# Second Place Solution of WSDM2023 Toloka
Visual Question Answering Challenge

Xiangyu Wu1 Zhouyang Chi1 Yang Yang1 Jianfeng Lu1 1 Nanjing University of
Science and Technology
<EMAIL_ADDRESS>
###### Abstract

In this paper, we present our solution for the WSDM2023 Toloka Visual Question
Answering Challenge. Inspired by the application of multimodal pre-trained
models to various downstream tasks(e.g., visual question answering, visual
grounding, and cross-modal retrieval), we approached this competition as a
visual grounding task, where the input is an image and a question, guiding the
model to answer the question and display the answer as a bounding box on the
image. We designed a three-stage solution for this task. Specifically, we used
the visual-language pre-trained model OFA as the foundation. In the first
stage, we constructed a large-scale synthetic dataset similar to the
competition dataset and coarse-tuned the model to learn generalized semantic
information. In the second stage, we treated the competition task as a visual
grounding task, loaded the weights from the previous stage, and continued to
fine-tune the model on the competition dataset, transferring the semantic
information learned in the first stage to the competition task. Finally, we
designed a bounding box matching and replacing post-processing strategy to
correct the model’s prediction results. Our team achieved a score of 76.342 on
the final leaderboard, ranking second.

##  1 Introduction

Visual-language pretraining (VLP) [26, 25, 15, 5, 21, 10] models have seen
rapid development and significant advancements in recent years. These models
aim to bridge the gap between visual and linguistic information, enabling
machines to understand and generate contextually rich content combining images
and text. Early work, such as OFA [14] and BLIP [6], laid the groundwork for
integrating visual and textual information. OFA aimed to unify vision-language
tasks using large-scale pretraining, while BLIP improved data efficiency and
model performance through self-supervised learning. Recent advancements,
including ChatGPT-4 [11], have led to more powerful models capable of tasks
like image generation from text, multimodal conversation, and advanced visual
reasoning.

One key application is Visual Question Answering (VQA) [4, 2, 13, 22, 8, 16],
where the model answers questions based on an image. This task requires
understanding both the image and the natural language question, combining
image recognition, language processing, and reasoning. Visual grounding [7,
12, 24, 1, 9, 3] is a specific task within the broader domain of VQA. In VQA,
the primary objective is to answer questions about an image using natural
language understanding. Visual grounding within VQA focuses on precisely
locating and identifying objects or regions in the image that correspond to
specific elements mentioned in the textual query. This task requires the model
to effectively link the textual description with relevant visual features in
the image, enabling accurate and contextually relevant answers to questions
posed about visual content.

VLP models [26, 25, 20, 17] achieve visual grounding tasks by first
pretraining on large-scale datasets containing paired image and text data.
These models extract feature embeddings from images using CNNs and process
textual descriptions using transformer architectures like BERT. Through cross-
modal attention mechanisms, they align visual and textual features, enabling
precise linking of natural language queries to specific visual elements in
images. Fine-tuning on task-specific datasets further refines their ability to
understand and respond to queries that require nuanced visual comprehension
within applications such as VQA and multimodal interaction systems.

With the rapid development of multimodal pre-trained models, they have shown
strong generalization capabilities in various downstream tasks, such as visual
grounding, visual question answering, cross-modal retrieval, image captioning,
and more. We found that the visual grounding task refers to predicting the
bounding box for a given text in an image, which inspired us to transform the
competition task, namely visual question grounding, into a visual grounding
task, effectively leveraging the power of multimodal pre-trained models.

In the first stage, we collected and constructed a large amount of external
data for coarse tuning of the model, with image distributions, question
distributions, and label distributions similar to the competition data.
Secondly, we used the OFA model as the foundation and coarse-tuned a model
with strong generalization and rich semantics. In the second stage, we loaded
the coarse-tuned weights from the previous stage, treated the competition task
as a visual grounding task, constructed different question templates, and
continued fine-tuning the OFA model on the competition dataset. Finally, we
designed a bounding box matching and replacing the post-processing strategy.
The bounding box position predicted by visual grounding is roughly correct,
but the accuracy of coordinates is not higher than that of an object detector.
Therefore, by calculating the IoU, we replaced the predicted bounding box with
the object detector’s bounding box to correct the model’s prediction results.
Our team secured the runner-up position on the final leaderboard with a score
of 76.342.

##  2 Related Works

###  2.1 Visual-Language Pretraining (VLP)

Recent developments in VLP [26, 25, 15, 5, 18, 19] have been propelled by
pioneering models such as OFA [14] and BLIP [6]. These models have
innovatively utilized large-scale datasets to pretrain transformer-based
architectures on paired image-text data. OFA aims to unify various vision-
language tasks by leveraging comprehensive pretraining, thereby enhancing
performance in applications such as VQA and image-text retrieval. Meanwhile,
BLIP focuses on optimizing data efficiency and model performance through
advanced self-supervised learning techniques, contributing significantly to
the robustness of multimodal understanding. In this evolving landscape,
ChatGPT-4 [11] has emerged as a notable advancement, showcasing remarkable
capabilities in generating nuanced natural language responses and pushing the
boundaries of language modeling tasks.

###  2.2 Visual Question Answering (VQA)

VQA [4, 2, 13, 22] involves answering questions about images using natural
language understanding, which has been a pivotal area of research in
multimodal AI. These tasks require models to comprehend both the visual
content of images and the semantic context of textual queries. Early
approaches focused on integrating vision and language through methods like
joint embeddings and attention mechanisms. More recent advancements,
leveraging models such as OFA [14] and BLIP [6], have significantly improved
the accuracy and efficiency of VQA systems by employing large-scale
pretraining on diverse datasets. These models aim to enhance the model’s
ability to reason about complex scenes and provide accurate responses based on
multimodal inputs. VQA continues to evolve with the introduction of
transformer-based architectures like ChatGPT-4, which further pushes the
boundaries of multimodal understanding and response generation in AI systems.

###  2.3 Visual Grounding (VG)

Visual grounding [7, 12, 24, 1, 9, 23] tasks involve the localization and
identification of specific objects or regions within an image based on textual
descriptions. This task is crucial in multimodal AI applications, where models
need to link natural language queries to corresponding visual elements
effectively. By leveraging deep learning techniques, such as convolutional
neural networks (CNNs) for image feature extraction and transformer
architectures for textual understanding, models can align visual and textual
modalities. This alignment enables precise object localization, scene
understanding, and context-based reasoning, enhancing applications like VQA
[4, 2], image retrieval, and interactive systems that require accurate
interpretation and response generation based on visual content.

##  3 Methods

The solution of this competition is based on the OFA [14] visual language pre-
training model, so we introduce the OFA model first. OFA is a large multi-
modal pre-training model that transforms all pre-training tasks into text
generation tasks so that all pre-training tasks can be performed by one
decoder module. For example, VG, visual grounding pre-training task construct
the template which region does the text ”Man in white shirt” describe?
bounding box coordinates are generated by the decoder module; ITM, image text
match pre-training task, construct the template, Does the image describe ”Two
boys playing frisbee on the grass”? yes or no is generated by the same decoder
module. It can be seen, that the visual grounding task is very similar to the
competition, which are both output bounding box coordinates. Therefore, we
transformed the competition task into visual Grounding task and used the large
pre-training model for fine-tuning.

Our methods mainly include three parts, respectively Coarse tuning, Fine
tuning, and Postprocessing. In the first part, Coarse tuning aims to build a
synthetic dataset similar to the competition dataset and train a weak
semantics but strong generalization model on the synthetic dataset. The weak
semantics is because the synthetic dataset contains dirty data and labels so
the semantic learning is not accurate enough. Strong generalization is due to
the large scale of the synthetic dataset, so the generalization ability is
relatively strong. In the second part, the Fine-tuning stage loads the coarse-
tuning part weight and continues to train the competition dataset. The third
part, post-processing, through bounding box matching, replacing, and model
ensemble, further improves the accuracy of model prediction.

Figure 1: Coarse Tuning Stage.

###  3.1 Coarse Tuning Stage

The first part is the coarse tuning stage. We construct the coarse-tuning
dataset through coco images. There are several features of constructing
synthetic datasets. First, the image distribution, question distribution, and
bounding box distribution of the coarse tuning dataset should be as close as
possible to the competition dataset, so that the model can avoid learning the
wrong data distribution; Secondly, any sampling operation must be Random
Sampling, which can ensure that the model will not learn any data bias.
Finally, do not sample any data in the test public set, which can avoid
overfitting the model to the test public set. The coarse-tuning paradigm
should be the same as the competition task, similar to the pre-training, save
the coarse-tuned model weight for the next fine-tuning part. similar to the
pre-training, the more coarse tuning epochs, the stronger generalization, and
the better performance.

This figure illustrates our process of constructing the synthetic dataset. For
each sample in the training set, we directly input images and questions into
the multi-modal pre-training model to obtain textual answers, which we define
as pseudo-answers. Now, each sample consists of an image, a question, and a
pseudo-answer; therefore, we can build a mapping table of pseudo-answers and
questions, where one pseudo-answer corresponds to multiple questions, for
example, the pseudo-answers clock and vase. Then, randomly selected an image
from the coco and detected several objects by the object detector. Each
detected object includes confidence, class counts, class name, and bounding
box, where class number is defined as the number of the object in the image,
such as the number of clocks is one and the number of roll paper is two. Next,
we sorted the detected objects according to confidence, selected an object
class with the largest confidence, the class count is one, and belonging to
the pseudo answer, then, randomly selected a question corresponding to the
pseudo answer from the mapping table. Now, a new sample is obtained, the
question of the sample is randomly selected question, the pseudo-answer is the
selected object class, and the target bounding box is obtained by the object
detector. After the synthetic dataset is constructed, a model with weak
semantics but strong generalization can be coarse tuning in the form of visual
grounding.

Figure 2: Fine Tuning Stage.

###  3.2 Fine-tuning Stage

The second part is the Fine-tuning stage. In the form of a visual grounding
task, load the trained weight obtained by the last Coarse tuning part and
continue to train the model on the competition dataset. Each sample consists
of an image, a question, and a pseudo-answer. Question and pseudo answer are
combined into the template, which is used as text input of the model. For the
four templates we constructed, we finally adopted the second template, and the
first word of the question, such as what, where, and which, was replaced with
which region. After the template construction, the template and image are
input into the OFA model, through text encoder, image encoder, and cross-modal
fusion, the coordinates of the bounding box are finally output by text
decoder.

Figure 3: Postprocessing Stage.

###  3.3 Postprocessing Stage

The third part is the post-processing stage, the bounding box position
predicted by OFA is roughly correct, but the accuracy of coordinates is not
higher than object detector. Therefore, by calculating the iou, we replace the
predicted bounding box with the object detector’s bounding box. For each
image, all bounding boxes in the image are detected by object detectors yolor
and vitDet, and sorted according to the confidence, which are called candidate
Bounding boxes. Then, for the predicted bounding box, the first candidate
bounding box with iou higher than zero point six is selected to replace the
predicted bounding box. Finally, the model ensemble includes three ways, the
first is five folds with standard Corase tuning, the second is ten folds with
standard Corase tuning, and the third is five folds with back translation
Corase tuning. The back translation was applied to the coarse tuning stage,
which expanded the diversity of question data.

##  4 Experiments

###  4.1 Dataset.

The Toloka dataset comprises images paired with textual questions, where each
entry includes a question-image pair annotated with ground truth bounding box
coordinates pinpointing the visual answer. In total, the dataset consists of
45,199 instances distributed across three subsets: 38,990 instances in the
training set, 1,705 instances in the public test set, and 4,504 instances in
the private test set.

The dataset is structured with several key columns: ”image” contains URLs
linking to images hosted on a public content delivery network; ”question”
provides English-language queries associated with each image. Additional
metadata includes ”width” and ”height” integers representing the dimensions of
each image. For bounding box annotation, the dataset includes ”left,” ”top,”
”right,” and ”bottom” integers detailing the coordinates that define the
spatial extent of the object or region in the image that corresponds to the
answer to the question.

###  4.2 Leadboards.

Method | Score
---|---
Baseline | 71.0
Pseudo Answer | 73.5
Template | 74.2
Coarse Tuning | 75.1
Postprocessing | 75.8
Test Public | 76.5
Test Private | 76.342
Table 1: Results of each component.

Table 1 shows the improvement in model performance by each of our components.
The baseline is defined as the OFA model which directly inputs the competition
dataset and reasoning. The performance of coarse tuning and pseudo answer
increased the most because the pseudo answer showed the category of objects
corresponding to the bounding box. On the test public set, our method obtained
a seventy-six point five score, and on the test private set, our method
obtained a seventy-six point three score, which shows that our method has
strong generalization.

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# Index Modulation-Based Flexible Non-Orthogonal Multiple Access

Emre Arslan, Ali Tugberk Dogukan,
Ertugrul Basar E. Arslan, A. T. Dogukan and E. Basar are with the
Communications Research and Innovation Laboratory (CoreLab), Department of
Electrical and Electronics Engineering, Koç University, Sariyer 34450,
Istanbul, Turkey. Email<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Non-orthogonal multiple access (NOMA) is envisioned as an efficient candidate
for future communication systems. This letter proposes a novel orthogonal
frequency division multiplexing (OFDM) with index modulation (IM)-based NOMA
scheme, called OFDM-IM NOMA, for future multi-user communication systems.
Inspired by IM and classical OFDM-NOMA, users utilize flexibility by adjusting
power allocation factors and subcarrier activation ratios. Our new scheme
allows different service users to share available resources as in classical
NOMA, more efficiently. It is shown that OFDM-IM NOMA reliably supports a high
and low data rate user at the same resources by adjusting their subcarrier
activation ratios.

###### Index Terms:

5G, 6G, NOMA, OFDM, index modulation (IM), Internet-of-things (IoT), waveform
design, multiple access.

##  I Introduction

Wireless communication networks (5G and beyond) demand stringent requirements
with diverse users and rich use-cases. For instance, 6G wireless networks are
estimated to support up to $10^{7}$ devices/km2, about ten times the
connectivity density when compared to 5G [1]. To meet these demands, multiple
access schemes are being developed to allow multiple users to share the
available bandwidth for spectrum efficiency. Recently, non-orthogonal multiple
access (NOMA) has been proposed as a promising multiple access candidate, most
popularly in the power domain, to enhance spectrum efficiency [2]. Power-
domain NOMA allows multiple users to share the same time and frequency
resources separating them by their different power levels [3]. The non-
orthogonality in NOMA allows the transmission of multiple signals through
superposition coding (SC). Upon reception, successive interference
cancellation (SIC) is employed to remove the interference of other users’
signals for efficient detection. NOMA additionally introduces flexibility in
the power domain and fairness to users with worse channel conditions as well
as achieves low-latency. As a result, NOMA is envisioned as a potential
candidate for a fair, efficient, low-latency, and flexible multiple access
technique allowing wireless connectivity for billions of devices. The
literature on NOMA is very rich and many interesting concepts on power domain
NOMA have been studied [4, 5, 6, 7]. However, state-of-the art NOMA studies
usually do not take into consideration of imperfections in SIC detection for
bit error rate (BER) analysis and consider both users with the same
application demands allowing no flexibility in spectral and energy efficiency.
In other words, both users consider the same system parameters in almost all
studies. In this paper, we challenge this status quo by providing a flexible
waveform design for users with different requirements.

Figure 1: Block diagram of the proposed OFDM-IM NOMA system.

Index modulation (IM) appears as a simple, spectral and energy efficient
scheme to transmit additional information bits through the indices of
communication systems [8, 9]. A novel multi-carrier waveform called orthogonal
frequency division multiplexing with IM (OFDM-IM) [10], conveys additional
information through the indices of subcarriers in the frequency domain along
with $M$-ary modulated symbols. This provides an additional degree of freedom
by utilizing subcarrier activation ratios where the subcarriers of an OFDM
system can be turned on and off according to user applications; therefore, the
users may exploit the flexibility of IM. In [11], a NOMA multicarrier index
keying (NOMA-MCIK) scheme, which combines IM and NOMA, is proposed. NOMA-MCIK
applies IM to subblocks which consist of a certain number of subcarriers and
transmits the same modulated symbol through the active subcarriers. Using the
subcarrier activation feature of OFDM-IM and flexibility of NOMA in the power
domain to multiplex users, it is possible to construct a novel and flexible
waveform to ensure high spectrum efficiency depending different user
requirements.

The aim of this paper is to propose a flexible scheme by incorporating IM to
the subcarriers of OFDM-NOMA users, where the users exploit the same or
different number of active subcarriers. The flexibility provided from both
NOMA by adjusting the power allocation factors and OFDM-IM with adjustable
subcarrier activation ratios, is taken advantage of, to provide a promising
and alternative waveform called OFDM-IM NOMA. Different from NOMA-MCIK, OFDM-
IM NOMA applies IM to the subcarriers in a subblock and transmits different
symbols over active subcarriers to increase spectral efficiency. The proposed
scheme is based on the simultaneous transmission of two users’ OFDM-IM signals
with different power levels where the information is conveyed through both the
active subcarrier indices and $M$-ary modulated symbols. In this setup, a main
user (the near user) that needs higher data rates, and multiple far users that
have low data rate requirements, i.e., Internet-of-things (IoT) devices, share
the same spectrum. Classical OFDM-NOMA provides the same amount of subcarriers
for both users while assigning different power levels [12]. Using IM, the
proposed scheme activates most of the subcarriers for the near user and a
fewer number of ones for the IoT-based far users. Since in OFDM-IM NOMA the
far user has a fewer number of activated subcarriers, it may exploit lower
order modulations without SIC decoding. As a result, the far user utilizes
only a small amount of the spectrum according to its modest requirements while
enjoying a reliable and energy efficient transmission. Meanwhile, the near
user may continue to use the spectrum with a higher data rate benefiting from
the flexibility provided by OFDM-IM. At the near user, SIC is used to
eliminate the high power far user interference. Benefits of the proposed
scheme to classical OFDM-NOMA include higher flexibility with different
subcarrier activation ratios which allow adjustable spectral efficiencies and
controllable inter-user interference, higher energy efficiency, improved
reliability and higher spectrum efficiency. For the proposed scheme, an
optimum power allocation search is performed and theoretical error performance
is investigated to confirm our computer simulations. Taking a different
approach from the current NOMA literature, this paper focuses particularly on
BER analyses and flexibility in the waveform domain for the case of two users
rather than sum-rate and spectral efficiency analyses.

The rest of the paper can summarized as follows. In Section II, the system
model of OFDM-IM NOMA is presented. In Section III, the theoretical error
performance of the proposed scheme is investigated along with the optimum
power allocation method. Our computer simulation results are presented in
Section IV. Finally, Section V concludes the paper.

##  II System Model

In this section, the system model of the proposed OFDM-IM NOMA scheme is
given. First the transmitter architecture is presented, then the receiver
model is explained.

###  II-A Transmitter Side

Let us consider an OFDM-based downlink (DL) NOMA system operating under
frequency-selective Rayleigh fading channels. The base-station (BS) generates
OFDM-IM signals to serve $U$ users independently through the same frequency
and time slots by SC. The BS implements SC by allocating different power
levels to multiple users and transmitting a composite signal. This paper
considers a scenario with only two users $(U=2)$ as shown in Fig. 1. For each
user, a total of $m_{u}$ bits are transmitted, where $u\in\\{NU,FU\\}$, and NU
and FU denote near and far users, respectively. These $m_{u}$ bits are split
into $g_{u}$ groups, each containing $p_{u}=m_{u}/g_{u}$ bits. Since the same
procedures are applied for the creation of each subblock, it is sufficient to
consider the $\xi^{\text{th}}$ subblock
${\mathbf{x}}_{u}(\xi)\in\mathbb{C}^{n_{u}\times 1}$ of any user,
$\xi\in\\{1,\cdots,g_{u}\\}$. The $p_{u}$ bits are mapped into subblocks with
sizes $n_{u}$, where $n_{u}=N/g_{u}$ and $N$ is the number of total
subcarriers, that is, the size of fast fourier transform (FFT). For OFDM-IM
subbblock creation, the $p_{u}$ bits are separated into two parts. First,
$p_{u,1}=\lfloor\log_{2}\binom{n_{u}}{k_{u}}\rfloor$ bits determine $k_{u}$
active subcarriers in a subblock using a look-up table or the combinatorial
method [10], and produces the active subcarrier index set as
$\mathcal{I}_{u}(\xi)=\\{i_{u,1}(\xi),\cdots,i_{u,k_{u}}(\xi)\\}$ where
$i_{u,\lambda}(\xi)\in\\{1,\cdots,n_{u}\\}$ and $\lambda=1,\cdots,k_{u}$.
Then, the $p_{u,2}=k_{u}\log_{2}(M_{u})$ bits determine the vector of
modulated symbols
$\mathbf{q}_{u}(\xi)=[q_{u,1}(\xi),\cdots,q_{u,k_{u}}(\xi)]$,
$q_{u,\lambda}(\xi)\in\mathcal{Q}_{u}$, conveyed through the active
subcarriers, $\mathcal{Q}_{u}$ is the complex signal constellation of user $u$
with the size of $M_{u}$ and is normalized to unit average power.
Consequently, a total of

$p_{u}=p_{u,1}+p_{u,2}=\lfloor\log_{2}\binom{n_{u}}{k_{u}}\rfloor+k_{u}\log_{2}(M_{u})$
(1)

bits are transmitted via each subblock. The $N\times 1$ OFDM-IM signal block
of each user is given by
${\mathbf{z}}_{u}=[\mathbf{x}_{u}^{\mathrm{T}}(1)\,\mathbf{x}_{u}^{\mathrm{T}}(2)\,\cdots\,\mathbf{x}_{u}^{\mathrm{T}}(g_{u})]^{\mathrm{T}}=[x_{u}(1)\,x_{u}(2)\,\cdots\,x_{u}(N)]^{\mathrm{T}}$
and it is created by considering $\mathcal{I}_{u}(\xi)$ and
$\mathbf{q}_{u}(\xi)$, subblock by subblock, where
$x_{u}(\varphi)\in\\{0,\mathcal{Q}_{u}\\}$, $\varphi=1,\cdots,N$ and
$(.)^{\mathrm{T}}$ denotes transposition. Then, SC is applied in the frequency
domain to obtain the overall transmission vector as:

${\mathbf{x}}_{SC}=\sqrt{\alpha
P_{BS}}\mathbf{z}_{NU}+\sqrt{(1-\alpha)P_{BS}}\mathbf{z}_{FU}$ (2)

where $P_{BS}$ and $\alpha$ is the total transmit power of the BS (per
subcarrier) and the power allocation factor, respectively. Here, we consider
$P_{BS}=1$ and $0\leq\alpha\leq 1$. The average power of the NU and the FU per
subcarrier are $P_{NU}=\alpha P_{BS}$ and $P_{FU}=(1-\alpha)P_{BS}$,
respectively.

After this point, the procedures as in OFDM are applied. A block-type
interleaver is employed to eliminate the correlation effect of the channel in
a subblock as in [13]. The inverse fast fourier transform (IFFT) is applied to
obtain the time domain OFDM block $\mathbf{x}_{TI}$:

${\mathbf{x}}_{TI}=\mathrm{IFFT}\big{\\{}{\mathbf{x}}_{SC}\big{\\}}=\begin{bmatrix}X(1)&X(2)&\cdots&X(N)\end{bmatrix}^{\mathrm{T}}.$
(3)

After the IFFT operation, a cyclic prefix (CP) of length $C$ samples
$[X(N-C+1)\cdots X(N-1)X(N)]^{\mathrm{T}}$ is added to the beginning of the
OFDM block. Once parallel to serial (P/S) and digital/analog conversions are
applied, the signal is transmitted over a frequency-selective Rayleigh fading
channel, which can be represented by the channel impulse response (CIR)
coefficients

$\mathbf{t}=\begin{bmatrix}t(1)&\cdots&t(v)\end{bmatrix}^{\mathrm{T}}$ (4)

where $t(\zeta),\zeta=1,\dots,v$ are circularly symmetric complex Gaussian
random variables with the $\mathcal{C}\mathcal{N}(0,\frac{1}{v})$
distribution. With the assumption that the channel remains constant during
transmission of an OFDM block and the CP length $C$ is larger than $v$, the
received vector of two users can be given by

$\mathbf{y}_{u}=[y_{u}(1)\cdots
y_{u}(N)]^{\mathrm{T}}=\mathbf{H}_{u}\mathbf{x}_{SC}+\mathbf{w}_{u}$ (5)

where
$\mathbf{H}_{u}=\mathrm{diag}(\mathbf{h}_{u})=\mathrm{diag}([h_{u}(1)\,\cdots\,h_{u}(N)]^{\mathrm{T}})$
and $\mathbf{w}=[w_{u}(1)\,\cdots\,w_{u}(N)]^{\mathrm{T}}$ are the channel
matrix and the noise vector for the two users in the frequency domain,
respectively, and $\mathrm{diag}(\cdot)$ converts a vector into a diagonal
matrix. The distributions of $h_{u}(\varphi)$ and $w_{u}(\varphi)$ are
$\mathcal{C}\mathcal{N}(0,\sigma^{2}_{u})$ and
$\mathcal{C}\mathcal{N}(0,N_{0})$, respectively, where $N_{0}$ is the noise
variance in the frequency domain, which is equal to the noise variance in the
time domain. The signal-to-noise ratio (SNR) is defined as $1/N_{0}$. The
spectral efficiency of the users is given by

$\vspace{-0.15cm}\eta_{u}=m_{u}/(N+C)\hskip 5.69046pt\text{[bits/s/Hz]}.$ (6)

###  II-B Receiver Side

In this subsection, the receiver structure is presented for both users. It is
assumed that the channel gain for the NU is higher than FU
$(\sigma^{2}_{NU}\geq\sigma^{2}_{FU})$ due to the distance difference between
them, which is a valid assumption in NOMA-based multi-user systems. At both
receivers, after obtaining $\mathbf{y}_{u}$, a block-type de-interleaver is
employed. For both users, we define the set of all possible subblock
realizations as
$\mathcal{B}_{u}=\\{\mathbf{b}_{u,1},\mathbf{b}_{u,2},\cdots,\mathbf{b}_{u,G_{u}}\\}$
and the total number of possible subblocks as ${G}_{u}=2^{p_{u}}$,
$u\in\\{NU,FU\\}$.

####  II-B1 Near User (NU)

Since the signal power of the NU is less than the FU $(\alpha<0.5)$, first the
FU signal is decoded through SIC. We can decode the $\xi^{\mathrm{th}}$
subblock of the FU using the set $\mathcal{B}_{FU}$. Finally, maximum-
likelihood (ML)-based detection rule for SIC operation can be employed as

$\hat{\mathbf{x}}_{FU,\text{SIC}}(\xi)=\underset{\mathbf{b}_{FU}\in\mathcal{B}_{FU}}{\arg\>\min}{\left\|\bar{\mathbf{y}}_{NU}(\xi)-\sqrt{P_{FU}}\bar{\mathbf{H}}_{NU}(\xi)\mathbf{b}_{FU}\right\|}^{2}$
(7)

where $\bar{\mathbf{y}}_{NU}(\xi)=[y_{NU}(n_{FU}(\xi-1)+1)\cdots
y_{NU}(n_{FU}\xi)]^{\mathrm{T}}\in\mathbb{C}^{n_{FU}\times 1}$ and
$\bar{\mathbf{H}}_{NU}(\xi)=\mathrm{diag}([h_{NU}(n_{FU}(\xi-1)+1)\cdots
h_{NU}(n_{FU}\xi)])\in\mathbb{C}^{n_{FU}\times n_{FU}}$, are the received
signal vector and the equivalent channel matrix of the FU at the NU for the
$\xi^{\mathrm{th}}$ subblock, respectively. Then, the decoded FU block is re-
constructed as
$\hat{\mathbf{z}}_{FU}=[\hat{\mathbf{x}}_{FU,\text{SIC}}(1)\dots\hat{\mathbf{x}}_{FU,\text{SIC}}(g_{FU})]^{T}\in\mathbb{C}^{N\times
1}$ and subtract it from the overall received OFDM block as follows:

${\mathbf{r}}_{NU}=\mathbf{y}_{NU}-\hat{\mathbf{z}}_{FU}=[r_{NU}(1)\cdots
r_{NU}(N)]^{\mathrm{T}}.$ (8)

Hence, the interference of the FU signal on the NU signal is eliminated.
Finally, the NU signal is decoded by ML-based detection rule with the NU
subblock set $\mathcal{B}_{NU}$:

$\hat{\mathbf{x}}_{NU}(\xi)=\underset{\mathbf{b}_{NU}\in\mathcal{B}_{NU}}{\arg\>\min}{\left\|\bar{\mathbf{r}}_{NU}(\xi)-\sqrt{P_{NU}}\tilde{\mathbf{H}}_{NU}(\xi)\mathbf{b}_{NU}\right\|}^{2}$
(9)

where $\bar{\mathbf{r}}_{NU}(\xi)=[r_{NU}(n_{NU}(\xi-1)+1)\cdots
r_{NU}(n_{1}\xi)]^{\mathrm{T}}\in\mathbb{C}^{n_{NU}\times 1}$ and
$\tilde{\mathbf{H}}_{NU}(\xi)=\mathrm{diag}([h_{NU}(n_{NU}(\xi-1)+1)\cdots
h_{NU}(n_{NU}\xi)])\in\mathbb{C}^{n_{NU}\times n_{NU}}$ are the interference
eliminated signal vector and the channel matrix corresponding to
$\xi^{\mathrm{th}}$ subblock for the NU. Note that for $n_{NU}=n_{FU}$, which
means that the same subblock size is used for both users, we have
$\bar{\mathbf{H}}_{NU}(\xi)=\tilde{\mathbf{H}}_{NU}(\xi)$ .

####  II-B2 Far User (FU)

Since the signal power of the FU is higher than the NU $(\alpha<0.5)$, it is
assumed that the interference of the NU signal on the FU signal is negligible.
Therefore, we can decode the $\xi^{\mathrm{th}}$ subblock of the FU directly
using the FU set $\mathcal{B}_{FU}$. As a result, ML-based detection rule can
be employed as:

$\hat{\mathbf{x}}_{FU}(\xi)=\underset{\mathbf{b}_{FU}\in\mathcal{B}_{FU}}{\arg\>\min}{\left\|\bar{\mathbf{y}}_{FU}(\xi)-\sqrt{P_{FU}}\bar{\mathbf{H}}_{FU}(\xi)\mathbf{b}_{FU}\right\|}^{2}$
(10)

where $\bar{\mathbf{y}}_{FU}(\xi)=[y_{FU}(n_{FU}(\xi-1)+1)\cdots
y_{FU}(n_{FU}\xi)]^{\mathrm{T}}\in\mathbb{C}^{n_{FU}\times 1}$ and
$\bar{\mathbf{H}}_{FU}(\xi)=\mathrm{diag}([h_{FU}(n_{FU}(\xi-1)+1)\cdots
h_{FU}(n_{FU}\xi)]^{\mathrm{T}})\in\mathbb{C}^{n_{FU}\times n_{FU}}$, are the
received signal vector and the channel matrix for the $\xi^{\mathrm{th}}$
subblock, respectively.

##  III Performance Analysis

###  III-A Theoretical BER derivation

In this subsection, a theoretical error probability analysis is provided and
an average bit error probability (ABEP) expression is obtained for both the NU
and the FU. It is sufficient to investigate the pairwise error probability
(PEP) events of a single subblock to derive the performance of OFDM-IM NOMA
since the error performance is identical for all subblocks. Thus, we remove
the subblock index $\xi$ in the sequel for simplicity.

From $(5)$, assume that $\mathbf{B}_{u}=\mathrm{diag}(\mathbf{b}_{u})$ is
transmitted and $\hat{\mathbf{B}}_{u}=\mathrm{diag}(\hat{\mathbf{b}}_{u})$ is
erroneously detected. In this case, the unconditional PEP (UPEP) can be given
by[14]

$\text{Pr}(\mathbf{B}_{u}\rightarrow\hat{\mathbf{B}}_{u})=\frac{1}{\pi}\int_{0}^{\pi/2}M_{\delta}\Big{(}-\frac{\sigma^{2}_{u}}{4N_{0}\sin^{2}{\theta}}\Big{)}d\theta.$
(11)

where
$\delta=\|(\mathbf{B}_{u}-\hat{\mathbf{B}}_{u})\bar{\mathbf{h}}_{u}\|^{2}$ and
$\bar{\mathbf{h}}_{u}\in\mathbb{C}^{n_{u}\times n_{u}}$ is the channel vector
corresponding to a subblock. Expressing $\delta$ in the quadratic form as
$\delta=\bar{\mathbf{h}}_{u}^{\mathrm{H}}\mathbf{Q}\bar{\mathbf{h}}_{u}$,
where
$\mathbf{Q}=(\mathbf{B}_{u}-\hat{\mathbf{B}}_{u})^{\mathrm{H}}(\mathbf{B}_{u}-\hat{\mathbf{B}}_{u})$
and $(.)^{\mathrm{H}}$ denotes Hermitian transposition, its moment generating
function can be calculated from [15] as
$M_{\delta}(t)=[\mathrm{det}(\mathbf{I}_{N}-t\mathbf{Q})]^{-1}=[\prod_{i_{1}}^{q}(1-t\lambda_{i})]^{-1}$,
where $q=\mathrm{rank}(\mathbf{Q})$ with non-zero eigenvalues of $\mathbf{Q}$
being $\lambda_{i},i=1,2,\cdots,q$ for $q\leq N$ and $\mathbf{I}_{N}$ is an
$N\times N$ identity matrix. Substituting $M_{\delta}(t)$ in $(10)$, we obtain

$\text{Pr}(\mathbf{B}_{u}\rightarrow\hat{\mathbf{B}}_{u})=\frac{1}{\pi}\int_{0}^{\pi/2}\prod_{i=1}^{q}\Bigg{(}\frac{\sin^{2}{\theta}}{\sin^{2}{\theta}+\frac{\sigma^{2}_{u}\lambda_{i}}{4N_{0}}}\Bigg{)}d\theta$
(12)

which has a closed form solution in Appendix$(5.\text{A})$ of [15]. After
obtaining UPEP of each user, the interference of the FU on the NU is ignored,
and ABEP of the NU can be approximated as:

$\displaystyle P_{b,NU}\approx 0.5P_{s,FU}+(1-P_{s,FU})\times$
$\displaystyle\frac{\sqrt{P_{NU}}}{p_{NU}G_{NU}}\sum_{\mathbf{B}_{NU}}\sum_{\hat{\mathbf{B}}_{NU}}\text{Pr}(\mathbf{B}_{NU}\rightarrow\hat{\mathbf{B}}_{NU})\times
e(\mathbf{B}_{NU},\hat{\mathbf{B}}_{NU})$ (13)

where

$P_{s,FU}=\frac{\sqrt{P_{FU}}}{G_{FU}}\sum_{\mathbf{B}_{FU}}\sum_{\hat{\mathbf{B}}_{FU}}\text{Pr}(\mathbf{B}_{FU}\rightarrow\hat{\mathbf{B}}_{FU})$
(14)

is the symbol error probability (SEP) of the FU and
$e(\mathbf{B}_{u},\hat{\mathbf{B}}_{u})$ stands for the number of bit errors
for the corresponding pairwise error event
$(\mathbf{B}_{u}\rightarrow\hat{\mathbf{B}}_{u})$. The interference of the NU
on the FU signal is neglected, therefore, ABEP of the FU can be lower bounded
by

$\displaystyle P_{b,FU}\geq$
$\displaystyle\frac{\sqrt{P_{FU}}}{p_{FU}G_{FU}}\sum_{\mathbf{B}_{FU}}\sum_{\hat{\mathbf{B}}_{FU}}\text{Pr}(\mathbf{B}_{FU}\rightarrow\hat{\mathbf{B}}_{FU})\times
e(\mathbf{B}_{FU},\hat{\mathbf{B}}_{FU}).$ (15)

As will be shown in next section, (13) and (15) can be used to predict the BER
of the NU and the FU, respectively.

###  III-B Optimum Power Allocation

Figure 2: Optimum $\alpha$ search from $0$ to $0.5$ with intervals of $0.05$
for a fixed SNR of $30$ dB.

Current NOMA literature mostly considers a fixed power allocation without any
search method. To obtain better error performance, in this subsection, the
power allocation factor $\alpha$ is determined according to the average BER of
both users 111Another criteria rather than average BER may be considered for
determining the optimum $\alpha$. For example, the error performance of FU can
be prioritized. in the presence of SIC errors and interference using Monte
Carlo simulations. For different $k_{NU}$ and $k_{FU}$ values, the performance
of the users may vary, therefore, the average performance of the NU and FU is
considered:

$\text{Avg}_{\text{BER}}=\frac{p_{FU}\text{BER}_{FU}+p_{NU}\text{BER}_{NU}}{p_{FU}+p_{NU}}$
(16)

where $\text{BER}_{FU}$ and $\text{BER}_{NU}$ stand for the bit error rate of
the far user and the near user, respectively. As shown in Fig. 2, the average
BER of both users for two cases are simulated at a fixed SNR value of $30$ dB
for $\alpha$ values varying from $0$ to $0.5$ with an increasing interval of
$0.05$. Then the $\alpha$ value that provides the minimum average BER is
selected. Fig. 2 shows our power allocation search for two different
configurations of the proposed scheme and also consists of the individual BER
of both users for each case. We refer to $k$ active out of $n$ subcarriers as
$u(n_{u},k_{u})$, $u\in\\{NU,FU\\}$. It is observed that different
configurations may provide different optimal power allocation factors where
for FU(4-2)-NU(4-2) and FU(4-1)-NU(4-3) the optimum $\alpha$ is obtained as
$0.15$ and $0.3$, respectively. As the activation ratio of user $u$ is
increased more power needs to be allocated to user $u$ and vice-versa as seen
in Fig. 2. Note that theoretical derivations of (13) and (15) cannot be used
to obtain the optimum $\alpha$ since they do not consider the interference of
the NU to the FU.

##  IV Simulation Results

Figure 3: Error performance of OFDM NOMA-IM with $n=4$ for (a) $k_{FU}=1$,
$k_{NU}=3$ and (b) $k_{FU}=2$, $k_{NU}=2$.

In this section, computer simulation results are presented for the OFDM-IM
NOMA scheme in the presence of Rayleigh fading channels and perfect channel
state information at the users. The system parameters are assumed to be:
$N=128$, $C=16$, $\sigma^{2}_{NU}=0$ dB, $\sigma^{2}_{FU}=-3$ dB and $v=10$.
Computer simulation results show the BER performance of these schemes using
Monte Carlo simulations. For all simulations, block interleaving of size of
$n_{u}\times g_{u}$, imperfect SIC detection and a fixed subblock size of
$n_{NU}=n_{FU}=4$ is considered. In our simulations, the same subblock size is
chosen for ease of presentation, however a generalization is possible. Optimum
power allocation factor $\alpha$ is obtained by simulating the averaged BER
values from $\alpha=0$ to $\alpha=0.5$ with an increasing interval of $0.05$
for a fixed SNR of $30$ dB and choosing the power allocation factor with the
minimum average BER as in Fig. 2.

Fig. 3 shows the simulation and theoretical results of the proposed OFDM-IM
NOMA scheme for two different setups. In Fig. 3(a), $k_{NU}=3$, $k_{FU}=1$,
$M_{NU}=4$ and $M_{FU}=4$ are considered. Here, the NU (main user) has a
higher spectral efficiency, while the FU (IoT user) has a lower spectral
efficiency. It can be seen that the FU exhibits a better BER performance due
to less interference along with a lower order modulation and a higher power
allocated to it. The use of a lower order modulation, no need for SIC and a
better error performance makes the FU more suitable for IoT applications
because it can also be more energy efficient due to a lower complex detector
architecture. In other words, this user would just need to communicate
reliably at low data rates, for example, to transmit sensor data. BER
performance of the NU is worse because of the employment of a higher
modulation order and remaining interference of the FU during the SIC process
along with its lower allocated power. The theoretical curve of the FU obtained
by $(15)$ acts as a lower bound due to an assumption of no interference from
the NU in the calculation. The theoretical BER curve of the NU is obtained by
$(13)$ and is an approximate one because we do not take into consideration of
the NU interference when decoding the FU first in the SIC process. From Fig.
3(b), it is also confirmed that the theoretical results match the simulation
results with different set of parameters: $k_{NU}=2$, $k_{FU}=2$, $M_{NU}=4$
and $M_{FU}=4$.

Fig. 4 shows the comparison of classical OFDM-NOMA and OFDM-IM NOMA with
varying parameters. All NUs and FUs have a spectral efficiency value of
$1.7778$ and $0.8889$ bps/Hz, respectively. It can be seen that along with the
main benefits of flexibility of the user applications and high spectral
efficiency, we additionally obtain a better error performance for the FU and,
most of the time, for the NU. The FU achieves a better error performance due
to characteristics of IM as in OFDM-IM. Due to the employment of higher
modulation orders, lower power allocation and significant interference at SIC
decoding, the NU error performance may be worse at certain configurations.
Another reason that negatively affects the error performance is that the
interference of the other user harms the OFDM-IM decoding process. This is
because in classical OFDM-IM, the inactive subcarriers are always zero, but in
OFDM-IM NOMA, there is a possibility they may not be completely zero and an
active subcarrier of the other user may act as interference to the main
signal. However, as in the case of FU$(4,1)$-NU$(4,3)$, even the NU exhibits a
better BER performance than classical OFDM-NOMA since the probability of an
active subcarrier of the FU overlapping with an empty subcarrier of the NU is
dramatically less than in the case of FU$(4,2)$-NU$(4,2)$.

Figure 4: Error performance of OFDM NOMA-IM with different configurations
compared to OFDM-NOMA.

##  V Conclusion

In this paper, OFDM-IM NOMA has been presented as a novel and flexible NOMA
scheme for different application users with varying subcarrier activation
ratios. The proposed scheme allows a main user with a higher data rate and
less data rate user such as an IoT device to share the spectrum in a more fair
manner. System performance has been shown in terms of BER and imperfect SIC
has been considered to investigate a more realistic NOMA scenario. OFDM-IM
NOMA has been shown to provide a better BER along with its flexibility
advantages. Future extensions may include research for more effective ways to
reduce interference between users, enabling more number of IoT users to work
with the main user instead of one. An additional improvement may be an
advanced optimum power allocation method and the development of an LLR
detection method with suitable thresholds to determine the activation
probabilities of subcarriers in the subblock for each user.

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