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# Interpretable AI-based Large-scale 3D Pathloss Prediction Model for enabling
Emerging Self-Driving Networks

Usama Masood, Hasan Farooq, Ali Imran, and Adnan Abu-Dayya This work was
supported in part by the National Science Foundation (NSF) under Grant
1559483, Grant 1619346, and Grant 1730650; and in part by the Qatar National
Research Fund (QNRF) under Grant NPRP12-S 0311-190302. A portion of this work
has been published in IEEE GlobeCom’19 [1]. Usama Masood and Ali Imran are
with the AI4Networks Research Center, School of Electrical & Computer
Engineering, University of Oklahoma, Tulsa, OK, 74135 USA. E-mail:
{usama.masood<EMAIL_ADDRESS>Hasan Farooq is with the Ericsson Research,
USA. E-mail<EMAIL_ADDRESS>Adnan Abu-Dayya is with the Electrical
Engineering Department, Qatar University. E-mail<EMAIL_ADDRESS>
###### Abstract

In modern wireless communication systems, radio propagation modeling to
estimate pathloss has always been a fundamental task in system design and
optimization. The state-of-the-art empirical propagation models are based on
measurements in specific environments and limited in their ability to capture
idiosyncrasies of various propagation environments. To cope with this problem,
ray-tracing based solutions are used in commercial planning tools, but they
tend to be extremely time-consuming and expensive. We propose a Machine
Learning (ML)-based model that leverages novel key predictors for estimating
pathloss. By quantitatively evaluating the ability of various ML algorithms in
terms of predictive, generalization and computational performance, our results
show that Light Gradient Boosting Machine (LightGBM) algorithm overall
outperforms others, even with sparse training data, by providing a 65%
increase in prediction accuracy as compared to empirical models and 13x
decrease in prediction time as compared to ray-tracing. To address the
interpretability challenge that thwarts the adoption of most ML-based models,
we perform extensive secondary analysis using SHapley Additive exPlanations
(SHAP) method, yielding many practically useful insights that can be leveraged
for intelligently tuning the network configuration, selective enrichment of
training data in real networks and for building lighter ML-based propagation
model to enable low-latency use-cases.

###### Index Terms:

Radio Propagation Model, Mobile Networks, Pathloss, Ray Tracing, Feature
Engineering, Interpretable Machine Learning, Explainable Artificial
Intelligence (XAI), LightGBM, Ultra-Reliable Low-Latency Communication
(URLLC).

##  1 Introduction

Emerging cellular networks are anticipated to witness a dramatic growth in
connected devices and exciting new vertical services. Artificial Intelligence
(AI) enabled end to end network automation vis-a-vis next generation Self
Organizing Network (AISON), as proposed in [2], is considered to be the key
enabler to meet the stringent performance requirements of increasingly complex
planning, operation, optimization and maintenance in emerging self-driving
networks.

The ultimate goal of AISON is to autonomously orchestrate the plethora of
network parameters to maintain optimal multi-faceted network performance in
terms of all important top level Key Performance Indicators, without much
human involvement [2]. Most of the high level KPIs such as capacity, Quality
of Service (QoS) and energy efficiency ultimately depend on one core low level
metric i.e., Received Signal Strength (RSS). Therefore, characterising RSS as
a function of network parameters is the very first step towards optimally
designing and operating a cellular network. Hence, a realistic propagation
model that is sensitive to the variations in network parameters (e.g., tilt)
and environment geography and can follow the spatio-temporal variation in the
network will be the cornerstone of AISON enabled future cellular networks (5G
and beyond).

The existing propagation models can be categorized into three classes:
deterministic, empirical and semi-empirical [3, 4]; deterministic models are
based on the principles of wave propagation that can be theoretically computed
using Maxwell’s equations. However, in practice approximate methods such as
ray tracing are used to model signal propagation, by taking into account the
interactions of rays with the environment and using the dominant ray path to
calculate the pathloss. These models can be very accurate depending on the
resolution of available topographical database, but unfortunately are
computationally inefficient. On the other hand, empirical and semi-empirical
models such as COST-Hata [5], Stanford University Interim (SUI) [6], Standard
Propagation Model (SPM) [7] and ITU-R P.452-15 [8] can be efficiently
computed. However, these empirical and semi-empirical models are less
sensitive to the actual physical and geometric structure of a given
propagation environment and require in-depth domain-specific knowledge and
technical expertise in radio signal propagation across electromagnetic fields.

To address the constraints and limitations of traditional propagation modeling
methods, Artificial Intelligence and ML techniques are being considered as
promising viable solutions and have been proven to be very effective for
approximating arbitrary functions with hidden features. As envisioned in [2],
AI is going to be indispensable in optimally designing and operating
increasingly complex cellular networks. Hence, AI can replace classical
mathematical models with a robust data-driven pathloss prediction model, that
is more accurate than empirical propagation models and more computationally
efficient than deterministic models, for system level intelligent network
planning and post-deployment optimization and automation in cellular networks.

###  1.1 Related Work

In recent years several studies have been conducted for pathloss prediction in
a particular environment using machine learning based models. Artificial
Neural Networks have been at the core of most ML-based pathloss prediction
models, however, the input features to the ANN model in these studies are
limited to a particular environment, such as rural [9], urban [10, 11] and
volcanic ocean islands [12], and seems unable to scale to other environment
settings. The authors in [13] went one step ahead and used evolutionary
algorithms to find the optimal hyper-parameters of the ANN based model, but
they assumed a uniformly structured simulation area, which is not the case in
practical scenarios. The authors in [14] incorporated features based on
clutter maps to differentiate between different environments, but the
presented model is still unable to capture the variation in coverage due to
the change in geometrical structure of the propagation path. Furthermore, the
authors in [15] tried to capture this variation by incorporating clutter
heights as input feature, but still their input feature set is very limited to
scale to different network configuration, as is the case in real networks. On
the other hand, supervised ML techniques have also been used for pathloss
prediction. The authors in [16] used Support Vector Regression to predict
pathloss. However, they trained their model on a drive test data from a single
serving Base Station (BS) in an urban environment. The authors in [17]
compared the performance of several supervised ML algorithms for estimating
cellular network coverage, using User Equipment (UE) measurement traces, BS
parameters and geographical information. However, instead of modeling the
pathloss or RSS, the authors classify the observation area as a good or a bad
coverage area, using a pre-defined coverage threshold. A recently proposed
data-driven model in [18] is the most relevant to our framework, using a
boosting ensemble learning method to predict RSS using UE data from
crowdsourcing applications. However, the environmental features used in the
model are very limited.

Figure 1: Proposed Framework of a Machine Learning-based 3D Radio Propagation
Model. Raw datasets such as BS sites topology, UE measurement traces and
geographical information are first pre-processed and then converted into right
data i-e- feature matrix comprising of key features/predictors that can
estimate pathloss (or RSS). These key features are then used to train state-
of-the-art ML algorithms for creating an RSS prediction model.

###  1.2 Contributions and Organization

In this paper, we present a framework for an AI-driven large-scale 3D pathloss
model (See Figure 1), that is scalable and robust to the variations in the
environment geography and addresses the limitations of aforementioned studies.
The contributions of this paper can be summarized as follows:

  1. 1.

A novel set of key predictors (features) are identified that can characterize
the physical and geometric structure of the environment traversed by a signal
in its propagation path (e.g., indoor distance, Manhattan distance, number of
building penetrations in each clutter type).

  2. 2.

Multi-faceted performance comparison of the current state-of-the-art ML
algorithms is done to evaluate the ability of proposed ML-based propagation
model for real-time implementation, that includes predictive performance,
generalization performance (robustness to unseen propagation scenarios using
sparse training data, as is the case in real networks) and computational
performance (i.e., training time and prediction time). In our investigation,
Light Gradient Boosting Machine (LightGBM) algorithm is found to be the most
optimal choice overall in modeling the complex propagation environment in real
networks, due to its lightning fast training process and robustness to
sparsity of training data.

  3. 3.

The baseline performance of LightGBM algorithm is further optimized by
investigating four different hyperparameter optimization approaches. These
include Grid Search, Random Search, Bayesian Optimization and Simulated
Annealing. These approaches are investigated in terms of performance gain and
computational complexity (convergence time), and Bayesian optimization seems
to be the best approach among them, as it converges in just 3 search
iterations and reduces the prediction RMSE by 10%.

  4. 4.

Performance comparison of the proposed model with state-of-the-art empirical
propagation models and ray-tracing approach is also provided. The results show
a 65% increase in prediction accuracy as compared to empirical propagation
models and 13x decrease in prediction time as compared to ray tracing.

  5. 5.

A key caveat of using ML is the lack of interpretability of resultant models,
i.e., the black box paradox. In this study we try to address this weakness of
the proposed RSS estimation models by performing extensive secondary analysis
of the proposed models through SHAP method to interpret the model’s
predictions and bring clarity in understanding the importance of each feature
(e.g., Azimuth, Tilt and Antenna Height) in the model. Utility of the insights
drawn from the secondary SHAP analysis are also provided, such as intelligent
optimization of network configuration, smart/selective enrichment of training
data in real networks and building lighter ML-based propagation model to
enable low-latency use-cases.

  6. 6.

Another key contribution of the paper is to leverage the SHAP interpretability
analysis to improve the various aspects of performance in the baseline model.
We leverage the insights from SHAP analysis to propose a second novel light
weight model for real-time implementation. This second model uses only the
most significant features (selected based on insights gained from SHAP
analysis) and as a result has $\sim$ 70% less computational complexity
compared to the base line model at the cost of negligible loss in performance
(around 3%).

The rest of the paper is organized as follows: Section 2 explains the proposed
framework, starting from raw data from the network, data pre-processing,
feature engineering and a comparison of various machine learning algorithms
for modeling RSS, whereas, Section 3 provides the performance comparison of
the proposed model with traditional propagation models. Interpretation of the
proposed AI-driven model using a recently proposed sensitivity analysis
technique is given in Section 4 and finally Section 5 concludes this paper.

##  2 Proposed Framework

The proposed framework for an AI-driven 3D propagation model (Figure 1) uses
raw data from the network consisting of network topology information, UE
measurement traces and geographic information of the area, pre-process them
and converts them into right data [2], which is then fed to a ML model to
estimate RSS at given locations in a radio propagation environment.

###  2.1 Network and Simulation Setup

TABLE I: Network Scenario Settings System Parameters |  Values
---|---
Air Technology | 4G LTE
Cellular Layout | 10 Macrocell sites
Sectors | 3 sectors per eNB
Simulation Location | Brussels, Belgium
Simulation Area | 3.80 km2
User Distribution | Poisson Distribution
Propagation Model | Aster (Ray Tracing)
Path Loss Matrix Resolution | 10m
Geographic Information |  (1-m Resolution GeoData) Ground Heights (DTM) + Building Heights (DHM) + Land Use Map (DLU)
Land Cover (Clutter) Types | 15 different classes
eNB Transmit Power (max) | 43 dBm
eNB Noise Figure | 5 dB
eNB Antenna Height | Actual site heights
eNB Antenna Model |  Kathrein Directional Antenna (Model 742 265)
eNB Antenna Gain | 18.3 dBi
eNB Antenna Horizontal Half Power Beamwidth | 63o
eNB Antenna Vertical Half Power Beamwidth | 4.7o
Frequency Band | 2110 FDD (E-UTRA Band 1)
Channel Bandwidth (CBW) | 5 MHz

(a) 3D Elevation Map

(b) 2D Elevation Map

(c) Propagation Path between a BS and UE

Figure 2: Area of Simulation showing (a) Building Heights (b) Transmitter
Positions and (c) Vertical Propagation Path

  * •

Network Scenario: A ray-tracing based industry standard radio network planning
and optimization platform “Atoll” [19] is used to create a sophisticated
network topology, consisting of 10 macro cell sites in the center of City of
Brussels, Belgium (See Figure 2(b)). Actual antenna pattern and antenna
heights are used in our analysis. Table I lists all the network and simulation
scenario settings used in our analysis.

  * •

Geographical Datasets: High resolution (1-m) geographical datasets containing
earth terrain, buildings heights and land use information (e.g., Open, Parks,
Block Buildings etc.) of the city are used in our analysis, enabling realistic
and accurate pathloss calculation using Aster high-performance propagation
model [20].

  * •

Ray Tracing: Aster utilizes advanced ray-tracing propagation techniques to
calculate various phenomena that affects radio wave propagation including
vertical diffractions over roof-tops, horizontal diffractions and reflections
based on ray-launching, atmospheric absorptions, rain attenuation and
vegetation through loss etc. Aster utilizes advanced ray-tracing propagation
techniques to calculate various phenomena that affects radio wave propagation
including vertical diffractions over roof-tops, horizontal diffractions and
reflections based on ray-launching, atmospheric absorptions, rain attenuation
and vegetation through loss etc.

  * •

Validation using Real Data: Furthermore, the parameters of the Aster
propagation model are pre-calibrated using more than 1.5 million real channel
measurement points from the real environment [21]. Therefore, the high-
fidelity RSS (or pathloss) data calculated by Atoll in the observation area
can be taken as ground truth for designing a realistic propagation model.

###  2.2 Raw Data

The following three different kinds of datasets are required as input data for
our proposed framework:

  1. 1.

Sites Topology: This dataset contains the Location, Height, Azimuth, Tilt,
Transmit Power, Frequency, Antenna Type of all the BSs in the observation
area. It is denoted by ${D}_{\textit{BS}}$ (See Table II).

TABLE II: Sites Topology Parameter |  Description
---|---
Location ($x_{\textit{BS}},y_{\textit{BS}}$) | Location coordinates of a BS site (See Figure 2(b))
Height ($h_{\textit{BS}}$) |  The height of BS antenna above the ground and building (if any)
Azimuth ($\theta_{\textit{BS}}$) |  Azimuth angle (in degrees) of the BS antenna, which is the direction of antenna w.r.t. North
Tilt ($\phi_{\textit{BS}}$) |  Tilt angle (in degrees) of the BS antenna, which is basically the angle below the horizontal plane
Tx Power ($P_{\textit{BS}}$) |  The power of the radio signal (in dBm) when it’s transmitted from the BS antenna
Frequency ($f$) |  Carrier frequency used by the BS antenna for transmission
Antenna Type |  The type of antenna used by the BS transmitter. It is differentiated by beamwidth, antenna gain etc
  2. 2.

Geographic Information: The geographical information of the propagation
environment can be captured using three types of geographical datasets:
Digital Terrain Model (DTM), Digital Height Model (DHM) and Digital Land Use
Map (DLU). These datasets are in a raster grid format, which means that the
whole observation area is divided into grids (or bins), each grid containing a
specific value (See Table III). These geographical datasets are routinely used
by mobile telecom industry for their planning and maintenance tasks, and can
be acquired on demand [22].

TABLE III: Geographic Information Parameter |  Description
---|---
Digital Terrain Model ($D_{\textit{DTM}}$) |  It provides the earth terrain (ground) height. It takes as an input the $x,y$ coordinates and outputs the ground height $z_{\textit{DTM}}$ at that place $z_{\textit{DTM}}=D_{\textit{DTM}}(x,y)$. (See Figure 2(c))
Digital Height Model ($D_{\textit{DHM}}$) |  It provides the building heights (above the ground) in the observation area. It takes as an input the $x,y$ coordinates and output the total height $z_{\textit{DHM}}$ of the user at that place $z_{\textit{DHM}}=D_{\textit{DHM}}(x,y)$. (See Figure 2(a))
Digital Land Use Map ($D_{\textit{DLU}}$) |  It provides the clutter (or land cover) type of each grid in the observation area. It takes as an input the $x,y$ coordinates and output the clutter type $c$ at that place $c=D_{\textit{DLU}}(x,y)$
  3. 3.

UE Traces: This dataset contains the RSS, Location, Timestamp, Network ID of
all the UEs in the observation area. It is denoted by ${D}_{\textit{UE}}$ (See
Table IV). The mobile operators can readily use the data from Drive Tests,
Minimization of Drive Tests (MDT) reports, crowdsourcing applications etc. to
generate this dataset, without the need for any new standardization.

TABLE IV: UE Traces Parameter |  Description
---|---
RSS |  Received Signal Strength ($P_{\textit{UE}}$) from the serving Base Station (BS)
Location |  Location coordinates ($x_{\textit{UE}},y_{\textit{UE}}$) of a UE
Timestamp |  Time at which the UE trace is recorded
Network ID |  Information regarding serving BS ID, Mobile Network Code etc.

###  2.3 Data Pre-processing

Raw UE traces from the network are first pre-processed by cleaning and
gridding, before using them for feature extraction.

####  2.3.1 Data cleaning

Data cleaning is the process of identifying missing and corrupt values in the
dataset and then handling them by modifying or deleting the relevant rows (or
entries) from the dataset. This pre-processing step ensures that the training
data for the proposed model is free from any anomalies and inconsistencies. In
our study, some UE traces containing missing values (e.g., out of coverage
UEs) are removed before using them for further analysis.

####  2.3.2 Data gridding

Data gridding is the process of mapping all UE traces into unique spatial bins
(of 10m width in our case) and then averaging the measurements inside each
spatial bin for every serving BS. The advantage of data gridding is twofold:

  1. 1.

Handling Randomness: Firstly, it can offset randomness in RSS due to fast
fading and slow fading (to some extent), by averaging all measurements from
the same BS, falling within a small bin, given the RSS within the bin is
expected to stay almost same due to its small size.

  2. 2.

Handling Positioning Error: Secondly, it handles positioning error in the user
reported measurements. However, gridding/binning has its costs i.e., it
introduces quantization error to say the least and also presents an accuracy
vs complexity trade-off.

In our study, UE traces in the observation area are first mapped into unique
spatial bins of 10m width, and then in each bin all UE traces corresponding to
a unique BS were averaged out. For further analysis, the averaged UE traces
are used to mitigate the effect of randomness from the original data.

For detailed analysis of the impact of gridding, reader is referred to a
recent study in [23] and [24]. Analysis presented in [23] and [24] shows that
there exists a trade-off between the quantization error introduced by gridding
and the positioning error from the incorrect GPS location tagged with the UE
measurements, and that there exists an optimal bin-width for gridding for a
given UE density and positioning error that maximizes the accuracy of UE
measurements data.

Figure 3: Propagation Path between a BS and UE, showing various features of
the proposed model

###  2.4 Feature Engineering (Raw Data to Right Data)

Feature engineering is a key process in ML, that leverages domain knowledge to
create features which can characterize the complex target model and greatly
enhance its learning performance.

In our study, several key predictors (features) are identified or engineered,
to better characterize the environment traversed by a signal in its
propagation path (See Figure 3). The raw network, UE and geographic datasets,
readily available to the mobile operators, are converted into right data (key
features) comprising of system as well as propagation environment features
that can then be leveraged to train an ML-based propagation model.

####  2.4.1 Propagation Distance

This is the horizontal distance (in meters) between a UE and its serving BS.
It is denoted by $d$.

$d=\sqrt{(x_{\textit{BS}}-x_{\textit{UE}})^{2}+(y_{\textit{BS}}-y_{\textit{UE}})^{2}}.$
(1)

####  2.4.2 Horizontal Angular Separation

This is the horizontal angular separation (in degrees) between the BS antenna
boresight and the direction of Line of Sight path to the UE. This feature
captures the attenuation due to horizontal antenna pattern of the BS. It is
denoted by $\theta_{hor}$.

$\theta_{\textit{hor}}=abs(\theta_{\textit{BS}}-\theta_{\textit{UE}}),$ (2)

where,

$\theta_{\textit{UE}}=atan2\left(\frac{x_{\textit{BS}}-x_{\textit{UE}}}{y_{\textit{BS}}-y_{\textit{UE}}}\right).$
(3)

Here $\theta_{\textit{UE}}$ is the azimuth angle of (UE) arrival and
$\theta_{\textit{BS}}$ is the azimuth angle of (BS) departure, or simply BS
azimuth angle, whereas, $atan2()$ calculates the four quadrant inverse
tangent.

####  2.4.3 Vertical Angular Separation

This is the vertical angular separation (in degrees) between the BS antenna
boresight and the direction of Line of Sight path to the UE. This feature
captures the attenuation due to vertical antenna pattern of the BS. It is
denoted by $\phi_{ver}$.

$\phi_{\textit{ver}}=\phi_{\textit{UE}}-\phi_{\textit{BS}},$ (4)

where,

$\phi_{\textit{UE}}=atan\left(\frac{z_{\textit{UE}}-z_{\textit{BS}}}{d}\right),$
(5)
$z_{\textit{UE}}=D_{\textit{DTM}}(x_{\textit{UE}},y_{\textit{UE}})+D_{\textit{DHM}}(x_{\textit{UE}},y_{\textit{UE}}),$
(6)

$z_{\textit{BS}}=D_{\textit{DTM}}(x_{\textit{BS}},y_{\textit{BS}})+D_{\textit{DHM}}(x_{\textit{BS}},y_{\textit{BS}}).$
(7)

Here $\phi_{\textit{UE}}$ is the tilt angle of (UE) arrival,
$\phi_{\textit{BS}}$ is the tilt angle of (BS) departure, or simply BS tilt
angle, $z_{\textit{UE}}$ is the total height of UE and $z_{\textit{BS}}$ is
the total height of BS (See Table III for details on $D_{\textit{DTM}}$ and
$D_{\textit{DHM}}$).

####  2.4.4 Effective BS Height

This is the vertical distance (in meters) between a UE and its serving BS. It
is denoted by $d_{\textit{vert}}$.

$d_{\textit{vert}}=z_{\textit{BS}}-z_{\textit{UE}}.$ (8)

####  2.4.5 Manhattan Distance

This represents the Manhattan distance between the BS and UE. As radio waves
also diffracts at the street corners and are more likely to travel along the
streets in urban areas, therefore Manhattan distance is a better metric to
calculate the distance traversed by the signal, especially in urban networks
[25, 26]. It is denoted by $d_{\textit{man}}$.

####  2.4.6 LoS / NLoS State

This represents the link status between a BS and a UE antenna. A UE can either
be in a Line of Sight (LoS) or Non Line of Sight (NLoS) region from the BS.
This feature is particularly useful in wireless channels, as LoS regions have
higher RSS, and vice versa. It is denoted by $L$.

####  2.4.7 First Diffraction Point

This is the horizontal distance (in meters) from a BS to the first diffraction
point in the propagation path between a BS and UE. This feature captures the
significance of diffracted rays at the receiver, as multiple rays from the
same BS are received and the ray having the highest signal strength is
selected as the dominant ray. It is denoted by $d_{\textit{FD}}$.

####  2.4.8 Last Diffraction Point

This is the horizontal distance (in meters) from a BS to the last diffraction
point in the propagation path between a BS and UE. This feature also tries to
learn the behavior of diffracted rays in the estimation of RSS. It is denoted
by $d_{\textit{LD}}$.

####  2.4.9 Number of Building Penetrations

This is the number of buildings penetrated by the signal in its direct path
between a BS and UE. This feature characterizes the penetration loss (dB)
experienced by the signal while crossing buildings. It is denoted by $N$.

####  2.4.10 Indoor Distance

Horizontal distance (in meters) in the direct path between a BS and UE that is
passing through buildings (indoor). This feature characterizes the linear loss
(dBm/m) experienced by the signal in an indoor area. It is denoted by
$d_{\textit{indoor}}$.

####  2.4.11 Outdoor Distance

Horizontal distance (in meters) in the direct path between a BS and UE that is
in open area (outdoor). This feature characterizes the linear loss (dBm/m)
experienced by the signal in an open area. It is denoted by
$d_{\textit{outdoor}}$.

####  2.4.12 BS Clutter Type

It is the clutter type (or land cover type) of the BS (For example: open
street, dense buildings, sparse buildings, trees, water etc.). This feature
tries to learn the effect of different land cover type on the signal around
the BS antenna. It is denoted by $c_{\textit{BS}}$.

####  2.4.13 UE Clutter Type

It is the clutter type (or land cover type) of the UE (For example: open
street, dense buildings, sparse buildings, trees, water etc.). Each clutter
type has its own effect on the signal and this feature tries to learn this
behavior. It is denoted by $c_{\textit{UE}}$.

####  2.4.14 Number of Building Penetrations in each Clutter Type

This is the number of buildings penetrated by the signal in each unique
clutter in the direct path between a BS and UE. Different clutters can be
different types of buildings, each having different penetration loss (dB). If
our observation area consists of 15 different clutter classes, then this
feature is subdivided into 15 different features, each representing the number
of building penetrations in that respective clutter, whose sum equals the
total number of building penetrations in the propagation path of that UE. It
is denoted by $N_{c}$.

####  2.4.15 Indoor Distance in each Clutter Type

Indoor distance (in meters) covered by each unique clutter in the direct path
between a BS and UE. This feature characterizes the linear loss (dBm/m)
experienced by the signal in different indoor environments. Again, this
feature is subdivided into the total number of clutters in the observation
area, whose sum equals the total indoor distance in the propagation path of
that UE. It is denoted by $d_{\textit{indoor}_{c}}$.

####  2.4.16 Outdoor Distance in each Clutter Type

Outdoor distance (in meters) covered by each unique clutter in the direct path
between a BS and UE. This feature characterizes the linear loss (dBm/m)
experienced by the signal in different outdoor environments. Again, this
feature is subdivided into the total number of clutters in the observation
area, whose sum equals the total outdoor distance in the propagation path of
that UE. It is denoted by $d_{\textit{outdoor}_{c}}$.

TABLE V: Key Symbol Definitions Symbol |  Units |  Definition |  Symbol |  Units |  Definition
---|---|---|---|---|---
$\theta_{\textit{BS}}$ | o | Azimuth Angle of (BS) Departure | $P_{\textit{BS}}$ | dBm | BS Transmit Power
$\phi_{\textit{BS}}$ | o | Tilt Angle of (BS) Departure | $P_{\textit{UE}}$ | dBm | RSS of a UE
$\theta_{\textit{UE}}$ | o | Azimuth Angle of (UE) Arrival | $d$ | $m$ | Propagation Distance
$\phi_{\textit{UE}}$ | o | Tilt Angle of (UE) Arrival | $d_{\textit{vert}}$ | $m$ | Effective BS Height
$\phi_{\textit{ver}}$ | o | Vertical Angular Separation | $d_{\textit{man}}$ | $m$ | Manhattan Distance
$\theta_{\textit{hor}}$ | o | Horizontal Angular Separation | $L$ | - | LoS/NLoS State
$f$ | MHz | Operating Frequency | $d_{\textit{FD}}$ | $m$ | Distance from BS to First Diffraction Point
$h_{\textit{BS}}$ | $m$ | BS Antenna Height | $d_{\textit{LD}}$ | $m$ | Distance from BS to Last Diffraction Point
$h_{\textit{UE}}$ | $m$ | UE Antenna Height | $N$ | - | Number of Building Penetrations
$c_{\textit{BS}}$ | int | BS Clutter Type | $d_{\textit{indoor}}$ | $m$ | Indoor Distance in the Propagation Path
$c_{\textit{UE}}$ | int | UE Clutter Type | $d_{\textit{outdoor}}$ | $m$ | Outdoor Distance in the Propagation Path
$D_{\textit{DHM}}$ | - | Raster Grid Data of Digital Height Model | $N_{c}$ | - | No. of Building Penetrations in each Unique Clutter
$D_{\textit{DTM}}$ | - | Raster Grid Data of Digital Terrain Model | $d_{\textit{indoor}_{c}}$ | $m$ | Indoor Distance in each Unique Clutter
$D_{\textit{DLU}}$ | - | Raster Grid Data of Digital Land Use Map | $d_{\textit{indoor}_{c}}$ | $m$ | Outdoor Distance in each Unique Clutter

###  2.5 RSS Modeling using Machine Learning Methods

RSS prediction is essentially a regression problem, where the key features
proposed earlier are used as input for training ML models, to learn the
complex behavior of a signal passing through a wireless channel. Algorithm 1
explains the process of removing randomness from the UE traces (to some
extent) by gridding (averaging all measurements in a spatial bin) and then
training the ML model using the computed key features as input and the
corresponding expected value of RSS as output.

In this paper, we investigate a range of different Parametric, Non-Parametric
and Ensembles of machine learning regression algorithms for their strengths
and weaknesses while modeling RSS and implementing them.

  * •

Parametric algorithms, such as Linear Regression, assumes training data to be
of a specific functional form with a fixed size of parameters.

  * •

Non-Parametric algorithms, on the other hand, such as k-Nearest Neighbors,
Decision Tree and Neural Networks, are free to assume any functional form of
the training data.

  * •

Ensemble algorithms are of two types: Bagging and Boosting, which further have
several variants.

Earlier works on propagation modeling [17] were mostly based on parametric
models and some ensemble learning models.

Algorithm 1 RSS Prediction Model Training Algorithm

1:$D_{\textit{UE}}$, $D_{\textit{BS}}$, $D_{\textit{DTM}}$,
$D_{\textit{DHM}}$, $D_{\textit{DLU}}$

2:RSS Prediction Model $\mathbfcal{M}(F)$

3:for all UE traces do

4: Map its location to pre-defined grids (e.g., 10m x 10m)

5:end for

6:for each unique grid do

7: for each unique serving BS do

8: Average out the RSS ($P_{\textit{UE}}$) of all users to offset randomness

9: Compute feature vector
$F=[d,\theta_{\textit{hor}},\phi_{\textit{ver}},d_{\textit{vert}},\\\
d_{\textit{man}},L,d_{\textit{FD}},d_{\textit{LD}},N,d_{\textit{indoor}},d_{\textit{outdoor}},c_{\textit{BS}},c_{\textit{UE}},N_{c},\\\
d_{\textit{indoor}_{c}},d_{\textit{outdoor}_{c}}]$

10: end for

11:end for

12:Train the Machine Learning model $\mathbfcal{M}$ using Feature Matrix
$\mathbfcal{F}$, whose each row corresponds to a feature vector $F$

13:return $\mathbfcal{M}(F)$

####  2.5.1 Criteria for Model Evaluation and Selection

In this work, we have done a comprehensive and multi-faceted performance
evaluation of the state-of-the art ML algorithms, that includes predictive
performance, generalization performance and computational performance, and
also provided insights from each of these algorithms to make this paper self-
contained.

  1. 1.

Predictive Performance: The predictive performance of a model indicates the
model accuracy for unseen data. In our analysis, we have used Root Mean Square
Error (RMSE) and coefficient of determination ($R^{2}$) performance metrics
defined below to judge the predictive performance of models.

$RMSE=\sqrt{\frac{\Sigma_{i=1}^{N}{(P_{\textit{UE}_{i}}-\hat{P}_{\textit{UE}_{i}})^{2}}}{N}},$

$R^{2}=1-\frac{{SS}_{res}}{{SS}_{total}}=1-\frac{\Sigma_{i}{(P_{\textit{UE}_{i}}-\hat{P}_{\textit{UE}_{i}})^{2}}}{\Sigma_{i}{(P_{\textit{UE}_{i}}-\bar{P}_{\textit{UE}_{i}})^{2}}}.$

Here $P_{\textit{UE}}$ is the actual RSS of a UE, $\hat{P}_{\textit{UE}}$ is
the predicted RSS of a UE, $\bar{P}_{\textit{UE}}$ is the mean value of RSS
and $N$ is the number of UE traces in the test data. ${SS}_{res}$ and
${SS}_{tot}$ corresponds to the residual sum of squares and total sum of
squares, respectively. $RMSE$ is measured here in dB, whereas $R^{2}=1$ in the
best case and $R^{2}=0$ when the model output is always equal to its mean
value in test data. In rare scenarios, $R^{2}<0$, when the model predictions
are even worse than the baseline mean value prediction.

  2. 2.

Generalization Performance: The generalization performance of a model
indicates its robustness in predictive performance for unseen data (or
scenarios). In our analysis, we have used 5-fold repeated cross-validation
technique along with its mean and standard deviation value for all iterations
to judge the generalization ability of a model on unseen data (propagation
scenarios) with a certain confidence, even when using very sparse training
data (2% in our analysis). In other words, the generalization ability of the
model can be judged both by the standard deviation of its mean RMSE or the
increase in its predictive performance when using sparse training data for all
cross-validation iterations.

  3. 3.

Computational Performance: Computational performance of a ML model can be
judged by its training time, which indicates the time and therefore resources
it takes to train the model and prediction time, which shows its prediction
latency. These values are extremely crucial in a production setting where we
have cost (or resources) and latency constraints. In our analysis, all the ML
methods are evaluated using the same number of CPU cores for a fair
comparison.

####  2.5.2 Model Evaluation

  1. 1.

Linear Regression: As evidenced by our experiments, linear regression method
[27] doesn’t seem to be suitable to capture the complex non-linear nature of
the wireless channel. In our results, we have shown (in Figure 4) that it
gives a high prediction RMSE of 5.45 dB and a low $R^{2}$ score of 0.65.

  2. 2.

k-Nearest Neighbors: k-Nearest Neighbors (k-NN) [28] doesn’t seem to handle
non-linearity well in case of sparse training data, as the prediction in test
data is basically the mean of $k$ nearest data points in the training data.
Also, it has the highest computation cost at run-time among the tested
algorithms, as evidenced in results (Figure 4).

  3. 3.

Decision Tree: A single Decision Tree (DT) [29] in our experiments, is unable
to generalize well, especially with sparse training data and seems to overfit,
therefore also doesn’t seem to be a suitable choice for a ML-based propagation
model.

  4. 4.

Random Forest: Random Forest [30] is an Ensemble learning method, which
combines several decision trees, using Bootstrap Aggregation (or Bagging)
technique, to improve the predictive performance of a single decision tree.
Here, each tree is trained on a random subset, with replacement, of training
data. Also, each node is split among a random subset of input features, which
may not be the best split among all features. This randomness increases the
bias of the forest, when compared to a single non-random tree. The output here
is the average prediction of all individual trees, and due to this averaging,
variance in the ensemble model decreases, which more than make up for the
increase in bias, hence improving performance of the overall model, RMSE of
3.46 dB as compared to 4.76 dB in a single decision tree. Another advantage is
that, as opposed to a single decision tree, random forest is robust to
outliers in the training data. The main drawback of using this method is the
slow prediction speed, as evidenced in our results (See Figure 4), due to a
large number of trees, making it unsuitable for real-time predictions.

  5. 5.

Extremely Randomized Trees: Extremely Randomized Trees is another Bagging
Ensemble learning method, which goes one step further in randomizing the
trees, as compared to Random Forest. In addition to each tree trained on a
random subset of data and best split at each node chosen on a random subset of
features, thresholds are also picked at random for every candidate feature at
a node. This increase in randomness, further decreases the variance of the
ensemble model, at the cost of slight increase in bias. It has all the pros of
Random Forest, plus a reduction in training time, but the major drawback is
still high prediction time, as evidenced in our results (See Figure 4).

  6. 6.

Adaptive Boosting: Adaptive Boosting (AdaBoost) is a Boosting Ensemble model.
In boosting, models are built in sequence, so that each subsequent model
learns from the mistakes of the previous model, to create a stronger model. In
AdaBoost, each subsequent model is forced to focus on samples which were badly
predicted in the previous model. This is done by giving higher weights to
those samples in the training set, whose prediction error was high in the
previous model, and vice versa. Weighted sampling is then used in the
subsequent model to generate a derived training set, using sampling with
replacement. The probability that a training example appears in the training
set is relative to its weight. The final output is a weighted average of all
the model’s output, where more weight is placed on stronger models.
Consequently, the bias of the combined model is reduced in boosting, as
opposed to bagging, where the variance was reduced, by averaging several weak
learners. As shown in Figure 4, bagging methods outperforms AdaBoost in terms
of higher prediction accuracy. The other disadvantage of this technique is
that it cannot be parallelized, since the training of each subsequent tree
model, depends on the output of previous model, therefore, its training time
is much higher as compared to bagging ensemble methods.

  7. 7.

Gradient Boosting Decision Trees: Gradient Boosting Decision Trees (GBDT) is
another Boosting ensemble model, which works on the same Boosting principle of
learning from the previous model’s mistake, but the difference lies in how to
learn from the mistakes of previous model. Gradient Boosting learns from the
error residuals (gradients) of the previous model directly, unlike AdaBoost,
which changes the sample distribution at every iteration, by giving higher
weights to under-fitted (or badly predicted) samples. The goal is to
iteratively minimize the prediction error, by training each subsequent
decision tree model, on the residual errors (prediction errors) made by the
previous model, this process is essentially a gradient descent optimization on
the overall composite model. The final output would then be the sum of
predictions from all the models. Our results show that Gradient Tree Boosting
has much better prediction performance (RMSE of 4.32 dB) as compared to
AdaBoost (See Figure 4).

  8. 8.

Extreme Gradient Boosting: Extreme Gradient Boosting (XGBoost) [31] is an
advanced implementation of gradient boosting and follows the same principle.
The main advantage of XGBoost is the ability of parallel processing, therefore
much faster as compared to GBDT. While it’s not possible to create trees in
parallel because each tree is dependent on the previous, it’s possible to
build a tree using all the cores, by building several nodes within each depth
of a tree, in parallel. To improve the performance of the model, Weighted
Quantile Stretch idea is used to reduce the search space while finding the
best split, by looking at the distribution of features across all instances in
a leaf. It further reduces the computational complexity by learning the
sparsity patterns in the data and skip samples with missing values while
making a split. Moreover, it includes regularization to prevent over-fitting
and improve overall performance of the model (See Figure 4), due to which it
is also sometimes called as regularized gradient boosting.

  9. 9.

Light Gradient Boosting: Light Gradient Boosting Machine (LightGBM) [32] is
another implementation of Gradient Boosting, which improves on XGBoost. It can
train on larger datasets in a fraction of time and with comparable accuracy,
as compared to XGBoost, hence the word Light is used. It uses a technique
called Gradient-based One-Side Sampling (GOSS) to intelligently extract the
most useful information as fast as possible, by randomly skipping the samples
with less information (small gradients) in the dataset. Moreover it has
introduced another method called Exclusive Feature Bundling (EFB) for reducing
model complexity, by combining similar features in a near lossless way. Our
results have shown that LightGBM has better accuracy as compared to XGBoost in
sparse training data scenario and 12x faster training speed (See Figure 4).

  10. 10.

Categorical Boosting: Categorical Boosting (CatBoost) [33] is a gradient
boosting algorithm whose power lies in processing categorical features in the
dataset. Categorical features have values which are discrete and not related
to each other. CatBoost incorporates several innovative methods to deal with
these features at training, instead of during data pre-processing.
Furthermore, it incorporates a modified gradient boosting algorithm called
ordered boosting, to avoid target leakage present in standard gradient
boosting algorithms, as they rely on the target of all training samples at
each iteration, resulting in biasness. Here, however, training is done on
independent random permutations of the dataset at each iteration, to avoid
this prediction shift. Therefore, CatBoost can outperform other gradient
boosting algorithms, specially if you have categorical variables in the data
(for instance, LOS State, BS and UE Clutter Types are the categorical features
used in our model). As shown in our results (Figure 4), prediction RMSE is
reduced to 3.74 dB at the cost of increase in training time. It is worth
mentioning here that the GPU implementation of this algorithm is faster than
both XGBoost and LightGBM, but in our results we have used CPU for training
these algorithms.

  11. 11.

Deep Neural Network: Deep Neural Network (DNN) algorithm belongs to a special
class of machine learning, called deep learning and creates a multi-layer
perceptron (MLP) to find the input-output associations. Its basic structure
consists of an input layer, output layer and one or more hidden layers between
them, each containing several neurons (or nodes). Neurons in the input layer
equals the number of input features, whereas output layer consists of one
neuron which holds the prediction output. Number of hidden layers and its
neurons are variable, and depends on the complexity of model it is trying to
learn. Our extensive investigations on DNN design show that, for learning the
behavior of RSS in a wireless channel, 6 hidden layers each consisting of 32
neurons provide the most optimal results, any increase or decrease in this
number results in over-fitting or under-fitting on the training data,
respectively. The DNN used in this study has Rectified Linear Unit (ReLu)
activation function in the hidden layers, whereas output layer uses linear
activation function. In our simulation results (Figure 4), DNN performs worse
than ensemble-based methods and also has the highest computational cost.

####  2.5.3 Model Selection

For selecting the best performing model, we should overall look at the
predictive, generalization and computational performance across all evaluated
models. For a fair comparison, all the ML methods are evaluated using the same
number of CPU cores. Furthermore, in all experiments, 5-fold repeated cross
validation is used so that the results are generalizable in all propagation
scenarios.

In Figure 4(a), training and prediction time of all the methods are normalized
to the highest value individually. DNN has the highest, whereas linear
regression has the lowest training and prediction time. In Figure 4(c),
comparison of $R^{2}$ value is given, where CatBoost and LightGBM algorithms
perform the best in capturing the variance of RSS (or pathloss) and learning
complex non-linear relationships in a wireless channel and have the lowest
Root Mean Squared Error (RMSE) in sparse training data scenarios (shown in
Figure 4(b)), whereas linear regression has the highest RMSE for RSS
prediction as the complex non-linear nature of wireless channel renders it
unsuitable.

All the models are also separately trained on only 2% of training data, to
evaluate their performance in case of data sparsity, as is the case in real
practical scenarios. DNN shows the highest impact (loss in accuracy) due to
data sparsity.

Overall, LightGBM algorithm outperforms others, especially for real-time
implementation, due to its lightning fast training process. RSS model trained
using LightGBM algorithm is used for further simulations and results.

(a) Training time (normalized by the highest value of DNN) and Prediction Time
(normalized by the highest value of k-NN)

(b) RSS Prediction Error

(c) Model R-Squared Value

Figure 4: Comparison of various Machine Learning Algorithms w.r.t (a) Training
Time, Prediction Time, (b) Prediction Error, (c) R-Squared Value and
Robustness to Sparsity of Training Data, for Modeling RSS (Height of bars
represent the mean value and Error bar represent the standard deviation using
5-fold Repeated Cross Validation)

####  2.5.4 Model Improvement using Hyperparameter Optimization

The baseline LightGBM model performance shown in Figure 4 is further improved
by optimizing its hyperparameters for the RSS (or pathloss) prediction task,
according to the special characteristics of the wireless channel.

The hyperparameters selected to be optimized are: 1) ‘number of estimators’ in
the range of $500-2500$, 2) ‘maximum tree depth’ in the range of $5-20$ and 3)
‘learning rate’ in the range of $0.1-0.001$. Furthermore, 5-fold repeated
cross validation is used for each combination of hyperparameters and model’s
performance is evaluated based on its RMSE and $R^{2}$. Four different
hyperparameter optimization approaches are evaluated (shown in Figure 5) in
terms of performance gain and convergence time:

  1. 1.

Grid Search: This approach does an exhaustive search over the entire search
space of hyperparameters. Figure 5(a) shows the mean RMSE and $R^{2}$ of
LightGBM model at different combinations of hyperparameters. The model
converges to its best RMSE after 50 iterations (as shown in Figure 5(e)).

  2. 2.

Random Search: This approach also does an exhaustive search over the entire
search space of hyperparameters, but picks them randomly, therefore its
convergence time is more likely to be less than grid search method, as shown
in Figure 5(e), where the model converges to its best RMSE after 25
iterations.

  3. 3.

Bayesian: In this approach, hyperparameters are tuned using a Bayesian
optimization algorithm, known as Tree-structured Parzen Estimator (TPE) [34].
This Bayesian approach is a model-based approach, and as search iterations
progresses, it switches from exploration to exploitation to minimize the
objective function loss (concentrating on the hyperparameter combinations that
resulted in lower loss, which in our case is the RMSE). This approach
sometimes gets trapped in the local minima of the objective function, an issue
which is not faced by grid or random search. Figure 5(c) and Figure 5(e) shows
the superior performance of this approach as it converges in only 3 search
iterations.

  4. 4.

Simulated Annealing: This approach is a meta-heuristic optimization algorithm
[35], that is simpler and is preferred over its Bayesian counterpart when the
objective function is simple to evaluate. But it seems to converge slowly than
the Bayesian approach (as evidenced in Figure 5(e), where it took 8 iterations
to converge). After these 8 iterations, our proposed ML algorithm shows a
significant performance gain, as its prediction RMSE is reduced to 3.54 dB, as
compared to 3.91 dB earlier in the baseline LightGBM algorithm using the
default hyperparameters.

(a) Grid Search

(b) Random Search

(c) Bayesian TPE

(d) Simulated Annealing

(e) Comparison of hyperparameter tuning approaches w.r.t. Performance Gain and
Convergence Time. Bayesian optimization performed the best here by achieving a
10% improvement in prediction RMSE as compared to baseline LightGBM model, in
just 3 search iterations

Figure 5: Comparison of different Hyper-parameter tuning approaches for
improving the performance of baseline LightGBM model, in terms of RSS
Prediction RMSE, $R^{2}$ and convergence time (In subplots (a)-(d), RMSE and
$R^{2}$ of the LightGBM model is plotted against different combinations of
hyperparameters, after performing 5-fold Repeated Cross Validation at each
search iteration of the tuning process (dotted line/curve represents the Mean
value and filled area/polygon around it represents the standard deviation
using 5-fold Repeated Cross Validation)

##  3 Comparison with Empirical Radio Propagation Models

We also compare the performance of our proposed AI-driven 3D propagation model
based on improved LightGBM algorithm with traditional empirical propagation
models, as they are currently used in state-of-the-art commercial planning
tools to characterize the propagation behavior of a radio signal in different
conditions. Empirical models offer a mathematical equation to calculate the
path loss at any given point from the BS, and are based on data collected in a
specific scenario.

###  3.1 COST-Hata Model

It is an empirical model for pathloss calculation [5], that extends the Hata
formulae [36] to frequencies upto 2 GHz and it also takes into account the
topo map (DTM) between the BS and UE and morpho map (DLU) only at the
receiver. The below equation is valid for urban environments with 1.5 m UE
height.

$\displaystyle
L_{\textit{path}}=A_{1}+A_{2}*log(f)+A_{3}*log(h_{\textit{BS}})+$
$\displaystyle(B_{1}+B_{2}*log(h_{\textit{BS}})+B_{3}*h_{\textit{BS}})*log(d).$
(9)

Here $L_{\textit{path}}$ is the pathloss (in dB), $A_{1}=46.3$, $A_{2}=33.9$,
$A_{3}=-13.82$, $B_{1}=44.9$, $B_{2}=-6.55$, $B_{3}=0$ are user-defined
parameters, $f$ is the carrier frequency (in MHz), $h_{BS}$ is the height of
BS and $d$ is the propagation distance between BS and UE.

For Urban Areas:

$\displaystyle
L_{\textit{path}}^{\prime}=L_{\textit{path}}-a(h_{\textit{UE}}).$

For Sub-Urban Areas:

$\displaystyle
L_{\textit{path}}^{\prime}=L_{\textit{path}}-a(h_{\textit{UE}})-2*(log(\frac{f}{28}))^{2}-5.4.$

For Quasi-Open Rural Areas:

$\displaystyle
L_{\textit{path}}^{\prime}=L_{\textit{path}}-a(h_{\textit{UE}})-4.78*(log(f))^{2}+18.33*log(f)$
$\displaystyle-35.94.$

For Open Rural Areas:

$\displaystyle
L_{\textit{path}}^{\prime}=L_{\textit{path}}-a(h_{\textit{UE}})-4.78*(log(f))^{2}+18.33*log(f)$
$\displaystyle-40.94.$

Where $L_{\textit{path}}^{\prime}$ is the corrected pathloss and
$a(h_{\textit{UE}})$ is the correction factor for UE height different from 1.5
m.

For Rural/Small Cities:

$\displaystyle
a(h_{\textit{UE}})=(1.1*log(f)-0.7)*h_{\textit{UE}}-(1.56*log(f)-0.8).$

For Open Rural Areas:

$\displaystyle a(h_{\textit{UE}})=3.2*(log(11.75*h_{\textit{UE}}))^{2}-4.97.$

###  3.2 Stanford University Interim (SUI) Model

It is derived from the Erceg-Greenstein propagation model [37] and is valid
for 1900-6000 MHz. It also takes into account the topo map (DTM). It uses the
following formula:

$\displaystyle
L_{\textit{path}}=-7366+26*log(f)+10*a(h_{\textit{BS}})*(1+log(d))$
$\displaystyle-a(h_{\textit{UE}}),$ (10)

where,

$\displaystyle
a(h_{\textit{BS}})=a-b*h_{\textit{BS}}+\frac{c}{h_{\textit{BS}}},$
$\displaystyle
a(h_{\textit{UE}})=X*log\left(\frac{h_{\textit{UE}}}{2}\right).$

Here $a(h_{\textit{BS}})$ and $a(h_{\textit{UE}})$ are the correction factors
for BS and UE antenna heights, respectively, $f$ is the operating frequency
and $d$ is the propagation distance (in km). $a=4.6$, $b=0.0075$, $c=12.6$ and
$X=10.8$ are the correction constants which depend on the terrain type [6].

###  3.3 Standard Propagation Model (SPM)

It is derived from the Hata formulae and is valid for 150-3500 MHz. It also
takes into account the topo map (DTM) and morpho map (DLU) between the BS and
UE. It is given by the following formula:

$\displaystyle
L_{\textit{path}}=K_{1}+K_{2}*log(d)+K_{3}*log(h_{\textit{BS}}^{\prime})+K_{4}*L_{\textit{diff}}$
$\displaystyle+K_{5}*log(d)*log(h_{\textit{BS}}^{\prime})+K_{6}*h_{\textit{UE}}^{\prime}$
$\displaystyle+K_{7}*log(h_{\textit{UE}}^{\prime})+K_{\textit{clutter}}*f(\textit{clutter}).$
(11)

Here $K_{1}=23.8$, $K_{2}=44.9$, $K_{3}=10.89$, $K_{4}=0.19$, $K_{5}=-10$,
$K_{6}=0$, $K_{7}=0$, $K_{\textit{clutter}}=1$ are user-defined parameters,
$h_{BS}^{\prime}$ and $h_{UE}^{\prime}$ are the effective BS and UE heights,
respectively, by taking into account the earth terrain. $L_{\textit{diff}}$ is
the diffraction loss calculated by Deygout method and $f(\textit{clutter})$ is
the weighted average of the user-specified clutter losses, in the propagation
path between BS and UE [7].

###  3.4 ITU 452 Model

It is based on the ITU-R P.452-15 recommendation [8] and is valid for
100-500,000 MHz band. It takes into account the LoS/NLoS state, diffraction,
tropospheric scatter, surface ducting and elevated layer reflection and
refraction. It is given by the following formula:

$\displaystyle
L_{\textit{path}}=-5*log\left(10^{-0.2*L_{a}}+10^{-0.2*(L_{b}+(L_{c}-L_{d})*F_{j})}\right)$
$\displaystyle+A_{\textit{BS}}+A_{\textit{UE}},$ (12)

where,

$\displaystyle
F_{j}=1-0.5*\left[1+tanh\left(2.4*\frac{\theta-0.3}{0.3}\right)\right].$

Here $L_{a}$ is the basic transmission loss due to troposcatter, $L_{b}$ is
the minimum basic transmission loss with LoS propagation and over-sea sub-path
diffraction, $L_{c}$ is the basic transmission loss associated with
diffraction and LoS or ducting/layer-reflection enhancements,
$A_{\textit{BS}}$ and $A_{\textit{UE}}$ are additional losses due to BS and UE
surroundings, respectively, $F_{j}$ is the interpolation factor to take into
account the path angular distance and $\theta$ is the path angular distance.
These parameters are further calculated from equations in ITU-R recommendation
P.452-15 [8].

###  3.5 Performance Comparison

The proposed ML-based propagation model is compared against traditional
empirical propagation models, in terms of predictive performance,
generalization performance and computational performance.

####  3.5.1 Predictive Performance

In Figure 6, a box-plot representation is used to compare the performance of
our proposed model with the state-of-the-art empirical propagation models, by
taking highly precise ray-tracing based RSS estimates as ground truth. The
data used here as benchmark is unseen and not used earlier in the training or
validation process of our proposed ML-based model. The RSS is calculated from
the empirical models using
$P_{\textit{UE}}=P_{\textit{BS}}-L_{\textit{path}}$, where $P_{\textit{UE}}$
is the UE’s RSS, $P_{\textit{BS}}$ is the BS’s transmit power and
$L_{\textit{path}}$ is the pathloss calculated using (3.1)-(3.4). We can see
that the predicted RSS using our proposed AI-driven model has much less error
as compared to other empirical models, showing a $65\%$ improvement over the
best performing empirical model (3.2 dB RMSE as compared to 9.1 dB for SUI).

####  3.5.2 Generalization Performance

The reason for the gain in accuracy of the proposed model lies in its
generalizability as compared to other empirical propagation models. Firstly,
ML-based model, thanks to its ability to incorporate higher degrees of freedom
compared to an empirical, has an intrinsic advantage over empirical model.
Empirical models are usually scenario-specific and have different fine-tuned
parameter values for different geographic scenarios (e.g., urban, sub-urban,
rural etc.) using extensive channel measurements from that scenario. The key
cost of this advantage is opaqueness or black box nature of model, which we
will address in the next section.

Secondly, through the feature engineering process, the proposed model
leverages a novel combination of key features, which are not included in
traditional empirical models, and can characterize the physical and geometric
structure of the environment traversed by a signal in its propagation path
(e.g., indoor distance, Manhattan distance, number of building penetrations in
each clutter type etc.), and are sensitive to the change in network parameters
(e.g., horizontal angular separation, vertical angular separation etc.). These
additional features (or degrees of freedom) enable the ML-model to be trained
on combined data from different geographic scenarios and hence provide more
scalability and generalizability.

Figure 6: Comparison of Proposed model with various Empirical Radio
Propagation Models in terms of RSS prediction error, showing a $65\%$
improvement over the best performing empirical model (3.2 dB RMSE as compared
to 9.1 dB for SUI) Figure 7: Comparison of Proposed model with various
Empirical Radio Propagation Models and Ray Tracing w.r.t. Prediction Time and
RSS Prediction Error. The proposed ML-based model is atleast 65% more accurate
than the investigated empirical models, and 13x faster than ray-tracing

####  3.5.3 Computational Performance

While the proposed model yields better accuracy than empirical models, our
analysis (shown in Figure 7) shows that its computational complexity and
therefore implementation cost is much lower than the highly sophisticated ray-
tracing based tools that are being widely used in commercial cell planning
tools, because it only uses the key features as input to the trained ML-based
model to predict the RSS, as compared to ray tracing, which approximates the
interactions of all rays with the neighboring environment to estimate the
pathloss, hence computationally inefficient. As a result, it’s much faster
than ray-tracing, and thereby addresses a much-complained problem in ray-
tracing based tools, by industry professionals. The preliminary implementation
of the proposed framework has demonstrated a 13x decrease in prediction time
as compared to ray-tracing approach, and can be further optimized to make it
more efficient (for instance, by using parallel computing).

##  4 Secondary Analysis for Interpretability and Sensitivity

One of the key caveats of applying machine learning is lack of
interpretability of the resultant models. This challenge often undermines the
uptake rate of ML based models, particularly in cellular networks where stakes
are high. Therefore, knowing why a model is predicting what it is predicting
can be a very useful auxiliary information on top of accuracy, prediction and
training agility and robustness to sparsity of training data. Model
interpretation is also a vital debugging tool, as it can help you learn about
the problems (e.g., biasness) in the model and for ensuring that small changes
in the input do not lead to large changes in the prediction. Therefore, in
this section, we try to make our proposed black-box machine learning model
more trustable, interpretable and robust [38].

###  4.1 Sensitivity Analysis

Sensitivity Analysis is a useful technique for investigating the model’s
behavior for specific scenarios of interest and for providing a global insight
into the model’s behavior. This is done by quantifying the contribution of
each input feature, in the variability of the model output. These values are
called sensitivity indices.

####  4.1.1 Sobol Indices

The most popular method of finding these sensitivity indices is Sobol Method
[39], which is based on the variance of model output. However, they are very
difficult to interpret if there is a statistical dependence between features.
For Instance, in the case of independent features, there exists a unique Sobol
Index for a feature, representing the variance in model output solely by that
feature, also called First Order Sobol Index. But if the features have
dependency between them, then the first order indices fail to capture the
contribution of each feature, and Second Order Sobol Indices are used to
express the contributions of the interactions between each pair of features,
and so on for higher orders.

####  4.1.2 LOCO Variable Importance

Leave-one-covariate-out (LOCO), or even Leave-one-feature-out (LOFO) [40] is
another method for finding variable importance (or sensitivity) in the model
output. It scores each row in the training data for each feature (or
covariate). In each scoring run, one feature is missed and its impact on the
output prediction is measured. The feature with the most impact on the
predicted outcome is taken to be the most important. However, its performance
can quickly deteriorate if there are complex non-linear dependencies in a
model, in which case Shapley values will be a better technique.

####  4.1.3 Shapley Values

The lack of accurate model interpretation using the above methods, when there
are complex non-linear interdependencies between features, can be overcome by
using Shapley values [41], which is a Nobel-laureate concept in cooperative
game theory and economics, to determine the contribution of each player in a
collaborative game to its success, but can be used to calculate feature
importance in a model and thus achieve a good degree of interpretability, even
for non-parametric models. In the case of dependence between a group of input
features, the effect of interaction between features is equally allocated to
each feature within the group.

###  4.2 Model Interpretation with SHAP

A recently introduced method called SHAP (SHapley Additive exPlanations) [42],
based on Shapley values, measures how much each feature contributes, either
positively or negatively, to the model output. An advantage of using SHAP is
that each sample in the data has its own set of SHAP values, unlike
traditional methods, which only tells the importance of a feature across the
whole dataset. This is particularly useful, as we can observe the effect on
model output, for the whole range of each input feature. In our further
analysis, we have used the TreeSHAP algorithm [43], which is an efficient
approach of calculating shapley values of ML models belonging to decision tree
family (e.g., LightGBM, XGBoost etc.).

####  4.2.1 Feature Importance using SHAP Summary Plots

(a) SHAP Value Distribution

(b) Mean SHAP Value

Figure 8: (a) SHAP Summary plots showing Top 9 Input Features (a) SHAP Value
(Impact on RSS) variance w.r.t respective feature values (b) Mean SHAP Values
(Average Impact on RSS)

Figure 9: Impact of various features and their inter-dependence in predicting
Received Signal Strength. Useful for model interpretability and finding
important feature regions (or values) for intelligent data collection and
network automation

In Figure 8(a), SHAP values of some features are plotted for all measurement
instances, which show the distribution of impacts on the predicted RSS value,
for each input feature. Here the points are colored by the respective
feature’s value and piled up vertically to show density. For each measurement
sample, the sum of SHAP values (for every feature) equals the variance in the
predicted output from its mean value across all samples. For instance, from
domain knowledge we know that the RSS of a user will be highest if its
horizontal angular separation from the BS antenna is close to zero and vice
versa, due to the impact of antenna beamwidth on its attenuation. Similarly,
the RSS of a user will be high if it’s close to the BS, therefore, the impact
of propagation distance is highest at its extreme values, same is the case for
indoor distance and outdoor distance. On the other hand, Vertical Angular
Separation is generally inversely proportional to the distance between BS and
UE, therefore its impact is highest when it has a high value and vice versa.
Also the impact of Effective BS Height is high, if the net vertical distance
between the UE and BS is high, and vice versa. Similar trends can be seen for
other features as well.

In Figure 8(b), the mean SHAP value for each input feature is plotted. These
results show the average impact of each feature on the model output (i.e.,
predicted RSS value). We can see that, contrary to the common understanding
where distance is considered and used in literature as the key determining
factor for pathloss (or RSS), the Indoor Distance has the highest feature
importance (or impact) in the RSS model. On the other hand, BS Clutter Type in
the propagation path has the lowest impact.

####  4.2.2 Feature Inter-Dependency using SHAP Dependency Plots

The interplay of combinations of features can be uncovered using SHAP
dependence plots. By plotting the SHAP value for many samples in the dataset
(See Figure 9), we can see that the SHAP value (attributed importance) of a
feature changes as its value varies. However, its interaction with other
features in the model is captured by its vertical dispersion. Unlike standard
partial dependence plots, that only plot a line, here each dot (sample) is
colored with the value of an interacting feature.

In Figure 9, we can see that the impact of propagation distance decreases as
its value increases. Whereas, as mentioned before, indoor distance has an
interaction with the propagation distance that affects its relative
importance. Figure 9 shows the effect of effective BS height on the attributed
feature importance of vertical angular separation, where high value of
effective BS height decreases the importance of vertical angular separation
when its value is greater than zero, and vice versa. Similarly, in Figure 9,
we can see the increase in feature importance of indoor distance at points
where vertical angular separation is high. Figure 9 shows that feature
importance of Manhattan distance and its interplay with horizontal angular
separation. In Figure 9, as we know that the increase in number of building
penetrations in the propagation path between a BS and UE, increase its indoor
distance as well in most cases, results in the decrease of its feature
importance (Figure 9). Lastly, Figure 9 shows the feature importance of
effective BS height and its interaction with vertical angular separation.

###  4.3 Insights from Interpretability/Sensitivity Analysis

To interpret the model predictions and gain insights into the black-box model
by turning it into rather grey-box model, SHAP algorithm is used. The SHAP
Summary plot (or the feature importance plot) in Figure 8 shows the mean
importance of each feature in the variability of the model output. This plot
is particularly useful for a system-level control as it shows that what
control knob (or network parameter) needs to be played the most for tuning
network configuration to get optimal performance. SHAP Dependency plots (shown
in Figure 9), on the other hand, shows the behavior of feature importance (or
SHAP value) with respect to the value of its corresponding feature and its
interaction with the most dependent feature. This plot is useful for observing
the range of values for a pair of features that has the highest impact on the
model output. For Example, Figure 9 shows that the indoor distance and
vertical angular separation have the highest impact on the model output when 0
< $d_{\textit{indoor}}$ < 20 m and $\phi_{\textit{ver}}>10^{\circ}$.

###  4.4 Utility of Insights Gained from the Proposed Model

The information yield by the SHAP analysis, that has transformed the
originally black-box model into a _grey-box model_ , can be exploited in real
networks for several use cases. Below we identify three key use cases:

  1. 1.

Addressing the Sparsity Challenge: A key challenge in applying ML to wireless
networks is sparsity of training data i.e., gathering data for complete
parameters ranges is often very difficult, if not impossible. For example, its
not viable to gather RSS measurements against all antenna tilt range (0-90) in
a live network. Furthermore, usually the process of gathering and enriching
training data is costly. The proposed framework builds a grey-box model
instead of a black box model, thanks to the insights provided by the SHAP
analysis, can be leveraged to address the aforementioned challenges of data
sparsity. The knowledge that what parameter ranges are more crucial to the
model can be exploited for selective collection and enrichment of training
data. This can provide a lower cost/benefit ratio as compared to a uniform or
random collection or enrichment of training data. For example, based on
observation from Figure 9, instead of uniform or random measurement campaigns,
more resources should be dedicated to data collection for Antenna Tilt and
UE’s RSS data pairs corresponding to $\phi_{\textit{ver}}>10^{\circ}$
(vertical angular separation) and Antenna Tilt/Azimuth and UE’s RSS data pairs
corresponding to 0 < $d_{\textit{indoor}}$ < 20 (indoor distance in the
propagation path).

  2. 2.

Intelligent Optimization: Current design and post deployment optimization
paradigm of cellular networks rely mostly on the domain knowledge. However,
given the large number of design and optimization parameters per site—already
roughly 1500/site in LTE — and growing complexity trend towards 5G and beyond,
achieving optimal design and operation in emerging cellular networks by solely
relying on domain knowledge is going to become inviable approach. The insights
gained from the semi transparency (vis-a-vis greyness) of the presented model
achieved through the proposed framework can be very helpful towards more
effective and resource efficient design and post deployment optimization of
the network. For example, while searching for optimal design and configuration
parameters, the parameters and regions of the search space with parameter
ranges identified by the proposed framework to be more influential on the
KPIs, can be explored more exhaustively, compared to other parameters and
parts of the parameter range. This approach is expected to improve the design
and optimization processes compared to uniform (brute force based) or pseudo
random or heuristic search algorithms (e.g., genetic algorithms, simulated
annealing) based design and optimization.

  3. 3.

Lighter ML model for low-latency use-cases: The insights gained from the SHAP
analysis can also be used to select the most important features for building
our proposed ML model. Therefore, a lighter version of the model can be built
using the selected key features to further reduce the computational complexity
of the model. The results from this analysis (in Table VI) show that by using
the top 5 features (from Figure 8(b)), i.e., indoor distance, propagation
distance, vertical angular separation, horizontal angular separation and
effective BS height, the training and prediction time of the resulting RSS
prediction model can be significantly reduced (by around 70%) at the cost of
negligible loss in accuracy (by around 3%) to enable low latency use-cases for
the proposed SHAP-enabled lighter model. By allowing real-time predictions,
such lightweight model can be used for real time AI-powered closed loop
optimization of the network, thus acting as a key enabler for the Ultra-
Reliable Low-Latency Communication (URLLC) in 5G networks.

TABLE VI: Performance Evaluation of the SHAP-enabled Lighter Model using 5-fold Repeated Cross Validation Performance Metric |  Baseline ML Model using all features |  Lighter ML Model using Top 5 features |  Net Gain
---|---|---|---
RMSE | $3.542\pm 0.036$ | $3.661\pm 0.038$ | $-3.35\%$
$R^{2}$ | $0.854\pm 0.003$ | $0.844\pm 0.003$ | $-1.17\%$
Training Time | $1.896\pm 0.090$ | $0.681\pm 0.049$ | $\mathbf{+64.07\%}$
Prediction Time | $0.077\pm 0.005$ | $0.023\pm 0.002$ | $\mathbf{+70.13\%}$

##  5 Conclusion and Future Works

In this paper, we propose a framework for a robust and scalable AI-driven 3D
propagation model for cellular networks. To enable this framework, we have
identified a novel set of key predictors, that can characterize the complex
physical and geometric structure of the propagation environment. Performance
comparison of several state-of-the-art machine learning algorithms including
Linear Regression, K-Nearest Neighbors, Decision Tree, Random Forest,
Extremely Randomized Trees, Adaptive Boosting (AdaBoost), Gradient Boosting
Decision Trees (GBDT), Extreme Gradient Boosting (XGBoost), Light Gradient
Boosting (LightGBM), Categorical Boosting (CatBoost) and Deep Neural network
(DNN) is done to highlight their strengths and weaknesses in modeling the
propagation through complex real environment using the proposed key predictors
as input features. The results show that LightGBM outperforms other ML tools,
including DNN, in terms of computational complexity and robustness to
extremely sparse training data (just 2%), as often is the case in real
networks. On the other hand, compared to other tested ML tools, DNN’s
performance deteriorates the most when the training data becomes sparse. The
proposed ML-Based model is compared against state-of-the-art empirical models
including COST-Hata, Stanford University Interim (SUI), Standard Propagation
Model (SPM) and ITU 452 Model. Proposed ML-based model yields 65% higher
accuracy in RSS estimation as compared to empirical propagation models, when
highly sophisticated ray-tracing based data for the city of Belgium from a
commercial planning tool is used as ground truth. On the other hand, proposed
model offers 13x reduction in prediction time as compared to ray-tracing based
commercial planning tool. The black box nature of the proposed model is
transformed into relatively more interpretable grey-box model using SHAP
method. The insights presented through interpretability analysis offer new
research directions such as intelligent data gathering for addressing the
challenge of training data sparsity, finding the optimal combination of
network configuration parameters and building lighter ML models for low-
latency use-cases.

The presented system level pathloss prediction model combined with the
interpretability analysis thus manifests a framework that can act as a corner
stone for the Artificial Intelligence driven Self Organizing Networks (AISON),
as opposed to current SON which lacks interpretable models for quantifying
network performance as function of the plethora of network configuration
parameters. Furthermore, in addition to system level pathloss model, the
proposed framework can be extended to an AI-driven link level channel model
for channel estimation, physical layer design etc. Such extension will require
incorporating many other channel parameters such as delay spreads and angular
spreads etc., that can be neglected in system level path lass model due to the
much larger temporal and spatial scale that can suffice for system level
planning and optimization, but cannot give meaningful insights for link level
design. Other possible extensions are developing both link level and system
level channel models for higher frequency bands. This is needed especially for
next-generation 3D heterogeneous cellular networks in mmWave/Terahertz bands
with flying Unmanned Aerial Vehicle (UAV)-based BSs [44, 45] and
Reconfigurable Intelligent Surfaces (RIS) [46], since propagation conditions
will be significantly different than sub-6 GHz bands and conventional network
planning using empirical model will cease to be a viable option.

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|  Usama Masood is currently working toward his Ph.D. degree in electrical and
computer engineering at the Artificial Intelligence for Networks Center,
University of Oklahoma (OU), Tulsa, OK. His research focus at AI4Networks
Center is on designing AI-enabled system-level solutions for Zero Touch
Automation in emerging networks. During his PhD, he has contributed to several
National Science Foundation (NSF) research and development projects on 5G
Cellular Networks including the design and development of 5G Testbed at OU-
Tulsa campus for enabling experimental research on different 5G use-cases and
designing advanced cell outage management framework for self-healing networks,
a multi-national project on AI-based Self Organizing 5G and beyond networks
and a industry collaboration project with Ericsson Research, CA for solving
the training data sparsity challenge to enable AI-based zero touch automation
in emerging networks.
---|---
|  Dr. Hasan Farooq received his B.Sc. degree in Electrical Engineering from
the University of Engineering and Technology, Lahore, Pakistan, in 2009, M.Sc.
by Research degree in Information Technology from Universiti Teknologi
PETRONAS, Malaysia in 2014 and his Ph.D. degree in Electrical and Computer
Engineering from the University of Oklahoma, USA in 2018. Hasan has developed
several methods to harness unprecedented intelligence from the wireless
communication network data that can be utilized for proactive dynamic network
orchestration and optimization. His dissertation was awarded Gallogly College
of Engineering Dissertation Excellence Award by University of Oklahoma in
2018. He has contributed to several NSF funded research projects in the domain
of self-organizing networks for 5G and beyond and has authored over 40 high
impact publications. He is currently working as AI Researcher at Ericsson
Research Silicon Valley.
---|---
|  Ali Imran (Senior Member, IEEE) is a Presidential Associate Professor and
Willams Professor in ECE and founding director of the Artificial Intelligence
(AI) for Networks (AI4Networks) Research Center and TurboRAN Testbed for 5G
and Beyond at the University of Oklahoma. His research interests include AI
and its applications in wireless networks and healthcare. His work on these
topics has resulted in several patents and over 100 peer-reviewed articles
including some of the highly influential papers in the domain of wireless
network automation. On these topics he has led numerous multinational
projects, given invited talks/keynotes and tutorials at international forums
and advised major public and private stakeholders and co-founded multiple
start-ups. He holds a B.Sc. degree in electrical engineering from the
University of Engineering and Technology Lahore, Pakistan, in 2005, and the
M.Sc. degree (Hons.) in mobile and satellite communications and the Ph.D.
degree from the University of Surrey, Guildford, U.K., in 2007 and 2011,
respectively. He is an Associate Fellow of the Higher Education Academy, U.K.
He is also a member of the Advisory Board to the Special Technical Community
on Big Data, the IEEE Computer Society.
---|---
|  Dr. Adnan Abu-Dayya has been serving as the Founding Executive Director of
the Qatar Mobility Innovations Center (QMIC) since 2009. It is one of the
first technology innovation institutions in the Middle East focused on
translating R&D and technology innovations into scalable digital platforms and
solutions in the field of Intelligent Mobility and Smart Cities. From 2007 to
2008, Adnan served as the Chairman of the Electrical Engineering Department at
Qatar University. Before moving to Qatar in 2007, Adnan worked for 10 years at
AT&T Wireless in Seattle, USA where he served in a number of senior management
positions covering product innovations, emerging technologies, systems
engineering, product realization, and intellectual property management. Before
that, Adnan worked as a Senior Manager at Nortel Networks in Ottawa, Canada in
the advanced technology group, and as a Senior Consultant at the
Communications Research Centre in Ottawa, Canada. Dr. Adnan serves as the
Chairman of the Advisory Board of the Electrical & Computer Engineering
Department of Texas A&M University at Qatar, he is a member of the Steering
Committee of the Smart Grid Research Center at Texas A&M University at Qatar,
and is a member of the advisory board of the Qatar Car Museum. Adnan received
his PhD in Wireless Communications (Electrical Engineering) from Queens
University, Kingston, Canada in 1992. He has 10 issued patents, and more than
100 referred publications.
---|---
  *[ML]: Machine Learning
  *[LightGBM]: Light Gradient Boosting Machine
  *[SHAP]: SHapley Additive exPlanations
  *[AI]: Artificial Intelligence
  *[QoS]: Quality of Service
  *[RSS]: Received Signal Strength
  *[SUI]: Stanford University Interim
  *[SPM]: Standard Propagation Model
  *[ANN]: Artificial Neural Network
  *[BS]: Base Station
  *[UE]: User Equipment
  *[BSs]: Base Station
  *[DTM]: Digital Terrain Model
  *[DHM]: Digital Height Model
  *[DLU]: Digital Land Use Map
  *[MDT]: Minimization of Drive Tests
  *[LoS]: Line of Sight
  *[NLoS]: Non Line of Sight
  *[RMSE]: Root Mean Square Error
  *[$R^{2}$]: coefficient of determination
  *[k-NN]: k-Nearest Neighbors
  *[DT]: Decision Tree
  *[URLLC]: Ultra-Reliable Low-Latency Communication
  *[UAV]: Unmanned Aerial Vehicle
  *[RIS]: Reconfigurable Intelligent Surfaces