# Learning to Profile: User Meta-Profile Network
for Few-Shot Learning

Hao Gong  0000-0002-9879-4595 Rakuten Institute of Technology, Rakuten, Inc.
Tokyo, Japan<EMAIL_ADDRESS>,  Qifang Zhao  Rakuten Institute of
Technology, Rakuten, Inc. Tokyo, Japan<EMAIL_ADDRESS>,  Tianyu Li
Rakuten Institute of Technology, Rakuten, Inc. Tokyo, Japan
<EMAIL_ADDRESS>,  Derek Cho  Rakuten Institute of Technology, Rakuten,
Inc. Tokyo, Japan<EMAIL_ADDRESS>and  DuyKhuong Nguyen  Data Science &
AI Department, Rakuten, Inc. Tokyo, Japan<EMAIL_ADDRESS>
(2020)

###### Abstract.

Meta-learning approaches have shown great success in solving challenging
knowledge transfer and fast adaptation problems with few samples in vision and
language domains. However, few studies discuss the practice of meta-learning
for large-scale industrial applications, e.g., representation learning for
e-commerce platform users. Although e-commerce companies have spent many
efforts on learning accurate and expressive representations to provide a
better user experience, we argue that such efforts cannot be stopped at this
step. In addition to learning a strong profile of user behaviors, the
challenging question about how to effectively transfer the learned
representation and quickly adapt the learning process to the subsequent
learning tasks or applications is raised simultaneously.

This paper introduces the contributions that we made to address these
challenges from three aspects. 1) Meta-learning model: In the context of
representation learning with e-commerce user behavior data, we propose a meta-
learning framework called the Meta-Profile Network, which extends the ideas of
matching network and relation network for knowledge transfer and fast
adaptation; 2) Encoding strategy: To keep high fidelity of large-scale long-
term sequential behavior data, we propose a time-heatmap encoding strategy
that allows the model to encode data effectively; 3) Deep network
architecture: A multi-modal model combined with multi-task learning
architecture is utilized to address the cross-domain knowledge learning and
insufficient label problems. Moreover, we argue that an industrial model
should not only have good performance in terms of accuracy, but also have
better robustness and uncertainty performance under extreme conditions. We
evaluate the performance of our model with extensive control experiments in
various extreme scenarios, i.e. out-of-distribution detection, data
insufficiency and class imbalance scenarios. The Meta-Profile Network shows
significant improvement in the model performance when compared to baseline
models.

Meta-learning; Representation learning; Multi-modal model; Multi-task learning

††journalyear: 2020††copyright: acmcopyright††conference: Proceedings of the
29th ACM International Conference on Information and Knowledge Management;
October 19–23, 2020; Virtual Event, Ireland††booktitle: Proceedings of the
29th ACM International Conference on Information and Knowledge Management
(CIKM ’20), October 19–23, 2020, Virtual Event, Ireland††price: 15.00††doi:
10.1145/3340531.3412722††isbn: 978-1-4503-6859-9/20/10††ccs: Computing
methodologies Learning latent representations††ccs: Computing methodologies
Transfer learning

##  1\. Introduction

Rakuten has one of the largest e-commerce ecosystems in the world, and serves
tens of millions of users by providing diverse cross-domain services from
online to offline. Like all other e-commerce platforms, a fundamental task is
to understand customers and serve better by using the gained knowledge from
huge amounts of collected user behavior data through applications, e.g.,
personalized recommendation, target prospecting, search ranking and customized
advertisement systems (hu2013personalized, ; perlich2014machine, ;
agichtein2006improving, ). Traditionally, this is done through intensive
feature engineering to create various features of users with machine learning
and deep learning algorithms. However, this strategy relies heavily on the
quality of data and prior domain knowledge. For the extracted features, as
many of them are generated to serve a particular task, this leads to huge
challenges when attempting to reuse it for new tasks.

Representation learning has been proposed to expand the scope of applicability
of machine learning, and reduce the dependence on feature engineering
(bengio2013representation, ). In the case of e-commerce, a well learned
representation could be task-agnostic and reflect the general interest of a
user. And the great success brought by deep learning has made significant
advances to support representation learning (radford2015unsupervised, ).
However, with the increase of input data size and the deepening of the model
structure, the cost of model training greatly increases, requiring many
iterations and weight updates during the training optimization
(sung2018relation, ). Meanwhile, to meet the diverse needs of different users
and services, we also face an increasing number of unknown tasks. Considering
resource limitations, training a large-scale model from scratch for new tasks
is impractical for business purposes due to time constraints. Moreover, the
standard deep learning does not offer a satisfactory solution to quickly learn
new tasks from small sample data, as the achievement of deep learning heavily
relies on the fact that it demands large amounts of labeled examples.

The problem of learning how to efficiently and quickly transfer learned
knowledge to new tasks with few training examples is referred to as few-shot
learning or meta-learning, and has become the subject of a lot of recent
studies (Bengio97onthe, ; Thrun1998, ). With human learning, people can
usually learn new concepts and skills successfully with only a few examples
(lake2015human, ). The research literature on meta-learning shows great
diversity, spanning from optimization-based learning (Ravi2017OptimizationAA,
; finn2017model, ), memory network-based learning (santoro2016meta, ;
munkhdalai2017meta, ), to metric-based learning (vinyals2016matching, ;
snell2017prototypical, ; sung2018relation, ). Among these research,
optimization-based and memory network-based learning approaches show many
advantages compared to traditional learning methods, but the training examples
still need to be slowly learned by the model into its parameters which limited
the universality of the model to solving realistic scenario problems
(yu2018diverse, ; sun2019meta, ). In contrast, the metric-based approach
allows the fast adaptation of new examples through non-parametric models
without causing catastrophic forgetting (vinyals2016matching, ).

Although previous studies demonstrate the successes of meta-learning with few-
shot settings, there are questions that still remain. Can meta-learning be
applied for user representation learning for e-commerce applications? For
example, can we perform target prospecting with a user’s sequential shopping
behavioral data? If so, how can we implement the idea to a production
environment, and evaluate the model performance appropriately?

In this work, we propose a cross-domain meta-learning framework called Meta-
Profile Network to solve the user profiling problem in representation learning
with e-commerce user behavior data, which empowers the model quickly adapt to
unseen tasks and leverages the experience from model training simultaneously.
We extend the idea of the matching network and relation network approaches
(vinyals2016matching, ; sung2018relation, ) in a realistic scenario.
Meanwhile, we propose the time-heatmap encoding strategy and deep network
architecture to boost the learning efficiency in user profiling with long-term
cross-domain data.

More importantly, we believe that a good industrial model should not only
perform well in terms of accuracy but also have strong robustness and
uncertainty performance under extreme conditions. By comparing to baseline
models, we conduct three sets of extensive control experiments to test the
performance of our model, i.e. uncertainty to out-of-distribution detection,
robustness to data insufficiency and class imbalance.

##  2\. Related Work

In this section, three directions of research are briefly described from
following aspects - encoding strategy, meta-learning and network architecture
- that are closely related to our proposed work.

###  2.1. Long-Term User Behavior Representation and Cross-Domain Data at
Rakuten

The development of long-term human behavior is a relatively slow but dynamic
procedure, which is subtly affected by the physical, mental, and social
activity during the phases of human life (bornstein2014interaction, ). For
most people, their long-term shopping behavior changes slowly over time.
Unlike short-term behavior, which is influenced by many uncertain emergent
factors, long-term behavior could be regarded as an internal attribute of
humans. Based on this understanding, to better comprehend the user needs, this
work assumes that general users have such potential internal behaviors which
are changing slowly with the time window moving. Instead of using the short-
term behavior data (e.g., 10 days click-through data) to learn the unexpected
interests of users, our model uses data from the past one-year time frame to
capture users’ long-term behaviors.

To create an effective user representation and alleviate the learning bias
from extreme data skew, it is essential to learn from multiple data sources
instead of a single data source. At Rakuten, there are over 70 unique
businesses including e-commerce, digital content communication and finical
tech services, and the cross-use ratio of all services are over 60%
(rakuten_global_website, ). For example, Rakuten Ichiba is the leading online
shopping website in Japan, Rakuten Travel provides hotel and flight booking
services, and Rakuten Points is a point system based on virtual currency which
links all of these services. Together these services build up a diverse
ecosystem that covers many aspects of users’ daily life. Behavior data derived
from the ecosystem is very rich and diverse, which allows for many
opportunities to improve customer satisfaction and generate business value. To
take advantage of this unique ecosystem, this study utilizes data from across
these various domains.

However, with the use of long-term and cross-domain data, problems regarding
representation learning with computation efficiency on large-scale data have
also arisen. Along with the rise in popularity of many embedding techniques
and neural networks in recent years, distributed representation
(Bengio2013RepresentationLA, ; lecun2015deep, ) has gained significant
attention and wide applications. Compared to traditional methods that assemble
and aggregate user preferences based on prior human knowledge, embedding with
carefully picked behavior sequences and sampling methods have shown success in
recommendation and similar item discovery (real-time-embeddings, ), and
improved the data processing efficiency as well. Such encoding-decoding
strategies are used to embed sequential user behavior data into low-
dimensional representations in this work (details described in Section 3.1).

###  2.2. Meta-Learning

Meta-learning models are trained over a variety of source tasks and optimize
the model to adapt for unknown tasks on the learned distribution space of
tasks. Few-shot (or one-shot) learning, the alternative term of meta-learning
on few-shot (or one-shot) settings, has shown the ability to generate novel
behavior based on inference from only one or few training examples which can
benefit real-world applications (santoro2016meta, ; finn2017model, ;
vinyals2016matching, ; munkhdalai2017meta, ; snell2017prototypical, ;
sung2018relation, ). However, based on our understanding, the model
scalability and flexibility limit the effectiveness of the memory network-
based methods and optimization-based methods in solving industry problems. The
memory network-based methods use specific structures to generalize the stored
experience to unseen tasks. Meanwhile, to avoid model overfitting with
training data in meta-training phase, optimization-based methods use a shallow
neural network which restrict its capability of using deeper structures. To
obviate the disadvantages of other meta-learning methods when facing real-
world few-shot classification problems, we use a metric-based method in our
work.

Our work extends the ideas of the matching network and the relation network.
The matching network proposes the idea that training in the same way as
testing, which means the training and testing conditions should match
(cai2018memory, ). It learns and encodes the meta-data to a low-dimension
embedding space in a feed-forward way without updating deep network weights,
and then maps the pair of sample datasets (a labeled support set and an
unlabelled prediction set) to its label by using the embedding. This design
can alleviate the requirement of fine-tuning for new task adaptation. The
relation network takes this idea one step further. It proposes a two-branch
framework to learn the distance metric with embeddings.

###  2.3. Multi-Modal Framework and Multi-Task Learning

Diverse cognition is critical to user understanding. The information from
various modalities is characterized by very different statistical properties.
In the field of e-commerce, due to the nature of each domain, data from each
service can be regarded as unimodal data. Many studies have shown that a
multi-modal framework can learn commonalities from multiple modality data and
support the task learning, like the semantic representation studies in vision
and language (feng-lapata-2010-visual, ; bruni2014multimodal, ). The cross-
domain data can be considered as one kind of multi-modal data. Due to the
difference in service coverage and distribution of active users in each
domain, to tackle such cross-domain data and make sure the model learning
ability not be limited by the diversity, the multi-modal framework are used to
build the deep neural network in the meta-training phase in our work. The
framework shows the tolerance and flexibility to exploit and synthesize the
redundant inherent information to reach understanding. The cross-domain data
are from three big domains, viz. user demographic data (numerical and
categorical data), behavior data of online shopping service (time series
sequential data), and point usage data from Rakuten Points service (time
series sequential data). All of these data are connected through a common ID
system under the Rakuten ecosystem.

Meanwhile, to avoid losing the learning ability of generalization when focused
on a particular single task, we introduce multi-task learning to the model to
provide an inductive bias, which allows the model not to learn from one task
but a distribution space of tasks. As Rich Caruana (caruana1997multitask, )
described ”Multi-task learning improves generalization by leveraging the
domain-specific information contained in the training signals of related
tasks.” Multi-task learning can be used to augment data to address data
insufficient problems, such as class imbalance, noisy, sparse, and
insufficient samples.

##  3\. Methodology

To learn effective user representations to provide better user experiences, we
propose a meta-learning framework called Meta-Profile Network, which learns
the similarity of embeddings with a two-branch framework. In this section,
first we describe the time-heatmap encoding strategy that is used to handle
long-term sequential shopping behavior data. Then it is followed by the
introduction of Meta-Profile training strategy and the technical details of
the deep network.

Figure 1. Time-heatmap encoding. Each channel of the ’image’ represents the
behavior pattern in certain perspective.

###  3.1. Time-heatmap Encoding Strategy

At present, the research on image processing with deep learning models has
progressed greatly. Inspired by the image data format, we propose the time-
heatmap encoding method. As a general digital image is formed by the
combination of RGB 3-color channels. Analogous to image data matrices, we use
an image-like format to embed the time-series based user behavior data into
’image’ channels as shown in Figure.1. Since we intend to use long-term
sequential behavior data (as Table.1 introduced), the time window of data is
exactly one year, which can treat equivalently as an image of dimension 24
(hours) × 365 (days). Each channel of the ’image’ reveals the behavior pattern
in a certain perspective. And the value of each cell in each channel can be
any value based on the extraction rule. For example, the first channel
represents fashion-related shopping behavior, while the second channel can
represent household-related behavior. And the cell value in the first channel
can represent the amount that the user spends on purchasing fashion products.
We can say each encoded channel is a snapshot of the user’s life in the past
year from a specific point of view. In general, this encoding strategy gives
us the ability to transform the processing of sequential behavior data into
image data processing problems. Meanwhile, as a more efficient format, the
image-like format reduces the resource requirements for processing large-scale
data, standardizes the data size, and enhances the flexibility and scalability
of data usage in implementation.

Table 1. Example of user shopping behavior sequence. The time-heatmap encoding
method will convert the raw data from sequence data to image channels.

UserID | Price | Datetime | Genre Name by Level
---|---|---|---
1 | 2200 | 20XX-XX-XX 21:30:00 | beauty/makeup/lipstick
2 | 3200 | 20XX-XX-XX 21:10:00 | beauty/makeup/lipstick
3 | 2200 | 20XX-XX-XX 14:40:00 | shoes/sandals/straps
4 | 4600 | 20XX-XX-XX 22:40:00 | fashion/outerwear/coat
4 | 1400 | 20XX-XX-XX 20:40:00 | fashion/tops/shirts/blouses
4 | 2000 | 20XX-XX-XX 20:40:00 | bedding/cushion/cushion

In our work, sequence data account for a large portion of all our data, e.g.,
Rakuten Ichiba user shopping behavior data and Rakuten Points usage data. The
shopping behavior data includes user purchases, canceled purchases and payment
amounts data. All these behavior data are genre-based shopping records as
introduced in the example table. The Rakuten Points data include user standard
owned points, limited-term points and used points datasets. Although the data
come from various domains and contain different internal information, we use
this encoding strategy to embed the time-series related sequence data and
standardize into image-like channel format. On the other hand, most users’
data are very sparse in reality. The time interval between two shopping
records can be very long. For the data storage and processing efficiency
considerations, we use the vectorized data storage method to reduce the
storage of redundant null values. For example, ”2, 10, 28: 5000; 100, 20, 25:
6000; …” it means that the user purchased the channel 28 item worth 5,000 at
10:00 on the 2nd day (relative time to one-year), then he purchased the
channel 25 item worth 6000 at 20:00 on the 100th day.

###  3.2. Meta-Profile Network

Figure 2. Meta-Profile Network architecture for N-way K-shot (N=9, K=1)
problem with one prediction example case.

To reduce the prediction error on unseen tasks, many studies point out that
the model training process can be induced with a small support set, making the
training process mimics what happens during inference, thus avoiding exposing
all target labels to the model and encouraging the model to optimize quickly
(vinyals2016matching, ). In our work, we define our source tasks as
$\tau=\\{T_{1},T_{2},...,T_{n}\\}$, and unknown target task as
$\tau^{\prime}$. We prepared three sets of data, i.e. a training set
$D^{train}$, a small support set $S$, and a prediction set $D^{predict}$. The
training set is associated with the label space of $\tau$ independently, while
the support set and the prediction set share the same label space of
$\tau^{\prime}$. We recognize each pair of support set $S$ and mini-batch $B$
sampled from training set as a data point $d=\langle S,B\rangle$. For the case
where the support set $S$ contains $K$ labeled examples for each of $N$
classes, we consider it as a $N$-way $K$-shot classification task.

The training procedure has to be chosen carefully to match inference at test
time (vinyals2016matching, ). We construct the Profile Network $g_{\theta}$
(details of the deep network architecture described in Section 3.3) to learn
to update model weights and optimize neural networks in each training
iteration with embedded data point $d$, and then encode the learned
representations to feature maps $g_{\theta}(D^{train},S)$. As metric-based
meta-learning aims to learn a similarity measuring function over objects, the
aim of our work is to learn such classifier for any given support set $S$ in
$N$-way $K$-shot classification. Similar to other metric-based models, the
predicted probability over known tasks $\tau$ is a weighted sum of labels of
support set samples. The weight is generated by a similarity measuring
function $f_{\theta}$ with two data points. Consequently, the generated
feature maps of $g_{\theta}(D^{train},S)$ and $g_{\theta}(D^{predict},S)$ are
fed into similarity module $f_{\theta}$ to produce a similarity score between
each other. Theoretically, the similarity module $f_{\theta}$ can be any kind
of distance measurement kernel function. Here, we use a fully connected neural
network with ReLU activation.

###  3.3. Network Architecture

This section introduces the deep network architecture of the profile network
part in Figure.2.

3.3.1 Justification of Model Selection. The information derived from the user
can be divided into two parts: intrinsic and extrinsic data. For instance, we
define the sequential behavior data from services A and B as extrinsic data,
and the demographic data from service C as intrinsic data. Regarding the
extrinsic data (Figure.2), it is natural to employ a recurrent neural network
(RNN) rather than a convolutional neural network (CNN) to tackle the
sequential property. However, the advantage of RNN on sequential data relies
on the assumption: items inside the sequence (e.g., words in NLP) have strong
short-range and long-range dependence (hochreiter1997long, ). In practice, the
dependence among different purchases from the same user is not strong. Two
purchases of a user behavior sequence are approximately independent events.
Besides, the frequency of user shopping behavior varies greatly. The huge
difference in the sequence length for each user would cause problems in the
implementation of the RNN model. Based on the above considerations, we use a
CNN to model behavioral data converted into the image-like format, viz. data
from domain A (Rakuten Ichiba) and B (Rakuten Points).

3.3.2 CNN Architecture for One Modality Model.  Each CNN model has a 5-level
structure, and each level of a convolutional layer consists of three parts in
order: convolution, batch normalization and ReLU activation. Analogous to the
division of the human life cycle, we expect each level of convolutional layer
can periodically capture the spatial and temporal dependencies by following
the patterns from 365 days, 52 weeks, 12 months, 4 seasons to 1 year. As each
channel of input is a fixed length 8760 (365×24 = 8760 hours), we set the
window size and max pooling size as Table.2 shows.

Table 2. Table shows the details of the CNN architecture. In general, each
convolutional layer consists of three parts in order: convolution, batch
normalization and ReLU activation.

Layer Name | Output Shape | Model Settings
---|---|---
Concat_0 | (32, 365, 24, ?) | Concatenate n-dim inputs
[0.5pt/2pt] Conv_1 | (32, 365, 24, 64) | filters=64, kernel_size=(7, 2), stride=1
Max_pool_1 | (32, 52, 12, 64) | pool_size=(7, 2)
[0.5pt/2pt] Conv_2 | (32, 52, 12, 128) | filters=128, kernel_size=(4, 2), stride=1
Max_pool_2 | (32, 13, 6, 128) | pool_size=(4, 2)
[0.5pt/2pt] Conv_3 | (32, 13, 6, 256) | filters=256, kernel_size=(3, 2), stride=1
Max_pool_3 | (32, 4, 3, 256) | pool_size=(3, 2)
[0.5pt/2pt] Conv_4 | (32, 4, 3, 512) | filters=512, kernel_size=(1, 1), stride=1
Max_pool_4 | (32, 1, 1, 512) | pool_size=(4, 3)
[0.5pt/2pt] Flatten | (32, 512) | Flatten

3.3.3 Source Task Settings.  To learn the high-level abstraction of users in
meta-training phase, we prepare two categories of tasks to induce the model to
learn the universal meta information, viz., surveyed user profile information
related tasks and various service usage related tasks. We use multi-task
learning to compensate for the lack of labels in certain tasks. Based on the
prior tests, we prune the number of source tasks from over one hundred to
nine.

Regarding the weighted losses of tasks in multi-task learning, we assign a
weights to users depending on whether users are labeled for each task. We
assign a weight 1 for true cases, otherwise 0. The overall loss for each mini-
batch is shown below:

(1)
$J(\theta)=\sum_{n=1}^{N}\sum_{i=1}^{B}\frac{w_{ni}}{\sum_{i=1}^{B}w_{ni}}J_{ni}(\theta)$

In Eq.1, $n$ denotes $n$-th task, $i$ is the $i$-th user, $w_{ni}$ is the
weight, and it is 1 if user $i$ has the label in the task $n$ , and 0
otherwise. $N$ is 9 in our case, $B$ is the mini-batch size, which is chosen
to be 32. $J_{ni}(\theta)$ is the loss for user $i$ in task $n$ , and $\theta$
is the model’s parameters.

##  4\. Evaluation and Experiments

In this section, we conduct experiments to evaluate the performance of our
model including uncertainty and robustness estimates. The model has been
implemented to the service called ”Rakuten AIris” to provide effective target
prospecting. We first explain the experiment settings. Then, we evaluate the
effectiveness of our model with three experiments by comparing it with the
baseline model. Finally, we briefly discuss the effectiveness of the model in
online services. We will not reveal the details of data and tasks due to the
data governance concerns.

Table 3. Out-of-distribution (OOD) detection performance with the normal
training model (baseline model trained from scratch) and with the Meta-Profile
Network model. AUROC is the Area Under the Receiver Operating Characteristic
curve. AUPR is the Area Under the Precision-Recall curve. Results are based on
9-way 1-shot classification on 8 unseen target tasks.

| AUPR | AUROC
---|---|---
Target Task | Normal Training | Meta-Profile (diff) | Growth Rate | Normal Training | Meta-Profile (diff) | Growth Rate
RAKU_BMW | 0.6166 | 0.6225(+0.0059) | 0.97% | 0.8479 | 0.8597(+0.0118) | 1.39%
RAKU_PRI | 0.4503 | 0.5361(+0.0858) | 19.06% | 0.7006 | 0.7712(+0.0706) | 10.08%
RAKU_MCD | 0.4470 | 0.4655(+0.0185) | 4.14% | 0.7486 | 0.7587(+0.0101) | 1.35%
RAKU_TYTP | 0.4456 | 0.4623(+0.0167) | 3.75% | 0.7006 | 0.7250(+0.0243) | 3.47%
RAKU_TYTA | 0.4200 | 0.4498(+0.0298) | 7.09% | 0.6849 | 0.7220(+0.0371) | 5.42%
RAKU_BK | 0.5498 | 0.5882(+0.0384) | 6.98% | 0.7942 | 0.7968(+0.0026) | 0.33%
RAKU_RB | 0.7041 | 0.7863(+0.0821) | 11.67% | 0.8741 | 0.8914(+0.0173) | 1.98%
RAKU_MB | 0.6891 | 0.7495(+0.0604) | 8.76% | 0.8669 | 0.8927(+0.0259) | 2.98%

###  4.1. Experiment Setup

Datasets and tasks: All of the experiments are performed on one-year of
Rakuten e-commerce online user behavior data (Dec 1st, 2018 - Dec 1st, 2019).
As explained in Section 3.1, our data come from three data sources: 1) user
online shopping behavior sequence data from Rakuten Ichiba including item
purchase and cancellation data, 2) point usage sequence data from Rakuten
Point service, 3) inherent data such as demographic information. The goal of
this work is to provide an efficient advertisement solution with
representation learning for e-commerce platform users, the source tasks $\tau$
are described in Section 3.3.3. The target tasks $\tau^{\prime}$ in meta-
testing are business-related, based on the understanding of potential
preference from user profiling, through a similarity check between existing
users and newly developed users to provide an accurate advertisement
recommendation. Here, 8 new unseen target tasks are tested. For the protection
of personal privacy information, data anonymization and user pseudonymization
processes are applied to all raw data.

Model settings: The model is built and trained with Keras on top of TensorFlow
using single GPU ’GeForce RTX 2080 Ti’. On average, initial meta-training
takes about 15 hours with a single-core GPU. As for the CNN model settings, we
choose the Adam optimizer, and apply the cyclic learning rate adaption
strategy introduced in paper (smith2017cyclical, ) to speed-up the
convergence, and then use ’the Stochastic Gradient Descent with Warm Restarts’
(loshchilov2016sgdr, ) to further reduce the loss. Our multi-modal profile
models show no overfitting during the training, and we think it is due to
three reasons: 1) the strong regularization effect of the 2-D CNN; 2) multi-
task learning; 3) a large training set. The number of model parameters is
about 2 million. Based on the results of our experiments, we found our model
performs well without using any additional regularization techniques like
dropout or L1/L2 regularization.

Baseline model: To fairly evaluate the performance of Meta-Profile Network,
all the following experiments are conducted by comparing the Meta-Profile
Network to a normal training strategy. The normal training strategy completely
copies the meta-testing part, which uses the exact same similarity module
$f_{\theta}$ and model parameter settings by training the prediction dataset
$D^{predict}$ from scratch.

###  4.2. Uncertainty of Out-of-Distribution Detection

The ability to distinguish abnormal data or data that is clearly far from
current distribution space is a crucial indicator to judge whether the
industrial model is successful, especially for deep learning and meta-learning
models (hendrycks2016baseline, ; hendrycks2019using, ). To evaluate the
performance of model in the uncertainty estimates, we consider using an out-
of-distribution (OOD) detection test to see whether any out-of-distribution
inputs are fed into the in-distribution classes. To measure the quality of
out-of-distribution detection, two standard metrics Area Under the Receiver
Operating Characteristic (AUROC) curve and Area Under the Precision-Recall
(AUPR) curve are employed in our work. The higher AUPR and AUROC values
indicate the stronger model’s ability to resist uncertainty.

Table.3 demonstrates the OOD detection performance of the baseline model and
the Meta-Profile model. Since the distribution space of each task is
different, we cannot just use a single unknown task to evaluate the
uncertainty of the model. Here we test 8 different unseen target tasks in this
estimation. Both the AUROC and AUPR scores of Meta-Profile Network
consistently improve over the baseline model on all 8 unseen target tasks. For
the most outstanding task ’RAKU_PRI’, Meta-Profile Network has more than 19%
AUPR and 10% AUROC performance improvement in the uncertainty test. Compared
to the normal training strategy, Meta-Profile Network has around 8% AUPR and
more than 3% AUROC improvement in 8 tasks on average. Consequently, Meta-
Profile Network can significantly improve the performance of the model in
resisting uncertainty compared to the normal training strategy.

###  4.3. Robustness to Data Insufficiency (Label Masking)

In practice, the data insufficiency problem is particularly prevalent. Like
the fuel to the engine, the success of a deep model is based on having enough
sufficient labeled samples. In extreme cases, when we have only a few samples
for a task, the effectiveness of the model will be greatly reduced. Meta-
learning has demonstrated that it can mitigate the side effects of the data
insufficiency problem. We design a label masking experiment to evaluate the
robustness of our model when it faces the insufficient data problem.

To quantitatively observe and analyze the performance of the model in
different levels of masking, we prepare two sets of test cases to simulate two
insufficient data scenarios, a moderate scenario and an extreme scenario. The
original size of unknown labeled samples is 10,000. The data size of the
moderate group gradually decreases from 100% in 20% decrements to 20%. The
extreme group tests the performance of the model under severely reduced
datasets with, 5%, 3%, 1%, 0.5%, of labels respectively. Figure.3 shows the
performance of two models in a data insufficiency scenario. Compared with the
normal training strategy, Meta-Profile Network shows relatively good
performance in all test cases. Even in the case of extremely small data, our
model can still improve task prediction performance by 10%. Similar results
are demonstrated in other pre-trained model related studies under low-resource
conditions (bhunia2019handwriting, ).

Figure 3. Robustness evaluation in a data insufficient scenario. To simulate a
situation with data insufficiency, the original labeled samples are manually
masked by percentage. We compare the performance of the two models under the
moderate and extremely low-resource situations. The value of x-axis represents
the percentage of labels available.

###  4.4. Robustness to Class Imbalance

In terms of model robustness evaluation, another common problem that needs
attention is the imbalance of class labels. Most machine learning algorithms
perform best with an equal number of class samples. In cases where the total
number of samples from a class is more abundant than samples from other
classes, it will induce the model to learn more about the prevalent class and
produce a result that looks good but is far from the ground truth.
Understanding the differences in the learning of new tasks caused by the
unequal distribution of minority and majority classes is important to this
work.

Figure 4. Robustness evaluation in a class imbalance scenario. The imbalance
ratio is defined as the ratio of positive class to negative class. We prepare
7 test cases with an exponentially increasing imbalance ratio starting at 0.5.
Dashed lines indicate the 2-period moving average.

An additional explanation to the task description in Section 4.1, for the new
brand advertisement recommendation task, we set the newly developed users as
the positive class. In contrast, users that never used this brand before are
considered the negative class (these users are not involved in the training
set $D^{train}$). The imbalance ratio is defined as the ratio of positive
class to negative class. By adjusting the imbalance ratio, we can test the
performance of the model under class imbalanced circumstances. We test 7 cases
with an exponentially increasing imbalance ratio starting at 0.5. Compared to
the baseline model, the figure illustrates (Figure.4) that Meta-Profile
Network significantly improves the performance with the imbalance ratio
increasing. Meanwhile, our model performs better compared to normal training
as the imbalance ratio increases, as shown by the slope of the line
representing the 2-period moving average of AUPR. According to the results of
two robustness estimates, our model can significantly improve the robustness
score compared to the normal training strategy, which can help the application
cope with more extreme conditions.

###  4.5. Model Deployment

Lastly, we have deployed our Meta-Profile Network online on Rakuten AIris
advertisement recommendation service (Figure.5). The service allows users to
do the target prospecting without training the entire model from scratch when
we have a new task (job), e.g., find the potential users with similar behavior
patterns to new brand’s existing users. According to the statistics, the
customer acquisition cost (CAC) for AIris target prospecting has a 30-50%
decrease compared to the standard data management platform (DMP) segments or
other platform’s lookalike solution. The customer conversion rate (CVR) has a
high improvement from 10-30% in comparison with the previous standard
solution, which is considered to be a big improvement for the service.

Figure 5. Rakuten AIris target prospecting service page. The proposed User
Meta-Profile Network running in its background enables fast adaptation to new
use cases, instead of training models from scratch.

##  5\. Conclusion

In this work, we introduced the Meta-Profile Network, a novel meta-learning
framework for learning how to profile user behaviors and fast adapt to
subsequent learning tasks. The proposed time-heatmap encoding strategy, multi-
modal combined with multi-task learning architecture proved to be highly
efficient for learning representation of user behavior with long-term cross-
domain data. Meta-Profile Network based on metric-based meta-learning and deep
neural networks empower the model to effectively and quickly transfer the
learned knowledge to unknown tasks while learning a good profile of user
behaviors.

Our extensive experiments demonstrate that the benefits of the Meta-Profile
Network extend beyond merely model accuracy and quick convergence in
comparison with training from scratch strategy. In fact, the proposed meta-
learning approach has better robustness and uncertainty under various extreme
conditions as well. Moreover, Meta-Profile Network also shows strong
flexibility and scalability in practice, which could promote meta-learning
research and development in large-scale industrial applications.

###### Acknowledgements.

This work is supported by Rakuten Institute of Technology, Tokyo, Japan. We
are grateful to cooperate with the Rakuten AIris science team. The authors
would also like to thank the anonymous reviewers for their valuable comments
and helpful suggestions.

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# Analogue Radio over Fiber aided Multi-service Communications for High Speed
Trains

Yichuan Li, Salman Ghafoor, Mohammed El-Hajjar, Senior Member, IEEE
Y. Li is with Harbin Institute of Technology (Shenzhen), Shenzhen, China
(e-mail: liyichuan@hit.edu.cn).S. Ghafoor is with the National University of
Sciences and Technology, Pakistan (e-mail: salman.ghafoor@seecs.edu.pk).M. El-
Hajjar is with the School of Electronics and Computer Science, University of
Southampton, SO17 1BJ, United Kingdom (meh@ecs.soton.ac.uk).

###### Abstract

High speed trains (HST) have gradually become an essential means of
transportation, where given our digital world, it is expected that passengers
will be connected all the time. More specifically, the on-board passengers
require fast mobile connections, which cannot be provided by the currently
implemented cellular networks. Hence, in this article, we propose an analogue
radio over fiber (A-RoF) aided multi-service network architecture for high-
speed trains, in order to enhance the quality of service as well as reduce the
cost of the radio access network (RAN). The proposed design can simultaneously
support sub-6GHz as well as milimeter wave (mmWave) communications using the
same architecture. Explicitly, we design a photonics aided beamforming
technique in order to eliminate the bulky high-speed electronic phase-shifters
and the hostile broadband mmWave mixers while providing a low-cost RAN
solution. Finally, a beamforming range of 180∘ is demonstrated with a high
resolution using our proposed system.

###### Index Terms:

Optical fiber, radio access network, Beyond 5G, High speed train, analogue
radio over fiber, mmWave beamforming.

##  I Introduction

The high speed train (HST) operating at a speed above 300 km/hour has
fundamentally changed the individuals’ life-style. It is reported that HST has
the second-highest internet streaming after household environments, such as
homes and offices [1, 2], where the majority of this streaming is used for
supporting the on-board activities, such as on-demand video, online-gaming,
and voice or video calling. Furthermore, since the 4G and 5G use the sub-6GHz
band and then the millimeter wave (mmWave) communications will coexist with
these frequency bands [3], a railway network supporting multi-service is
required, where the passengers are capable of being connected to 4G, 5G,
Beyond 5G or even Wi-Fi networks all the time [4, 3, 5]. On the other hand,
HST requires high capacity due to the increasingly high number of passengers
and the severe Doppler effects caused by the high speed [6, 7]. As a result,
this requires more base-stations and an efficient cellular handover technique,
which has several challenges [6, 7, 8, 9]. First, the denser deployment of
base stations (BS) can provide seamless connection for the passengers by
increasing the capacity per cell, which by contrary would impose more inter-
cell interference (ICI) [6, 7]. Then, the severe Doppler effects seriously
undermine the system as the train is moving extremely fast, impacting the
handover process of the cellular networks [4, 5]. Besides, the channel
estimation might not be accurate due to the rapid channel variations,
influencing the quality of service (QoS) and hence, the user experience [8,
9].

Figure 1: Multi-service HST System Architecture

As a solution, mmWave beamforming has been proposed for mitigating the ICI,
while enhancing the capacity, especially in ultra-dense cellular networks
[10]. On the other hand, two-hop relay communications are advocated by [1, 4]
to address the handover failure and the rapid channel variation in HSTs, where
several relay antennas can be installed on the rooftop of the train cars for a
stable handover. However, in order to have a decent quality of service (QoS),
a large number of base-stations must be deployed, increasing the total cost of
the radio access networks (RANs) including both the Capital Expenditure
(CAPEX) and the Operational Expenditure (OPEX). Hence, ultra-light RANs are
required [11]. In addition, mmWave communications beamforming requires high-
speed mmWave phase-shifters [12], which increases the overall RAN cost and
limits the tuning carrier frequency range [13, 14, 15], and the broadband
mixers, which affects achievable the bit error rate (BER) performance [13].
Furthermore, the phase-shifter based beamforming would impose beam-squinting
on the wideband signals111Beamsquinting is the beam-shifts caused by the
frequency shifts when applied with the constant phase-shift among neighbouring
antenna element (AE). This would be even severe in the context of wide-band
signal beamsteering [15]..

The analogue radio over (A-RoF) based true-time delay is a low-cost yet high-
performance RAN solution with ultra-light remote radio head (RRH) [16, 6, 17,
18, 19, 14, 20], where the RAN is separated between the central unit (CU) and
several RRHs and is capable of reducing both its power-consumption and
complexity. Explicitly, the A-RoF aided beamformer was proposed for providing
beam-squinting free beamforming using the uniform fiber Bragg grating (FBG)
[15, 21, 22] or a single chirped FBG (CFBG) [23, 24].

Figure 2: Conventional System Model (DML: Directly Modulated Laser; WDM Mux:
Wavelength Division Multiplexer; PD, Photo-detector; PSL: Power Splitter; BPF:
Bandpass Filter; EA: Electronic Amplifier; NS: Number of Services; NA: Number
of Antenna Element.)

In this article, we design a two-hop HST communications network combined with
the A-RoF aided beamforming techniques, where multi services, such as on-
demand video, online-gaming, and voice or video calling, which are carried by
mmWave and sub-6GHz signals using 4G, 5G or Wi-Fi networks are delivered to
the train. Explicitly, the multi service signals generated in the CU of Fig. 1
are transmitted through a short-length fiber of upto 20km to the RRHs, which
communicate with the antennas on the top of the HST to provide the required
service to the on-board passengers. The beam pattern is controlled in the CU
using the CFBG, instead of the costly and bulky phase-shifters in the RRHs,
alleviating the size and cost of the RRH and facilitating the densely deployed
RRHs along the railways. The proposed system enables both cost-reduction by
simplifying the RAN design and performance-improvement by exploiting
centralised optical processing and multi-service signal generation as a
benefit of the A-RoF architecture [14]. The novel contributions of our system
are as follow:

  1. 1.

Photonic aided true-time delay beamforming: We conceive a multi-service true-
time-delay transmit beamforming for HST two-hop network, while also
eliminating the beam-squinting phenomenon.

  2. 2.

Energy-efficient RRHs: The large-scale power-thirsty phase shifters and costly
mmWave phase shifters are removed, while the beam is optically controlled
using the passive FBGs in the proposed design, hence improving the OPEX-
savings and enabling ultra-light RRHs deployment.

  3. 3.

Multi-service signal generation: multi-service signals carried by mmWave and
sub-6GHz frequency band can be optically generated and beam-steered to the HST
in the same direction.

  4. 4.

Centralised optical processing: unlike the phase-shifter used in conventional
wireless transmit beamforming, the beam control module is located in the
central unit, potentially facilitating the coordinated multipoint (CoMP)
transmission.

The rest of the paper is organised as follows. We introduce the multi-service
two-hop train system in Section II, while the A-RoF aided beamforming
technique and its time delay principle are detailed in Section III. Then, we
present the cost-benefits and the beamforming performance of our proposed
system in Section IV, followed by the conclusion in Section V.

Figure 3: Proposed A-RoF aided Multi-service Architecture.

##  II Multi-service HST System Architecture

In this section, we present a general architecture for the two-hop HST system
shown in Fig. 1, which can be exploited in our design. As shown in Fig. 1, the
signal is generated in the CU and transmitted via fiber to several RRHs, where
only optical-to-electronic conversion, amplification and filtering are
performed, thus substantially reducing the RRH size. Explicitly, the RRH
receives the signal from the CU using fiber and then transmits this signal to
the HST using a set of antenna arrays, as shown in Fig. 1, where the RRHs are
placed along the train line and will communicate with the antenna arrays on
the rooftop of the HST.

The signals transmitted from the RRHs to the HST are beamformed and
transmitted to the antenna arrays fixed on the rooftop of the HST, as shown in
Fig. 1. Then, the signals are relayed to the on-board passengers to fulfill
the users demands through the indoor communication system [25]. It has been
verified using field tests that the two-hop relay communication in HST setup
outperforms the conventional 4G cellular system in terms of signal quality
[25].

Since the 4G and 5G signals would co-exist in the non-standalone 5G deployment
proposed by the 3GPP in the recent Releases [26], multi-service signal
transmission using different frequency bands and wireless standards are of
importance to support the users’ daily streaming, on-line gaming, voice or
video call and on-demand video [3].

Conventionally, the A-RoF aided multi-service system can be supported using
the architecture of Fig. 2 [1, 4, 9, 27, 25], where different services carried
by different frequencies are directly modulated by individual lasers before
being coupled into an optical fiber. At the end of the fiber, each optical and
radio frequency (RF) chain are used for optical-to-electronic conversion,
amplification, filterings. Furthermore, when analogue beamforming is employed
for improving the signal-to-noise ratio performance, a large number of phase-
shifters, band-pass filter (BPFs), electronic amplifiers (EAs) are required,
which increases the cost and power-consumption of the whole system.
Explicitly, let us take service 1 as an example, as shown in Fig. 2, assuming
the RF of $f_{3}$ carries service 1, $f_{3}$ is used to directly modulate a
laser operating at the center wavelength of $\lambda_{1}$. Then, coupled with
other services carried by $\lambda_{2}$ to $\lambda_{6}$ into the fiber, the
wavelength division multiplexing (WDM) signal of the spectrum shown in Fig. 2
feeds the optical fiber for transmission, after which the WDM Demultiplexer
(WDM Demux) separates each wavelength. Then, the modulated optical signal of
$\lambda_{1}$ is photo-detected and the $f_{3}$ carrying service 1 is
recovered, followed by the power splitter (PSL) which splits the power of the
RF frequency, where, each BPF and EA is used for filtering out the wanted
signal and for the amplification of each port of the PSL, respectively.
Finally, several phase-shifters are used to phase-shift each output to form a
desired beam pattern, leading to the analogue beamforming with large amount of
power-thirsty and bulky phase-shifter deployment. In the next section, we will
introduce our A-RoF system based on the two-hop transmission, while invoking a
lower-cost photonic aided multi-service solution.

Figure 4: The proposed network’s multi-service signal generation and their
time-delay imposed.

##  III A-RoF aided Beamforming for High-speed Train Multi-service
Communications

###  III-A A-RoF aided HST System Model

As mentioned in section II, the RRH beamforms the multi-service signals,
composed of sub-6GHz and mmW signals, to the HST rooftop antenna arrays. Fig.
3 shows the proposed A-RoF design, where the sub-6GHz and mmW signals are
beamformed in the same direction to the antenna array placed on the rooftop of
the train. The proposed design avoids the beam-squinting as well as considers
low-complexity RRH.

In Fig. 3, the access network is divided into CU and RRH, where the CU
performs the baseband signal processing as well as the radio modulations [14],
while the RRH is simplified to only radio functions such as amplifications and
filtering. Explicitly, in the CU of Fig. 3, the RF signals of $f_{1}$, $f_{2}$
and $f_{3}$222The number of frequencies can be readily extended, which depends
on the bandwidth of the LD. directly modulate a laser diode (LD) operating at
$\lambda_{1}$. The signal at the output of the directly modulated laser is
given at the optical input of a Mach-Zehnder modulator (MZM) that is being
driven by a sinusoidal signal of frequency $\Delta f1$. The nonlinear transfer
function of the MZM results in the generation of multiple spectral copies of
the directly modulated optical signal that have a frequency spacing of $\Delta
f_{1}$ as shown in Fig. 3 [13]. The resulting WDM signal is time-delayed using
a CFBG, which is capable of reflecting different wavelengths with a linear
time-delay. Then, as shown in Fig. 3, another laser diode operating at
$\lambda_{2}$ is intensity modulated by a sinusoidal signal having frequency
of $\Delta f_{2}$ through a MZM to generate multiple sidebands by using the
nonlinear function of the MZM [13]. The two WDM signals are coupled into a
single mode fiber using a fiber coupler.

As shown in the RRH of Fig. 3, the combined WDM signal is separated by a two-
port optical interleaver, which filters the desired signals to two individual
dense wavelength division demultiplexers (DWDM Demux), each of which would be
used for either sub-6GHz signal generation or mmWave signal generation. The
upper DWDM Demux of Fig. 3 filters the spectrum which can generate a beat
frequency of sub-6GHz bands. Then, the photodetected sub-6GHz frequency after
each PD is band-pass filtered and amplified, while the inter-element time
delay is dependent on the chirped FBG 1 and FBG 2 strains as tested by [28].
Similarly, the bottom DWDM Demux in the RRH of Fig. 3 is used for mmWave
signal generation, where an extra chirped FBG, namely chirped FBG 3 of Fig. 3,
is implemented for adjusting the beam direction to be the same as the sub-6GHz
bands, which will be elaborated in the next section.

To elaborate further on the RF and mmWave signals generation, as shown in Fig.
4, the optical interleaver, which is a periodic optical filter, separates the
combined WDM signals of spectrum ③ of Fig. 3. The spectrum of the two outputs
of the optical interleaver is depicted in Fig. 4, where port 1 maps the
spectrum ④ of Fig. 4 to the sub-6GHz spectrum of $f_{1}$, $f_{2}$ and $f_{3}$,
with port 2 mapping the spectrum ⑤ to the mmWave frequencies of
$f_{1}+\frac{\Delta f}{2}$, $f_{2}+\frac{\Delta f}{2}$ and $f_{3}+\frac{\Delta
f}{2}$333Note that if $\frac{\Delta f}{2}=f_{o1}-f_{o2}$ is upto 25 GHz,
$f_{1}+\frac{\Delta f}{2}$ is the mmWave signal of at least 25 GHz. The
spectrum ④ and ⑤ of Fig. 4 corresponds to spectrum ④ and ⑤ of Fig. 3.. Let us
now consider a four-antenna-element system for both the sub-6GHz and mmWave
transmission. The beating frequencies of the red boxes of Fig. 4 would be
mapped to antenna elements 1-4 of both the mmWave antenna array and the
sub-6GHz antenna array dispensing with the mmWave mixers and phase shifters,
since they have been performed using the above optical link with the aid of
WDM signal and CFBG.

Thus, a multi-service communication system transporting sub-6GHz and mmWave
signals in the same direction is built for the two-hop HST systems. In the
next section, we will detail the true-time delay principles and its mapping
rule from the optical domain to the electronic domain as well as the multi-
service generation.

###  III-B True-time Delay Principle

Instead of exploiting the conventional phase-shifting schemes for analogue
beamforming [29], our proposed system invokes the true-time delay, which
relies on the constant time-delay among the RF signal fed into the adjacent
antennas elements to introduce the beam steering, which is capable of
mitigating the wide-band beam-squinting problems [15]. While undermining the
codebook design of the phased-array systems [30], beam-squinting is also
detrimental for the channel estimation and precoding, which further degrades
the wireless communication transmission rate [31].

In the following, with the aid of the mathematical derivation, we will prove
how the imposed optical linear time-delay is used for introducing the constant
time-delay among the RF signal fed into the adjacent antennas elements of each
antenna array of Fig. 3. In the upper line of the CU in Fig. 3, where the
spectrum ① is generated, the multi-service RF signals are used to directly
modulate a laser diode and the input optical field of the MZM can be
formulated as [13]:

$E_{in}(t)=\sqrt{P_{Laser}}e^{j\omega_{\lambda_{1}}t}[1+cos(\omega_{f_{1}}t)+cos(\omega_{f_{2}}t)+cos(\omega_{f_{3}}t)],$
(1)

where $P_{Laser}$ is the LD output power and $\omega_{f_{1}}$,
$\omega_{f_{2}}$ and $\omega_{f_{3}}$ denote the optical carrier’s angular
frequency corresponding to $\lambda_{1}$, $\lambda_{2}$ and $\lambda_{3}$ of
Fig. 3. Then, the MZM output field [13] is as follows:

$\begin{array}[]{lcl}E_{MZM_{up}}(t)\\\ =cos(\pm\frac{\pi}{4}+\frac{\pi
V_{dr}cos(\omega_{\Delta f_{1}})}{2V_{\pi}})E_{in}(t)\\\
=\frac{\sqrt{P_{laser}}[1+cos(\omega_{f_{1}}t)+cos(\omega_{f_{2}}t)+cos(\omega_{f_{3}}t)]e^{j\omega_{\lambda_{1}}t}}{\sqrt{2}}[J_{0}(\frac{\pi|V_{dr}|}{2V_{\pi}})\\\
+2\sum_{n=1}^{\infty}(-1)^{n}J_{2n}(\frac{\pi
V_{dr}}{2V_{\pi}})cos(2n\omega_{\Delta f_{1}}t)\\\ \pm
2\sum_{n=1}^{\infty}(-1)^{n}J_{2n-1}(\frac{\pi
V_{dr}}{2V_{\pi}})cos((2n-1)\omega_{\Delta f_{1}}t)]\\\
=\frac{\sqrt{P_{laser}}}{\sqrt{2}}[J_{0}(\frac{\pi|V_{dr}|}{2V_{\pi}})[e^{j\omega_{\lambda_{1}}t}+e^{j(\omega_{\lambda_{1}}+\omega_{f_{1}})t}/2\\\
+e^{j(\omega_{\lambda_{1}}t-\omega_{f_{1}}t)}/2+e^{j(\omega_{\lambda_{1}}+\omega_{f_{2}})t}/2+e^{j(\omega_{\lambda_{1}}t-\omega_{f_{2}}t)}/2\\\
+e^{j(\omega_{\lambda_{1}}+\omega_{f_{3}})t}/2+e^{j(\omega_{\lambda_{1}}t-\omega_{f_{3}}t)}/2]\\\
+2\sum_{n=1}^{\infty}(-1)^{n}J_{2n}(\frac{\pi V_{dr}}{2V_{\pi}})\\\
\times[e^{j(\omega_{\lambda_{1}}+2n\omega_{\Delta
f_{1}})t}/2+e^{j(\omega_{\lambda_{1}}-2n\omega_{\Delta f_{1}})t}/2\\\
+\frac{e^{j(\omega_{\lambda_{1}}+2n\omega_{\Delta
f_{1}}+\omega_{f_{1}})t}/2+e^{j(\omega_{\lambda_{1}}-2n\omega_{\Delta
f_{1}}-\omega_{f_{1}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+2n\omega_{\Delta
f_{1}}-\omega_{f_{1}})t}/2+e^{j(\omega_{\lambda_{1}}-2n\omega_{\Delta
f_{1}}+\omega_{f_{1}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+2n\omega_{\Delta
f_{1}}+\omega_{f_{2}})t}/2+e^{j(\omega_{\lambda_{1}}-2n\omega_{\Delta
f_{1}}-\omega_{f_{2}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+2n\omega_{\Delta
f_{1}}-\omega_{f_{2}})t}/2+e^{j(\omega_{\lambda_{1}}-2n\omega_{\Delta
f_{1}}+\omega_{f_{2}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+2n\omega_{\Delta
f_{1}}+\omega_{f_{3}})t}/2+e^{j(\omega_{\lambda_{1}}-2n\omega_{\Delta
f_{1}}-\omega_{f_{3}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+2n\omega_{\Delta
f_{1}}-\omega_{f_{3}})t}/2+e^{j(\omega_{\lambda_{1}}-2n\omega_{\Delta
f_{1}}+\omega_{f_{3}})t}/2}{2}]\\\ \pm
2\sum_{n=1}^{\infty}(-1)^{n}J_{2n-1}(\frac{\pi V_{dr}}{2V_{\pi}})\\\
\times[\frac{e^{j(\omega_{\lambda_{1}}+(2n-1)\omega_{\Delta
f_{1}})t}+e^{j(\omega_{\lambda_{1}}-(2n-1)\omega_{\Delta f_{1}})t}}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+(2n-1)\omega_{\Delta
f_{1}}+\omega_{f_{1}})t}/2+e^{j(\omega_{\lambda_{1}}-(2n-1)\omega_{\Delta
f_{1}}-\omega_{f_{1}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+(2n-1)\omega_{\Delta
f_{1}}-\omega_{f_{1}})t}/2+e^{j(\omega_{\lambda_{1}}-(2n-1)\omega_{\Delta
f_{1}}+\omega_{f_{1}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+(2n-1)\omega_{\Delta
f_{1}}+\omega_{f_{2}})t}/2+e^{j(\omega_{\lambda_{1}}-(2n-1)\omega_{\Delta
f_{1}}-\omega_{f_{2}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+(2n-1)\omega_{\Delta
f_{1}}-\omega_{f_{2}})t}/2+e^{j(\omega_{\lambda_{1}}-(2n-1)\omega_{\Delta
f_{1}}+\omega_{f_{2}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+(2n-1)\omega_{\Delta
f_{1}}+\omega_{f_{3}})t}/2+e^{j(\omega_{\lambda_{1}}-(2n-1)\omega_{\Delta
f_{1}}-\omega_{f_{3}})t}/2}{2}\\\
+\frac{e^{j(\omega_{\lambda_{1}}+(2n-1)\omega_{\Delta
f_{1}}-\omega_{f_{3}})t}/2+e^{j(\omega_{\lambda_{1}}-(2n-1)\omega_{\Delta
f_{1}}+\omega_{f_{3}})t}/2}{2}]],\end{array}$

where $\omega_{\Delta f_{1}}$, $V_{dr}$ and $V_{pi}$ are the angular frequency
of $\Delta f_{1}$, the amplitude of the drive frequency of the MZM and its
switching voltage. $J_{n}(\frac{\pi V_{dr}}{2V_{\pi}})$ is the Bessel function
of the first kind and order n, which determines both the number and the
amplitude of the side-bands. The spectrum of the MZM output is marked as ① of
Fig. 3, where the same RF signals subsuming $f_{1}$, $f_{2}$ and $f_{3}$ are
carried by each wavelength, generating a WDM signal spaced with $\Delta
f_{1}$. Similarly, the WDM signal at the output of the second MZM represented
by spectrum ② in Fig. 3 can be expressed as follows, where the input optical
field of the bottom MZM $E_{in2}(t)$ and an unmodulated WDM signal
$E_{MZM_{bottom}}(t)$ is generated:

$E_{in2}(t)=\sqrt{P_{Laser}}e^{j\omega_{\lambda_{2}}t},$ (2)
$\begin{array}[]{lcl}E_{MZM_{bottom}}(t)\\\ =cos(\pm\frac{\pi}{4}+\frac{\pi
V_{dr}cos(\omega_{\Delta f_{2}})}{2V_{\pi}})E_{in2}(t)\\\
=\frac{\sqrt{P_{laser}}e^{j\omega_{\lambda_{2}}t}}{\sqrt{2}}[J_{0}(\frac{\pi
V_{dr}}{2V_{\pi}})\\\ +2\sum_{n=1}^{\infty}(-1)^{n}J_{2n}(\frac{\pi
V_{dr}}{2V_{\pi}})cos(2n\omega_{\Delta f_{2}}t)\\\ \pm
2\sum_{n=1}^{\infty}(-1)^{n}J_{2n-1}(\frac{\pi
V_{dr}}{2V_{\pi}})cos((2n-1)\omega_{\Delta f_{2}}t)]\\\
=\frac{\sqrt{P_{laser}}}{\sqrt{2}}[J_{0}(\frac{\pi|V_{dr}|}{2V_{\pi}})(e^{j\omega_{\lambda_{2}}t})\\\
+2\sum_{n=1}^{\infty}(-1)^{n}J_{2n}(\frac{\pi V_{dr}}{2V_{\pi}})\\\
\times[e^{j(\omega_{\lambda_{2}}+2n\omega_{\Delta
f_{2}})t}/2+e^{j(\omega_{\lambda_{2}}-2n\omega_{\Delta f_{2}})t}/2]\\\ \pm
2\sum_{n=1}^{\infty}(-1)^{n}J_{2n-1}(\frac{\pi V_{dr}}{2V_{\pi}})\\\
\times[\frac{e^{j(\omega_{\lambda_{2}}+(2n-1)\omega_{\Delta
f_{2}})t}+e^{j(\omega_{\lambda_{2}}-(2n-1)\omega_{\Delta
f_{2}})t}}{2}]].\end{array}$ (3)

Then, the two WDM signals are combined using the fiber coupler and transmitted
through a single mode fiber. By assuming $\Delta f=\Delta f_{1}=\Delta f_{2}$
and $\Delta f=2(f_{02}-f_{01})$, the combined WDM signal has a wavelength
spacing of $\frac{\Delta f}{2}.$ As shown in spectrum ③ of Fig. 3, the
combined WDM signal would be filtered to two ports, with each being fed into a
WDM Demux. Each output of the DWDM Demux would be fed into a photo detector to
obtain either sub-6GHz signal or mmWave signal. Then, assuming the time delays
imposed in the different frequencies are $t_{n}$ and $T_{n}$ as shown in Fig.
4 and by filtering the unwanted low frequency, we are capable of obtaining
three frequencies in the mmWave spectrum as $S_{mmPD_{1}}$, $S_{mmPD_{2}}$ and
$S_{mmPD_{3}}$ after the PD as shown in Fig. 3, which are then input to a BPF
and then EA444Here, we use three photo-detected signals as an example, which
can be readily extended to any number of photo detectors.. These mmWave
signals can be represented as follows:

$\begin{array}[]{lcl}S_{mmPD_{1}}=\frac{P_{laser}}{2}\\\
(cos((\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{1}}})(t+\frac{\omega_{\lambda_{2}}T_{1}-\omega_{{\Delta
f}}T_{1}-\omega_{\lambda_{1}}t_{3}+\omega_{\Delta
f}t_{3}+\omega_{f_{1}}t_{3}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{1}}})}))+\\\
cos((\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{2}}})(t+\frac{\omega_{\lambda_{2}}T_{1}-\omega_{{\Delta
f}}T_{1}-\omega_{\lambda_{1}}t_{2}+\omega_{\Delta
f}t_{2}+\omega_{f_{2}}t_{2}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{2}}})}))+\\\
cos((\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{3}}})(t+\frac{\omega_{\lambda_{2}}T_{1}-\omega_{{\Delta
f}}T_{1}-\omega_{\lambda_{1}}t_{1}+\omega_{\Delta
f}t_{1}+\omega_{f_{3}}t_{1}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{3}}})})))\end{array}$
(4)

$\begin{array}[]{lcl}S_{mmPD_{2}}\\\
=\frac{P_{laser}}{2}(cos((\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{1}}})(t+\frac{\omega_{\lambda_{2}}T_{2}-\omega_{\lambda_{1}}t_{3}^{{}^{\prime}}+\omega_{f_{1}}t_{3}^{{}^{\prime}}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{1}}})}))\\\
+cos((\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{2}}})(t+\frac{\omega_{\lambda_{2}}T_{2}-\omega_{\lambda_{1}}t_{2}^{{}^{\prime}}+\omega_{f_{2}}t_{2}^{{}^{\prime}}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{2}}})}))\\\
+cos((\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{3}}})(t+\frac{\omega_{\lambda_{2}}T_{2}-\omega_{\lambda_{1}}t_{1}^{{}^{\prime}}+\omega_{f_{3}}t_{1}^{{}^{\prime}}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{3}}})})))\end{array}$
(5)

Components | Proposed System | Conventional System
---|---|---
Passive Components
Optical Interleaver | 1 | 0
CFBG | 1 | 0
DWDM Demux | 2 | 1
Active Components
PD |  8 ($2N_{A}$) |  6 ($N_{s}$)
BPF |  8 ($2N_{A}$) |  24 ($N_{s}N_{A}$)
EA |  8 ($2N_{A}$) |  24 ($N_{s}N_{A}$)
Phase shifters | 0 |  12 mmWave PSs+12 Sub-6GHz PS ($N_{s}N_{A}$)
PSL | 0 |  6 ($N_{s}$)

Table I: RRH Complexity Comparison

$\begin{array}[]{lcl}S_{mmPD_{3}}=\frac{P_{laser}}{2}\\\
(cos((\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{1}}})(t+\frac{\omega_{\lambda_{2}}T_{3}+\omega_{{\Delta
f}}T_{3}-\omega_{\lambda_{1}}t_{3}^{{}^{\prime\prime}}-\omega_{\Delta
f}t_{3}^{{}^{\prime\prime}}+\omega_{f_{1}}t_{3}^{{}^{\prime\prime}}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{1}}})}))\\\
+cos((\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{2}}})(t+\frac{\omega_{\lambda_{2}}T_{3}+\omega_{{\Delta
f}}T_{3}-\omega_{\lambda_{1}}t_{2}^{{}^{\prime\prime}}-\omega_{\Delta
f}t_{2}^{{}^{\prime\prime}}+\omega_{f_{2}}t_{2}^{{}^{\prime\prime}}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{2}}})}))\\\
+cos((\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{3}}})(t+\frac{\omega_{\lambda_{2}}T_{3}+\omega_{{\Delta
f}}T_{3}-\omega_{\lambda_{1}}t_{1}^{{}^{\prime\prime}}-\omega_{\Delta
f}t_{1}^{{}^{\prime\prime}}+\omega_{f_{3}}t_{1}^{{}^{\prime\prime}}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{3}}})}))),\end{array}$
(6)

where
$\omega_{mmWave_{n}}=\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{n}}}$
is the generated mmWave signal frequency. Then, if we take
$\omega_{mmWave_{1}}$ as an example, according to Equations (4), (5) and (6),
the time-delay difference between AE2 and AE1 can be referred to as
$\Delta_{1}$, and between AE3 and AE2 as $\Delta_{2}$, which can be
represented as:

$\begin{array}[]{lcl}\Delta_{1}=\frac{\omega_{\lambda_{2}}T_{2}-\omega_{\lambda_{1}}t_{3}^{{}^{\prime}}+\omega_{f_{1}}t_{3}^{{}^{\prime}}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{1}}})}\\\
-\frac{\omega_{\lambda_{2}}T_{1}-\omega_{{\Delta
f}}T_{1}-\omega_{\lambda_{1}}t_{3}+\omega_{\Delta
f}t_{3}+\omega_{f_{1}}t_{3}}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{1}}})}\\\
=\frac{\omega_{mmWave_{1}}(T_{2}-T_{1})+(n(T_{2}-T_{1})/(2\pi))(2\pi\omega_{mmWave_{1}}/n)}{-\omega_{mmWave_{1}}}\\\
=-2(T_{2}-T_{1}),\end{array}$ (7)

and

$\begin{array}[]{lcl}\Delta_{2}\\\
=\frac{\omega_{\lambda_{2}}(T_{3}-T_{2})-\omega_{\lambda_{1}}(t_{3}^{{}^{\prime\prime}}-t_{3}^{{}^{\prime}})+\omega_{f_{1}}(t_{3}{{}^{\prime\prime}}-t_{3}^{{}^{\prime}})+\omega_{\Delta
f}(T_{3}-t_{3}^{{}^{\prime\prime}})}{-(\omega_{\lambda_{2}}-\omega_{\lambda_{1}}+\omega_{{f_{1}}})}\\\
=-2(T_{3}-T_{2}).\end{array}$ (8)

As mentioned in Section I, CFBG is capable of obtaining a linear relation
between the time delay and the optical spectrum fed into it, which would be
elaborated in Section IV. Then, we obtain $\Delta T=T_{3}-T_{2}=T_{2}-T_{1}$
as the time-delay difference of two frequencies with a spacing of $\Delta f$.
Hence, we conclude that the optical time-delay of $\Delta T$ can result in a
$-2\Delta T$ constant time-delay difference among the neighbouring AEs as
verified by (7) and (8). This rule also applies to $\omega_{mmWave_{1}}$ and
$\omega_{mmWave_{2}}$. Similarly, by repeating the process of the above
derivation, we can have the time-delay difference relationship in terms of
sub-6GHz as $\tau=-2\Delta T$. Then, we attempt to solve the problem of the
beam-squinting for the mmWave and the sub-6GHz signals, where we implement the
CFBG3 of Fig. 3, where the beam angle and the time delay relation is as
follows:

$\tau=\frac{dcos(\theta)}{c},$ (9)

where the $\theta$ is the beam angle to the perpendicular orientation of the
antenna array. In order to obtain the same beam direction for both mmWave and
sub-6GHz, the time delay difference of the sub-6GHz and the mmWave service
must satisfy the following:
$cos(\theta_{1})=cos(\theta_{2})=c\tau_{1}/d_{1}=c\tau_{2}/d_{2}$, where we
have $\tau_{2}=\frac{d_{2}\tau_{1}}{d_{1}}$, with $d_{1}$ and $d_{2}$ being
the inter-element distance of each antenna array. The CFBG3 of the RRH is
capable of tuning the time delay of the mmWave service from $\tau_{1}$ to
$\tau_{2}$.

Figure 5: The Time Delay and its Corresponding Beam coverage Figure 6: Multi-
service Beam in the same direction. (a) The beam direction of mmWave signals
at 28 GHz, 30 GHz and 31 GHz, when the true-time-delay $\Delta T$ of Section
III-B is 5.0748. (b) The beam direction of sub-6GHz signals at 3 GHz, 5 GHz
and 6 GHz, when the true-time-delay $\Delta T$ of Section III-B is 47.3647.

Simulation Parameters | Values
---|---
Number of Antenna Element ($N_{A}$) | 4
Combined WDM Wavelength Spacing | 25 GHz
Length of the Chirped FBG | 40 mm
$f_{1}$, $f_{2}$ and $f_{3}$ | 3, 5, 6 GHz
$f_{o1}$, $f_{o2}$ | 193.500, 193.525 GHz
WDM Central Frequencies | 193.450, 193.475, 193.500, 193.525 GHz
193.550, 193.575, 193.600, 193.625 GHz
RF signal Generation ($N_{s}$) | 3, 5, 6, 28, 30, 31 GHz
Simulation Platform | Optisystem, OptiGrating

Table II: RRH Complexity Comparison Figure 7: The total chirp versus the beam
angle

Therefore, by assuming a linear relation of $t=nf+m$ between the optical
frequency and the time delay imposed by the CFBG1 and CFBG2 of the CU of Fig
3, where $n$ and $m$ are constants and the new linear relation imposed by the
CFBG3 in the RRH is $t=fk+j$, we have a new relation of frequency and time-
delay as $t=f(k+n)+m+j$ for the mmWave WDM signal. As mentioned above, we have
the following relationship:

$\tau_{1}=-2(T_{2}-T_{1})=-2n\Delta f,$ (10)
$\tau_{2}=-2(T_{2}^{new}-T_{1}^{new})=-2(n+k)\Delta f.$ (11)

Thus, $\frac{d_{2}\tau_{1}}{d_{1}}=-2(n+k)\Delta f$, and we obtain the
relation $k=-\frac{d_{2}\tau_{1}}{2d_{1}\Delta
f}-n=\frac{d_{2}-d_{1}}{d_{1}}n$. Then, by simply tuning the CFBG3 of the RRH
according to the CFBG1 and CFBG2 of the CU of Fig. 3 to the new relation as
$t=fk+j$, the multi-service communications including sub-6GHz and mmWave can
be beamsteered to the same direction. Note that the linear relation can be
tuned by changing the supported beam’s deflection as demonstrated in [28],
resulting in a tunable chirp rate of the linear CFBG, which is capable of
obtaining a linear true-time delay of the WDM signals [28].

In this section, we verified mathematically that a double time-delay of the
neighbouring wavelength of the WDM signal can be translated into the inter-
element time-delay difference of the antenna array, justifying the feasibility
of A-RoF aided beamforming control using optical true-time delays, while
removing the electronic phase-shifters and avoiding the beam squints. In the
next section, we will evaluate our system in terms of cost and performance.

##  IV System Evaluation

In this section, the system evaluation of our proposed system of Fig. 3 is
presented. We will compare the cost and complexity of the proposed system with
that of the conventional system of Fig. 2, following by a beamforming analysis
of Fig. 3.

###  IV-A Cost and Complexity Analysis

In this section, we analyse the cost benefits of our proposed design over the
conventional system, where the multi-service bands are modulated using 6 LDs
and beam-steered using 6 sets of phase-shifter array as shown in Fig. 2. As
mentioned above, our design benefits from its ultralight RRH design, hence
reducing the power-consumption and the OPEX. As shown in Table I, we list the
number of components implemented in our proposed A-RoF system of Fig. 3 and
the conventional system as shown in Fig. 2, where $N_{S}$ denotes the number
of services while $N_{A}$ is the number of antenna elements of each antenna
array. Assuming we transmit sub-6GHz spectrum of $f_{1}$, $f_{2}$ and $f_{3}$
and the mmWave frequencies of $f_{1}+\frac{\Delta f}{2}$, $f_{2}+\frac{\Delta
f}{2}$ and $f_{3}+\frac{\Delta f}{2}$ using the four-antenna-element array, it
is shown in Table I that in the proposed design of Fig 3, in contrast to the
conventional design of Fig. 2, the bulky phase-shifters and the power splitter
are totally removed, while the number of BPF, EA is substantially reduced.
Instead, some passive components such as optical interleaver, CFBG and an
extra DWDM Demux are introduced, but the number of which is not dependent on
either the services or the antenna elements. Explicitly, as seen in Table I,
regarding the active components, the power-thirsty phase-shifter and power
splitters are reduced from 24 and 6 to 0 and 0, respectively, while the number
of BPFs and EAs are decreased from 24 and 24 to 8 and 8, respectively,
resulting in a reduced power-comsumption in the RRH of Fig. 3. Therefore, we
can conclude that the power-consumption can be substantially reduced with the
removal of the phase-shifters and the introduction of the passive optical
components, while the total hardware cost would be reduced due to the optical
mmWave generation without using the mmWave phase-shifters, simplifying the BPF
and the EA.

###  IV-B Beamforming Performance Analysis

Let us now analyse the system performance of our proposed system. In this
section, we use the uniform linear antenna array having four elements555Note
that any number can be used and the four-element system is just an example.
The simulation parameters are listed in Table II. We directly modulate the
laser diode using different frequencies of $f_{1}=3$, $f_{2}=5$ and $f_{3}=6$
GHz. Then, after the true-time-delay process and the optical interleaver, a
photonic RF generation of sub-6GHz at $f_{1}=3$, $f_{2}=5$ and $f_{3}=6$ GHz
and mmWave at $f_{1}+\frac{\Delta f}{2}=28$, $f_{2}+\frac{\Delta f}{2}=30$ and
$f_{3}+\frac{\Delta f}{2}=31$ GHz can be obtained without the bulky and RF
mixers, where $\Delta f=\Delta f_{1}=\Delta f_{2}$.

In this section, we present our novel beamforming design, where we obtain a
relation between the optical signal after the CFBG1 and CFBG2 in the CU of
Fig. 4 and its time delay imposed in Fig. 5(a). Explicitly, as portrayed in
Fig. 5 by tuning a supported beam’s deflection as detailed in [28], we are
capable of changing the total chirp, resulting in a linear relation between
time-delay and the optical frequency as depicted in Fig. 5(a), hence resulting
in a multi-service beam coverage around 180∘ as shown in Fig. 5(b).

Moreover, to prove that our design can provide the same directive beam for
both sub-6GHz and mmWave spectrum, as analysed in Section III, the CFBG1 and
CFBG2 of Fig. 3 are required to impose the same degree of time-delay
difference, while CFBG 3 is tuned to a time-delay related to the CFBG 1 and
CFBG 2. As shown in Fig 6, the sub-6GHz beams are directed to the same
direction at $\Delta T_{1}=47.3647$ to the mmWave beam at $\Delta
T_{2}=5.0748$, where the relation happens to be $\Delta T_{1}=d_{2}*\Delta
T_{2}/d_{1}$ 666In our example, $d_{1}=\lambda_{3GHz}/2$ and
$d_{2}=\lambda_{28GHz}/2$ are the inter-element distances of the sub-6GHz
antenna array and mmWave antenna array, respectively, where we assume the
center frequencies are 3 GHz and 28 GHz. Then we have $d_{2}/d_{1}=0.107$..

Explicitly, it is shown in Fig. 7(a) and 7(b) that the sub-6GHz and mmWave
band are capable of being mapped to the same beamforming angle, thanks to the
introduction of CFBG 3 in the RRH of Fig. 3. When the total chirp of both the
CFBG 1 and CFBG 2 ranges from 0.7 to 4 nm with a step-size of 0.05, the time
delay difference of sub-6GHz and mmWave spans from 77.6 ps to 13.4 ps and from
8.3 to 1.4 ps, respectively, which results in a beam angle from 158.48 to
99.23 ∘ as shown in Fig. 7(a) and 7(b). Thus, by controlling the total chirp
of the CFBG 3 in the RRH according to the total chirp in the CU, we can direct
the multi-service to the same direction as shown in Fig. 6.

Then, as shown in Fig. 6(b) and Fig. 5, the corresponding multi-service beam
coverage, which is around 180∘ with a high precision, verifies that our
photonic beamforming system can radiate the wideband beam flexibly and widely,
while substantially simplifying the RRH designs as analysed in Section III.

##  V Conclusion

In this article, we have proposed a low-cost A-RoF aided multi-service
communications in the two-hop relay train system, where we implemented the
photonic beamformer using the CFBGs, enabling a centralised and low-cost RAN
design. In this paper, we designed a double time-delay mapping rule of the
optical signals and the corresponding RF signals and verified that the
proposed system was capable of reducing the total cost of the RAN by
simplifying the RRHs. Finally, a single beam transmitting the multi-service
signals with a 180∘ beamfroming range was presented.

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|  Yichuan Li is an Assistant Professor with Harbin Institute of Technology
(Shenzhen), Shenzhen, China. He received B.Sc. degree in Optics Information
Science and Technology from China University of Petroleum (East China),
Qingdao, China, in 2012, and M.Sc. degree in wireless communications from the
University of Southampton, Southampton, UK., in 2014. He was a research
assistant in the Lightwave Communication Lab of the Chinese University of Hong
Kong (CUHK) from July to October in 2017. He received his Ph.D. degree in
wireless communications from the University of Southampton, Southampton, UK.
in 2019. His research is focused on the the radio over fiber for backhaul,
fronthaul and indoor communication network. His research interests are
millimeter wave over fiber, optical fiber aided analogue beamforming
techniques, Multi-functional MIMO, mode division multiplexing in multimode
fiber and fiber-based C-RAN system.
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|  Salman Ghafoor received the B.Sc. Electrical Engineering degree from UET
Peshawar, Peshawar, Pakistan, in 2006, the M.Sc. degree in electronic
communications and computer engineering from the University of Nottingham,
Nottingham, U.K, and the Ph.D. degree from the University of Southampton,
Southampton, U.K. He was a Research Student at the Optoelectronics Research
Centre (ORC), University of Southampton, U.K for two years. In 2010, he joined
the School of Electronics and Computer Science (ECS), University of
Southampton where he completed his Ph.D in 2012. He is currently an Associate
Professor with National University of Sciences and Technology (NUST),
Islamabad, Pakistan. His areas of research include Free space optical
communications, all-optical signal processing, ultra-wideband over fibre, and
radio over fibre systems.
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|  Mohammed El-Hajjar is an Associate Professor in the School of Electronics
and Computer Science in the University of Southampton. He received his PhD in
Wireless Communications from the University of Southampton, UK in 2008.
Following the PhD, he joined Imagination Technologies as a design engineer,
where he worked on designing and developing Imagination’s multi-standard
communications platform, which resulted in three patents. He is the recipient
of several academic awards and has published a Wiley-IEEE book and in excess
of 80 journal and conference papers. Mohammed’s research interests include the
development of intelligent communications systems, energy-efficient
transceiver design, MIMO, millimeter wave communications and Radio over fiber
network design.
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