Energy Efficient MIMO-NOMA HCN with IoT for

Wireless Communication Systems

Sunil Chinnadurai and Dongweon Yoon∗
Department of Electronic Engineering,
Hanyang University, Seoul, 133-791, Korea.
Email: dwyoon@hanyang.ac.kr

Abstract—In this paper, the energy efficiency maximization networks. User scheduling and power control algorithm have
problem is tackled in a multiple-input multiple-output (MIMO)- been proposed in [6] to maximize the spectral efficiency of a
non-orthogonal multiple access (NOMA) heterogeneous cellular downlink NOMA HetNet system. Authors in [7] analyzes the
network (HCN) with Internet of Things (IoT) for wireless
communication systems. A fractional non-convex optimization achievable rate and coverage probability of a two tier NOMA
problem is formulated to maximizes the energy efficiency (EE) network with the deployment of non-uniform small cells.
subject to the transmit power constraints and the minimum In addition to SE, EE is becoming a decisive performance
rate requirement for the cell edge (CE) users present in both metric for an IoT system due to the abrupt increase of energy
macro base station (MBS) and pico base station (PBS). The
above problem is hard to solve due to its nonlinear fractional
usage in wireless HetNets [8]. For instance, the authors in [9]
objective function. Fractional programming properties is firstly proposed a new framework for NOMA enabled cloud radio
employed to convert the non-convex problem into its parametric access network (CRAN) to maximizes the energy efficiency
form. In addition, an efficient iterative algorithm is proposed in advanced wireless communication systems. Energy efficient
established on the branch and reduced bound (BRB) approach user scheduling and power allocation scheme for NOMA
that achieves convergence to the above problem, mitigates the
inter tier interference and also improves the fairness between
is presented in [10] with not only imperfect channel state
the users. Comprehensive numerical results emphasize that the information, but also cross-tier interference in HetNets. EE
proposed scheme achieves higher energy efficiency as compared was maximized in a MIMO-NOMA HetNet system by imple-
with the existing NOMA scheme and the conventional orthogonal menting the iterative power allocation algorithm employing
multiple access (OMA) scheme. branch and reduced bound (BRB) approach [11], [12]. Joint
Index Terms—Energy efficiency, heterogeneous network (Het-
Net), power allocation, MIMO, IoT, NOMA.
user scheduling and power allocation schemes was proposed in
[13] to improve the energy efficiency of the downlink NOMA
heterogeneous network while considering both perfect CSI
I. I NTRODUCTION
and imperfect CSI. The performance of data rate and energy
Wireless networks have become dense in last decade due consumption tradeoff was also examined in the above work. A
to different communication services. Data traffic is expected joint subcarrier and power allocation algorithm was proposed
to increase thousand-fold in wireless communication systems in [14] to examine the tradeoff among the fairness, energy
[1]. Heterogeneous network (HetNet) has been implemented to efficiency and sum-rate of the power domain NOMA based
increase the throughput, spectrum efficiency (SE) and energy HetNet system. Among the ongoing research contribution
efficiency (EE) to overcome the huge data traffic by deploying towards 5G, energy efficiency of NOMA based HetNets with
low power small cells along with macro base stations (MBS) IoT has not been very much examined yet and is still in its
[2]. Communication system will be facing on challenges early stages. Motivated by the aforementioned statements, the
from Internet of Things (IoT) as billions of devices will main contributions in this paper are summarized as follows.
be connected in the coming decade. NOMA has created an
• Energy efficiency maximization problem is examined for
immense attraction as it can meet the demanding requirements
a single cell MIMO-NOMA heterogenous system while
of supporting dense wireless HetNet by providing ultra low
satisfying the transmission power and rate constraints of
latency, enhancing EE and SE [3]. NOMA exploits the same
the CE users. We firstly employ the fractional program-
radio resources to serve multiple users simultaneously, which
ming properties to convert the non-convex problem into
produces better throughput, spectral efficiency and fairness
its equivalent parametric form.
than the conventional orthogonal multiple access (OMA)
• Furthermore, an efficient iterative algorithm is proposed
scheme. At the transmitter, NOMA utilize superposition cod-
established on the branch and reduced bound (BRB)
ing to superimpose the multiple users signal using a power
approach that achieves convergence to the above problem
domain which causes inter user interference (IUI). Successive
and attains an optimal solution. The proposed iterative
interference cancellation (SIC) technique is deployed at the
algorithm helps to mitigates the inter tier interference and
receiver side to mitigates the IUI and decode the transmitted
also improves the fairness between the users.
signal [4]. A unified NOMA framework is investigated in
[5] to maximize the sum-rate in heterogeneous ultra dense The rest of this paper is organized as follows. Section II

978-1-5386-5041-7/18/$31.00 ©2018 IEEE 856 ICTC 2018

describes the considered system model and problem formu- The achievable sum rate of the total MIMO-NOMA Hetnet
lation for the downlink of a single cell massive MIMO- system is given as
NOMA system. The proposed algorithm is given in section III.  
Numerical results are presented to show the effectiveness of Rsum = Rp,n , (6)
p∈{i,j,k} n∈{Up }
our proposed algorithm for single cell MIMO-NOMA system
in Section IV, and Section V concludes this paper. where {Up } represents the users connected with MBS, PBS
and FBS. The total transmission power at the BS is given as
2
 4

PT = Pi + Pj + Pk + Pc , (7)
II. S YSTEM M ODEL
j=1 k=1

where Pi , Pj and Pk are the transmit power at the MBS, PBS

We consider the downlink transmission in an MIMO- and FBS respectively. Pc is the circuit power consumption
NOMA heterogeneous network, which consists of NI macro at all base stations. Therefore, the energy efficiency (EE) is
base stations (MBS) , NJ pico base stations (PBS), NK femto defined as the ratio of the overall sum rate to the power
base stations (FBS), N mobile stations (MSs) and K IoT consumption as expressed in the below equation
devices as shown in Fig. 1. Two single antenna users form Rsum
a cluster and are served by multiple antenna MBS and PBS. EE = . (8)
PT
MBS is located at the center of the cell. PBS and FBS are
present at the edges of the cell. For our convenience, i, j and A. Problem Formulation
k are represented as MBS, PBS and FBS, respectively. There The energy efficiency maximization problem for MIMO-
are Ui macro cell users (CUs), Uj pico CUs and Uk femto NOMA HetNet system is formulated as follows
CUs respectively, where i ∈ {1, 2, 3, .., I}, j ∈ {1, 2, 3, .., J}
and k ∈ {1, 2, 3, .., K}. The transmission power emitted from max EE
p2,i,n ≥0,p2,j,n ≥0
the FBS is too low to create interference to the CUs served Γ2,i,n ≥ Γthd
s.t. 2,i,n , n ∈ Ui (C1)
by MBS and PBS. Successive interference cancellation is
implemented at both near user (NU) and cell edge (CE) user. Γ2,j,n ≥ Γthd
2,j,n , n ∈ Uj (C2)
Each user receives its desired signal as well as interference p2,x,n ≥ 0, x ∈ i, j, n ∈ Ui , Uj (C3)
signals from the cross tier base staions (BSs). The transmission tr{E(xp xH
p )} ≤ Pp , p ∈ NB (C4), (9)
power constraints for BSs are given by
where EE is defined in Eq.(9) and Γthd 2,x,n is the signal-
tr{E(xp xH
p )} ≤ Pp , p ∈ NB , (1) to-interference-plus-noise ratio (SINR) threshold for the CE
where Pp is the maximum transmission power at each BS and users, where x ∈ {i, j}. The objective function in (9) max-
NB = {NI + NJ + NK }. The received signal at Up,n is given imizes the energy efficiency of the considered system. The
as constraints C1 and C2 given in (9) represent the minimum
Uj
data rate requirement for CE users present at MBS and PBS
Ui
 
  respectively. C3 indicates the power allocation coefficient for
yp,n = pi,a Pi hi,p,n + pj,b Pj hj,p,n
the CE users at MBS and PBS. The total power constraints
a=1 b=1
Uk  for each BS is given in the constraint C4.

+ Pk hk,p,n + zp,n , (2)
III. J OINT R ESOURCE AND P OWER A LLOCATION
c=1
A LGORITHM
where hi,i,n represents the channel fading coefficient between
the ith BS and users served by that BS. zp,n is the AWGN The formulated EE maximization in Eq.(9) is difficult to
noise with CN (0, σp,n
2
), p ∈ {i, j, k} . The attainable downlink solve due to its non-convex rate constraint of the CE users (for
rate of transmission from the BS to nth user is obtained as both MBS and PBS separately) and the non-linear fractional
objective function. The above problem is first converted into
Rp,n = W log2 (1 + SIN Rp,n ), (3) a DC programming problem. Branch and reduced bound
where (BRB) algorithm is then implemented to solve the above
optimization problem and also to find the optimal power
pp,n Pp αp,n
SIN Rp,n = n−1 . (4) allocation coefficients for the CE users present in both MBS
2
pp,u Pp αp,n + σp,n
u=1 and PBS. The proposed joint resource and power allocation
The channel gain is given as algorithm enhances the fairness between the near and CE
2 users. Joint resource and power allocation (JRPA) algorithm
|hi,p,n | also maximizes the EE by mitigating the inter-tier interference.
αp,n =  2  2 .
|h |
n∈U j j,n j j,p,n +
p P 2
n∈U k Pk |hk,p,n | + σp,n Inter user interference (IUI) is eliminated based on the user
(5) pairing algorithm proposed in [15]. In order to apply BRB

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 IV. N UMERICAL R ESULTS
In this section, the performance of the proposed joint
resource and power allocation (JRPA) scheme is compared
with the existing scheme proposed in [16] and the conventional
OMA scheme [18]. The scheme proposed in [16] is referred to
as majorization minimization non-orthogonal multiple access
(MMNOMA) scheme. A single cell MIMO-NOMA downlink
system is considered as shown in Fig. 1. We assume that
there are 1 MBS, 2 PBS and 4 FBSs each with multiple
transmit antennas and receiver equipped with a single antenna.
MBS is located at the center of the cell whose size of 500
m is considered. Each BS is subject to the transmit power
constraint. Unless otherwise specified, we assume Γthd 2,i,n =
10 dB, Γthd2,j,n = 4 dB, N = 30, nM = 20, nP = 8, nF =
4, PP = Pi = 30 dBm, Pj = 20 dBm, Pk = 5 dBm, PC
= 1 W, and σp,n 2
= 1. EE performance will be attained by
taking average of the energy efficiency over the fading channel
matrices. Unless explicitly stated, all results are presented
for 200 channel fading realizations. Jain’s fairness index [17]
is employed to measure the fairness between the near and
Fig. 1. MIMO-NOMA HetNet Downlink System
CE users served only MBS and PBS. We also presume that
the elements of the channel matrices between the user and
BS follow independent and identically distributed complex
Gaussian distribution. There are only two users are considered
approach, the above problem in Eq.(9) is reformulated into in every pair to decrease the decoding complexity at SIC
the non-convex objective function over the rectangle (Rinit ), receivers. Convergence criteria is set to 10−2 , i.e., we assume
where R = {SIN R|SIN Rp,n min
≤ SIN Rp,n ≤ SIN Rp,n max
}. that the proposed JRPA algorithm comes to halt when the
The achieved SINR values are denoted by SIN Rp,n from difference between the attained upper bound Un and lower
Eq.(6) for all the BSs are enclosed within initial rectangle. bound Ln values within the successive iterations are less than
i.e., SIN Rp,n ⊆ Rinit , where p ∈ NB . The optimum power 10−2 .
allocation coefficient for the FU in MBS and PBS are found EE performance and Jain’s fairness index are plotted versus
by the tight lower and upper bounds for φmin (Rinit ). By total transmission power in Fig. 2 and Fig. 3 respectively. It is
substituting the value of optimal power allocation coefficients observed from the results that the proposed scheme attains
px,n , where x ∈ {i, j} is obtained from Algorithm 1 in EE performance gain of around 2.5 [Mbits/joule] at 12.5
Eq.(8), the energy efficiency for the MIMO-NOMA HetNet dBm compared to MMNOMA scheme and 5 [Mbits/joule]
System can be obtained. Algorithm 1 summarizes the steps of compared to OMA Scheme. This observation can be justified
proposed JRPA algorithm which is given as follows for the reason that the transmission power is greatly reduced
due to the proposed BRB scheme which increases the EE. It
is also good to note that the fairness index of the proposed
Algorithm 1 Proposed JRPA Algorithm scheme is better than the fixed (Fixed PA is employed in MM-
Step 1. Initialization: Set n = 1, D1 = Rinit , NOMA Scheme) and exhaustive power alloacation scheme for
U 1 = ψub (Rinit ) and L1 = ψlb (Rinit ). Tolerance � ≥ 0 all transmission power due to the attained optimal PA coeffi-
Step 2. Convergence Criteria: If Un − Ln ≥ �, Go to Step cients for both macro and pico cell users by BRB approach.
3. Otherwise, Stop the algorithm In addition, the proposed BRBNOMA scheme consistently
Step 3. Branching: 1. R ∈ Dn , Set Rn = R where outperforms OMA scheme in terms of energy efficiency.
φlb (R) = Ln 2. Split the latest Rn into Rn1 and Rn2 3. V. C ONCLUSION
Remove Rn and add Rn1 and Rn2 to form Dn+1 from Dn In this paper, a joint resource and power allocation scheme
Step 4. Bounding: Compute the upper bounds was examined to maximizes the EE with IoT in a MIMO-
(φub (Rn1 ), φub (Rn2 )) and lower bounds (φlb (Rn1 ), φlb (Rn2 )) NOMA system for wireless communication systems. An effi-
1. Set Un+1 = minUn , φub (Rn1 ), φub (Rn2 ) 2. Set Ln+1 = cient iterative algorithm established on the BRB approach was
minLn , φlb (Rn1 ), φlb (Rn2 ) proposed to optimize the transmit power allocation coefficients
Step 5. Reduction: Choose R ∈ Dn+1 when for the CE users served by MBS and PBS. In addition, the
φlb (R) ≥ Un+1 and remove all R obtained to update proposed BRB algorithm improves the fairness between the
Dn+1 users and maximizes the EE of the considered MIMO-NOMA
Step 6. Repeat: Set n = n + 1 and go back to step 2. HetNet system. Via numerical results, it was also proved

858
 Research Center) support program (IITP-2018-2017-0-01637)
26
supervised by the IITP(Institute for Information and com-
Proposed BRBNOMA scheme
25 MMNOMA scheme
munications Technology Promotion. (Corresponding author:
BRBOMA scheme Dongweon Yoon (dwyoon@hanyang.ac.kr))
24
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ACKNOWLEDGMENT
This research was supported by the MSIT(Ministry of
Science, ICT), Korea, under the ITRC(Information Technology

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