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MS. THESIS

Joint User Scheduling and Power

Allocation for Energy Efficient

Millimeter Wave NOMA Systems

밀리미터파 비직교 다중접속 시스템에서 사용자

스케줄링과 전력 할당

BY

Sunyoung Lee

AUGUST 2018

DEPARTMENT OF ELECTRICAL AND

COMPUTER ENGINEERING

COLLEGE OF ENGINEERING

SEOUL NATIONAL UNIVERSITY

i

Abstract

Joint User Scheduling and Power Allocation

for Energy Efficient Millimeter Wave NOMA

Systems

Sunyoung Lee

Department of Electrical and Computer Engineering

The Graduate School

Seoul National University

Non-orthogonal multiple access (NOMA) and millimeter wave (mmWave)

communications are promising technologies for the fifth generation (5G)

wireless communication systems. NOMA is able to serve multiple users in

the same resource block by exploiting successive interference cancellation

(SIC). MmWave communications can use wide bandwidth available in the

mmWave frequency band.

ii

In this thesis, we investigate the user scheduling and power allocation

scheme for a mmWave NOMA system. To reduce the feedback overhead,

random beamforming is adopted at a base station. The optimization problem

is formulated to maximize the energy efficiency. To solve this problem, we

first address the user scheduling problem and power allocation problem

separately, then an iterative algorithm is proposed to jointly optimize the user

scheduling and power allocation. Simulation results show that the proposed

scheme achieves higher energy efficiency than the conventional scheme.

Keywords: NOMA, mmWave, random beamforming, resource allocation,

power allocation, user scheduling, energy efficiency.

Student Number: 2016-24274.

iii

Contents

Abstract i

Contents iii

List of Figures iv

Chapter 1 Introduction 1

Chapter 2 System Model 5

2.1 Channel Model 7

2.2 Random Beamforming 8

2.3 Data Transmission Model 9

Chapter 3 Energy Efficient User Scheduling and Power Allocation 13

3.1 User Scheduling 15

3.2 Power Allocation 18

3.3 Joint User Scheduling and Power Allocation 27

Chapter 4 Simulation Results 28

Chapter 5 Conclusion 38

iv

List of Figures

Figure 2.1 Downlink mmWave NOMA system. . . . . . . . . . . . . . . . . . . 27

Figure 3.1 A system diagram for the addressed mmWave NOMA

system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Figure 4.1. Energy efficiency versus maximum transmission power maxP for

proposed and conventional schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 4.2. Energy efficiency versus maximum transmission power maxP for

different values of the number of beams M . . . . . . . . . . . . . . . . . . . . . . . . 34

Figure 4.3. Energy efficiency versus maximum transmission power maxP for

v

different values of the number of antennas N . . . . . . . . . . . . . . . . . . . . . . 35

Figure 4.4. Energy efficiency versus maximum transmission power maxP for

different values of the number of antennas N . . . . . . . . . . . . . . . . . . . . . . . 36

1

Chapter 1

Introduction

Non-orthogonal multiple access (NOMA) has been recognized as a

promising candidate for the fifth generation (5G) wireless communication

systems. In NOMA, multiple users are served in the same resource block by

applying power domain multiplexing at the transmitter and successive

interference cancellation (SIC) at the receiver [1], [2]. Since the communica-

tion resources are shared by users, NOMA improves the spectral efficiency

compared with orthogonal multiple access [3].

Recently, multiple input multiple output (MIMO) has been applied to

2

NOMA systems to further increase spectral efficiency. In a MIMO-NOMA

system, users are paired into clusters and users in each cluster share the same

beamforming vector. The performance is enhanced when users with high

channel correlation are paired into a cluster [4].

Millimeter wave (mmWave) communication is another promising

technology for 5G wireless communication systems. MmWave communica-

tion operates in the band of 30-300 GHz, where the available bandwidths are

much wider than the microwave bands used in current wireless

communications [5]. However, mmWave signals suffer from severe path loss

compared to microwave signals. To compensate the large path loss, proper

beamforming schemes are needed [6].

The use of NOMA in mmWave communications is desirable due to the

highly directional nature of mmWave propagation, which makes users'

channel highly correlated [7]. Furthermore, due to the large bandwidth

available at mmWave frequencies, mmWave NOMA system can achieve high

capacity.

Most of previous works on the coexistance of NOMA and mmWave

communications focus on the spectral efficiency [7]-[9]. In [7], the sum rate

and outage probabilities were analyzed for mmWave NOMA systems when

random beamforming is used at the BS. In [8], the capacity of mmWave

massive MIMO NOMA systems was analyzed in the low signal-to-noise ratio

(SNR) and high SNR regimes. In [9], user scheduling and power allocation

3

schemes are proposed to maximize the spectral efficiency of mmWave

NOMA systems.

As the energy consumption of wireless communications increases due to

the explosive growth of data traffic [10], an energy efficient resource

allocation is needed. There has been few works on the energy efficiency of

mmWave NOMA systems. In [11], an energy efficient power allocation

scheme is proposed for mmWave massive MIMO NOMA systems.

In this thesis, we investigate a joint user scheduling and power allocation

for a mmWave NOMA system to maximize the energy efficiency. A base

station (BS) transmits signals to users by NOMA and adopt random

beamforming to reduce the channel feedback overhead [12]. We formulate

the joint user scheduling and power allocation optimization problem with the

objective of maximizing energy efficiency under the quality-of-service (QoS)

constraints, SIC constraints, and the transmission power constraint. To solve

this challenging problem, we first decouple the problem into two subproblems,

the user scheduling problem and the power allocation problem. For the user

scheduling problem, a suboptimal algorithm is proposed to reduce the

complexity. For the power allocation problem, the problem is approximated

and reformulated into a convex problem. Then an iterative algorithm is

proposed to obtain the optimal solution. We jointly optimize the user

scheduling and power allocation by solving the user scheduling and the power

allocation subproblems iteratively.

4

The rest of this thesis is organized as follows. In chapter 2, the system

model and channel model are described. In chapter 3, the optimization

problem is formulated and a joint user scheduling and power allocation

algorithm is proposed. In chapter 4, simulation results are shown. Finally,

conclusions are drawn in chapter 5.

Equation Section (Next)

Equation Section (Next)

5

Chapter 2

System Model

Consider a downlink mmWave NOMA system which consists of one BS

and K users 1,2, , ,ku k K . The BS has a uniform linear array (ULA)

with N antennas, and each user has a single antenna. Suppose that the BS

forms M beams where M N and / 2M K . Suppose that a user is

scheduled on at most one beam and a beam serves at most two users. When

two users are scheduled on a beam, the users are served by NOMA.

6

BS

Figure 2.1. Downlink mmWave NOMA system

7

2.1 Channel Model

As discussed in [13], [14], the mmWave channel has a characteristic of

limited scattering to have a few number of paths. We adopt a mmWave

channel model with L paths including a line-of-sight (LOS) path [15]. The

channel vector between the BS and ku is given by

,

,

1 ,

( ),L

k l

k k l

l k l

aN

L g

h a (2.1)

where 1l for the LoS path, 1l for non-line-of-sight (NLoS) paths, and

,k la is the small scale fading gain which is distributed according to (0,1) .

,k lg denotes the path loss, which is given by

, 1010log ( ) [dB],k l kg d (2.2)

where kd is the distance between the BS and ku , 2~ (0, ) , and ,

, are parameters which depend on whether the path is LoS or NLoS.

,( )k la denotes the array response vector which is given by

, ,( 1)

,

1( ) [1, , , ] ,k l k lj j N T

k l e eN

a (2.3)

8

where , [ 1,1]k l is the normalized angle of departure (AoD) for the l -th

path of the channel between the BS and ku .

2.2 Random Beamforming

Suppose that random beamforming is adopted at the BS that does not

require full channel state information (CSI) of all users. The random

beamforming vector at the BS is given by [7], [16]

2( 1)

, 1, , ,m

mm M

M

w a (2.4)

where is a random variable uniformly distributed over [-1,1]. For

simplicity, let m denote the direction of the m -th beam, i.e.,

2( 1)m

m

M

.

Suppose that each user knows the beamforming vectors so that it feeds back

the effective channel gains for all beams, 2{| | | 1, 2, , }H

k m m Mh w , instead

of full CSI.

9

2.3 Data Transmission Model

For two users scheduled on each beam, the user with larger and smaller

effective channel gains are referred to as the strong user and the weak user,

respectively. Let ( )

,

i

k m , 1, 2, ,k K , 1, 2i , 1, 2, ,m M , denote the

scheduling indicators. The indicator (1)

, 1k m if ku is scheduled for the

strong user of the m -th beam and (1)

, 0k m otherwise. The indicator

(2)

, 1k m if ku is scheduled for the weak user of the m -th beam and

(2)

, 0k m otherwise. The transmit signal at the BS is given by

2

( )

, ,

1 1 1

,M K

i

n j n n i j

n j i

P s

x w (2.5)

where ks is the data symbol transmitted to ku , ,1mP and ,2mP are the

transmission power allocated to the strong user and the weak user of the m

-th beam, respectively.

Suppose that ku is scheduled on the m -th beam. The received signal at

ku is given by

10

2 2( ) ( )

, , , ,

1 1 1

disred signal

intra-beam interference

2( )

, ,

1 1 1

inter-beam interference

,

KH i H i

k k m k m m i k k m j m m i j

i j ij k

M KH i

k n j n n i j k

n j in m

y P s P s

P s n

h w h w

h w

(2.6)

where kn is an additive white Gaussian noise with zero-mean and variance

2 . When ku is the strong user of the m -th beam, the signal-to-

interference-plus-noise ratio (SINR) for ku to decode the weak user's signal

is given by

2 (2)

, ,2

12 1

, 22 (1) 2 ( ) 2

, ,1 , ,

1 1 1

| |

.

| | | |

KH

k m j m m

jj k

k m M KH H i

k m k m m k n j n n i

n j in m

P

P P

h w

h w h w

(2.7)

The decoding rate for ku to decode the weak user's signal is given by

2 1 2 1

, 2 ,log (1 ).k m k mR (2.8)

If 2 1

,k mR is higher than the target rate minR , ku decodes the weak user's

signal successfully [17]. Removing the weak user's signal by successive

interference cancellation (SIC), the SINR and data rate of ku are given by

11

2 (1)

, ,11

, 22 ( ) 2

, ,

1 1 1

| |

| |

H

k m k m m

k m M KH i

k n j n n i

n j in m

P

P

h w

h w

(2.9)

and

1 1

, 2 ,log (1 ),k m k mR (2.10)

respectively.

When ku is the weak user of the m -th beam, the SINR and data rate of

ku are given by

2 (2)

, ,22

, 22 (1) 2 ( ) 2

, ,1 , ,

1 1 1 1

| |

| | | |

H

k m k m m

k m K M KH H i

k m j m m k n j n n i

j n j ij k n m

P

P P

h w

h w h w

(2.11)

and

2 2

, 2 ,log (1 )k m k mR (2.12)

respectively.

The energy efficiency of the system is given by

2

,

1 1 1

2

,

1 1

( , ) ,

M Ki

k m

m k i

M

c m i

m i

R

P P

ρ P (2.13)

12

where cP is the circuit power consumption, 2K M ρ is the user

scheduling matrix whose ( , , )k m i -th element is ( )

,

i

k m , and 2MP is the

power allocation matrix whose ( , )m i -th element is ,m iP .

Equation Section (Next)

13

Chapter 3

Energy Efficient User Scheduling

and Power Allocation

For joint user scheduling and power allocation, the optimization problem

to maximize the energy efficiency is formulated as follows.

,

max: ( , )ρ P

ρ1 PP (3.1)

( )

, , mins.t. , , , {1,2},i i

k m k mR R k m i (3.2)

2 1 (1)

, , min , , ,k m k mR R k m (3.3)

2

, max

1 1

,M

m i

m i

P P

(3.4)

14

2

( )

,

1 1

2, ,K

i

k m

k i

m

(3.5)

2

( )

,

1 1

1, ,M

i

k m

m i

k

(3.6)

( )

, {0,1}, , ,i

k m k m (3.7)

where {1, 2, }K , {1, 2, }M , and maxP is the maximum

transmission power of the BS. (3.2) is the QoS requirement for users, (3.3)

is the SIC constraint, and (3.4) is the total transmission power constraint.

(3.5) is a constraint that at most two users are scheduled on a beam, and (3.6)

is a constraint that each user is scheduled on at most one beam.

The joint optimization problem P1 is a mixed-integer programming

which is difficult to solve [18]. To obtain a solution for this problem, we

decouple the problem into two subproblems: a user scheduling problem for

the given power allocation and a power allocation problem for the given user

scheduling. We first address two subproblems separately, then propose an

algorithm in which user scheduling and power allocation are performed

iteratively to obtain a solution for the joint optimization problem.

15

3.1 User Scheduling

Obtaining an optimal solution of user scheduling problem by exhaustive

search requires high computational complexity [19]. To reduce the

complexity, we propose a novel suboptimal user scheduling algorithm, as

shown in Algorithm 1.

The first step is to find out the set of candidate users, m . Define m as

a set of users whose AoD of the LoS path, ,1k , is in the range of [ ,m

]m , i.e., ,1{ | | }m k k mC u , where is the maximum angle

difference. Due to the directional nature of mmWave channel, the users in m

can have large beamforming gain for the m -th beam [7]. At most two users

among m will be scheduled on the m -th beam.

The next step is to select one beam and two users iteratively. In each

iteration, one beam and two users are selected to maximize the energy

efficiency with all the chosen pairs in all the previous iterations. Let

denote the set of indices of beams on which no user is scheduled. Initially, set

{1, , }M . Let 2

, ,

K M

k m i

J denote the single entry matrix,

, , {1, 2},k m i whose ( , , )k m i -th element is one and the other

elements are zero [20]. Schedule *1k

u and *2k

u on the *m -th beam which

16

Figure 3.1. A system diagram for the addressed mmWave NOMA system.

17

satisfy 1 2

1 2

* * *

1 2 , ,1 , ,2, ,

( , , ) arg max ( , )k k m

k m k mm u u C

m k k

ρ J J P . Then remove

*m from , and remove *1k

u and *2k

u from m , m . The above

procedure is repeated until all beams are scheduled, i.e., or less than

two users remains in m for all m , i.e., | | 1m , m . In the case

of and m , | | 1m , the remaining user in m , m , is

scheduled on the m -th beam.

Algorithm 1 Proposed User Scheduling

1: Initialize ρ 0 , ,1{ | | }m k k mC u for m and

{1, , }M

2: repeat

3: 1 2

1 2

* * *

1 2 , ,1 , ,2, ,

( , , ) arg max ( , )k k m

k m k mm u u

m k k

ρ J J P .

4: * * * *1 2, ,1 , ,2k m k m

ρ ρ J J .

5: *\ .m

6: Remove *1k

u and *2k

u from m , m .

7: until or | | 1m , m

8: if and m , | | 1m

9: Schedule k mu on the m -th beam.

10: end if

18

3.2 Power Allocation

For a given user scheduling matrix ρ , the power allocation problem to

maximize the energy efficiency is formulated as follows.

( ): max ,P

ρP P2 (3.8)

( )

, , mins.t. , , , {1,2},i i

k m k mR R k m i (3.9)

2 1 (1)

, , min , , ,k m k mR R k m (3.10)

2

, max

1 1

.M

m i

m i

P P

(3.11)

To solve this non-convex problem, we propose a power allocation algorithm.

First, we employ the successive convex approximation technique to

sequentially approximate constraints by using the following inequality [21]:

2 , , 2 , ,log (1 ) log ,i i i i

k m k m k m k ma b (3.12)

where

,

,

,1

i

k mi

k m i

k m

a

(3.13)

and

,

, 2 , 2 ,

,

log (1 ) log ,1

i

k mi i i

k m k m k mi

k m

b

(3.14)

19

for a given ,

i

k m . The equality in (3.12) is satisfied when , ,

i i

k m k m . Using

the lower bound of (3.12), 1

,k mR and 2

,k mR are approximated to

1 1 2 1 1 1

, , 2 , ,1 , 2 ,

(1)log (| | ) logH

k m k m k m k m m mk m k mR a a P a b h w (3.15)

and

2 2 2 2 2 2

, , 2 ,

(2

,2 , 2 ,

)log (| | ) log ,H

k m k m k m k m m k m k mmR a a P a b h w (3.16)

respectively, where , 2 ,logm i m iP P ,

,

2(1) 2 ( ) 2

,

1 1 1

| | 2 ,n i

M KPH i

m k n j n

n j in m

h w (3.17)

and

,1 ,

2(2) 2 (1) 2 ( ) 2

, ,

1 1 1 1

| | 2 | | 2 .m n i

K M KP PH H i

m k m j m k n j n

j n j ij k n m

h w h w (3.18)

Similarly, 2 1

,k mR is approximated to

2 1 3 2 3 (2)

(

, , 2 , , ,2

1

3 3

,

3

2 ,

)

log (| | )

log ,

KH

k m k m k m k m j

m

m m

jj k

k m k m

R a a P

a b

h w

(3.19)

20

where

,1 ,

2(3) 2 (1) 2 ( ) 2

, ,

1 1 1

| | 2 | | 2 ,m n i

M KP PH H i

m k m k m k n j n

n i jn m

h w h w (3.20)

2 1

,3

, 2 1

,

,1

k m

k m

k m

a

(3.21)

and

2 1

,3 2 1 2 1

, 2 , 2 ,2 1

,

log (1 ) log1

,k m

k m k m k m

k m

b

(3.22)

for a given 2 1

,k m . Note that (3.15), (3.16) and (3.19) are concave with

respect to ,m iP , since a log-sum-exponential function is a convex function.

From (3.15), (3.16) and (3.19), the problem P2 is approximated to

,

2

,

1 1 1

2

1 1

ma: x

2 m i

M Ki

k m

m k i

MP

c

m i

R

P

P

P3 (3.23)

( )

, , mins.t. , , , {1,2}, i i

k m k mR R k m i (3.24)

2 1 (1)

, , min , , ,k m k mR R k m (3.25)

,

2

max

1 1

,2 m i

MP

m i

P

(3.26)

21

where P is a 2M matrix whose ( , )m i -th element is ,m iP . However, the

objective function (3.23) is still non-concave function. We first introduce

slack variables ,

i

k m , k , m , {1, 2}i , so that the problem P3 is

reformulated as

,

2

,

1 1 1

2,

1 1

max

2

:m i

M Ki

k m

m k i

MP

c

m i

P

P ξ

P4 (3.27)

( )

, , mins.t. , , , {1,2},i i

k m k mR k m i (3.28)

( )

, , , , , , {1,2},i i i

k m k m k mR k m i (3.29)

(3.25), (3.26).

Note that , 0i

k m if ( )

, 0i

k m . The problem P4 is equivalent to the

following problem.

,

2 2

,,

1 1 1 1 1

2 2mi: lo 2g l gn om i

M M KP i

c k m

m i m k i

P

P ξP5 (3.30)

s.t. (3.25), (3.26), (3.28), (3.29).

Since the objective function (3.30) is a convex function, the problem P4 is

a convex problem. Next, we apply Lagrange dual method [22] to solve it. The

Lagrangian of the problem P5 is given by

22

,

,

2 2

2 2 ,

1 1 1 1 1

2 2( )

, min max

1 1 1 1 1

2( ) 3

, , min ,

1 1 1

, ,

, , ,

( , , , , )

log 2 log

( ) 2

( ) (

m i

m i

k m k m

k m k m k m

M M KP i

c k m

m i m k i

M K Mpi i i

k m

m k i m i

M Ki i i i

k m k m k

m k i

L

P

R P

R R

P ξ λ μ

(1) 2 1

,

1 1

),K M

m k m

k m

R

(3.31)

where ,

i

k m , ,

i

k m , are non-negative Lagrange multipliers, and λ , μ

are collections of ,

i

k m , ,

i

k m , respectively. The Lagrange dual function is

given by

,

( , , ) min ( , , , , ).g L P ξ

λ μ P ξ λ μ (3.32)

The Lagrange dual problem is formulated as

, ,

max ( , , ): g

λ μ

P λ μ6 (3.33)

, 0,s.t. , , {1,2},i

k m k m i (3.34)

, , , {1,2,3}0, ,i

k m k m i (3.35)

0. (3.36)

The subgradient method is utilized to solve the problem P6 [23]. The

Lagrange multipliers in the t -th iteration are given by

23

,

2

max

1 1

( 1) ( ) ( 2) ,m i

MP

m i

t t t P

(3.37)

, min ,

( )

,

( )

,

,

( ) ( ) , 1,( 1)

0, 0,

i i

k m k mi

k

i

k

m

k m

i

m

t t Rt

(3.38)

and

3

, mi

2 1 (1)

, ,

( )

n

,

3

,

( ) ( ) , 1,( 1)

0, 0,

k m k m

i

m

m

k

k

k m

t t Rt

R

(3.39)

where ( )t is the positive step size and [ ] max{ ,0}a a . The Karush-

Kuhn-Tucker (KKT) conditions result in

, ,2

,,

1 1 1

10

ln 2

i i

k m k mM Kiik mk m

m k i

L

(3.40)

for ( , , )k m i that satisfies ( )

, 1i

k m . From the above equation, we obtain

( )

,2

,

,

1 1 1

( )

,

,

1

l

( 1) , 1,

( 1)

0 0

n

.

2

i

k mM Ki

k m

m k i

i

k

i

k m

i

k

m

m

t

t

(3.41)

For fixed λ , μ , and , the optimal solutions are obtained by KKT

conditions, which lead to

24

,1

,1

,1

,1

(1) 1

, , ,

1,1

2(1) 1 1

, , , (1)1

23( )

, , , ( )1 1 1

12ln 2 2

| | 2

| | 20

m

m

m

m

P KP

k m k m k m

km tot

PHKk m

k m k m k m

k m

PHM Ki i i k m

k m k m k m im k i m

La

P P

a

a

h w

h w

(3.42)

and

,2

,2

,2

(2) 2 2 (3) 3 3

, , , , , ,

1,2

23( )

, , , ( )1 1 1

2ln 2 2

| | 20,

m

m

m

P KP

k m k m k m k m k m k m

km tot

PHM Ki i i k m

k m k m k m im k i m

m m

La a

P P

a

h w

(3.43)

where ,

2

1 1

2 m i

MP

tot

m i

P

and (3) (1)

, ,k m k m . From (3.42) and (3.43), the

power allocation coefficients are given by

(1) 1

,1 , , , ,1

1

1 /K

m k m k m k m m

k

P a A

(3.44)

and

(2) 2 2 (3) 3 3

,2 , , , , , , ,2

1

/ ,K

m k m k m k m k m k m k m m

k

P a a A

(3.45)

where

25

2(1) 1 1

,1 , , , (1)1

23( )

, , , ( )1 1 1

| |ln 2

| |

1HKk m

m k m k m k m

ktot m

HM Ki i i k m

k m k m k m im k i m

A aP

a

h w

h w (3.46)

and

,223

( )

, , , ( )1 1

,2

1

| | 21ln 2 .

mPHM Ki i i k m

k m k m k m im k itot mm m

mA aP

h w

(3.47)

The power allocation algorithm is summarized in Algorithm 2.

26

Algorithm 2 Proposed Power Allocation

1: Set the initial point (0)P , the maximum error tolerance , the maximum

number of iterations maxL , and the outer iteration counter 1l .

2: Calculate (0)( , ) ρ P ,

(0)

,

i

k m , and 2 1(0)

,k m based on (0)

P .

3: repeat

4: Set ( 1)

, ,

i i l

k m k m , 2 1 2 1( 1)

, ,

l

k m k m .

5: Calculate ,

i

k ma and ,

i

k mb according to (3.13), (3.14), (3.21), and

(3.22).

6: Set the inner iteration counter 1t and the inner iteration initial

point ( 1)(0) lP P .

7: repeat

8: Obtain ( )t , , ( )i

k m t , and , ( )i

k m t , according to (3.37)-(3.39),

and (3.41) based on ( 1)t P .

9: Calculate ( )i

m according to (3.17), (3.18), and (3.20).

10: Calculate totP .

11: Obtain ( )tP from (3.44) and (3.45) based on ( )t , , ( )i

k m t ,

, ( )i

k m t , ( )i

m , and totP .

12: 1t t .

13: until convergence

14: Set ( ) ( 1)l t P P .

15: Calculate ( )( , )l ρ P ,

( )

,

i l

k m , and 2 1( )

,

l

k m based on ( )l

P .

16: 1l l .

17: until ( ) ( 1)| ( , ) ( , ) |l l ρ P ρ P or maxl L

27

3.3 Joint User Scheduling and Power

Allocation

To solve the original joint user scheduling and power allocation problem

P1 , we perform Algorithm 1 and Algorithm 2 iteratively. Setting the power

allocation coefficients ,1 max / (3 )mP P M and ,2 max2 / (3 )mP P M initially

in Algorithm 3, find user scheduling indicators by Algorithm 1. Then, given

the user scheduling, find power allocation coefficients by Algorithm 2. This

procedure is repeated until the energy efficiency converges or the maximum

number of iterations is reached.

Algorithm 3 Joint User Scheduling and Power Allocation

1: Set the maximum error tolerance , the maximum number of iterations

maxL , and the iteration counter 1l .

2: Initialize (0)P with ,1 max / (3 )mP P M and ,2 max2 / (3 )mP P M .

3: Initialize (0) ρ 0 .

4: repeat

5: Given ( 1)lP , obtain user scheduling

( )lρ by Algorithm 1.

6: Given ( )l

ρ and the initial point ( 1)lP , obtain ( )l

P by Algorithm 2.

7: 1l l .

8: Calculate ( ) ( )( , )l l

ρ P .

9: until ( ) ( ) ( 1) ( 1)| ( , ) ( , ) |l l l l ρ P ρ P or maxl L

28

Chapter 4

Simulation Results

Consider a mmWave NOMA system with random beamforming at the BS.

Suppose that users are uniformly distributed in a cell with radius 100 m.

Suppose that number of paths 3L , the rate requirement of users min 0.1R

bits/s/Hz, the noise variance 2 90 dBm, the circuit power 10cP

dBm, the maximum angle difference 0.2 , the maximum error tolerance

0.05 , and the maximum number of iterations max 10L . Suppose that

path loss parameters 61.4 , 2 , and 5.8 for LoS paths, and

72 , 2.92 , and 8.7 for NLoS paths [15].

Figure 4.1 shows the energy efficiency versus the maximum transmission

29

power at the BS for the number of users 40K . In Figure 4.1 (a), the

number of antennas 8N , and the number of beams 8M . In Figure 4.1

(b), the number of antennas 16N , and the number of beams 8M . In

Figure 4.1 (c), the number of antennas 8N , and the number of beams

4M . The performance of conventional algorithms, such as the matching

algorithm for user scheduling [9] and the fixed power allocation (PA) are

presented for comparison. For fixed PA, set ,1 max / (3 )mP P M and

,2 max2 / (3 )mP P M . It is shown that the proposed joint user scheduling and

power allocation scheme achieves higher energy efficiency than the

conventional algorithms. It is also shown that for the schemes which involve

the proposed power allocation algorithm, the energy efficiency first increases

and then converges to a constant value as the maximum transmission power

increases. The reason is that when maxP is large, using the maximum power

is not desirable in the perspective of energy efficiency.

Figure 4.2 shows the energy efficiency versus the maximum transmission

power at the BS for the number of users 40K and the number of antennas

8N . It is shown that for small maxP , the energy efficiency for small M

is larger than that for large M and for large maxP , the energy efficiency for

large M is larger than that for small M . This is because if M is large

when maxP is small, relatively small power is allocated to one user.

Figure 4.3 shows the energy efficiency versus the maximum transmission

30

power at the BS for the number of users 40K , and the number of beams

8M . It is shown that energy efficiency for large N is larger than that of

small N .

Figure 4.4 shows the energy efficiency of the system versus for max 25P

dBm. In Figure 4.4 (a), the number of antennas at the BS 8N and in

Figure 4.4 (b), the number of antennas at the BS 16N . It is shown that the

energy efficiency increases as the number of users increases. This is because

the number of users with good channel condition increases as the number of

users increases. It is also shown that the energy efficiency increases as the

number of beams increases. The reason is that the number of served users

increases as the number of users increases.

31

(a) 8N and 8M

32

(b) 16N and 8M

33

(c) 8N and 4M

Figure 4.1. Energy efficiency versus maximum transmission power maxP for

proposed and conventional schemes.

34

Figure 4.2. Energy efficiency versus maximum transmission power maxP for

different values of the number of beams M .

35

Figure 4.3. Energy efficiency versus maximum transmission power maxP for

different values of the number of antennas N .

36

(a) 8N

37

(b) 16N

Figure 4.4. Energy efficiency versus maximum transmission power maxP for

different values of the number of antennas N .

38

Chapter 5

Conclusion

In this thesis, we investigate resource allocation for a mmWave NOMA

system with random beamforming. A new joint user scheduling and power

allocation scheme is proposed to maximize the energy efficiency.

The joint optimization problem is formulated and it is decoupled into user

scheduling and power allocation subproblems. We propose a suboptimal user

scheduling algorithm for a given power allocation. We also propose an

optimal power allocation algorithm for given user scheduling based on the

successive convex approximation and Lagrangian dual method. Then the

algorithms are performed iteratively to obtain a solution of the joint

optimization problem. By computer simulations it is shown that the energy

efficiency increases as either the maximum transmission power or the number

39

of users increases. It is also shown that the proposed algorithms achieves

higher energy efficiency than the conventional algorithms.

40

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45

Korean Abstract

본 논문에서는 밀리미터파 비직교 다중접속 시스템에서 사용자

스케줄링과 전력 할당 방법을 다룬다. 피드백 오버헤드를 줄이기

위하여 기지국에서 랜덤 빔포밍을 사용한다. 각 빔으로는 비직교

다중접속을 통하여 최대 두 명의 사용자에게 신호를 보낸다. 에너

지 효율을 최대화하는 사용자 스케줄링과 전력할당 문제를 만들고

이 문제를 풀기 위한 알고리즘을 제안한다. 모의실험을 통해 제안

한 방법이 기존의 방법보다 에너지 효율이 좋음을 확인한다.

주요어: 비직교 다중접속, 밀리미터파, 랜덤 빔포밍, 자원 할당, 전

력 할당, 사용자 스케줄링, 에너지 효율.

학번: 2016-24274