Repeated index modulation for ofdm systems

MINISTRY OF EDUCATION & TRAINING MINISTRY OF NATIONAL DEFENSE
MILITARY TECHNICAL ACADEMY
LE THI THANH HUYEN
REPEATED INDEX MODULATION
FOR OFDM SYSTEMS
A Thesis for the Degree of Doctor of Philosophy
HA NOI - 2020
MINISTRY OF EDUCATION & TRAINING MINISTRY OF NATIONAL DEFENSE
MILITARY TECHNICAL ACADEMY
LE THI THANH HUYEN
REPEATED INDEX MODULATION
FOR OFDM SYSTEMS
A Thesis for the Degree of Doctor of Philosophy
Specialization: Electronic Engineering
Specialization code: 9 52 02 03
SUPERVISOR
Prof. TRAN XUAN NAM
HA NOI - 2020
ASSURANCE
I hereby declare that this thesis was carried out by myself under the
guidance of my supervisor. The presented results and data in the the-
sis are reliable and have not been published anywhere in the form of
books, monographs or articles. The references in the thesis are cited in
accordance with the university’s regulations.
Hanoi, May 17th, 2019
Author
Le Thi Thanh Huyen
ACKNOWLEDGEMENTS
It is a pleasure to take this opportunity to send my very great appre-
ciation to those who made this thesis possible with their supports.
First, I would like to express my deep gratitude to my supervisor,
Prof. Tran Xuan Nam, for his guidance, encouragement and meaningful
critiques during my researching process. This thesis would not have been
completed without him.
My special thanks are sent to my lecturers in Faculty of Radio - Elec-
tronics, especially my lecturers and colleagues in Department of Com-
munications who share a variety of difficulties for me to have more time
to concentrate on researching. I also would like to sincerely thank my
research group for sharing their knowledge and valuable assistance.
Finally, my gratitude is for my family members who support my stud-
ies with strong encouragement and sympathy. Especially, my deepest
love is for my mother and two little sons who always are my endless
inspiration and motivation for me to overcome all obstacles.
Author
Le Thi Thanh Huyen
TABLE OF CONTENTS
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 1. RESEARCH BACKGROUND . . . . . . . . . . . . . . . 8
1.1. Basic principle of IM-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.1. IM-OFDM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1.2. Sub-carrier mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.1.3. IM-OFDM signal detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.1.4. Advantages and disadvantages of IM-OFDM. . . . . . . . . . . . 16
1.2. Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 2. REPEATED INDEX MODULATION FOR OFDM
WITH DIVERSITY RECEPTION . . . . . . . . . . . . . . . . . . . . . . 24
2.1. RIM-OFDM with diversity reception model . . . . . . . . . . . . . . . . 24
2.2. Performance analysis of RIM-OFDM-MRC/SC under perfect CSI
28
2.2.1. Performance analysis for RIM-OFDM-MRC . . . . . . . . . . . . 29
i
2.2.2. Performance analysis for RIM-OFDM-SC . . . . . . . . . . . . . . . 34
2.3. Performance analysis of RIM-OFDM-MRC/SC under imperfect
CSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.1. Performance analysis for RIM-OFDM-MRC . . . . . . . . . . . . 35
2.3.2. Performance analysis for RIM-OFDM-SC . . . . . . . . . . . . . . . 40
2.4. Performance evaluation and discussion . . . . . . . . . . . . . . . . . . . . . 41
2.4.1. Performance evaluation under perfect CSI . . . . . . . . . . . . . . 41
2.4.2. SEP performance evaluation under imperfect CSI condition .
48
2.4.3. Comparison of the computational complexity . . . . . . . . . . . 49
2.5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Chapter 3. REPEATED INDEX MODULATION FOR OFDM
WITH COORDINATE INTERLEAVING . . . . . . . . . . . . . . . 51
3.1. RIM-OFDM-CI system model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2. Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.1. Symbol error probability derivation . . . . . . . . . . . . . . . . . . . . . 56
3.2.2. Asymptotic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.3. Optimization of rotation angle . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3. Low-complexity detectors for RIM-OFDM-CI. . . . . . . . . . . . . . . 62
3.3.1. Low-complexity ML detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.3.2. LLR detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.3. GD detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4. Complexity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.5. Performance evaluations and discussion. . . . . . . . . . . . . . . . . . . . . 69
ii
3.6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . 76
PUBLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
iii
LIST OF ABBREVIATIONS
Abbreviation Definition
AWGN Additive White Gaussian Noise
BEP Bit Error Probability
BER Bit Error Rate
CI Coordinate Interleaving
CS Compressed Sensing
CSI Channel State Information
D2D Device to Device
ESIM-OFDM Enhanced Sub-carrier Index Modulation for Or-
thogonal Frequency Division Multiplexing
FBMC Filter Bank Multi-Carrier
FFT Fast Fourier Transform
GD Greedy Detection
ICI Inter-Channel Interference
IEP Index Error Probability
IFFT Inverse Fast Fourier Transform
IM Index Modulation
IM-OFDM Index Modulation for OFDM
iv
IM-OFDM-CI Index Modulation for OFDM with Coordinate
Interleaving
IoT Internet of Things
ISI Inter-Symbol Interference
ITU International Telecommunications Union
LowML Low-complexity Maximum Likelihood
LLR Log Likelihood Ratio
LUT Look-up Table
M2M Machine to Machine
Mbps Megabit per second
MGF Moment Generating Function
MIMO Multiple Input Multiple Output
ML Maximum Likelihood
MM-IM-OFDM Multi-Mode IM-OFDM
MRC Maximal Ratio Combining
NOMA Non-Orthogonal Multiple Access
OFDM Orthogonal Frequency Division Multiplexing
OFDM-GIM OFDM with Generalized IM
OFDM-I/Q-IM OFDM with In-phase and Quadrature Index
Modulation
OFDM-SS OFDM Spread Spectrum
PAPR Peak-to-Average Power Ratio
PEP Pairwise Error Probability
PIEP Pairwise Index Error Probability
v
PSK Phase Shift Keying
QAM Quadrature Amplitude Modulation
RIM-OFDM Repeated Index Modulation for OFDM
RIM-OFDM-MRC Repeated Index Modulation for OFDM with
Maximal Ratio Combining
RIM-OFDM-SC Repeated Index Modulation for OFDM with Se-
lection Combining
RIM-OFDM-CI Repeated Index Modulation for OFDM with Co-
ordinate Interleaving
SC Selection Combining
SEP Symbol Error Probability
SIMO Single Input Multiple Output
S-IM-OFDM Spread IM-OFDM
SNR Signal to Noise Ratio
SM Spatial Modulation
SS Spread Spectrum
UWA Underwater Acoustic
V2V Vehicle to Vehicle
V2X Vehicle to Everything
xG x-th Generation
vi
LIST OF FIGURES
1.1 Block diagram of an IM-OFDM system. . . . . . . . . . . . 10
2.1 Structure of the RIM-OFDM-MRC/SC transceiver. . . . . . 25
2.2 The SEP comparison between RIM-OFDM-MRC and the
conventional IM-OFDM-MRC system when N = 4, K =
2, L = 2, M = {4, 8}. . . . . . . . . . . . . . . . . . . . . . . 42
2.3 The SEP performance of RIM-OFDM-SC in comparison
with IM-OFDM-SC for N = 4, K = 2, L = 2, M = {4, 8}. . 43
2.4 The relationship between the index error probability of
RIM-OFDM-MRC/SC and the modulation order M in
comparison with IM-OFDM-MRC/SC for N = 4, K = 2,
M = {2, 4, 8, 16}. . . . . . . . . . . . . . . . . . . . . . . . . 44
2.5 The impact of L on the SEP performance of RIM-OFDM-
MRC and RIM-OFDM-SC for M = 4, N = 4, K = 2 and
L = {1, 2, 4, 6}. . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.6 The SEP performance of RIM-OFDM-MRC under influ-
ence of K for M = {2, 4, 8, 16}, N = {5, 8}, K = {2, 3, 4, 5}. 46
2.7 The SEP performance of RIM-OFDM-SC under influence
of K when M = {2, 4, 8, 16}, N = {5, 8}, K = {2, 3, 4, 5}. . . 46
2.8 Influence of modulation size on the SEP of RIM-OFDM-
MRC/SC for N = 5, K = 4, and M = {2, 4, 8, 16, 32}. . . . . 47
vii
2.9 The SEP performance of RIM-OFDM-MRC in compari-
son with IM-OFDM-MRC under imperfect CSI when N =
4, K = 2, M = {4, 8}, and 2 = {0.01, 0.05}. . . . . . . . . . 48
2.10 The SEP performance of RIM-OFDM-SC in comparison
with IM-OFDM-SC under imperfect CSI when N = 4,
K = 2, M = {4, 8}, and 2 = 0.01. . . . . . . . . . . . . . . . 49
3.1 Block diagram of a typical RIM-OFDM-CI sub-block. . . . . 52
3.2 Rotated signal constellation. . . . . . . . . . . . . . . . . . . 60
3.3 Computational complexity comparison of LLR, GD, ML
and lowML detectors when a) N = 8,M = 16, K =
{1, 2, . . . , 7} and b) N = 8, K = 4,M = {2, 4, 8, 16, 32, 64}. . 68
3.4 Index error performance comparison of RIM-OFDM-CI,
IM-OFDM, IM-OFDM-CI and ReMO systems at the spec-
tral efficiency (SE) of 1 bit/s/Hz, M = {2, 4}, N = 4,
K = {2, 3}. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5 SEP performance comparison between RIM-OFDM-CI,
IM-OFDM and CI-IM-OFDM using ML detection at the
spectral efficiency of 1 bit/s/Hz when M = {2, 4}, N = 4,
K = {2, 3}. . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6 BER comparison between the proposed scheme and the
benchmark ones when N = 4, K = {2, 3}, M = {2, 4}. . . . 72
3.7 BER comparison between the proposed and benchmark
schemes at SE of 1.25 bits/s/Hz when N = {4, 8}, K =
{2, 4}, M = {2, 4, 8}. . . . . . . . . . . . . . . . . . . . . . . 73
viii
3.8 SEP performance of RIM-OFDM-CI and benchmark sys-
tems using different detectors. . . . . . . . . . . . . . . . . . 74
ix
LIST OF TABLES
1.1 An example of look-up table when N = 4, K = 2, p1 = 2 . . 13
2.1 Complexity comparison between the proposed schemes
and the benchmark. . . . . . . . . . . . . . . . . . . . . . . . 50
3.1 Example of LUT for N = 4, K = 2, pI = 2. . . . . . . . . . . 54
3.2 Complexity comparison between ML, LowML, LLR and
GD dectectors. . . . . . . . . . . . . . . . . . . . . . . . . . 68
x
LIST OF SYMBOLS
Symbol Meaning
a A complex number
aR Real part of a
aI Imaginary part of a
|a| Modulus of a
a A vector
A A matrix
AH The Hermitian transpose of A
AT The transpose of A
c Number of possible combinations of active in-
dices
f (.) Probability density function
G Number of sub-blocks
K Number of active sub-carriers
N Number of sub-carriers in each sub-block
NF Number of sub-carriers in IM-OFDM system
L Number of receive antennas
P (.) The probability of an event
PI Index symbol error probability
PM M -ary modulated symbol error probability
xi
Ps Symbol error probability
Q (.) The tail probability of the standard Gaussian
distribution
γ¯ Average SNR at each sub-carrier
I Set of possible active sub-carrier indices
M (.) The moment generating function.
S Complex signal constellation
Sφ Rotated complex signal constellation
α Index of an active sub-carrier
 Channel estimation error variance
Θ Big-Theta notation
φ Rotation angle of signal constellation
φopt Optimal rotation angle of signal constellation
‖.‖2F Frobenius norm of a matrix
diag(.) Diagonal matrix
C (N,K) Binomial coefficient, C (N,K) = N !
K!(N−K)!
bxc Rounding down to the closest integer
log2 (.) The base 2 logarithm
E {.} Expectation operation.
xii
INTRODUCTION
Motivation
Wireless communication has been considered to be the fastest devel-
oping field of the communication industry. Through more than 30 years
of research and development, various generations of wireless communi-
cations have been born. The achievable data rate of wireless systems
has increased to several thousands of times higher (the fourth genera-
tion - 4G) than that of the second generation (2G) wireless systems.
Particularly, the 4G wireless communication systems, supported by key
technologies such as multiple-input multiple-output (MIMO), orthogonal
frequency division multiplexing (OFDM), cooperative communications,
have already achieved the data rate of hundreds Mbps [1].
The MIMO technique exploits the diversity of multiple transmit an-
tennas and multiple receive antennas to enhance channel capacity with-
out either increasing the transmit power or requiring more bandwidth.
Meanwhile, OFDM is known as an efficient multi-carrier transmission
technique which has high resistance to the multi-path fading. The
OFDM system offers a variety of advantages such as inter-symbol in-
terference (ISI) resistance, easy implementation by inverse fast Fourier
transform/fast Fourier transform (IFFT/FFT). It can also provide higher
spectral efficiency over the single carrier system since its orthogonal sub-
1
carriers overlap in the frequency domain.
Due to vast developments of smart terminals, new applications with
high-density usage, fast and continuous mobility such as cloud services,
machine-to-machine (M2M) communications, autonomous cars, smart
home, smart health care, Internet of Things (IoT), etc, the 5G sys-
tem has promoted challenging researches in the wireless communication
community [2]. It is expected that ubiquitous communications between
anybody, anything at anytime with high data rate and transmission re-
liability, low latency are soon available [3]. Although there are several
5G trial systems installed worldwide, so far there have not been any
official standards released yet. The International Telecommunications
Union (ITU) has set 2020 as the deadline for the IMT-2020 standards.
According to a recent report of the ITU [3], 5G can provide data rate
significantly higher, about tens to hundreds of times faster than that of
4G. For latency issue, the response time to a request of 5G can reduce
to be about ... FDM to the MIMO and cooperative com-
munication systems is a challenging topic and very attractive for
future works.
• The performance of the RIM-OFDM-CI system in Chapter 3 is in-
vestigated under the perfect CSI condition. Evaluating the impacts
of channel estimation errors on the system performance is a signifi-
cantly meaningful topic for future research.
• The proposals in Chapter 2 and Chapter 3 of the thesis consider the
uncoded systems, it is more interesting when evaluating the SEP
and BER performance of the system with channel coding.
• The performance in terms of SEP and BER is analyzed for the two
proposed systems. Further analysis using other evaluated parame-
ters would probably give additional insights into the performance of
the proposed systems.
78
PUBLICATIONS
[J1] L. T. T. Huyen, and T. X. Nam, “Performance Analysis of
Repeated Index Modulation for OFDM with MRC Diversity over
Nakagami-m Fading Channel,” Journal of Science and Technology,
No.196, pp. 90–102, Feb., 2019.
[J2] T. T. H. Le, X. N. Tran, “Performance Analysis of Repeated
Index Modulation for OFDM with MRC and SC diversity Under
Imperfect CSI,” AEU - International Journal of Electronics and
Communications, (ISI-SCI, Q2, IF=2.853), Vol. 107, pp. 199-208,
Jul. 2019, https://doi.org/10.1016/j.aeue.2019.05.022, Available on-
line 23 May, 2019.
[J3] L. T. T. Huyen, and T. X. Nam, “Performance Analysis of Re-
peated Index Modulation with Coordinate Interleaving over Nakagami-
m Fading Channel,” Research and Development on Information and
Communication Technology (RD-ICT) of Journal of Information
and Communication Technology, Vol. 2019, No. 1, pp. 23-30, Jun.
2019.
[J4] T. T. H. Le, V. D. Ngo, M. T. Le, X. N. Tran, “Repeated Index
Modulation-OFDM with Coordinate Interleaving: Performance Op-
timization and Low-Complexity Detectors,” IEEE Systems Journal,
79
(ISI - SCI, Q1, IF=4.463), vol. , no. , pp. , 20xx. (Under review).
[C1] T. T. H. Le, X. N. Tran, “Repeated index modulation for OFDM
with space and frequency diversity,” Advanced Technologies for Com-
munications (ATC), 2017 International Conference on. IEEE, pp.
97–102, Oct., 2017 (Scopus).
[C2] T. T. H. Le, V. D. Ngo, M. T. Le, X. N. Tran, “Repeated Index
Modulation with Coordinate Interleaved OFDM,” 2018 5th NAFOS-
TED Conference on Information and Computer Science (NICS), pp.
115-119, Nov., 2018 (Scopus).
80
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