2
2 6 8 10 12
Hard
decision
Channel
decoder
-
+
BP based
MUD
A priori
LLR
Constellation
probability
calculator
LLRs
out
LLRs
in
Extrinsic
LLRs LLR: log-likelihood ratio
y
Outer-it = 0
Outer-it = 1
Outer-it = 2
Outer-it = 3
IEEE Wireless Communications • April 2018
58
QPSK is employed; thus, it is less attractive for
practical applications. Therefore, a PDMA scheme
with pattern matrix S
dm
(2
×
3) achieves an attractive
performance-complexity tradeoff to realize the
required overload of 150 percent.
comPlexIty-constrAIned cAPAcIty-AchIevIng
nomA desIgn PrIncIPle
Assuming Gaussian MAC (GMAC), the sum-rate
of the NOMA system can be expressed as
Rsum =
1
Nlog det I+
1
σ2SSH
⎛
⎝
⎜⎞
⎠
⎟
⎡
⎣
⎢⎤
⎦
⎥.
Rsum achieves the upper bound of the GMAC
when SSH = KI. The BP-based receiver can
achieve near-perfect interference cancellation for
properly designed S and the associated computa-
tional complexity is
O X df
max (s)
⎛
⎝
⎜⎞
⎠
⎟
[12]. Therefore, it is highly desirable to design that
fulfills: 1) SSH = KI and 2) exhibits low dfmax(s) as
much as possible. We can thus rigorously summa-
rize these two design targets as follows:
min
s
d
f
max (S)
s.t. SSH=KI, df
max (S)<K, sk
2=N.
(3)
The PDMA matrix provided in work exhibits
good performance-complexity tradeoff as demon-
strated later. However, the approach to the com-
plexity-constrained capacity-achieving NOMA
design defined in Eq. 3 still remains an open prob-
lem.
PdmA For mAssIve connectIvIty APPlIcAtIons
A key performance indicator (KPI) for 5G is the
ability to support massive connectivity with a large
number of devices such as smartphones, tablet
computers, and IoT devices. In this section, we
first provide the link-level simulation of a PDMA
system with different overload factors. We then
carry out the system-level simulation to illustrate
its advantages over conventional OMA schemes
for massive connectivity applications.
suPPort oF FlexIble And lArge overloAd
For a PDMA system, the maximum overload fac-
tor increases as the length of pattern N increases.
For the number of orthogonal radio resource ele-
ments N = 2, 3, and 4, the maximum overload
factor can be 150, 233, and 375 percent, respec-
tively. Therefore, by varying N, we can accommo-
date a flexible overload for versatile applications.
We evaluated the performance of the PDMA
via a link-level simulation. The ITU Urban Macro
(UMa) channel with a 2 GHz carrier frequency
was adopted. The maximum Doppler frequency,
fd, was set to 5.55 Hz, which corresponds to 3
km/h at the carrier frequency of 2 GHz. A perfect
channel state information is assumed. In all sce-
narios, QPSK was employed, and the maximum
throughput of each user was assumed to be the
same. Figure 4 illustrates the curves of average
BLER of all users of PDMA with the overload fac-
tors 150, 233, and 300 percent (the first 12 col-
umns of
Sdm
(4
×
15)
), respectively. The BLER results of
the OMA-based 4G system were also provided as
a baseline.
It is shown from Fig. 4 that the BLER perfor-
mance of the PDMA degrades as the overload
factor increases in the intermediate SNR region.
As the SNR increases, the BLER performance of
the PDMA approaches that of the 150 percent
case, indicating a near-perfect interference cancel-
lation for PDMA even with a high overload. The
maximum network throughput can be increased
by 200 percent (this is not shown due to space
constraints). The better performance of PDMA
over OFDMA is explained as follows: The PDMA
users exhibit either better diversity order (for
those with df>1) or better frequency diversity than
that of OFDMA.2
robustness In PAttern collIsIon cAses
Machine type communications (MTC) are nor-
mally battery powered, and low power con-
sumption is essential for its implementation. The
excessive transmission delay and large signaling
overhead in the current scheduling-based grant
access mechanism are too expensive for low-cost
MTC equipment. To address this issue, the con-
tention-based grant-free access can be applied
to substantially reduce the transmission latency
and signaling overhead by eliminating the conven-
tional “request-and-grant” procedure. However,
such an “arrive-and-send” mechanism will inevi-
tably introduce collisions among users. It is thus
essential to design a multiple access scheme with
tolerance to multi-user collisions, which can fortu-
nately be realized by the PDMA scheme due to
its convergence-amenable property.
In Fig. 5, we evaluate the link-level perfor-
mance of PDMA with user pattern collision. The
FIGURE 3. Comparison of CC sum-rate of the
PDMA scheme and the OMA scheme.
PDMA with Sdm
(46)
PDMA with Sdm
(23)
Conventional OMA
SNR (dB)
50
1
CC sum-rate (b/s/Hz)
1.5
2
2.5
3
10 15 20 25
FIGURE 4. BLER performance of the PDMA with
different overload factors in the uplink.
SNR (dB)
-2
10-2
10-3
BLER
10-1
0 2 4 6
PDMA, 150%
PDMA, 233%
PDMA, 300%
OFDMA
2 We applied localized
mapping for OFDMA since
it closely resembles that
of the localized mapping
DFT-spread OFDM. The
distributed-mapping of the
PDMA thus exhibits better
frequency diversity.
e structural
irregularity of the
PDMA pattern matrix
is beneficial for initi-
ating the convergence
of the iterative detec-
tion, especially for the
most difficult
equi-powered
case.
IEEE Wireless Communications • April 2018 59
ideal case is no user collision, while user collision
happens when any two users randomly select the
same user pattern. It is shown in Fig. 5 that the
performance degradation due to pattern collision
is about 0.25 dB at the BLER of 10-2, which is
acceptable for practical applications.
suPPort oF mAssIve connectIvIty In
contentIon-bAsed scenArIos
In this subsection, we present a system-level sim-
ulation of the potential gains of PDMA over the
OFDMA scheme (currently used by 4G) in con-
tention-based scenarios. We consider an applica-
tion scenario for small packet transmission with
tight latency constraints. We employ a 19-hex-
agonal macrocell model with 3 sectors per cell.
The cell radius of each macrocell is set to be
500 m. The locations of the users are randomly
assigned with uniform distribution. The system
bandwidth is set to 10 MHz, and the transmis-
sion power of the macrocell is 46 dBm. The
antenna gains at the macrocell and user equip-
ment (UE) are 17 dBi and 0 dBi, respectively.
The contention region is set to be 6 resource
block (RB) pairs. Uplink traffic for each user fol-
lows Poisson distribution with a mean packet
inter-arrival time of 120 ms per user. The turbo
BP receiver is employed for PDMA, while a lin-
ear MMSE receiver is employed for OFDMA.
The system performance is evaluated in terms
of outage probability, where the system outage
is defined as the user’s packet drop rate being
larger than 1 or 5 percent.
Figure 6 illustrates that PDMA can support 116
users for system outage of 5 percent, while con-
ventional OFDMA can only accommodate 46
users; that is, about 1.5 times more users can be
supported by PDMA. For a system outage of 1
percent, PDMA is able to achieve a more prom-
inent performance gain; that is, about 2.2 times
more users can be accommodated by PDMA.
Thus, PDMA demonstrates an obvious advantage
over OFDMA in terms of supported number of
users while achieving the same system outage
performance.
conclusIons
In this article, we first introduce the complexi-
ty-constrained capacity-achieving NOMA design
principle. Then a new NOMA scheme named
PDMA was devised. The PDMA scheme is based
on a joint transmitter and receiver design that
facilitates low-complexity SIC-based MUD with
substantially improved performance over con-
ventional OMA schemes. The PDMA scheme is
flexibly designed to accommodate various over-
loads and is thus suitable for diverse applications.
Furthermore, PDMA exhibits robust collision tol-
erance and is amenable to grant-free scenarios,
which is essential for IoT applications. Numerical
results from link-level and system-level simulations
illustrate that PDMA is a promising candidate
technique for 5G multiple access due to it being
able to triple the overall system throughput while
keeping a link performance close to orthogonal
transmissions.
Acknowledgment
The Project Supported by Beijing Municipal
Commission of Science and Technology
(D171100006317004）
reFerences
[1] L. Dai et al., “Non-Orthogonal Multiple Access for 5G: Solu-
tions, Challenges, Opportunities, and Future Research Trends,”
IEEE Commun. Mag., vol. 53, no. 9, Sept. 2015, pp. 74-81.
[2] T. Cover, “Broadcast Channels,” IEEE Trans. Info. Theory, vol.
18, no. 1, Jan. 1972, pp. 2–14.
[3] P. Wang, J. Xiao, and P. Li, “Comparison of Orthogonal and
Non-Orthogonal Approaches to Future Wireless Cellular Sys-
tems,” IEEE Vehic. Tech. Mag., vol. 1, no. 3, Sept. 2006, pp. 4–11.
[4] S. Yuya et al., “Non-Orthogonal Multiple Access (NOMA)
for Cellular Future Radio Access,” Proc. IEEE VTC-Spring
2013, May, 2013, pp. 1–5.
[5] K. Higuchi and A. Benjebbour, “Non-Orthogonal Multiple
Access (NOMA) with Successive Interference Cancellation
for Future Radio Access,” IEICE Trans. Commun., vol. E98-B,
no. 3, Mar. 2015, pp. 403–14.
[6] B. Wang et al., “Spectrum and Energy Efficient Beamspace
MIMO-NOMA for Millimeter- Wave Communications Using
lens Antenna Array,” IEEE JSAC, vol. 35, no. 10, Oct. 2017,
pp. 2370–82.
[7] X. Dai et al. “Successive Interference Cancelation Amenable
Multiple Access (SAMA) for Future Wireless Communica-
tions,” Proc. IEEE ICCS, Nov. 12–15, 2014, pp. 222–26.
[8] S. Chen et al., “Pattern Division Multiple Access-A Novel
Nonorthogonal Multiple Access for Fifth-Generation Radio
Networks,” IEEE Trans. Vehic. Tech., vol. 66, no. 4, Apr.
2017, pp. 3185–96.
[9] A. J. Viterbi, “Very Low Rate Convolutional Codes for Max-
imum Theoretical Performance of Spread-Spectrum Multi-
ple-Access Channels,” IEEE JSAC, vol. 8, no. 3, Mar. 1990,
pp. 641–649.
[10] N. Jindal and A. Goldsmith, “Dirty Paper Coding vs. TDMA
for MIMO Broadcast Channels,” IEEE Trans. Info. Theory, vol.
51, no. 7, May 2004, pp. 1783–94.
[11] X. Wang and H. V. Poor, “Iterative (Turbo) Soft-Interference
Cancellation and Decoding for Coded CDMA,” IEEE Trans.
Commun., vol. 47, no. 7, July 1999, pp. 1046–61.
[12] F. R. Kschischang and B. J. Frey, “Iterative Decoding of
Compound Codes by Probability Propagation in Graphical
Models,” IEEE JSAC, vol. 16, no. 2, Feb. 1998, pp. 219–30.
[13] G. Caire and S. Shamai (Shitz), “On the Achievable
Throughput of A Multi-Antenna Gaussian Broadcast Chan-
nel,” IEEE Trans. Info. Theory, vol. 49, no. 7, July 2003, pp.
1691–1706.
[14] Z. Ding, P. Fan, and H. V. Poor, “Impact of User Pairing
on 5G Non-Orthogonal Multiple Access Downlink Trans-
missions,” IEEE Trans. Vehic. Tech., vol. 19, no. 8, 2015, pp.
1462–65.
FIGURE 5. Performance of user collision.
SNR (dB)
-2
10-1
BLER
10-2
-1 0 1 2 3 4
Collision
No collision
5
FIGURE 6. Number of supported users by PDMA
and OFDMA under different outage probability
constraints.
System outage
1% outage
20
0
Number of suppor
ted users
40
60
80
100
120
5% outage
OFDMA
PDMA
Numerical results from
link-level and sys-
tem-level simulations
illustrate that PDMA is
a promising candidate
technique for 5G mul-
tiple access due to it
being able to triple the
overall system through-
put while keeping a
link performance
close to orthogonal
transmissions.
IEEE Wireless Communications • April 2018
60
[15] F. Kschischang, B. Frey, and H. Loeliger, “Factor Graphs
and the Sum-Product Algorithm,” IEEE Trans. Info. Theory,
vol. 47, no. 2, Feb. 2001, pp. 498–519.
bIogrAPhIes
Xiaoming Dai is currently a professor in the Department of Tele-
communications at the University of Science and Technology
Beijing (USTB), China. His research interests expand on modula-
tion and coding, space-time coding, signal processing, and code
designs. His research activity has led to numerous publications
in leading international journals and to fruitful industrial applica-
tions, most notably the pattern division multiple access (PDMA)
scheme.
Zhenyu Zhang is a Ph. D. student, majoring in information and
communication engineering at USTB. His research interests are
signal detection in massive MIMO systems and non-orthogonal
multiple access.
Baoming B ai is a professor with the State Key Laboratory of
Integrated Services Networks, School of Telecommunication
Engineering, Xidian University, China. His research interests
include information theory and channel coding, wireless com-
munication, and quantum communication.
ShanZ hi Chen is the director of the State Key Laboratory of
Wireless Mobile Communications and is a board member of
Semiconductor Manufacturing International Corporation. He
has devoted his work to the research and development of
TD-SCDMA third-generation industrialization and TD-LTE-Ad-
vanced fourth-generation standardization.
Shaohui S un received his Ph.D. degree in communication and
information systems from Xidian University in 2003. Since January
2011, he has been the chief technical officer of Datang Wireless
Mobile Innovation Center, Datang Telecom Technology and Indus-
try Group. His current research areas of interest include multiple
antenna technology, heterogeneous wireless networks, and relays.
