Stochastic Geometry Based Performance Study on
5G Non-Orthogonal Multiple Access Scheme
Zekun Zhang
†
, Haijian Sun
†
,Rose Qingyang Hu
†
,YiQian
‡
†
Department of Electrical and Computer Engineering, Utah State University, Logan, UT
‡
Department of Computer and Electronics Engineering, University of Nebraska-Lincoln, NE
Email:
†
{zekun.zhang.z@ieee.org, h.j.sun@ieee.org, rosehu@ieee.org},
‡
yqian@ieee.org
Abstract—To achieve a significant boost on capacity perfor-
mance in the next generation (5G) cellular network, novel radio
access technologies (RAT) are demanded to make the system
more spectrum efficient. As a promising multiple access scheme
for 5G cellular network, non-orthogonal multiple access (NOMA)
has attracted extensive research attention recently. Existing works
show that NOMA posses the potential to further improve system
spectrum efficiency compared with the orthogonal multiple access
(OMA), which is predominantly adopted by existing wireless
networks. In this paper, we develop the analytical framework on
system coverage and average user achievable rate in a downlink
NOMA system. We explicitly consider the inter-cell interference
in the study, which is a capacity limiting factor in most wireless
networks but less addressed in most existing analytical work
for NOMA. Additional to NOMA, the analysis on an OMA
access scheme, i.e., orthogonal frequency division multiple access
(OFDMA), is also conducted for comparison. Owing to the
tractability of Poisson Point Process (PPP) model used in this
work, all the analytical results are derived and expressed in a
pseudo-closed form or a succinct closed form. The analytical
results are validated by simulations and demonstrate that NOMA
can bring considerable performance gain compared to OMA
when success interference cancellation (SIC) error is low.
Index Terms—5G, NOMA, PPP, coverage probability, average
achievable rate
I. INTRODUCTION
Orthogonal multiple access (OMA) has been widely ap-
plied in current wireless communications systems, such as
orthogonal frequency division multiple access (OFDMA) or
single carrier frequency division multiple access (SC-FDMA)
adopted in Long-Term Evolution (LTE) [1] and LTE-Advanced
[2]. Although OMA eliminates inter-user interference with a
low-complexity implementation, its spectrum efficiency has
room to be further improved [3]. One of the most challenging
requirements in the next generation (5G) cellular network is
to offer data rate 1000 × of the current 4G technology [4].
As such, novel radio access technologies (RAT) with higher
spectral efficiency are expected.
Non-orthogonal multiple access (NOMA), as a promising
candidate RAT in 5G network, has received considerable
attention recently [5]–[8]. Specifically, NOMA allocates the
same frequency/time/spatial resource to multiple user equip-
ments (UEs) by multiplexing these UEs on the power domain
at the transmitter and extracting the intended signals from
the composite data using successive interference cancellation
(SIC) at the receiver [9]. Many problems about NOMA have
been studied by published work. In [10], authors considered
user fairness in the downlink NOMA and investigated power
allocation (PA) techniques that ensure fairness for users.
Authors of [11] investigated the system level performance
of NOMA in various environments including macro cells
and small cells, and showed that the performance gain of
NOMA can be obtained in both macro cell and small cell
deployments. In [12], the performance of a cellular network
that jointly considers multiuser multi-input multi-output (MU-
MIMO) and NOMA with underlaid device-to-device (D2D)
communications is studied. In [13], authors proposed two
user pairing schemes and investigated how to further enhance
the performance gain of NOMA over conventional OMA.The
study shows that NOMA can be applied on both downlink and
uplink [14].
To the best of our knowledge, [6] is the only one that
focuses on evaluating the performance of NOMA by using
the stochastic geometry method. Authors in [6] developed
analytical results on outage probability for 𝑚-th UE and of the
ergodic sum rate in a single cell downlink NOMA. However,
due to less tractability of the model used in [6], the clear
closed form expression for the ergodic sum rate is difficult to
derive. Moreover, inter-cell interference, which is a pervasive
problem in most of the existing wireless networks, is not
explicitly considered in [6] and neither do many other work
on NOMA. In this paper, we evaluate the performance of
downlink NOMA on coverage probability and average achiev-
able rate using a stochastic geometry model. More specifically,
Poisson Point Process (PPP) model is used in the study. The
advantages of adopting PPP model are summarized in [15]: i)
It models the real network deployment quite accurate; ii) Inter-
cell interference can be explicitly considered; iii) It provides
tractable and accurate results. Without loss of generality, we
start our analysis with a 2-UE NOMA case and further extend
the results to a general 𝑀 -UE NOMA scenario. Owing to
the tractability of PPP model, all the analytical results are
expressed in a pseudo-closed form with computable numerical
integration, or in a nice closed form under some special cases.
We expect our developed work can be used as a frame work for
downlink NOMA and to incorporate more advanced schemes
such as optimal NOMA power allocation and user pairing.
The rest of the paper is organized as follows. In section II
the system model and configurations are lay out. In section
III, we derive the statistical coverage probability and average
achievable rate for NOMA UEs. The analytical results for
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