Adaptive successive transmission in virtual full-duplex cooperative NOMA

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Adaptive Successive Transmission in Virtual
Full-Duplex Cooperative NOMA
Young-bin Kim
Future Access Network Division
KDDI Research, Inc.
Fujimino-shi, Japan
yo-kim@kddi-research.jp
Kosuke Yamazaki
Future Access Network Division
KDDI Research, Inc.
Fujimino-shi, Japan
ko-yamazaki@kddi-research.jp
Bang Chul Jung
Department of Electronics Engineering
Chungnam National University
Daejeon, South Korea
bcjung@cnu.ac.kr
Abstract—In this paper, we propose a novel virtual full-duplex
cooperative non-orthogonal multiple access (NOMA) technique
for a downlink two-hop cellular network which consists of a
single base station (BS), two mobile stations (MSs), and Khalf-
duplex decode–and–forward (DF) relay stations (RSs). In the
proposed technique, the BS sends super-imposed signals for two
MSs via the RSs in each transmission phase, while a selected RS
via two-stage relay selection sends the signals to two MSs. Thus,
the multiplexing loss due to half-duplex operation of RSs can be
overcome by allowing for both the BS and a selected RS to send
data at the same time. In the proposed cooperative NOMA, we
adaptively reset the successive transmission according to decoding
status at RSs. As main results, we mathematically analyze outage
probability and diversity-multiplexing tradeoff (DMT) of the
proposed technique. Extensive computer simulations show that
the proposed technique significantly outperforms the existing
schemes in terms of both outage probability and DMT.
I. INT ROD UC TI ON
Non-orthogonal multiple access (NOMA) is considered as
a promising candidate of 5G technologies [1] in order to meet
the requirements of 5G, massive connectivity, low latency,
high spectral efficiency, etc [2]. The merit of NOMA comes
from the capability of support for multi-user utilizing a single
domain, i.e., power, code domain [3]–[6].
Based on the existing conventional NOMA, various coop-
erative NOMA systems have also been focused due to the
additional spatial diversity through relay communications [6]–
[9]. The authors in [6] coped with relay selection for NOMA
in the presence of multiple half-duplex decode-and-forward
(DF) relay stations (RSs) and analyzed the proposed two-
stage relay selection scheme in terms of outage probability.
The work in [7] introduced NOMA in coordinated direct and
relay transmission (CDRT) in order to improve the user having
relatively poor channel where one user communicates with a
base station (BS) directly, whereas the other user can receive
message from the half-duplex DF RSs. In [8], a cooperative
NOMA scheme in which two half-duplex DF RSs forward the
messages to two users simultaneously using dirty paper coding
was analyzed in terms of outage probability. Achievable rate of
cooperative half-duplex relaying scheme for NOMA was also
This work was supported by the Basic Science Research Program
through the NRF funded by the Ministry of Science and ICT (NRF-
2016R1A2B4014834).
analyzed using efficient approximation via Gauss-Chebyshev
Integration in Rician fading environments [9].
However, aforementioned works inherently suffer from a
multiplexing loss since half-duplex RSs cannot transmit and
receive simultaneously. That is, at least two transmission
phases are necessary to transmit a signal to users in the absence
of channels between a BS and users. Motivated on compensat-
ing a multiplexing loss due to half-duplex RSs, we consider a
downlink cooperative NOMA scenario and propose spectrally
efficient multi-hop successive relaying with multiple half-
duplex RSs based on the proposed two-stage relay selection for
virtual full-duplex (VFD) operation. In the proposed protocol,
since inter-relay interference exists due to successive relaying,
it is critical how to deal with inter-relay interference. Hence,
we design the dynamic inter-relay interference management
based on [10], which is the scheme known as achieving best
diversity-multiplexing tradeoff (DMT) in the DF half-duplex
multi-relay scenario without a direct link to the best of our
knowledge so far.
In this paper, we propose the protocol that can operate VFD
with multiple half-duplex DF RSs leveraging dynamic inter-
relay interference management in the downlink cooperative
NOMA environments. The proposed protocol is based on
the two techniques: two-stage relay selection and adaptive
reset. For relay selection, RSs which will not be selected are
weeded out via two conditions. Adaptive reset enables a restart
of the transmission protocol even if there exist candidates
of relay selection in order to enhance diversity gain in the
moderate and high multiplexing gain regime. We analyze
the proposed protocol in terms of both outage probability
and DMT, and obtain the closed form exploiting Markov
chain in order to resolve the dependency of all transmission
phases. Based on the analysis, we confirm that the proposed
protocol outperforms the existing schemes in terms of outage
probability, especially the scheme proposed in [6] which is
asserted as outage-minimal in the same environment. We also
obtain the closed form of DMT of the proposed protocol and
show it approaches its upper bound in low multiplexing gain
regime.
The rest of this paper is organized as follows. In Section
II, we present system model of the proposed protocol. The
description of our proposed protocol, VFD cooperative NOMA
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.
.
.
BS
MS 1
MS 2
RS 1
RS 2
RS K
n-th TX phase
x[n]
x[n−1]
hb,1[n]
hb,2[n]
hb,K[n]
g2,1[n]
g2,2[n]
h2,1[n]
h2,K[n]
Fig. 1. System model
is given in Section III. Outage probability analysis using a
Markov chain are provided in Section IV. In Section V, the
proposed protocol is analyzed in asymptotic view. Numerical
results are given in Section VI. In Section VII, conclusions
are drawn.
II. SY ST EM M OD EL
We consider a single-cell downlink network consisting
of a single BS, two MSs, and Khalf-duplex decode-and-
forward (DF) relay stations (RSs) as depicted in Fig. 1. Each
node is assumed to be equipped with a single antenna, and we
assume there is no direct link between the BS and two MSs as
in [6]. In this paper, we assume a VFD operation at the RSs,
in which a particular RS sends a packet while the other RSs
receive a packet from the BS at the same time. Specifically,
the number of total successive transmission phases is assumed
to be N. The received signal at the k-th RS in the n-th
transmission phase is given by
yr
k[n] = hb,k[n]x[n] + hj,k [n]x[n−1] + zr
k[n],(1)
where x[n]and hb,k[n]denote the signal transmitted from the
BS in the n-th transmission phase and the channel coefficient
from the BS to the k-th RS in the n-th phase, respectively (1≤
k≤K,1≤n≤N). Note that x[0] = 0. We assume that
hb,k[n]is an i.i.d. complex Gaussian random variable, i.e.,
hb,k[n]∼ CN(0,1) and zr
k[n]represents the thermal noise at
the k-th RS in the n-th phase, which follows an i.i.d. complex
Gaussian distribution, i.e., zr
k[n]∼ CN(0, N0). We assume
that E[|x[n]|2] = P, and then the average signal-to-noise ratio
(SNR) is given by ρ=P/N0. In (1), without loss of generality,
we assume that the j-th RS (j6=k) is chosen to send the
(n−1)-th packet to two MSs and hj,k denotes the channel
coefficient from the j-th RS to the k-th RS, which is also
an i.i.d. complex Gaussian random variable, i.e., hj,k[n]∼
CN(0,1). In NOMA, the BS sends the superimposed signal
that is given by x[n] = √a1s1[n] + √a2s2[n], where si[n]
and √aidenote the desired signal of the i-th MS in the n-
th phase and the power allocation coefficient for the i-th MS
(a1+a2= 1), respectively.
Let D[n]be the index set of the RSs that successfully decode
the n-th packet from the BS during the n-th transmission
phase. Then, |D[n]|indicates the cardinality of the decoding
set. A RS among the RSs included in D[n−1] is selected to
send the decoded packet to two MSs in the n-th transmission
phase. Thus, in (1), the j-th RS is assumed to succeed to
decode the (n−1)-th packet from the BS, i.e., j∈ D[n−1].
The RS selection algorithm will be explained in the next
section.
At the i-th MS, the received signal is given by ym
i[n] =
gj,i[n]x[n−1] + zm
i[n], where gj,i[n]denotes the channel
coefficient from the j-th RS to the i-th MS (i= 1,2),
which is an i.i.d. complex Gaussian random variable, i.e.,
gj,i[n]∼ CN(0,1), and x[n−1] denotes the (n−1)-th packet
from the BS. At RSs, we also assume that E[|x[n−1]|2] = P
and zm
i[n]represents the thermal noise at the i-th MS in
the n-th phase, which follows an i.i.d. complex Gaussian
distribution, i.e., zm
i[n]∼ CN (0, N0).
We assume that two MSs are categorized not by chan-
nel quality but by different QoS requirements as in [6]. In
this paper, perfect CSI at the receiver (CSIR) is assumed.
Throughout this paper, the priority of the first MS is assumed
to be higher than that of the second MS. Dynamic power
allocation strategies in each transmission phase may improve
the performance, but it is out of the scope of this paper. Hence,
we assume that a1and a2are fixed over Ntransmission
phases.
III. VIRT UAL FU LL -D UP LE X COO PE RATI VE N OM A
Basically, the BS broadcasts the superposed signals for
two MSs in each transmission phase except for the last
transmission phase (i.e., n=N) in order to overcome the
throughput loss due to half-duplex operation of RSs. Mean-
while, a selected RS among which RSs successfully decode the
received packet from the BS in the previous transmission phase
(i.e., k∈ D[n−1]) forwards the packet to the MSs. Hence,
N−1packets are sent to two MSs from the BS during N
transmission phases in the proposed VFD cooperative NOMA.
In this section, we first investigate conditions for the successful
decoding of the received packet at the RSs, and then describe
the proposed relay selection algorithm.
A. Conditions for Successful Decoding at RSs
When the decoding set is empty, i.e., |D[n−1]|= 0, the
conditions for the k-th RS to successfully decode the received
signals, s1[n]and s2[n], at the n-th transmission phase are
given by represented as
(C1) : log 1+ a1|hb,k[n]|2
a2|hb,k[n]|2
+1/ρ!≥NR1
N−1,(2)
(C2) : log1+a2ρ|hb,k [n]|2≥N R2
N−1,(3)
where R1and R2denote the target rate for the first and
second MSs, respectively. Note that (2) and (3) represents the
conditions of successful decoding at RSs when there is no
inter-RS interference signals. At the first transmission phase,
these conditions are used at RSs since |D[0]|= 0.
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When the inter-RS interference exists, i.e., |D[n−1]| 6= 0,
all RSs except for the selected RS suffer from the interference
signals from the selected RS at the n-th transmission phase. In
this case, the conditions for the successful decoding at the RS
depends on whether it is included in the previous decoding set
or not. If the k-th RS is not selected to relay signals to MSs
and belongs to the previous decoding set, i.e., k∈ D[n−1],
then the conditions for the successful decoding are the same
as (2) and (3) because it already has the interference signals
from the selected RS and knows the channel coefficient from
the selected RS to itself by the assumption of local CSI.
On the other hand, if k /∈ D[n−1], then the k-th RS tries to
perform joint decoding of both the n-th desired signal from the
BS and the (n−1)-th interference signal from the selected RS.
In this case, a multiple-access channel (MAC) becomes formed
at the RSs except for the selected RS, consisting of the BS
(superposed desired signals) and the selected RS (superposed
interference signals). In order to obtain the conditions for suc-
cessful decoding of the n-th transmission phase at the k-th RS
such that k /∈ D[n−1], we need to investigate the achievable
rate region of the MAC channel consisting of 4users who send
√a1s1[n−1],√a2s2[n−1],√a1s1[n], and √a2s2[n], respec-
tively. Note that √a1s1[n−1] and √a2s2[n−1] are transmitted
through hj,k[n], whereas √a1s1[n]and √a2s2[n]are sent
through hb,k[n]for RS kas a MAC channel receiver. Let
m1=a1|hj,k[n]|2,m2=a2|hj,k [n]|2,m3=a1ρ|hb,k [n]|2,
and m4=a2|hb,k[n]|2. Also, R0
iis assumed to be R1and R2
when iis and odd and even number, respectively. Base on the
rate region of a MAC channel, in the joint decoding case for
the relays not in the decoding set except for the selected relay
(k /∈ D[n], k 6=j), the conditions of decoding are represented
as the intersection of the all possible cases of 15:
log 1 + ρX
i∈M
mi!≥NPi∈M R0
i
N−1,∀M ⊂ {1,2,3,4}.(4)
B. Relay Selection
Of relays in the decoding set in the (n−1)-th phase, which
decoded the received signals successfully based on (2) and (4),
a single relay is selected in every phase to forward (broadcast)
the received signals, known as opportunistic reactive DF
relaying. For relay selection, we propose the two-stage relay
selection criterion. At the first stage, we define the subset S[n]
based on cardinality of the decoding set in the previous phase
under the following conditions for 2≤n≤N:S[n] = nk∈
D[n−1]
log 1 + a1|gk,i[n]|2
a2|gk,i[n]|2+1
ρ≥NR1
N−1,∀i= 1,2o.In the
sequel, relay jis selected in the n-th phase by the following
criterion:
j= arg max
k∈S[n]|gk,2[n]|2,2≤n≤N. (5)
Note that (5) focuses on channel gain of MS2 since S[n]
already picked up RSs which are capable of decoding s1[n]
before relay selection. Finally, the selected relay jforwards
the received signals to the users in the n-th phase.
Fig. 2. An example of adaptive reset: The case for K= 3 and Nc= 1
The main difference of relay selection in this paper and [6]
is whether the subset S[n]includes the relays decoding s2[n−
1] successfully or not. That is, the two-stage relay selection
scheme in [6] can select the relays failing decoding s2[n−
1]while the proposed protocol can select the relays decoding
both s1[n−1] and s2[n−1] successfully.
C. Adaptive Reset
In order to improve the reliability of the proposed protocol,
we consider adaptive reset. The main idea of adaptive reset,
similarly considered in [10], is to allow refreshing and restart-
ing of the proposed protocol even before S[n]is empty. Let
Ncbe the cardinality of the decoding set which determines the
time to restart the transmission protocol. For example, Nc= 1
means that the protocol restarts when |S[n]| ≤ 1, as shown
in Fig. 2. The dotted red arrow from state 1 (Nc) to state
3 (K) corresponds to adaptive reset, whereas the arrow does
not exist if adaptive reset is not adopted. As a result, adaptive
reset secures diversity gain even in the high multiplexing gain
regime, which will be justified via asymptotic analysis in
Section V.
IV. OUTAG E PROBAB IL IT Y ANALYSIS
In this section, we analyze the proposed protocol in terms
of outage probability. In order to compute outage probability
in the n-th phase, we should consider the (n−1) states of the
subset in all previous phases. However, outage probability in
the n-th phase follows Markovity, where it depends on only the
(n−1)-th phase. Owing to the Markovity, outage probability
in the n-th phase denoting Pr{On}is given by
Pr{On}=
K
X
t=0
Pr On|S[l]|=t, l = 2, . . . , n
×Pr {|S[l]|=t, l = 2, . . . , n}
(a)
=
K
X
t=0
Pr On|S[n]|=tPr {|S[n]|=t}
=
K
X
t=0 Pr (|gj,2[n]|2
<2NR2
N−1−1
a2ρ)!t
Pr {|S[n]|=t}
where (a) follows from the Markovity. Outage probability in
the n-th phase is simplified but it is still intractable because
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outage probability in each phase depends on cardinality of
S[n−1] in the previous phase. Thus, we adopt Markov chain
in order to obtain the closed form of Pr {|S[n]|=t}so that
outage analysis is tractable which means Pr{On}=Pr{O} in
steady state.
Theorem 1: When there are half-duplex single-antenna K
relays in the absence of direct links between the BS and
users with single antenna at each, the outage probability of
the proposed protocol is given by
Pr{O} =
K
X
t=0 1−exp −2NR2
N−1−1
a2ρ!!t
πt(6)
where πt,∀t∈ {0, . . . , K}denotes an element of a
(K+ 1)-dimensional stationary distribution vector π(=
[π0, π1, ..., πK],PK
i=0 πi= 1) for the Markov chain and
exp(x) = ex.
Proof: Consider the Markov chain whose states are re-
lated to cardinality of the subset S, defined by
PK=










P0,0. . . P0,K−1P0,K
.
.
..
.
..
.
..
.
.
P0,0. . . P0,K−1P0,K
PK−Nc,0. . . PK−Nc,K −10
.
.
.. . . .
.
..
.
.
PK,0. . . PK,K−10










(7)
where Pi,j is the transition probability from state ito jwhich
more specifically means Pr{|S[l−1]|=i→ |S[l]|=j}
for the arbitrary phase, l= 2, . . . , N . Note that the first Nc
columns are the same since they are transition probabilities
from the initial state due to refreshing and the elements except
for first Nc+ 1 P0,Ks in the last column is zero since a
selected relay always forwards the received signals and thus
the cardinality of Scannot be Kexcept for when adaptive
reset is adopted.
Each element of PKcan be formulated as (8) shown
on the top of the next page, where poand point are the
probability that a relay does not belong to Sin the absence
(SIC or silent relays case) and presence (joint decoding case)
of inter-relay interference signals, respectively. We can easily
confirm that the Markov chain reaches a steady state as in
[10]. That is, πPK=πholds. Then, solving πPK=π
subject to PK
i=0 πi= 1, we can obtain the closed form
of Pr {|S[n]|=t}exploiting property of the stationary distri-
bution since Pr {|S[n]|=t}=πtin steady state. |hj,2[n]|2
follows exponential distribution. Finally, we can attain (6).
Corollary 1: When K= 3,
Pr{O} =
3
X
t=0 1−exp −2NR2
N−1−1
a2ρ!!t
πt,(9)
where π0={P2,0P0,2+P0,0(1−P2,2)}π2+(P3,0P0,2−P3,2P0,0)π3
P0,2, π1=
1−π0−π2−π3, π2=
P0,2−P3,2(P0,0+P1,1+P0,2)
(1+P0,3)(1−P2,2)−P0,2+P3,2(P0,0+P1,1+P0,2)andπ3=P0,3(1−π2)
1+P0,3,
where T=P0,2+P0,3P3,2−P1,2−P1,2P0,3and
C= 1 −P1,1−P0,3P1,1+P0,1+P0,3+P0,3P3,1.
Proof: Plugging K= 3 in (6) and solving πP3=π, we
can easily obtain (9).
Remark 1: It can be empirically confirmed that Pn
KPK=
Pn
Kholds within single-digit non average. That is, the Markov
chain reaches a steady state after a negligible number of
phases compared to sufficient N, and it validates the snap-
shop approach for outage probability analysis of the proposed
protocol.
V. AS YM PT OTI C ANALYSI S
In this section, we asymptotically analyze the proposed pro-
tocol with respect to ρ,Nand Kbased on outage probability
analysis. Basically, we exploit DMT [11] the main metric.
For DMT analysis, note that multiplexing gain and diversity
gain are defined, respectively, by r= limρ→∞ log Ri(ρ)
log ρand
d= limρ→∞ −log Pout(ρ)
log ρwhere Ri(ρ)represents the transmis-
sion rate of MS i, and Pout denotes outage probability. Let
us define f(ρ).
=ρvif limρ→∞ log(f(ρ))
log ρ=v. a+denotes
max(0, a)for any real value a, and log(·)denotes the base-2
logarithm. Focusing on DMT performance, substitute Riwith
rilog ρand define πt.
= ˜πtwhere ˜πt, a element of ˜
π, is the
dominant scale of πt. Then, the outage probability scales like
Pr{O} .
=
K
X
t=0 2¯r2log ρ
a2ρt
˜πt.
=
K
X
t=0
ρ−t(1−¯r2)·˜πt,(10)
where ¯riis effective multiplexing gain of MS i(¯ri=cri),
determined by the further asymptotic analysis shown later. In
order to represent ˜πt, it is necessary to formulate the dominant
scale of the outage probabilities conditioned on the decoding
status of RS kin the previous phase. For the case when
RS ksucceeded decoding in the previous phase, the outage
probability for RS kis the same as the case in the absence of
inter-relay interference due to SIC. Hence, we have
po= 1 −Pr |hb,k [n]|2>2¯r2log ρ
ρ
×Pr |hb,k[n]|2>2¯r1log ρ−1
{a1−(2¯r1log ρ)a2}ρ
×Pr |gk,1[n]|2>2¯r1log ρ−1
{a1−(2¯r1log ρ)a2}ρ
×Pr |gk,2[n]|2>2¯r1log ρ−1
{a1−(2¯r1log ρ)a2}ρ
= 1 −exp −2¯r2log ρ
ρ−32¯r1log ρ−1
{a1−(2¯r1log ρ−1)a2}ρ
.
=2¯r2log ρ
ρ+ 3 2¯r1log ρ
{a1−(2¯r1log ρ)a2}ρ
.
=ρ¯r2−1+ 3 ρ¯r1
ρ−ρ¯r1+1
.
=ρ−(1−¯r2),(11)
since ρ¯r1
ρ−ρ¯r1+1 goes to zero when ρis sufficiently large.
Meanwhile, assuming PMAC denotes the probability that (4)
holds,
point = 1 −PMACPr |gk,1[n]|2>2¯r1log ρ−1
{a1−(2¯r1log ρ)a2}ρ
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Pi,j =(K
jpK−j
o(1 −po)j,if i= 0
Pmin(i,j)
x=0 i−1
xpi−1−x
o(1−po)xK−i
j−xpK−i−j+x
oint (1−point )j−x,if i6= 0 ,(8)
×Pr |gk,2[n]|2>2¯r1log ρ−1
{a1−(2¯r1log ρ)a2}ρ
.
=ρ−(1−¯ri)+ρ−2(1−2 ¯ri)+ρ−(1−Pl¯rl)+ρ−2(1−¯r1−2¯r2)
+ρ−2(1−2¯r1−¯r2)+ρ−2(1−2Pl¯rl)+ 2 ρ¯r1
ρ−ρ¯r1+1
.
=ρ−min(1−¯ri,2(1−2¯ri),1−
Pl¯rl,2(1−¯r1−2¯r2),2(1−2 ¯r1−¯r2),2(1−2Pl¯rl
))
(12)
for all i= 1,2where Pl¯rl= ¯r1+ ¯r2.
However, it is intractable and complicated to attain the
dominant scale of stationary probability of the Markov chain,
˜πt. Hence, as assumed in [12], [13] in order to effectively
characterize DMT for each individual multiplexing gain, we
deal with symmetric multiplexing gain case (r1=r2=r).
It is noted that the symmetric multiplexing case is acceptable
since multiplexing gain of each user can be the same though
achievable rat of each user is different for NOMA, i.e., we
can say r1=r2=rif R1> R2and R1.
=R2.
=ρr. Since
r1=r2=rimplies ¯r1= ¯r2= ¯r, under the assumption of
symmetric multiplexing gain, (11) and (12) are reduced to
po.
=ρ−min(1−¯r), point
.
=ρ−min(1−2¯r,2(1−4¯r)),(13)
respectively.
Theorem 2: When each node has one antenna, the DMT of
the proposed protocol for Ncis given by (14) on the top of
the next page.
Proof: Plugging (13) into (7), we will obtain ˜
πwhich
PK.
=Pn
KPKholds. In order to find the dominant scale of
converged transition probability, three mainly different multi-
plexing gain region should be classified since point
.
=ρ−(1−2¯r)
for 0≤¯r≤1
6,point
.
=ρ−2(1−4¯r)for 1
6<¯r≤1
4, and
point
.
=ρ0for 1
4<¯r. Computations of Pn
Kis similar to the
way in Appendix A of [10], and we skip the details of matrix
computations due to the page limit. Consequently, we have
˜
π.
=hρ−((K−1)−K¯r), ρ−((K−2)−(K−1) ¯r), ρ−((K−3)−(K−2) ¯r),
·· · , ρ0, ρ−((K−1)−K¯r)iT
for 0≤¯r≤1/6(15)
˜
π.
= min
i=1,...,K−1−N˜
π(i),for 1/6<¯r≤1/4, where
˜
π(i)=hρ−{(K−i−1)(1−¯r)+(i2+i)(1−4 ¯r)},
ρ−{(K−i−2)(1−¯r)+(i2+i)(1−4 ¯r)}, . . . , ρ−2(1−4 ¯r), ρ0,
ρ−{(K−i−1)(1−¯r)+(i2+i)(1−4 ¯r)}i,(16)
˜
π.
=hρ−Nc(1−¯r),· ·· , ρ−(1−¯r), ρ0,··· , ρ0ifor 1/4<¯r.
(17)
For 0≤¯r≤1
4, since ρ0is only in the K-th element of ˜
π,
limρ→∞ ˜
π≈[0 0 ··· 0 1 0]. That is, limρ→∞ πK−1≈1
and limρ→∞ πt≈0,∀t6=K−1where πtis the steady
state probability of state tcorresponding to (t+ 1)-th element
of π. It implies that no refreshing is needed in asymptotic
region, thus ¯rfor 0≤¯r≤1
4Note that two limits about nand
ρare independent so that the order of limits is irrelevant to
the DMT results throughout this paper. Meanwhile, for 1
4<¯r,
since ρ0appears in the last K−Nc+1 elements, limρ→∞ ˜
π≈
[0 0 · ·· cNc··· cK−1cK]and it is easily shown that all the
coefficients of ρ0are the same. Therefore, cNc=·· · =cK=
1
K−Nc+1 and ¯r=K−Nc+1
K−Ncrfor 1
4<¯rbecause adaptive reset
occurs when |S[n]| ≤ Nc.
Replacing ˜πtin (10) by the elements of ˜
π, we can obtain
(14).
Corollary 2: The proposed protocol approximately achieves
the upper bound of DMT For 0< r ≤1
4as Kincreases given
the optimal value of Nc=K−2.
Proof: For 0< r ≤1
4, since limρ→∞ πK−1≈1,Nc=
K−2maximizes d(r, K, Nc). Then, we have
lim
K→∞
d(r,K,Nc)|Nc
=K−2= lim
K→∞
min{(K−1)−Kr,K−(K+6)r}
'min{(K−1)(1−r), K (1 −r)}=(K−1)(1−r) = du(r, K).
(18)
Note that the upper bound reflects that a selected relay always
cannot contribute to diversity gain.
VI. NU ME RI CA L RES ULTS
In this section, we evaluate the proposed protocol and
compare it with the referential schemes including the protocol
in [6] in terms of outage probability and DMT as metrics
of non-asymptotic and asymptotic analysis, respectively. ‘The
proposed’, ‘Two-stage RS’, and ‘Successive’ stand for the
proposed protocol in this paper, the protocol in [6], and
successive transmission based on relay selection dealing with
inter-relay interference as noise, respectively.
Fig. 3 characterizes outage probability of the schemes when
K= 10 according to specific examples of a1.R1and R2
are assumed to be 0.5 bit/s/Hz and 2 bit/s/Hz, respectively.
Period of refreshing successive transmission regardless of the
status of decoding set, N, determining spectral efficiency, is
set to 20 for ‘The proposed’ and ‘Successive’, respectively.
When K= 10 as shown in Fig. 3, the proposed technique
outperforms both the two-stage RS technique and the succes-
sive relaying technique especially for various values of a1. It is
worth noting that the optimal a1, resulting in the lowest outage
probability, is different for the proposed technique and the
two-stage RS technique. For example, the outage performance
of the proposed technique when a1= 0.5is better than
the case when a1= 0.75 and a1= 0.95. However, the
outage performance of the two-stage RS selection algorithm
2018 IEEE Wireless Communications and Networking Conference (WCNC)

d(r, K, Nc) = 




K−1−Kr, if 0≤r≤1
6
min
i=1,...,K−1−Nc(K−1−i)(1 −r)+(i2+i)(1 −4r),if 1
6< r ≤1
4
Nc(1 −K−Nc+1
K−Ncr)+,if 1
4< r ≤1
(14)
0 5 10 15 20 25 30 35
SNR[dB]
10-6
10-5
10-4
10-3
10-2
10-1
100
Outage Probability
a1=0.5, Proposed
a1=0.5, Two-stage RS [6]
a1=0.75, Proposed
a1=0.75, Two-stage RS [6]
a1=0.95, Proposed
a1=0.95, Two-stage RS [6]
a1=0.75, Successive
K=10
Fig. 3. Outage probability when K= 10 and Nc= 0 for R1= 0.5bit/s/Hz
and R2= 2 bit/s/Hz.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
5
10
15
20
25
30
MultiplexingGain(r)
DiversityGain(d)


Upperbound(K=30)
Theproposedprotocol(K=30)
Two-stageRS[6](K=30)
Upperbound(K=10)
Theproposedprotocol(K=10)
Two-stageRS[6](K=10)
Fig. 4. DMT when K= 10,30.
with a1= 0.75 is better than the case when a1= 0.5and
a1= 0.95.
Fig. 4 compares DMT of the proposed protocol and two-
stage relay selection when K= 10 and 30. The upper bounds
are plotted based on (18). In the both K= 10 and 30 cases, the
proposed protocol outperforms the two-stage relay selection in
terms of DMT except for the low multiplexing gain regime. It
comes from the inherent difference of diversity gain between
the proposed protocol and two-stage relay selection, which
a single relay in the proposed protocol is always excluded
to be selected for VFD operation. For 0≤r≤1
4, DMT of
proposed protocol approaches the upper bound, and it validates
Corollary 2.
VII. CON CL US IO NS
In this paper, we proposed the protocol that can operate
VFD with multiple half-duplex DF RSs leveraging dynamic
inter-relay interference management in the downlink cooper-
ative NOMA framework. We also introduced the two-stage
relay selection as well as adaptive reset. We analyzed the
proposed protocol in terms of outage probability and DMT,
and obtain the closed form of the both metrics. Numerical
results validated the analysis, and we confirmed that outage
probability of the proposed protocol surpassed that of the con-
ventional cooperative NOMA in the same environment. Also,
the proposed protocol almost outperformed the conventional
cooperative NOMA in terms of DMT.
REF ER EN CE S
[1] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K.
Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future
radio access,” Proc. IEEE Vehicular Technology Conference, Dresden,
Germany, Jun. 2013.
[2] W. Shin, M. Vaezi, B. Lee, D. J. Love, J. Lee, and H. V. Poor,
“Non-Orthogonal Multiple Access in Multi-Cell Networks: Theory, Per-
formance, and Practical Challenges,” IEEE Commun. Magazine, DOI:
10.1109/MCOM.2017.1601065
[3] Z. Ding, Z. Yang, P. Fan, and H. V. Poor, “On the performance of
nonorthogonal multiple access in 5G systems with randomly deployed
users,” IEEE Signal Processing Letters, vol. 21, no. 12, pp. 15011505,
Dec. 2014.
[4] S. Timotheou and I. Krikidis, “Fairness for non-orthogonal multiple
access in 5G systems,” IEEE Signal Processing Letters, vol. 22, no. 10,
pp. 16471651, Oct. 2015.
[5] Z. Ding, L. Dai, and H. V. Poor, “MIMO-NOMA design for small packet
transmission in the internet of things,” IEEE Access, vol. 4, pp. 1393-
1405, Apr. 2016.
[6] Z. Ding, H. Dai, and H. V. Poor, “Relay selection for cooperative NOMA,”
IEEE Wireless Commun. Letters, vol. 5, no. 4, pp. 416-419, Aug. 2016.
[7] J. -B. Kim and I. -H. Lee, “Non-Orthogonal multiple access in coor-
dinated direct and relay transmission,” IEEE Wireless Commun. Letters,
vol. 19, no. 11, pp. 2037-2040, Nov. 2015.
[8] H. Sun, Q. Wang, R. Q. Hu, and Y. Qian, “Outage probability study
in a NOMA relay system,” Proc. IEEE Wireless Communications and
Networking Conference, San Francisco, CA, USA, Mar. 2017
[9] R. Jiao, L. Dai, R. MacKenzie, and M. Hao, “On the performance of
NOMA-based cooperative relaying systems over Rician fading channels,”
IEEE Trans. Vehicular Technology, DOI: 10.1109/TVT.2017.2728608
[10] Y.-b. Kim, W. Choi, B. C. Jung, and A. Nosratinia, “A dynamic paradigm
for spectrally efficient half-duplex multi-antenna relaying,” IEEE Trans.
Wireless Commun., vol. 12, no. 9, pp. 4680-4691, Sep. 2013.
[11] L. Zheng and D.N.C Tse, “Diversity and multiplexing: A fundamental
tradeoff in multiple-antenna channels,” IEEE Trans. Inf. Theory, vol. 49,
no. 5, pp. 1073-1096, May 2003.
[12] H. Ebrahimzad and A. K. Khandani, “On diversity-multiplexing tradeoff
of the interference channel,” Proc. IEEE International Symposium on
Information Theory, Seoul, Korea, Jun.-Jul. 2009.
[13] H. Ebrahimzad and A. K. Khandani, “On the optimum diversity-
multiplexing tradeoff of the two-user Gaussian interference channel with
Rayleigh fading” IEEE Trans. Information Theory, vol. 58, no. 7, pp.
4481-4492, Jul. 2012.
2018 IEEE Wireless Communications and Networking Conference (WCNC)