=Paper=
{{Paper
|id=Vol-3793/paper23
|storemode=property
|title=Channel Modeling for Millimeter-Wave UAV
Communication based on Explainable Generative
Neural Network
|pdfUrl=https://ceur-ws.org/Vol-3793/paper_23.pdf
|volume=Vol-3793
|authors=Ladan Gholami,Pietro Ducange,Pietro Cassará,Alberto Gotta
|dblpUrl=https://dblp.org/rec/conf/xai/GholamiDCG24
}}
==Channel Modeling for Millimeter-Wave UAV
Communication based on Explainable Generative
Neural Network==
https://ceur-ws.org/Vol-3793/paper_23.pdf
Channel Modeling for Millimeter-Wave UAV
Communication based on Explainable Generative
Neural Network
Ladan Gholami1,2,* , Pietro Ducange1 , Pietro Cassará2 and Alberto Gotta2
1
Department of Information Engineering, University of Pisa, Pisa, Italy
2
Institute of Information Science and Technologies, CNR, Pisa, Italy
Abstract
This paper proposes an enhanced method for channel modeling in millimeter-wave wireless UAV-assisted
communication networks. It addresses the need for accurate, data-efficient, and interpretable channel
models for user-centric networks, obtained by integrating the Generative Adversarial Network (GAN)
framework with eXplainable AI (XAI) systems. The methodology incorporates Deep SHAP to optimize
the generator’s gradient descent process, improving model accuracy. By comparing metrics such as
Kullback-Leibler divergence and Wasserstein Distance, the model demonstrates superiority in capturing
real parameter distributions. Moreover, it indicates robust performance with significantly fewer training
samples, making it a promising solution for real-world deployment.
Keywords
Unmanned aerial vehicles, Channel modeling, Generative neural network, XAI, Shapley additive expla-
nations
1. Introduction
Unmanned Aerial Vehicles (UAVs) have emerged as integral components in various industries due
to their remarkable maneuverability, adaptability, and cost-effectiveness. Functioning as aerial
Base Stations (BSs) or mobile relays within three-dimensional (3D) wireless communication
networks, they ensure the provision of ubiquitous connectivity for the ground User Equipment
(UE), even in challenging environments where direct Line-Of-Sight (LOS) transmission links
are not feasible. Integrating UAVs into cellular networks represents a significant step toward
advancing fifth-generation (5G) and beyond 5G (B5G) mobile networks, ensuring continuous,
high-capacity broadband connectivity even in catastrophic scenarios.
The rise of time-critical communication services alongside the proliferation of internet
users and IoT devices, has led to a surge in data traffic, straining traditional radio spectrum
resources. Leveraging higher frequencies such as the millimeter Wave (mmWave) spectrum
not only addresses the issue but also offers advantages such as enhanced throughput and
lower latency, making them a promising solution for UAV networks. Moreover, accurate
Late-breaking work, Demos and Doctoral Consortium, colocated with The 2nd World Conference on eXplainable Artificial
Intelligence: July 17–19, 2024, Valletta, Malta
*
Corresponding author.
$ ladan.gholami@phd.unipi.it (L. Gholami); pietro.ducange@unipi.it (P. Ducange); pietro.cassara@isti.cnr.it
(P. Cassará); alberto.gotta@isti.cnr.it (A. Gotta)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
channel modeling is crucial in designing optimized air-to-ground (A2G) or air-to-air (A2A)
UAV-based communication systems. It involves developing a model that predicts or simulates
the parameters of mmWave links, considering phenomena including reflection, diffraction, and
scattering. However, the inherent susceptibility of mmWave to atmospheric absorption and
blockage significantly complicates their channel modeling in UAV-assisted networks.
Numerous studies have been conducted to develop accurate channel parameter models.
Conventional approaches are categorized into empirical, deterministic, and stochastic models.
For ground-to-air (G2A) communication, [1] proposed a mathematical path loss prediction model,
while [2] examined an empirical path loss two-ray model and modified Log-Distance model for
A2A communication. [3] introduced a map-based model for A2G mmWave communication,
considering all three direct, reflection, and diffraction rays. The work of [4] developed a hybrid
parameter estimation method for UAV-to-Vehicle (U2V) communication, integrating geometric-
based and stochastic approaches. Moreover, [5] presents a geometry-based stochastic model
for Multiple-Input Multiple-Output (MIMO) UAV communications, considering the movement
of the transmitter, receiver, and all reflectors within the propagation environment by using a
two-stage continuous-time Markov model.
In recent years, Machine Learning (ML) methods have gained great popularity in the channel
modeling domain. The ML approaches excel in generalizing to new data and adapting to
changing environmental conditions. In the study [6], a deep Long Short-Term Memory (LSTM)
model was proposed for predicting path loss in A2A UAV communication. In [7] authors
utilized Random Forest and K-nearest-neighbors techniques, along with a feature selection
scheme, for path loss and propagation delay predictions. [8] introduced a neural network-based
model for path loss prediction, focusing on the relationship between reflection angle, path
delay, and path loss factor. Additionally, [9] shows a rapid Angle-Of-Arrival (AOA) estimation
approach employing a Support Vector Machine (SVM) tailored for MIMO beamforming in
dynamic vehicular communication scenarios.
ML-based approaches, particularly Neural Networks (NNs), have proven to be valuable tools
for channel modeling, with Generative Neural Networks, such as Variational AutoEncoder (VAE)
and Generative Adversarial Networks (GAN) standing out for their ability to capture the complex
dynamics of mmWave UAV channels [10, 11, 12]. However, these models typically require
extensive training datasets, exceeding 10,000 records, which are costly and time-consuming to
acquire. Addressing this challenge, this paper exploits the potential of eXplainable Artificial
Intelligence (XAI) to enhance the training process of Conditional GANs (CGAN) for estimating
channel parameters between UAVs and UEs. By integrating the XAI approach with the deep
CGAN, a data-efficient model suitable for mmWave communication is developed, which achieves
comparable results with much fewer records. For evaluation purposes, we utilize ray tracing
simulation data, related to different urban characteristics. To our knowledge, such methodology
represents a unique contribution to UAV channel modeling, paving the way for user-centric
sixth-generation (6G) networks that require efficient, fast, and explainable AI mechanisms for
network management.
The rest of this paper is structured as follows: Section II elaborates on the basic concept of
XAI methods in greater depth. Section III outlines the proposed XAI-based CGAN channel
model. Then, Section IV presents the results, demonstrating the practicality of the proposed
technique. Section V concludes the paper.
2. XAI methods
XAI methods represent efforts to provide the users with a straightforward explanation of the
black-box ML models’ internal functionality or identify the key factors influencing their outputs.
This understanding empowers experts to refine and optimize the training procedure of ML-based
models, rendering XAI a prominent area of research across various fields. Within the realm of
XAI systems, model-agnostic techniques are typically categorized into visualization methods
such as surrogate models, knowledge extraction methods (e.g., rule extraction techniques),
influence methods including feature importance analysis, and example-based explainable tech-
niques. One notable feature importance analysis method is the SHapley Additive exPlanations
(SHAP) method, an additive feature attribution approach, which computes Shapley values (or
SHAP values) for each feature within the input dataset [13]. Shapley value for a feature "i" is
the average marginal contribution of that individual feature to the model prediction across all
possible feature subsets 𝑆 ⊆ 𝑀 ∖ {𝑖}, where 𝑆 is any subset of 𝑀 , the set of all input features.
All additive feature attribution methods try to provide an explanation model 𝑔 that explains
the output of the original model (𝑓 (𝑥)). For explanation, simplified inputs, denoted as 𝑥 ´ , are
typically employed, which can be transformed into the original input space via a mapping
function (𝑥 = ℎ𝑥 (𝑥 ´ )). The 𝑥
´ vector, with the length of M, constitutes zeros and ones, showing
a possible subset of features within x, where 𝑥 ´ 𝑖 = 1 indicates the presence of the feature
in the subset. The additive attribution approach yields ∑︀ an explanation model which 𝑀 satisfies
´ ) ≈ 𝑓 (ℎ(𝑥
𝑔(𝑥 ´ )) and is expressed as 𝑔(𝑥 ´ ) = 𝜑0 + 𝑀 𝜑 𝑥
´
𝑖=1 𝑖 𝑖 , where the 𝑥
´ 𝑖 = {0, 1} is the
simplified input and 𝜑𝑖 ∈ R is the importance value of feature 𝑖. The feature importance is
determined as follows:
∑︁ |𝑧´|!(𝑀 − |𝑧´| − 1)!
𝜑𝑖 (𝑓, 𝑥) = [𝑓𝑥 (𝑧´) − 𝑓𝑥 (𝑧´ ∖ 𝑖)] (1)
𝑀!
𝑧´⊆𝑥
´
In the Equation (1), 𝑧´ is the subset vector of 𝑥 ´ (𝑧´ ⊆ 𝑥
´ ), meaning the non-zero components are
a subset of non-zero elements in 𝑥 ´ . The |𝑧´| is the number of ones in 𝑧´ and 𝑀 is the cardinality
of the original input features. 𝑓 (𝑧´) = 𝑓 (ℎ𝑥 (𝑧´)) = 𝑓 (𝑧𝑆 ) since 𝑧𝑆 = ℎ𝑥 (𝑧´), where S is the set
of non-zero elements’ indexes in 𝑧´ vector. So, the calculation of Shapley values faces a problem
when computing 𝑓 (𝑧𝑆 ) as most models cannot approximate the patterns of missing features.
To tackle this limitation, the SHAP methods use the conditional expectation 𝐸 [𝑓 (𝑧)|𝑧𝑆 ] to
approximate 𝑓 (𝑧𝑆 ). Additionally, SHAP methods assume features independence and linearity
in the model for the sake of simplicity, which means 𝐸 [𝑓 (𝑧)|𝑧𝑆 ] approximates as 𝑓 (𝑧𝑆 , 𝐸 [𝑧𝑆¯ ]).
This implies that the missing feature can be estimated using the average values of this feature
in the provided background samples. It is important to note that, despite this assumption, SHAP
methods are capable of capturing feature correlations by considering all possible feature subsets
within each coalition.
There are various SHAP explainers inside the SHAP library, such as Kernel SHAP, which is
model-agnostic, while Linear SHAP, Tree SHAP, and Deep SHAP are specialized for specific
types of ML models. Deep SHAP provides global and local explainability for Deep Learning
(DL) models by combining the Shapley values concept with the DeepLIFT method. Functioning
as a SHAP method, it assumes the DL model is a linear model with independent input features,
so it treats each DL layer as a linear model and backward the computed Shapley values through
the network.
3. mmWave Channel Model
In this paper, we define a model to generate the parameters of the bidirectional channel linking
a transmitter to a receiver, focusing on key parameters, namely path loss, arrival and departure
angles, and propagation time delay. We assume the UAV is endowed with a cellular Base Station
(gNB), while UE serves the stationary receiver; however, the transmitter and receiver roles
can be interchanged. There are three distinct channel states to characterize the mmWave
channel between the transmitter and receiver: LOS, non-LOS, and no-link availability. Note
that our main focus is on modeling the channel parameters for non-LOS paths since the basic
trigonometry can be used to calculate angles and delay and Friis’ Law for path loss parameter
in the straight LOS paths [14]. Each link (n) is represented by six parameters, namely the path
loss (𝑃 𝑙𝑛 ), the azimuth and elevation angles of the receiver (𝜑𝑅 𝑛 , 𝜃𝑛 ), the azimuth and elevation
𝑅
angles of the transmitter (𝜑𝑛 , 𝜃𝑛 ) and the propagation delay (𝑑𝑛 ). The main objective is to
𝑇 𝑇
develop a data-driven model capable of producing parameters that closely resemble real-world
ones. The channel parameters of ray tracing simulation data from [10] are used for training and
evaluation purposes. This dataset considers 20 non-LOS paths within each link (channel), so the
model must generate 120 parameters for each link (20 paths * 6 parameters), with a maximum
loss of 200 dB.
Given that the estimation of channel parameters relies on the channel state (LOS, non-LOS,
or no-link), firstly, a two-hidden-layer deep classifier is used, as reference [10], to estimate
the probability of UE being in the LOS of the UAV. This model utilizes the link distances
𝑑 = [𝑑𝑥 , 𝑑𝑦 , 𝑑𝑧 ] and the cell type (terrestrial in our case) and generates the probability of the
link state.
3.1. Channel modeling via XAI-GAN
In GANs, the generator (G) attempts to produce more realistic synthetic data from random
noise (z), while the task of the discriminator (D) is to differentiate between real and synthetic
ones. Through adversarial training, GANs improve in generating better synthetic data with
a distribution close to the training data. In CGAN, both the generator and discriminator
receive additional conditioning information, to guide the generation process. In this work,
we opt for CGAN, conditioned on the link’s state, for mmWave A2G UAV channel parameter
estimation for the given urban environment. This choice is motivated by CGAN’s demonstrated
success in capturing complex input data distributions and generating high-quality synthetic
data for mmWave channel modeling, compared to CVAE, as evidenced in prior research [12, 11].
However, we seek to enhance the CGAN performance by integrating the XAI methods, leading
to XAI-GAN. We specifically employ the Deep SHAP approach due to its compatibility with the
deep structure of CGAN, as the reference [15].
To enhance the CGAN channel model, we augment the training procedure of CGAN by
integrating the XAI methods. In the original CGAN, the generator’s loss, (𝐷(𝐺(𝑧))), is computed
based on the discriminator’s assessment of the generated synthetic data 𝐺(𝑧). In XAI-GAN,
after the calculation of the generator’s loss, the generated synthetic data 𝐺(𝑧), along with the
discriminator and its prediction 𝐷(𝐺(𝑧)) are fed into the Deep SHAP. Its output reveals the
synthetic features’ influence on the resulting loss. This will allow the generator to learn which
features help the discriminator identify the synthetic data and use this knowledge to guide its
gradient descent process.
After obtaining the feature importance (SHAP value) of synthetic data on the discriminator
output via the Deep SHAP method, we transform it into a matrix, referred as the "explanation
matrix". Each element of this matrix falls within the range of [0,1], denoting the impact of
the corresponding feature. Values closer to zero indicate minimal impact on prediction, while
those approaching one signify greater influence. Following this, both the discriminator loss for
generated data and the explanation matrix 𝑀𝑒𝑥 are fed to the generator as feedback. The matrix
𝑀𝑒𝑥 and the generator’s gradient ∇ are subjected to a Hadamard’s product, as in the equation
(2), ensuring that the features’ significance is considered when updating the generator’s weights,
causing more control over the training process.
∇𝑛𝑒𝑤 = ∇ + 𝛼𝑀𝑒𝑥 ∇ (2)
The parameter 𝛼 serves as a regularizer and the product helps guide the gradient descent
more effectively, leading to the generation of synthetic data closer to the real parameters.
4. Experimental Results
In this section, we outline the experiments conducted to evaluate the efficiency of our generative
approach. We utilize the ray tracing simulation dataset from [10] for evaluation. This dataset
encompasses vectors connecting UAVs to terrestrial or aerial gNBs. We assume the terrestrial cell
only, considering the UE instead of terrestrial gNB and UAV with an aerial BS for our analysis.
Additionally, using different city blueprints, this dataset captures diverse environmental and
building characteristics of various cities. Our evaluation focuses on three key cities: Boston,
London, and Beijing. The ray tracing simulations conducted at 28GHz in [10] also involve UAVs
positioned at various heights of 30, 60, 90, and 120 meters for each environment.
To assess our channel parameter model, we compare it with two models of literature, namely
CGAN [12] and CVAE [10]. The hyperparameters and architecture employed for training these
models are detailed in Table 1. It’s worth noting that these generative models are conditioned
on the predictions of the link state model for the specified link. Hence, the link model is initially
trained individually on the local city datasets.
4.1. Performance evaluation metric
At first, the two metrics of Kullback-Leibler (KL) divergence and Wasserstein Distance (WD) are
selected to evaluate the efficiency of the XAI-GAN model. These metrics quantify the disparity
between the path loss distribution of the original test dataset and the distribution of synthetic
path loss generated by various generative models. The comparative results are presented in
Table 2. The results demonstrate that the distribution of synthetic path loss produced by the
XAI-GAN is much closer to the true distribution compared to other alternatives, in terms of
Table 1
Model summary and hyperparameters for all the evaluated models
Link state prediction XAI-GAN CGAN CVAE
Hidden units [50,25] gen-[280,560,1120] gen-[280,560,1120] enc-[200,80]
dsc-[1120,560,280] dsc-[1120,560,280] dec-[80,200]
Optimizer Adam Adam Adam Adam
Epochs 10 5 5 5
Batch size 100 280 280 280
Learning rate 10−3 10−4 10−4 10−4
Table 2
KL and WD distances between path loss distribution of real data and synthetic data
City Distance XAI-GAN CGAN CVAE
Boston KL 0.029 0.044 0.135
WD 9.653 9.717 9.798
London KL 0.055 0.060 0.122
WD 9.758 9.926 10.217
Beijing KL 0.032 0.048 0.115
WD 10.637 10.984 10.967
(a) (b)
Figure 1: KL distances between London’s path loss distribution and synthetic distribution achieved by
trained models
both criteria, underscoring the accuracy of the proposed model in representing the channel
parameters.
In the second stage, we train XAI-GAN and CGAN channel models on the London channel
parameter dataset with 70%, 50%, and 35% proportion of the dataset, respectively. The results
for these trained models are shown in Fig 1. For the model trained with 70% of the dataset, the
KL distance of the original CGAN is 0.085, while the XAI-GAN distance is 0.070, showing an
improved performance of 17%. Similar improvements are observed for the 50% and 35% data
subsets. This demonstrates that the XAI-GAN can achieve the same level of accuracy with
significantly less training data.
5. Conclusion
Our paper presents a modified model for wireless UAV-based channel parameter generation
using CGAN integrated with the XAI method. Our experimental findings demonstrate the
effectiveness of the proposed XAI-GAN framework in generating synthetic data with more
resemblance to real ones. Integrating the Deep SHAP explainer enhances the gradient descent
process of the generator, leading to a more data-efficient model. Experimental results on
models trained with different proportions of the dataset illustrate the superiority of XAI-GAN
in accurately modeling the link between UE and UAV, even with a 35% reduction in training
samples.
Acknowledgments
Work supported by the European Union under the Italian National Recovery and Resilience Plan
(PNRR) PE00000001 - program "RESTART", Mission 4 Issue 2 Investment 1.4 “Potenziamento
strutture di ricerca e creazione di ”campioni nazionali di R&S” CN00000023 – “Sustainable
Mobility Center (CNMS)”, and by the HORIZON-CL4-2021-SPACE-01 project "5G+ evoluTion
to mutioRbitAl multibaNd neTwORks" (TRANTOR) No. 101081983
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