Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
10.1109/ACCESS.2017.DOI

This work was supported by the Royal Academy of Engineering under Grant
Reference RF\201920\19\191.

Corresponding author: Nidhi Simmons (e-mail: nidhi.simmons@qub.ac.uk).

# AI-Based Channel Prediction in D2D Links: An Empirical Validation

NIDHI SIMMONS1  SAMUEL B. FERREIRA GOMES2  MICHEL DAOUD YACOUB2  OSVALDO
SIMEONE3  SIMON L. COTTON1  and DAVID E. SIMMONS4  Institute of Electronics,
Communications and Information Technology, Queen’s University Belfast, BT3
9DT, UK (e-mail: {nidhi.simmons<EMAIL_ADDRESS> Wireless Technology
Laboratory, School of Electrical and Computer Engineering, University of
Campinas, Campinas 13083-970, Brazil (e-mail<EMAIL_ADDRESS>and<EMAIL_ADDRESS> King’s Communications, Learning and Information
Processing (KCLIP), Centre for Telecommunications Research, Department of
Informatics, King’s College, London, WC2R 2LS, UK (e-mail:
<EMAIL_ADDRESS> Senior software engineer working in the area of
machine learning in Belfast, UK, (e-mail<EMAIL_ADDRESS>
###### Abstract

Device-to-Device (D2D) communication propelled by artificial intelligence (AI)
will be an allied technology that will improve system performance and support
new services in advanced wireless networks (5G, 6G and beyond). In this paper,
AI-based deep learning techniques are applied to D2D links operating at 5.8
GHz with the aim at providing potential answers to the following questions
concerning the prediction of the received signal strength variations: i) how
effective is the prediction as a function of the coherence time of the
channel? and ii) what is the minimum number of input samples required for a
target prediction performance? To this end, a variety of measurement
environments and scenarios are considered, including an indoor open-office
area, an outdoor open-space, line of sight (LOS), non-LOS (NLOS), and mobile
scenarios. Four deep learning models are explored, namely long short-term
memory networks (LSTMs), gated recurrent units (GRUs), convolutional neural
networks (CNNs), and dense or feedforward networks (FFNs). Linear regression
is used as a baseline model. It is observed that GRUs and LSTMs present
equivalent performance, and both are superior when compared to CNNs, FFNs and
linear regression. This indicates that GRUs and LSTMs are able to better
account for temporal dependencies in the D2D data sets. We also provide
recommendations on the minimum input lengths that yield the required
performance given the channel coherence time. For instance, to predict 17 and
23 ms into the future, in indoor and outdoor LOS environments, respectively,
an input length of 25 ms is recommended. This indicates that the bulk of the
learning is done within the coherence time of the channel, and that large
input lengths may not always be beneficial.

###### Index Terms:

1DCNNs, 5G, 6G, channel prediction, coherence time, CNNs, deep learning, dense
networks, device-to-device communications, feedforward networks, GRUs, LSTMs,
low-latency communications, neural networks, URLLC, wireless channel
prediction.

=-15pt

##  I Introduction

Advanced wireless networks—5G, 6G, and beyond—aim to provide a multitude of
new services, many of them supporting low-latency communications. One way to
deliver low-latency communications is to enable wireless terminals to
communicate with each other through direct, usually short device-to-device
(D2D) links. These links can also be conveniently used to provide for
additional features such as increase reliability and/or extension of radio
coverage [1].

The characteristics of signal propagation in D2D links can often be very
different to those encountered in traditional wireless communications. In the
latter, the base station is fixed with antennas elevated above rooftops, and
the link is therefore, usually, free of local scatterings. D2D communications
occur in an infrastructure-less network, with fixed or mobile terminals at low
elevations, immersed in rich scattering environments. Furthermore, mobile
terminals may be in close proximity to the human body, whose motion is bound
to cause stochastic shadowing on the radio link [2, 3]. Shadowing and
scattering may be caused by a number of different radio obstructions present
in the local environment, such as vehicles and buildings (outdoor), internal
walls and furniture (indoor), and pedestrians (indoor and outdoor) [4].

This paper is concerned with the problem of predicting radio channel
conditions encountered by D2D links. Given the difficulty in modelling D2D
links, we explore the use of artificial intelligence (AI) tools and rely on
extensive experiments.

###  I-A Related Work

Several works have previously addressed the wireless channel prediction
problem using AI techniques [5, 6, 7, 8]. In [5], a hybrid deep learning model
for spatiotemporal prediction in cellular networks was presented. It was shown
that the proposed model, which included an autoencoder-based deep network for
spatial modeling and long short-term memory network (LSTM) for temporal
modeling, significantly improved prediction accuracy when compared to two
commonly used baseline methods, namely autoregressive integrated moving
average, and support vector regression. Channel prediction using LSTMs and
autoregressive methods was also applied to vehicular measurements in [6].
Unlike in [5], where it was observed that ‘learning more’ (i.e., increasing
the number of stacked layers and hidden units in each layer) helped improve
prediction performance, it was found in [6] that LSTMs with just a small
number of hidden units performed better when compared to increasing the number
of hidden units in each layer. Reference [6] only compared a single deep
learning model with a single baseline model.

An initial study on channel prediction in body area networks (BANs) was
carried out in [7]. It was shown that an LSTM based framework performed better
on BAN measurements when compared with existing approaches such as moving
average and adaptive prediction. However, these studies did not include
comprehensive experiments using real data from a mobile device. Wireless
channel quality prediction was also studied in [8] where an encoder-decoder
based sequence-to-sequence deep learning model was used, and its performance
was compared with linear regression for multiple networks and communication
standards. It was observed that sequence lengths of size 20 captured most of
the useful information in the data, and sequences of greater lengths did not
improve prediction performance.

Concerning D2D communications, reference [9] focused on deep learning
approaches for content caching in cache-enabled D2D networks. Two recurrent
neural network approaches, namely echo state networks and LSTMs, were employed
to predict users’ mobility and content popularity, so as to determine which
content to cache and where to cache. However, these results were not tested on
real-world channel measurements. In [10], a deep learning approach was
proposed to predict D2D channel gains from independent cellular channel gains
in order to solve various problems related to radio resource management. All
predictions were based on the assumption of the channel being Gaussian.

###  I-B Main Contributions

This paper explores AI-based deep learning techniques on D2D links with the
aim at providing potential answers to the following questions concerning the
prediction of the received signal strength variations:

  1. 1.

How effective is the prediction as a function of the coherence time of the
channel?

  2. 2.

What is the minimum number of input samples required for a target prediction
performance?

To address these questions, four deep learning models are explored. These
include dense or feedforward networks (FFNs), convolutional neural networks
(CNNs), gated recurrent units (GRUs), and LSTMs. It is worth mentioning that
CNNs are commonly applied to analyse image data, but they also find
application in predicting time series data [11]. Furthermore, recurrent neural
networks (RNNs) are powerful in discovering the dependency in sequential data.
Specifically, GRUs and LSTMs work well on sequential data with long-term
dependencies [12, 13, 14] due to their internal memory mechanisms.

Accordingly, unlike prior work, we focus on understanding empirically the
relationship between channel coherence time and number of samples used in the
prediction models, as well as the minimum input length required to achieve a
target prediction performance for a given coherence time. To this end, we
compare and validate the prediction performances of the deep learning models
on real-world D2D field measurements conducted for a variety of environments
and scenarios at 5.8 GHz. These include an indoor open office area
environment, an outdoor open space environment, LOS, non-LOS (NLOS) and mobile
scenarios.

The remainder of this paper is organized as follows. Section II describes the
D2D channel measurements conducted at 5.8 GHz. Section III discusses the the
data preprocessing steps applied. Section IV discusses the deep learning
models used for prediction and their implementation details. Section V
presents the experimental results. Lastly, Section VI finishes the paper with
some concluding remarks.

Figure 1: D2D measurements in (a) an indoor open office environment and (b) an
outdoor open space environment showing different locations of person B for the
LOS and NLOS cases.

Figure 2: Small-scale fading variations in (a) Indoor LOS environment (b)
Indoor NLOS environment (c) Outdoor LOS environment and (d) Outdoor NLOS
environment.

##  II D2D Channel Measurements

The wireless channel measurement system used in this study was based on the
ML5805 transceivers, manufactured by RFMD (Qorvo)111https://ir.qorvo.com/news-
releases/news-release-details/rfmdr-releases-industrys-first-58-ghz-ism-band-
transceiver. The transceiver boards were interfaced with a PIC32MX which acted
as a baseband controller and allowed the analog received signal strength (RSS)
to be sampled with a 10-bit quantization depth. A D2D link was formed between
two persons, namely person A (an adult female of height 1.65 m and weight 53
kg) and person B (an adult male of height 1.83 m and weight 73 kg). The user
equipment (UE) positioned on person A acted as the transmitter and was
configured to output a continuous wave signal with a power level of +17.6 dBm
at 5.8 GHz. The UE positioned on person B acted as the receiver and sampled
the channel at a rate of 10 kHz.

The RSS data was downsampled by averaging 10 consecutive samples to improve
the signal to noise ratio (SNR) performance, thus giving an effective sampling
rate of 1 kHz after downsampling. Furthermore, the antennas used by the
transmitter and receivers were +2.3 dBi sleeve dipole antennas (Mobile Mark
model PSKN3-24/55S). The antennas were housed in a compact acrylonitrile
butadiene styrene (ABS) enclosure (107 × 55 × 20 mm). This setup was
representative of the form factor of a smart phone which allowed the user to
hold the device as they normally would to make a voice call. Each antenna was
securely fixed to the inside of the enclosure using a small strip of Velcro®.

The D2D channel measurements were obtained within an indoor open office area
and an outdoor open space environment, as shown in Fig. 1. The indoor open
office was located on the first floor of the Institute of Electronics
Communications and Information Technology (ECIT) building at Queen’s
University Belfast in the United Kingdom. The building mainly consists of
metal studded dry walls with metal tiled floors covered with polypropylene-
fiber, rubber backed carpet tiles, a metal ceiling with mineral fiber tiles
and recessed louvered luminaries suspended 2.7 m above floor level. The office
contained a number of chairs, metal storage spaces, doors and desks
constructed from medium density fibreboard. These desks were vertically
separated by soft wooden partitions. During the measurements, the office area
was unoccupied in order to facilitate pedestrian free D2D channel
measurements. The outdoor D2D measurements were conducted in an outdoor car
parking area adjacent to the ECIT building.

As shown in Fig. 1, during the D2D measurements [15], person A and B held
their UE at their left-ears to imitate making a voice call. For the LOS D2D
measurements, person B was positioned directly in front of person A whilst for
the NLOS D2D measurements, person B was positioned around an adjacent corner.
It is worth noting that both test subjects were initially stationary after
which they were instructed to walk around randomly within a circle of radius
0.5 m from their starting points. For the LOS D2D measurements in both
environments, while there may have been a direct LOS between the two person’s
bodies during the trials, in actual fact, the link between the hypothetical
UEs would have been subject to quasi-LOS conditions due to the random
movements undertaken. For the NLOS case, person B was always positioned around
an adjacent corner to ensure that the NLOS conditions (i.e. no direct signal
path between persons A and B) were maintained irrespective of the random
movements.

##  III Data Preprocessing

Once the RSS measurements were obtained, the small-scale fading data was
extracted for analysis. Specifically, the large-scale fading component was
removed by applying a low-pass filter to the raw RSS data in linear scale. To
determine the window size for extraction of the local mean signal, the raw
data was visually inspected and overlaid with the local mean signal for
differing window sizes. A smoothing window of 50 samples was then used. Fig. 2
shows the small-scale fading variations for a 4 s window observed in the
indoor LOS, indoor NLOS, outdoor LOS and outdoor NLOS environments,
respectively. The overall measurement data set consisted of approximately
62300 samples, equivalently 62.3 s length in time. This included the
measurement data for all scenarios.

Data scaling was then applied to transfer the data into ranges and forms that
are appropriate for modeling. It is well known that models trained on scaled
data perform significantly better when compared to models trained on unscaled
data [16]. As well as this, the gradient descent converges much faster with
scaled data than without it [17]. In this paper, the data sets were scaled
using min-max normalisation (which performs a linear transformation on the
original data) [18] before being input to the model for training. Let
$x_{min}$, and $x_{max}$ be the minimum and maximum values for attribute $X$.
Min–max normalization maps a value $v$ of $X$ to $\acute{v}$ in the range
[${\rm{new}}~{}x_{min}$, ${\rm{new}}~{}x_{max}$] using (1), as follows:

$\acute{v}\\!=\frac{v-x_{min}}{x_{max}-x_{min}}\left({\rm{new}}~{}{x_{max}}-{\rm{new}}~{}{x_{min}}\right)+{\rm{new}}~{}{x_{min}}.$
(1)

Note that the normalization output was customised to be in the range [-1, 1]
by rewriting (1), as follows

$\acute{v}=2\frac{v-x_{min}}{x_{max}-x_{min}}-1.$ (2)

##  IV Methodology

This work focuses on a univariate time series forecasting problem. Here, data
sets comprised of only a single variable are observed at each time step, and a
model is used to exploit the values seen at prior time steps to predict the
subsequent time step values. A sliding window222Is a statistical method in
which a window of specified length moves over the data, sample by sample, and
the statistic is computed over the data in the window. approach is adopted to
restructure the time series data as a supervised learning
problem.333Supervised learning is the most popular way of framing problems for
machine learning as a collection of observations with inputs and outputs.
Thus, the models here make a set of predictions based on a window of
consecutive samples from the data sets.

This section first discusses how the prediction problem in this paper is
framed in a supervised learning manner through data windowing. Then, the
baseline and deep learning models used here are explained. Following this,
their implementation details are presented.

###  IV-A Data Windowing

Data windowing of the models is represented in Fig. 3. The input size, also
called as the input width, is the number of time steps considered by the
window as an input, and is denoted by $T_{x}$. The number of output steps to
be predicted, also called as the horizon, is represented as $T_{y}$.

Linear and feedforward flatten the input data as a vector to convey the
previous time steps with size $T_{x}$. The main drawback of this approach is
that the resulting model can only be executed on input windows of exactly the
same shape. The CNN model also takes multiple time steps as input to produce
one-shot $T_{y}$ out steps predictions. However, different than feedforward
networks, CNNs can be run on inputs of any length, and the predictions are
based on a fixed-width history controlled by their kernel sizes. This might
result in better performance

Figure 3: Input-output relationship in (a) Linear and Feedforward models (b)
CNN model with kernel size of 3 and (c) LSTM and GRU models.

since it can see how things are changing over time. Recurrent neural networks
such as LSTMs and GRUs are intrinsically well-suited to process sequential
data. This is done by maintaining an internal state from time step to time
step. At each time step an input size of $T_{x}$ is fed into the model
producing $T_{y}$ output steps as predictions. For the next time step, the
data window is shifted by $T_{y}$ samples.

###  IV-B Linear Regression Baseline Model

This model assumes that the relationship between the independent variables (or
features) $\boldsymbol{x}$ and the dependent variable $y$ is linear i.e., $y$
can be expressed as a weighted sum of the elements in $\boldsymbol{x}$, given
some noise on the observations. It should be noted that the baseline model
here refers to a univariate linear regression model.

Assuming that the inputs consist of $T_{x}$ features, the prediction
${\hat{y}}$ is expressed as

${\hat{y}}={w_{1}}{x_{1}}+\dots+{w_{T_{x}}}{x_{T_{x}}}+b$ (3)

where $w_{1},\dots,w_{T_{x}}$ are called weights, and $b$ is called a bias
(also called an offset or intercept). The weights determine the influence of
each feature on the prediction, and the bias indicates the value that the
prediction should take when all of the features take value 0. Models whose
output prediction is determined by the affine transformation of input features
are linear models, where the affine transformation is specified by the chosen
weights and bias [19]. Now collecting all features into a vector
$\boldsymbol{x}\in{\mathbb{R}}^{T_{x}}$ and all weights into a vector
$\boldsymbol{w}\in{\mathbb{R}}^{T_{x}}$, the model in (3) can be expressed as
[19, eq. 3.1.3],

${\hat{y}}={\boldsymbol{w}^{\top}}{\boldsymbol{x}}+b.$ (4)

Here, the vector $\boldsymbol{x}$ corresponds to features of a single data
example and $(\cdot)^{\top}$ is the vector transpose. For a collection of
features fed into the model in a batch size444It is the number of samples
processed before the model is updated. of $N$,
$\boldsymbol{X}\in{\mathbb{R}}^{N\times T_{x}}$ and
$\boldsymbol{w}\in\mathbb{R}^{T_{x}\times T_{y}}$, the predictions
${\boldsymbol{\hat{y}}}\in{\mathbb{R}}^{N\times T_{y}}$, can be expressed via
the matrix-vector product [19, eq. 3.1.4]

${\boldsymbol{\hat{{y}}}}={\boldsymbol{{X}}}{\boldsymbol{{w}}}+\boldsymbol{b}.$
(5)

with $\boldsymbol{b}\in\mathbb{R}^{1\times T_{y}}$.

Figure 4: Dense/feed-forward network with one hidden layer with $h$ hidden
units.

###  IV-C Feedforward Network

These networks are also known as dense networks, and are capable of handling a
more general class of functions by incorporating one or more hidden layers.
These layers create non-linear representations of the data and are able to
capture complex interactions among the input. The final (output) layer is
usually a linear predictor.

The network layers are connected in a fully connected manner, meaning that
every input influences every neuron in the hidden layer, and each of these
influence every neuron in the output layer. A dense network with one hidden
layer is illustrated in Fig. 4. The inputs
$\boldsymbol{X}\in\mathbb{R}^{N\times T_{x}}$ are being fed into the model in
a batch size of $N$ training instances where each instance has $T_{x}$ inputs.
Considering one hidden layer network whose hidden layer has $h$ hidden units,
the hidden representation, $\boldsymbol{H}\in\mathbb{R}^{N\times h}$, and the
network output, $\boldsymbol{Y}\in\mathbb{R}^{N\times T_{y}}$, are given as
[19, eq. 4.1.3]

${\boldsymbol{H}}={g\left(\boldsymbol{X}\boldsymbol{W}^{(1)}+\boldsymbol{b}^{(1)}\right)}$
(6)

and

${\boldsymbol{Y}}={\boldsymbol{H}\boldsymbol{W}^{(2)}+\boldsymbol{b}^{(2)}},$
(7)

respectively. The weights and biases of the hidden layer are
$\boldsymbol{W}^{(1)}\in\mathbb{R}^{T_{x}\times h}$ and
$\boldsymbol{b}^{(1)}\in\mathbb{R}^{1\times h}$, respectively, whereas the
weights and biases of the output layer are
$\boldsymbol{W}^{(2)}\in\mathbb{R}^{h\times T_{y}}$ and
$\boldsymbol{b}^{(2)}\in\mathbb{R}^{1\times T_{y}}$, respectively. Finally,
the activation function $g(\cdot)$ is responsible for introducing non-
linearity in the model. In this work, we adopt rectified linear units (ReLU),
$g(x)=\max\\{0,x\\}$, as the hidden layer activations.

###  IV-D Long Short-Term Memory Network

The LSTM network is a type of RNN that is well known for its time series
prediction capabilities. In a standard RNN, the nodes i.e., the building
blocks of a neural network architecture are composed of basic activation
functions such as tanh and sigmoid. As indicated in [11], because RNN weights
are learned by backpropagating errors through the network, the use of these
activation functions can cause RNNs to suffer from the vanishing gradient
problem that causes the gradient to have either infinitesimally low or high
values. This affects a recurrent neural network’s ability to learn long-term
dependencies [20]. The LSTM network is able to partially overcome the
vanishing gradient problem by creating paths through time that have
derivatives that neither vanish nor explode [11] by incorporating the ability
to forget.

Figure 5: Block diagram of the LSTM cell.

As explained in [11], LSTM recurrent networks have LSTM cells, which includes
a memory cell (or cell for short), designed to record additional information
(which allows it to handle long-term dependencies). Each cell has the same
inputs and outputs as an ordinary recurrent network, and also has more
parameters and a system of three gating units that controls the flow of
information, namely the output gate, input gate, and forget gate. These gates
were specifically designed inspired by logic gates of a computer. The output
gate reads out the entries from the cell. The input gate decides when to read
data into the cell. Lastly, the forget gate represents a mechanism for
resetting the cell’s content. The main motivation of this gating design is to
be able to decide when to remember and when to ignore inputs in the hidden
state. Fig. 5 shows the block diagram of a single LSTM cell which has an
internal recurrence (a self-loop), in addition to the outer recurrence of the
RNN. The most important component is the memory cell state unit
${\boldsymbol{c}^{(t)}\in\mathbb{R}^{N\times h}}$ that captures the internal
state of the LSTM cell and has a linear self-loop given by [19, eq. 9.2.3]

${\boldsymbol{c}^{(t)}}={\boldsymbol{f}^{(t)}}\odot{\boldsymbol{c}^{(t-1)}}+{\boldsymbol{i}^{(t)}}\odot{\boldsymbol{\tilde{c}}^{(t)}},$
(8)

where $\odot$ is the Hadamard (elementwise) product operator.

The memory cell is updated by partially forgetting the existing memory and
adding a new memory content. This candidate memory cell
${\boldsymbol{\tilde{c}}^{(t)}\in\mathbb{R}^{N\times h}}$ represents the
degree to which the new memory content is added to the memory cell and is
modulated by the input gate ${\boldsymbol{i}^{(t)}\in\mathbb{R}^{N\times h}}$.
The new memory content is given as [19, eq. 9.2.2]

${\boldsymbol{\tilde{c}}^{(t)}}={\rm{tanh}}\\!\left(\\!{\boldsymbol{x}^{(t)}}{\boldsymbol{W}}_{xc}+\\!{\boldsymbol{h}^{(t-1)}}{\boldsymbol{W}_{hc}}\\!+\\!{\boldsymbol{b}_{c}}\\!\right),$
(9)

where ${\boldsymbol{W}_{xc}}\in\mathbb{R}^{T_{x}\times h}$ and
${\boldsymbol{W}_{hc}}\in\mathbb{R}^{T_{x}\times h}$ are input weight
parameters and recurrent weights with respect to the cell gate, respectively,
and ${\boldsymbol{b}_{c}}\in\mathbb{R}^{1\times h}$ is a bias parameter. The
batch size is denoted by $N$, $T_{x}$ is the number of inputs,
$\boldsymbol{x^{(t)}}\in\mathbb{R}^{N\times T_{x}}$ is the current input
vector and $\boldsymbol{h^{(t)}}\in\mathbb{R}^{N\times h}$ is the current
hidden layer vector with $h$ hidden units containing the outputs of all the
LSTM cells. The self-loop weight is controlled by a forget gate unit
${\boldsymbol{f}^{(t)}\in\mathbb{R}^{N\times h}}$ (for time step $t$), that
sets this weight to a value between 0 and 1 via a sigmoid unit. It is
expressed as [19, eq. 9.2.1]

${\boldsymbol{f}^{(t)}}=\sigma\\!\left(\\!{\boldsymbol{x}^{(t)}}{\boldsymbol{W}_{xf}}+\\!{\boldsymbol{h}^{(t-1)}}{\boldsymbol{W}_{hf}}\\!+\\!{\boldsymbol{b}_{f}}\\!\right).$
(10)

The biases, input weights and recurrent weights for the forget gates are
denoted by ${\boldsymbol{b}_{f}}\in\mathbb{R}^{1\times h}$,
${\boldsymbol{W}_{xf}\in\mathbb{R}^{T_{x}\times h}}$, and
${\boldsymbol{W}_{hf}\in\mathbb{R}^{h\times h}}$, respectively.

The external input gate unit ${\boldsymbol{i}^{(t)}\in\mathbb{R}^{N\times h}}$
is computed similar to the forget gate and is expressed as [19, eq. 9.2.1]

${\boldsymbol{i}^{(t)}}=\sigma\\!\left(\\!{\boldsymbol{x}^{(t)}}{\boldsymbol{W}_{xi}}+\\!{\boldsymbol{h}^{(t-1)}}{\boldsymbol{W}_{hi}}\\!+\\!{\boldsymbol{b}_{i}}\\!\right),$
(11)

with ${\boldsymbol{W}_{xi}}\in\mathbb{R}^{T_{x}\times h}$ being the input
weights, ${\boldsymbol{W}_{hi}}\in\mathbb{R}^{h\times h}$ the recurrent
weights, and ${\boldsymbol{b}_{i}}\in\mathbb{R}^{1\times h}$ the bias for the
input gate. The output ${\boldsymbol{h}^{(t)}\in\mathbb{R}^{N\times h}}$ of
the LSTM cell, also called hidden state, and the output gate
${\boldsymbol{o}^{(t)}\in\mathbb{R}^{N\times h}}$, are expressed as [19, eq.
9.2.4 and 9.2.1],

${\boldsymbol{h}^{(t)}}={\rm{tanh}}\left({\boldsymbol{c}^{(t)}}\right)\odot{\boldsymbol{o}^{(t)}}$
(12)

and

${\boldsymbol{o}^{(t)}}=\sigma\\!\left(\\!{\boldsymbol{x}^{(t)}}{\boldsymbol{W}_{xo}}+\\!{\boldsymbol{h}^{(t-1)}}{\boldsymbol{W}_{ho}}\\!+\\!{\boldsymbol{b}_{o}}\\!\right),$
(13)

respectively. Again, the input weights, recurrent weights, and bias for the
output gate are respectively denoted as
${\boldsymbol{W}_{xo,}}\in\mathbb{R}^{T_{x}\times h}$,
${\boldsymbol{W}_{ho,}}\in\mathbb{R}^{h\times h}$, and
${\boldsymbol{b}_{o}}\in\mathbb{R}^{1\times h}$. The hidden state vector is
simply a gated version of the hyperbolic tangent of the memory cell. This
ensures that ${\boldsymbol{h}^{(t)}}$ is always between -1 and 1. Whenever the
output gate approximates to 1, all information is effectively passed from
memory to the predictor, while for the output gate close to 0, all the
information is retained within the memory cell and no further processing is
performed.

###  IV-E Gated Recurrent Unit

GRUs are a newer generation of RNNs and work similar to LSTMs. Both have a
dedicated mechanism composed by gating units to decide when to memorize and
when to ignore inputs in the hidden state [13]. The key difference is that
GRUs have only two gates that control the flow of information, namely the
reset gate, and update gate. Furthermore, the cell state (memory unit) is not
part of its gating unit, and uses only the hidden state
${\boldsymbol{h}^{(t)}\in\mathbb{R}^{N\times h}}$ to transfer information.

Figure 6: Block diagram of the GRU model.

The core functionality of GRUs rely on a single gating unit simultaneously
controlling the forgetting factor and the decision to update the state unit.
This update is expressed as [11, eq. 10.45]

${\boldsymbol{h}^{(t)}}={\boldsymbol{u}^{(t)}}\odot{\boldsymbol{h}^{(t-1)}}+{(1-\boldsymbol{u}^{(t)})}\odot{\boldsymbol{\tilde{h}}^{(t)}}.$
(14)

The update gate ${\boldsymbol{u}^{(t)}\in\mathbb{R}^{N\times h}}$ and the
reset gate ${\boldsymbol{r}^{(t)}\in\mathbb{R}^{N\times h}}$ are expressed as
[19, eq. 9.1.1],

${\boldsymbol{u}^{(t)}}=\sigma\\!\left(\\!{\boldsymbol{x}^{(t)}}{\boldsymbol{W}}_{xu}+\\!{\boldsymbol{h}^{(t-1)}}{\boldsymbol{W}}_{hu}+\\!\boldsymbol{b}^{u}\right)$
(15)

and

${\boldsymbol{r}^{(t)}}=\sigma\\!\left(\\!{\boldsymbol{x}^{(t)}}{\boldsymbol{W}}_{xr}+\\!{\boldsymbol{h}^{(t-1)}}{\boldsymbol{W}}_{hr}+\\!\boldsymbol{b}^{r}\right)$
(16)

respectively, where
${\boldsymbol{W}_{xu}},{\boldsymbol{W}_{xr}}\in\mathbb{R}^{T_{x}\times h}$ and
${\boldsymbol{W}_{hu}},{\boldsymbol{W}_{hr}}\in\mathbb{R}^{h\times h}$ are
weight parameters and
${\boldsymbol{b}^{u}},{\boldsymbol{b}^{r}}\in\mathbb{R}^{1\times h}$ are
biases. The current input vector is
$\boldsymbol{x^{(t)}}\in\mathbb{R}^{N\times T_{x}}$ with batch size of $N$ and
input size $T_{x}$. The current hidden layer containing the GRU outputs is
denoted as $\boldsymbol{h^{(t)}}\in\mathbb{R}^{N\times h}$ with $h$ hidden
units.

The candidate hidden state $\boldsymbol{\tilde{h}}^{(t)}\in\mathbb{R}^{N\times
h}$ at time step $t$ is given as [19, eq. 9.1.2]

${\boldsymbol{\tilde{h}}^{(t)}}={\rm{tanh}}\left({\boldsymbol{x}^{(t)}}{\boldsymbol{W}_{xh}}+{(\boldsymbol{r}^{(t)}\odot\boldsymbol{h}^{(t-1)})\boldsymbol{W}_{hh}}\\!+\boldsymbol{b}^{h}\right),$
(17)

with ${\boldsymbol{W}_{xh}}\in\mathbb{R}^{T_{x}\times h}$,
${\boldsymbol{W}_{hh}}\in\mathbb{R}^{h\times h}$ denoting weight parameters
and ${\boldsymbol{b}^{h}}\in\mathbb{R}^{1\times h}$ bias.

###  IV-F Convolutional Neural Network

The name convolutional neural network indicates that the network employs a
mathematical operation called convolution, which is a specialised kind of
linear operation. CNNs exploit spatial locality by enforcing a local
connectivity pattern between neurons of adjacent layers. As well as this, the
convolution of the input with a set of filters (called kernels) is used as the
main operation in at least one of its layers. A convolution of a general time
series with a kernel of size 5 is shown in Fig. 7. Each kernel convolves with
the input producing a representation of the input as an output (this is
illustrated as a dashed line in Fig. 7). These representations are then
flattened and fed into a feedforward network with one hidden layer with
$T_{y}$ hidden units, producing the outputs.

The discrete convolution of an input $x$ with a kernel $w$ results in the
output $y$, given by [11, eq. 9.3]

${y\left(t\right)}=\left(x*w\right)(t)=\sum_{a=-\infty}^{\infty}{x\left(a\right)}{w\left(t-a\right)},$
(18)

where $*$ represents the convolutional operator, $t$ is the time index, and
$x$ and $w$ are defined only on integer $t$.

Unlike GRUs and LSTMs, CNNs are not a type of RNN due to the lack of self-loop
mechanisms. Instead, CNNs are well established in the literature and industry
as an efficient feature extractor, leading to important progress in computer
vision and related tasks [21, 22, 23].

Figure 7: Convolution of a time series with a kernel of size 5 producing a
representation of the input (dashed line). Here, the solid line indicates the
analysed time series and the arrow indicates the direction in which the kernel
is being convolved with the signal.

It is worth highlighting that although CNNs are not RNNs they are known for
processing data that have grid-like topology. In particular, one-dimensional
convolutional neural networks (1DCNN) are efficient in processing information
present in one-dimensional data, such as time series [11]. The benefit of
using 1DCNNs for sequence classification is that they can learn directly from
the raw time series data and do not require domain experience to manually
design input characteristics.

###  IV-G Implementation Details

The models used in this paper were built using Ubuntu 20.04.2 LTS and
Tensorflow®555https://www.tensorflow.org/ 2.5. The data was split into three
independent sets, namely training (70%), validation (20%) and test sets (10%).
The models were trained and tested in parallel on three computing systems
which include:

  1. 1.

a 9th Generation Intel® CoreTM i7-9750H consisting of 6 cores, 16 GB RAM, 512
GB solid state hard drive and an NVIDIA® GeForce® GTX 1650 4 GB GDDR5 GPU,

  2. 2.

a 10th Generation Intel® CoreTM i9-10885H consisting of 8 cores, 64 GB RAM, 1
TB solid state hard drive and an NVIDIA® GeForce® GTX 1650 Ti 4 GB GDDR6 GPU
and

  3. 3.

a 10th generation Intel® CoreTM i9-10900KF consisting of 10 cores, 64 GB RAM,
2 TB solid state hard drive and an NVIDIA® GeForce® RTX 2080 Ti 11 GB GDDR6
GPU.

TABLE I: Parameter space investigated for the deep learning models.

| FFN | 1DCNN | GRU | LSTM
---|---|---|---|---
Kernels/hidden units | 8 - 256 | 1 - 500 | 1 - 500 | 1 - 500
Layers | 1-2 | 1-2 | 1-2 | 1-2
Input lengths | 1, 4, 8, 11, 14, 17, 23, 25, 35, 50, 75, 100

TABLE II: Predicted output sequence lengths for D2D measurements in different
environments and conditions.

Time Correlation Function | Indoor LOS | Indoor NLOS | Outdoor LOS | Outdoor NLOS
---|---|---|---|---
| Coherence
---
time (s)
| Output sequence
---
length (samples)
| Coherence
---
time (s)
| Output sequence
---
length (samples)
| Coherence
---
time (s)
| Output sequence
---
length (samples)
| Coherence
---
time (s)
| Output sequence
---
length (samples)
| 0.1
---
0.3
0.5
0.7
0.9
| 0.017
---
0.014
0.011
0.008
0.004
| 17
---
14
11
8
4
| 0.018
---
0.015
0.012
0.008
0.004
| 18
---
15
12
8
4
| 0.023
---
0.019
0.014
0.010
0.005
| 23
---
19
14
10
5
| 0.016
---
0.014
0.011
0.008
0.004
| 16
---
14
11
8
4

Each of the models mentioned in the previous subsections were trained by
optimizing a mean square error (MSE) objective function. The Adam [24]
optimization algorithm was used as an adaptive learning rate method with a
step size of 0.001. Depending on the configuration of the parameters and
computer used, training the deep learning models (i.e., a single experiment)
took a maximum of 1 hour whilst the testing phase of the model took only a few
minutes. Furthermore, due to the high computational requirement of the deep
learning models, the parameter space was extensively investigated over a few
months before empirically666It is worth highlighting that determining the
optimal parameter values theoretically for a particular data set is still an
open research question. Hence, for the work carried out here, the parameters
were determined empirically [8]. deciding upon the optimal parameters of the
model. Table I provides the parameter space explored for the deep learning
models on which the predictions here are based. A batch size of 32 was chosen
as no significant improvements were noticed when the batch size was increased
from 32 to 64. A dropout size of 0.3 was chosen to reduce overfitting of the
model to the training data, and the models were trained for 150 epochs.777The
number of epochs is the number of complete passes through the training data
set. Assume that a data set has $x$ number of samples (rows of data), a batch
size of $y$ and $z$ epochs. This means that the data set will be divided into
$x/y$ batches, each with $y$ samples. The model weights will be updated after
each batch of $y$ samples. This also means that one epoch will involve $x/y$
batches or $x/y$ updates to the model. With $z$ epochs, the model will be
exposed to or pass through the whole data set $z$ times i.e., a total of
$x/y\times z$ batches during the entire training process.,888In this study,
there was no significant improvement in the performance noticed when the
number of epochs was raised above 150. Besides dropout, early stopping with
patience of 15 epochs was used to regularize the models.

As shown in Table II, for each of the D2D data sets the output lengths to be
predicted were varied between 4 and 23 samples depending on the coherence time
of the channel and time correlation function. According to [25], the coherence
time is defined as the time over which the time correlation function is above
0.5. However, in this study the time correlation function was varied from 0.1
to 0.9 to obtain a range of output lengths for prediction, and to evaluate the
prediction performance of the models. For instance, for the indoor LOS
measurements when the time correlation function is 0.5, the coherence time of
the channel was found to be 11 ms. Since each sample is equal to 1 ms, the
corresponding output length is computed to be 11 samples. In the experiments
conducted here (at both training and test times), single shot predictions were
made where the model predicted out steps time steps in the future, given RSS
measurement samples of length between 1 and 100.

##  V Experimental Analysis and Results

This section discusses the main metrics used for evaluation in this study, the
experiments performed on each of the D2D data sets to determine the model and
parameters that provide the best prediction performance, and the results.

The main metrics used for evaluation in this study include the mean absolute
error (MAE) and root mean squared error (RMSE). MAE measures the average
magnitude of the errors in a set of predictions without considering their
direction. It is the average over the test sample of the absolute differences
between prediction and actual observation where all individual differences
have equal weight. RMSE also measures the average magnitude of the error. It
is the square root of the average of squared differences between prediction
and actual observation. Since the errors are squared before they are averaged,
the RMSE gives a relatively high weight to large errors. This means that the
RMSE should be more useful when large errors are particularly undesirable.
Both MAE and RMSE express average model prediction error in units of the
variable of interest. They are negatively-oriented scores, which means lower
values are better. Let $y_{mn}$ be the $m$th test sample for the $n$th
prediction step where $n\in\left[1,z\right]$ and $z$ is the total number of
prediction steps. Let ${\hat{y}}_{mn}$ be the predicted value of $y_{mn}$.
Then, the RMSE and MAE are given by (19) and (20) as follows:

${\rm{RMSE}}_{n}=\sqrt{\frac{{\sum_{m=1}^{i}\left({\hat{y}}_{mn}-y_{mn}\right)}^{2}}{i}}$
(19)

${\rm{MAE}}_{n}={\frac{{\sum_{m=1}^{i}\left|{\hat{y}}_{mn}-y_{mn}\right|}}{i}}$
(20)

where $i$ is the number of test samples.

Figure 8: Comparison of MAEs and RMSEs of the deep learning models with each
other and linear regression for varying input lengths in indoor LOS and NLOS
environments. Here, (a), (b), (c) and (d) are obtained for an indoor LOS
environment for output lengths 8, 11, 14 and 17, respectively, whilst (e),
(f), (g) and (h) are obtained for an indoor NLOS environment for output
lengths 8, 12, 15 and 18, respectively.  Figure 9: Comparison of MAEs and
RMSEs of the deep learning models with each other and linear regression for
varying input lengths in outdoor LOS and NLOS environments. Here, (a), (b),
(c) and (d) are obtained for an outdoor LOS environment for output lengths 10,
14, 19 and 23, respectively, whilst (e), (f), (g) and (h) are obtained for an
outdoor NLOS environment for output lengths 8, 11, 14 and 16, respectively.
Figure 10: Comparing the RMSEs of all deep learning and baseline models, for
varying input lengths, for single and multiple LSTM, GRU, 1DCNN and FFN layers
in D2D indoor and outdoor LOS environments. Here, (a), (b) and (c) were
obtained for an indoor LOS environment for output prediction lengths of 11, 14
and 17 samples, whilst (d), (e) and (f) were obtained for an outdoor LOS
environment for output prediction lengths of 14, 19 and 23 samples,
respectively.

Recall that for each data set, the model parameters were tuned by varying the
number of stacked layers and hidden units/ kernels in each layer as indicated
in Table I. Following extensive experimentation on the parameter space, in
general, it was observed that a single LSTM, GRU and FFN layer with 25 hidden
units, and a single 1DCNN layer with 128 kernels and kernel size of 5,
provided the best prediction performance across all environments and
scenarios. Increasing the number of hidden units to more than 25, and the
number of kernels to beyond 128, significantly increased the time taken to
train the networks without providing any substantial performance improvements.
Likewise, when the number of layers were increased to two, in general, the
best prediction performances were obtained when the number of hidden units in
each layer for the FFNs were 5; 25 for GRUs and LSTMs; and 64 kernels for
1DCNNs.

Once the number of hidden units and kernels for the deep learning models were
chosen, their MAEs and RMSEs were compared with each other and the linear
regression baseline model for varying input and output lengths, for single and
multiple layers, across different D2D environments and scenarios. These
results are discussed in detail next.

Figure 11: Comparing the MAEs of all deep learning and baseline models, for
varying input lengths, for single and multiple LSTM, GRU, 1DCNN and FFN layers
in D2D indoor and outdoor LOS environments. Here, (a), (b) and (c) were
obtained for an indoor LOS environment to predict output lengths of 11, 14 and
17 samples, whilst (d), (e) and (f) were obtained for an outdoor LOS
environment to predict output lengths of 14, 19 and 23 samples, respectively.

###  V-A Comparing Errors vs Input Lengths

Figure 12: Comparing the prediction errors for all deep learning and baseline
models, for the optimal number of hidden units/kernels, for different output
time steps across all D2D environments and scenarios. The plots have been
obtained for a single LSTM, GRU, 1DCNN and FFN layer when the input length was
25 samples. RMSE results are shown for (a) indoor LOS, (b) indoor NLOS, (c)
outdoor LOS and (d) outdoor NLOS. MAE results are presented for (e) indoor
LOS, (f) indoor NLOS, (g) outdoor LOS, and (h) outdoor NLOS.

Figs. 8 and 9 compare the RMSEs and MAEs of the deep learning models with each
other, and linear regression999Linear regression is a statistical model that
fits the best line to the input data. Similar to the deep neural networks, the
baseline also considers a history of 1 - 100 samples to predict the required
out steps time steps in the future., for a range of input lengths. Figs. 8
(a), (b), (c) and (d) were obtained for an indoor LOS environment for output
lengths 8, 11, 14 and 17, respectively, whilst Figs. 8 (d), (e), (f) and (g)
were obtained for an indoor NLOS environment for output lengths 8, 12, 15 and
18, respectively. Likewise, Figs. 9 (a), (b), (c) and (d) were obtained for an
outdoor LOS environment for output lengths 10, 14, 19 and 23, respectively,
whilst Figs. 9 (d), (e), (f) and (g) were obtained for an outdoor NLOS
environment for output lengths 8, 11, 14 and 16, respectively.

Interestingly, it is observed that a fine-tuned GRU performs very similar to
the LSTM. GRUs control the flow of information in essentially the same way as
LSTMs. The difference is that LSTMs use a specifically designed memory cell to
capture the long-term dependencies in sequences whilst the GRUs use the update
gate. Furthermore, these models outperformed FFNs and 1DCNNs for all measured
data sets in this study. This points to the importance of accounting for long-
term temporal dependencies for channel prediction, which FFNs and 1DCNNs are
unable to capture. It is also seen that GRUs and LSTMs significantly
outperform linear regression in all environments and scenarios. The basic idea
behind linear regression is to provide a model which can observe linear trends
in the data. It is possible that this baseline model did not perform well here
because: 1) the D2D data sets in this paper are composed of real-world
measurements, possibly with nonlinearities introduced due to factors such as
the presence of obstacles in the environment, and the direction in which the
receiver moved as a result of the random movement undertaken; 2) it very
closely follows the trend captured by the previous value, which predicted
values may not necessarily follow.

###  V-B Recommendations on Input Length for Coherence Time Prediction

From Figs. 8 and 9 it is possible to see how little input a model requires to
achieve a target prediction performance. For instance, to predict 17 and 23
samples into the future, corresponding to coherence times of 17 and 23 ms in
indoor and outdoor LOS environments, respectively, an input length of 25
samples is recommended. Likewise, to predict 17 and 18 samples into the
future, corresponding to coherence times of 17 and 18 ms in indoor and outdoor
NLOS environments, respectively, input lengths of 25 and 75 samples are
recommended. Thus, through these figures, the interested reader can obtain
information on the minimum input length required to achieve a target
prediction performance for their chosen coherence time given the environments
being considered are similar to the ones presented in this work. It is also
worth highlighting that in most cases, a short input length of around 25
samples was found to achieve similar prediction performance when compared to
larger input lengths of 100 samples. Thus, indicating that large input lengths
(i.e., knowledge of a large number of past values) may not be always be
beneficial. This is intuitive because samples further in the past than the
coherence time of the channel are uncorrelated and therefore are less likely
to carry as much useful information.

###  V-C Comparing Errors vs Input Lengths for Multiple Layers’ Case

Observations discussed in the above two subsections for the single layers case
also hold when the number of stacked layers is increased to two as
demonstrated through Figs. 10 and 11. Fig. 10 shows the RMSEs of the deep
learning and baseline models vs varying input lengths for single and multiple
layers case, whilst Fig. 11 shows the MAEs of the deep learning and baseline
models vs varying input lengths for single and multiple layers case.
Furthermore, it can be seen that, just a single LSTM or GRU layer provides
good prediction performance and increasing the number of stacked layers will
increase the training times without providing any considerable performance
benefits.

###  V-D Comparing Errors vs Output Lengths

Fig. 12 compares the prediction errors for all deep learning and baseline
models for different output lengths, across all D2D environments and
scenarios. These plots have been obtained for a single LSTM, GRU, FFN and
1DCNN layer when the input length was 25 samples, number of hidden units = 25
and number of kernels = 128. As before, it can be seen that LSTMs and GRUs
perform comparably across all environments and scenarios. Furthermore, these
models significantly outperform FFNs, 1DCNNs and linear regression for all of
the D2D data sets considered here. It is also seen that the prediction errors
associated with the outdoor LOS scenario were the lowest. This could be
because of: 1) the overall low fluctuations in the small scale fading data
observed here when compared to the indoor LOS, NLOS and outdoor NLOS cases
(see Fig. 2), which means that the model has less difficulty making
predictions, and 2) the fades observed here are not as deep when compared to
the indoor LOS, NLOS and outdoor NLOS cases, again making it easier for the
models to predict.

###  V-E Qualitative Comparison

Fig. 13 shows a qualitative comparison between the actual and prediction
results for linear regression, FFN, 1DCNN, GRU and LSTM models. This figure
has been obtained for the outdoor LOS environment and illustrates an input
time-frame of 25 ms to predict 14 ms (or 14 samples) in the future. The number
of hidden units is equal to 25 whilst the number of kernels is equal to 128.
As indicated previously, the linear regression model is only able to capture a
low-dimensional slice of the behavior (i.e., it very closely follows the trend
captured by the previous value) resulting in poor prediction performance. GRUs
and LSTMs perform the best whilst FFNs and 1DCNNs are the worst performing
deep learning models for the given data sets.

Figure 13: Comparison of real and predicted values for outdoor LOS D2D measurements. Here, the output sequence length predicted = 14 samples, input sequence length = 25 samples, number of hidden units = 25 whilst the number of kernels = 128. Min-max normalisation has been applied to the data. TABLE III: Training times of LSTMs and GRUs for the indoor los and outdoor nlos D2D measurements when the input length is 25 samples. Environment | Indoor LOS | Outdoor NLOS
---|---|---
Model | LSTM | GRU | LSTM | GRU
Output (samples) | 17 | 16
Training time (sec) | 121 | 154 | 104 | 90
Output (samples) | 14 | 14
Training time (sec) | 121 | 153 | 123 | 101
Output (samples) | 11 | 11
Training time (sec) | 121 | 151 | 124 | 112
Output (samples) | 8 | 8
Training time (sec) | 134 | 149 | 90 | 115
Output (samples) | 4 | 4
Training time (sec) | 114 | 153 | 111 | 66

###  V-F Time Profiling

Profiling is a way to measure how the models behave in relation to the
resources (time and/or memory) they use. It is well known that deep learning
models are typically computationally expensive. Thus, quantifying the resource
consumption of these models can resolve performance bottlenecks and,
ultimately, make them execute faster. In this subsection, we implement time
profiling by comparing the training times of the two best performing deep
learning models here, namely LSTM and GRU. TensorBoard®
101010https://www.tensorflow.org/tensorboard, a visualization toolkit of
TensorFlow® was used to profile and track the performance of the models on the
device. The device used to evaluate the training times is an NVIDIA® GeForce®
GTX 1650 4 GB GDDR5 GPU.

Table III provides the training times of LSTMs and GRUs when the number of
hidden units is 25 in the indoor LOS and outdoor NLOS environments. Here, the
input length was equal to 25 samples. It is interesting to note that no clear
winner was found between LSTMs and GRUs with respect to their training times.
For instance, considering the indoor LOS environment and an output length of
17 samples, it can be seen from Table III that the training time associated
with the LSTMs was found to be 121 s whilst the GRUs was found to be 154 s.
This means that for these parameters in the indoor LOS scenario, the LSTMs
trained 27% faster when compared to the GRUs. Now, considering the outdoor
NLOS environment and an output length of 14 samples, it can be seen from Table
III that the training time associated with the LSTMs was found to be 123 s
whilst the GRUs was found to be 101 s. This means that for these parameters in
the outdoor NLOS scenario, the GRUs trained 22% faster when compared to the
LSTMs. Thus, by investigating the prediction performance and training times,
it was found that for the D2D measurements considered in this paper, both the
GRUs and LSTMs were the best performing models.

##  VI Conclusions

This paper investigated the capabilities of AI-based deep learning models
(LSTM, GRU, FFN and 1DCNN) to predict received signal strength variations in
D2D communications channels. A thorough investigation was performed on the
efficacy of the models to predict different output lengths chosen depending on
the coherence time of the channel and time correlation function. It was found
that, in general, GRUs and LSTMs consisting of a single layer with 25 hidden
units provided the best prediction performance. Training times of the models
were also compared with each other to pick the most suitable model for the D2D
data sets considered here. Interestingly, there was no clear winner found
between the LSTMs and GRUs.

The paper also investigated the minimum input length a model requires to
achieve a target prediction performance. It was found that to predict 17 and
23 ms into the future, corresponding to the coherence times observed in indoor
and outdoor LOS environments, respectively, an input length of 25 ms was
recommended. Likewise, to predict 17 and 18 samples into the future,
corresponding to coherence times of 17 and 18 ms in indoor and outdoor NLOS
environments, respectively, input lengths of 25 and 75 samples were
recommended. This indicates that large input lengths may not always be
necessary as samples further in the past than the coherence time of the
channel are uncorrelated and therefore are less likely to carry as much useful
information.

## References

  * [1] Z. Li, F. Sanchez Moya, F. Gabor, J. M. B. Da Silva Jr., K. Koufos, M. Dohler, and T. Nakamura, _Device-to-device (D2D) communications_. Cambridge University Press, 2016, p. 107–136.
  * [2] S. Obayashi and J. Zander, “A body-shadowing model for indoor radio communication environments,” _IEEE Transactions on Antennas and Propagation_ , vol. 46, no. 6, pp. 920–927, 1998.
  * [3] S. L. Cotton, A. McKernan, A. J. Ali, and W. G. Scanlon, “An experimental study on the impact of human body shadowing in off-body communications channels at 2.45 ghz,” in _Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP)_ , 2011, pp. 3133–3137.
  * [4] S. Cotton, “Human body shadowing in cellular device-to-device communications: Channel modeling using the shadowed fading model,” _Selected Areas in Communications, IEEE Journal on_ , vol. 33, pp. 111–119, 2015.
  * [5] J. Wang, J. Tang, Z. Xu, Y. Wang, G. Xue, X. Zhang, and D. Yang, “Spatiotemporal modeling and prediction in cellular networks: A big data enabled deep learning approach,” in _IEEE INFOCOM 2017 - IEEE Conference on Computer Communications_ , 2017, pp. 1–9.
  * [6] J. Joo, M. C. Park, D. S. Han, and V. Pejovic, “Deep learning-based channel prediction in realistic vehicular communications,” _IEEE Access_ , vol. 7, pp. 27 846–27 858, 2019.
  * [7] Y. Yang, D. B. Smith, and S. Seneviratne, “Deep learning channel prediction for transmit power control in wireless body area networks,” in _ICC 2019 - 2019 IEEE International Conference on Communications (ICC)_ , 2019, pp. 1–6.
  * [8] A. Kulkarni, A. Seetharam, A. Ramesh, and J. D. Herath, “Deepchannel: Wireless channel quality prediction using deep learning,” _IEEE Transactions on Vehicular Technology_ , vol. 69, no. 1, pp. 443–456, 2020.
  * [9] L. Li, Y. Xu, J. Yin, W. Liang, X. Li, W. Chen, and Z. Han, “Deep reinforcement learning approaches for content caching in cache-enabled d2d networks,” _IEEE Internet of Things Journal_ , vol. 7, no. 1, pp. 544–557, 2020.
  * [10] M. Najla, Z. Becvar, P. Mach, and D. Gesbert, “Predicting device-to-device channels from cellular channel measurements: A learning approach,” _IEEE Transactions on Wireless Communications_ , vol. 19, no. 11, pp. 7124–7138, 2020.
  * [11] I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio, _Deep learning_. MIT press Cambridge, 2016, vol. 1, no. 2.
  * [12] T. Lin, T. Guo, and K. Aberer, “Hybrid neural networks for learning the trend in time series,” in _Proceedings of the twenty-sixth international joint conference on artificial intelligence_ , 2017, pp. 2273–2279.
  * [13] J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” _arXiv preprint arXiv:1412.3555_ , 2014.
  * [14] S. Hochreiter and J. Schmidhuber, “Long short-term memory,” _Neural Computation_ , vol. 9, no. 8, pp. 1735–1780, 11 1997.
  * [15] N. Bhargav, S. L. Cotton, and D. Simmons, “Secrecy capacity analysis over $\kappa$-$\mu$ fading channels: Theory and applications,” _IEEE Trans. Commun._ , vol. 64, no. 7, pp. 3011–3024, July 2016.
  * [16] I. Guyon and A. Elisseeff, “An introduction to variable and feature selection,” _Journal of machine learning research_ , vol. 3, no. Mar, pp. 1157–1182, 2003.
  * [17] S. Aksoy and R. M. Haralick, “Feature normalization and likelihood-based similarity measures for image retrieval,” _Pattern recognition letters_ , vol. 22, no. 5, pp. 563–582, 2001.
  * [18] T. Poggio and S. Edelman, “A network that learns to recognize three-dimensional objects,” _Nature Publishing Group_ , vol. 343, no. 6255, pp. 263–266, 1990.
  * [19] A. Zhang, Z. C. Lipton, M. Li, and A. J. Smola, _Dive into Deep Learning_ , 2020, https://d2l.ai.
  * [20] F. Gers, J. Schmidhuber, and F. Cummins, “Learning to forget: continual prediction with lstm,” in _1999 Ninth International Conference on Artificial Neural Networks ICANN 99. (Conf. Publ. No. 470)_ , vol. 2, 1999, pp. 850–855 vol.2.
  * [21] A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” in _Advances in Neural Information Processing Systems 25_. Curran Associates, Inc., 2012, pp. 1097–1105.
  * [22] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in _2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)_ , 2016, pp. 770–778.
  * [23] C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Rabinovich, “Going deeper with convolutions,” in _Computer Vision and Pattern Recognition (CVPR)_ , 2015.
  * [24] D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” 2014, cite arxiv:1412.6980Comment: Published as a conference paper at the 3rd International Conference for Learning Representations, San Diego, 2015. [Online]. Available: http://arxiv.org/abs/1412.6980
  * [25] T. S. Rappaport _et al._ , _Wireless communications: principles and practice_. prentice hall PTR New Jersey, 1996, vol. 2.

|  Nidhi Simmons (S’14–M’18) received the B.E. degree (Hons.) in
telecommunications engineering from Visvesvaraya Technological University,
Belgaum, India, in 2011, the M.Sc. degree (Hons.) in wireless communications
and signal processing from the University of Bristol, U.K., in 2012, and the
Ph.D. degree in electrical engineering from Queen’s University of Belfast,
U.K., in 2018. From 2019 - 2020, she worked as a Research Fellow at Queen’s
University of Belfast, U.K. She then received a 5-year fellowship from the
Royal Academy of Engineering, and currently works as a Royal Academy of
Engineering Research Fellow at the Centre for Wireless Innovation, Queen’s
University Belfast. Her research interests include ultra-reliable low-latency
communications, channel characterization and modeling, machine learning for
wireless communications and blockchain technology.
---|---
|  Samuel Borges Ferreira Gomes received the B.Sc. degree in computer
engineering from the Federal University of Ceará (UFC), Brazil, in 2018, and
M.Sc. degree in electrical engineering from the State University of Campinas
(UNICAMP), Brazil, in 2021, where he is currently working toward the Ph.D.
degree. Since 2019, he has been a researcher assistant with the Wireless
Technology Laboratory (WissTek), UNICAMP. His research interests include
artificial intelligence and wireless communications.
---|---
|  Michel Daoud Yacoub was born in Brazil, in 1955. He received the B.S.E.E.
and M.Sc. degrees from the School of Electrical and Computer Engineering,
State University of Campinas, UNICAMP, Campinas, SP, Brazil, in 1978 and 1983,
respectively, and the Ph.D. degree from the University of Essex, U.K., in
1988. From 1978 to 1985, he was a Research Specialist in the development of
the Tropico digital exchange family with the Research and Development Center
of Telebras, Brazil. In 1989, he joined the School of Electrical and Computer
Engineering, UNICAMP, where he is currently a Full Professor. He consults for
several operating companies and industries in the wireless communications
area. He is the author of Foundations of Mobile Radio Engineering (Boca Raton,
FL: CRC, 1993), Wireless Technology: Protocols, Standards, and Techniques
(Boca Raton, FL: CRC, 2001), and the coauthor of the Telecommunications:
Principles and Trends (Sao Paulo, Brasil: Erica, 1997, in Portuguese). He
holds two patents. His general research interest includes wireless
communications.
---|---
|  Osvaldo Simeone (Fellow, IEEE) is a Professor of Information Engineering
with the Centre for Telecommunications Research at the Department of
Engineering of King’s College London, where he directs the King’s
Communications, Learning and Information Processing lab. He received an M.Sc.
degree (with honors) and a Ph.D. degree in information engineering from
Politecnico di Milano, Milan, Italy, in 2001 and 2005, respectively. From 2006
to 2017, he was a faculty member of the Electrical and Computer Engineering
(ECE) Department at New Jersey Institute of Technology (NJIT), where he was
affiliated with the Center for Wireless Information Processing (CWiP). His
research interests include information theory, machine learning, wireless
communications, and neuromorphic computing. Dr Simeone is a co-recipient of
the 2022 IEEE Communications Society Outstanding Paper Award, 2021 IEEE
Vehicular Technology Society Jack Neubauer Memorial Award, 2019 IEEE
Communication Society Best Tutorial Paper Award, the 2018 IEEE Signal
Processing Best Paper Award, the 2017 JCN Best Paper Award, the 2015 IEEE
Communication Society Best Tutorial Paper Award and of the Best Paper Awards
of IEEE SPAWC 2007 and IEEE WRECOM 2007. He was awarded a Consolidator grant
by the European Research Council (ERC) in 2016. His research has been
supported by the U.S. NSF, the ERC, the Vienna Science and Technology Fund, as
well as by a number of industrial collaborations. He currently serves in the
editorial board of the IEEE Signal Processing Magazine and is the chair of the
Signal Processing for Communications and Networking Technical Committee of the
IEEE Signal Processing Society. He was a Distinguished Lecturer of the IEEE
Information Theory Society in 2017 and 2018, and he is currently a
Distinguished Lecturer of the IEEE Communications Society. Dr Simeone is a co-
author of a textbook (to be published by Cambridge University Press), two
monographs, two edited books, and more than 160 research journal papers. He is
a Fellow of the IET and of the IEEE.
---|---
|  SIMON L. COTTON (S’04–M’07–SM’14) received the B.Eng. degree in electronics
and software from Ulster University, Ulster, U.K., in 2004, and the Ph.D.
degree in electrical and electronic engineering from the Queen’s University of
Belfast, Belfast, U.K., in 2007. He is currently a Professor of Wireless
Communications and the Director of the Centre for Wireless Innovation (CWI),
Queen’s University Belfast. He has authored and co-authored over 140
publications in major IEEE/IET journals and refereed international
conferences, two book chapters, and two patents. Among his research interests
are cellular device-to-device, vehicular, and body-centric communications. His
other research interests include radio channel characterization and modeling,
and the simulation of wireless channels. He was a recipient of the H. A.
Wheeler Prize, in 2010, from the IEEE Antennas and Propagation Society for the
best applications journal paper in the IEEE Transactions on Antennas and
Propagation, in 2009, and the Sir George Macfarlane Award from the U.K. Royal
Academy of Engineering in recognition of his technical and scientific
attainment since graduating from his first degree in engineering, in 2011.
---|---
|  David E. Simmons received the BSc in mathematics from the University of
Central Lancashire, in 2011, the M.Sc. degree in communications engineering
from the University of Bristol, U.K., in 2012, and D.Phil. degree in
Engineering from the University of Oxford, U.K., in 2016. His research has
focused on studying the information theoretic properties of relay networks as
they scale. During his D.Phil. studies, he was a recipient of the Best Paper
Award at the 23rd edition of EUCNC’14. From 2016 to 2017, he worked as a PDRA
within the Networked Quantum Information Technologies group at the University
of Oxford. From 2018 until present, he has worked as a Senior AI/ML Research
Scientist, Senior Software Engineer, and Engineering Team Lead in two startup
companies in Belfast, U.K. His research interests include communication and
network theory, information theory, AI/ML, and cryptography.
---|---