# Cellular Network Radio Propagation Modeling with Deep Convolutional Neural
Networks

Xin Zhang  Futurewei Technologies, Inc.BridgewaterNew JerseyUSA ,  Xiujun Shu
GTS R&D Algorithm Dept.Huawei Technologies, Co., Ltd.ShenzhenChina ,  Bingwen
Zhang  Futurewei Technologies, Inc.BridgewaterNew JerseyUSA ,  Jie Ren  GTS
R&D Algorithm Dept.Huawei Technologies, Co., Ltd.ShenzhenChina ,  Lizhou Zhou
GTS R&D Algorithm Dept.Huawei Technologies, Co., Ltd.ShenzhenChina and  Xin
Chen  GTS R&D Algorithm Dept.Huawei Technologies, Co., Ltd.ShenzhenChina

(2020)

###### Abstract.

Radio propagation modeling and prediction is fundamental for modern cellular
network planning and optimization. Conventional radio propagation models fall
into two categories. Empirical models, based on coarse statistics, are simple
and computationally efficient, but are inaccurate due to oversimplification.
Deterministic models, such as ray tracing based on physical laws of wave
propagation, are more accurate and site specific. But they have higher
computational complexity and are inflexible to utilize site information other
than traditional global information system (GIS) maps.

In this article we present a novel method to model radio propagation using
deep convolutional neural networks and report significantly improved
performance compared to conventional models. We also lay down the framework
for data-driven modeling of radio propagation and enable future research to
utilize rich and unconventional information of the site, e.g. satellite
photos, to provide more accurate and flexible models.

radio propagation, deep convolutional neural networks, path loss

††journalyear: 2020††copyright: acmcopyright††conference: Proceedings of the
26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining; August
23–27, 2020; Virtual Event, CA, USA††booktitle: Proceedings of the 26th ACM
SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’20), August
23–27, 2020, Virtual Event, CA, USA††price: 15.00††doi:
10.1145/3394486.3403287††isbn: 978-1-4503-7998-4/20/08††submissionid: 861

##  1\. Introduction

In a wireless communication system, signal transmitted by a base station can
undergo attenuation as it propagates through space before reaching a mobile
user equipment (UE). The difference in strength between the transmitted and
received signal is commonly referred to as path loss, usually measured in dB.

Path loss may be due to many effects, such as, free-space loss, refraction,
diffraction, reflection, aperture-medium coupling loss, and absorption. Path
loss can be influenced by terrain contours, environment (e.g., urban or rural,
vegetation or foliage, and the like), propagation medium (e.g., dry or moist
air), the distance between transmitter and receiver, the height and location
of antennas, the antenna radiation pattern, and other factors.

Path loss is often used in analysis and design of link budget of a
telecommunication system, and is fundamental for modern cellular network
planning, a process to optimize the number of base stations, the locations of
these base stations, antenna selection and parameter settings, etc, such that
maximum coverage is achieved with minimal cost.

Measuring path loss at all locations of interest is expensive, and sometimes
impossible when planning an area without existing base stations. Therefore, it
is desirable to predict path loss at a mobile UE using radio propagation
models without actual measurement. Conventional radio propagation models are
categorized into two types: empirical and deterministic models
(antenna_prop4_wireless_book, 1, 2).

Empirical models describe the relationship between path loss and environment
parameters using multiple equations, which are determined empirically using
coarse statistics of data measured under a limited number of settings,
specified by environment parameters. Empirical models are computationally
efficient, but are usually inaccurate because they use only very limited
parameters to describe the environment.

Deterministic models on the other hand describe the environment using detailed
information such as GIS maps, including building locations and shapes, terrain
of the area, land use (clutter layer), and antenna settings (location,
azimuth, tilt and radiation pattern). These models are derived from physical
laws of wave propagation, and in theory could be computed exactly by solving
Maxwell’s equations. Unfortunately, this approach requires unrealistically
complex mathematical operations and computing power. Ray tracing technique is
a popular approximation using geometrical optics and knife edge diffraction
theory (ikegami91_ray, 3, 4). Deterministic models are usually more accurate
than the empirical ones, at the cost of more computation. Furthermore, actual
path loss is determined by much richer information about the environment than
conventional GIS maps can provide, so the prediction by deterministic models
still has considerable error.

Radio propagation modeling is essentially a regression problem in machine
learning terms, and quite a few works have proposed to use machine learning
methods, mainly artificial neural networks, to predict path loss (mgbe15_ann,
5, 6, 7, 8, 9, 10). These works propose to use regression neural network to
predict path loss based on limited description of the environment and are
usually not site specific, similar to empirical models. Fully connected neural
networks with one or a few hidden layers are proposed, and the input
information are usually numerical vectors with 10 to 20 dimensions, only able
to capture very coarse characteristics of the environment.

Recently deep convolutional neural networks (ConvNet) have significantly
outperforms other machine learning techniques in computer vision related
tasks, such as image recognition (lenet_cnn, 11, 12, 13, 14, 15) and image
segmentation (fullyconv15_cnn, 16, 17, 18). These deep architectures have
exponentially more representation power and significantly outperform
conventional shallow learning methods. Usually much more training data is also
necessary for them to work properly.

In this article, a data-driven modeling framework is proposed to reformulate
path loss prediction to an image regression problem, and utilize recent
breakthrough of deep convolutional neural networks in computer vision related
tasks. We demonstrate how input information to the model, such as maps and
antenna parameters, can be translated into image tensors. We also proposed a
specific design of deep convolutional neural network architecture that is
tailored for radio propagation modeling. Results from large amount of
simulated and real field data show that the proposed data-driven model
performs significantly better than conventional radio propagation models.

It is also worth pointing out that the framework we proposed is flexible and
can accommodate a variety of future designs. One aspect is novel input
information design. For example, building materials and vegetation have large
effect in high frequency radio propagation, but they are expensive if not
impossible to include in conventional GIS maps. On the other hand, both
building materials and vegetation can be observed in satellite photos and can
be easily included into input tensors. Another aspect of future design is
researchers can invent better neural network architectures for more accurate
models.

The contribution of this work lies in the following aspects:

  * •

We reformulate the radio propagation modeling to an image regression problem
and propose to use deep ConvNet to solve it.

  * •

We apply radio propagation domain knowledge and design input tensors to
capture most relevant input information.

  * •

We select suitable neural network architectures based on the nature of radio
propagation modeling, as demonstrated in Section 3.3.

  * •

We tested the proposed model using both simulated and real field data to show
significant superiority over conventional models, and the proposed model has
already been deployed as a Huawei internal tool and is being used by field
engineers over the world.

##  2\. Conventional Radio Propagation Models

###  2.1. Empirical Models

There are a number of commonly used empirical models, for example, Okumura-
Hata model (hata80_emp, 19), Stanford University Interim model
(stanford_interim_emp, 20), standard propagation model (SPM) (spm_emp, 21) and
Walfisch-Ikegami model (antenna_prop4_wireless_book, 1, 2).

The above models all use a few parameters and equations to characterize
typical classes of radio links such as urban, suburb and rural. The parameters
are determined based on measured and averaged losses in the aforementioned
typical classes of ratio links. Thus empirical models are not site-specific,
i.e., they use exactly the same parameters for two different sites as long as
the sites fall in the same link category.

For example, the Okumura-Hata model is valid for microwave frequencies from
150 to 1500 MHz, and is suited for both point-to-point and broadcast
communications, and covers mobile station antenna heights of 1-10 m, base
station antenna heights of 30-200 m, and link distances from 1-10 km. The
Okumura-Hata model uses separate sub-models for the urban, suburban and rural
environments. The urban model is formulated as follows.

(1) $\begin{split}L_{U}=&\;69.55+26.16\log_{10}f-13.82\log_{10}h_{B}\\\
&-C_{H}+[44.9-6.55\log_{10}h_{B}]\log_{10}d\end{split}$

For small or medium-sized city,

(2) $C_{H}=0.8+(1.1\log_{10}f-0.7)h_{M}-1.56\log_{10}f$

For large cities and carrier frequency in $150\text{MHz}\leq f\leq
200\text{MHz}$,

(3) $C_{H}=8.29(\log_{10}(1.54h_{M}))^{2}-1.1$

And for large cities and carrier frequency in $200\text{MHz}\leq f\leq
1500\text{MHz}$,

(4) $C_{H}=3.2(\log_{10}(11.75h_{M}))^{2}-4.97$

$L_{U}$ is the path loss in urban areas in decibel (dB). $h_{B}$ is the height
of base station antenna in meter. $h_{M}$ is the height of mobile station
antenna in meter. $C_{H}$ is the antenna height correction factor. $f$ is the
carrier frequency in Megahertz. $d$ is the distance between the base and
mobile stations in kilometer.

The models for suburban and rural areas are just slightly modified version of
the above model and are omitted here.

SPM, derived from Okumura-Hata model with a few more parameters, is another
commonly used model in industry, and we will compare our proposed method with
SPM in Section 4.

As we can see, the disadvantage of empirical models is that they use very
limited input information and parameters to coarsely characterize radio links,
so the prediction can be very inaccurate. In our experience, the root-mean-
square error (RMSE) between the un-calibrated prediction and ground truth is
typical around $12$-$15$dB.

###  2.2. Deterministic Models

Ray tracing techniques based on geometrical optics (ikegami91_ray, 3, 4)
produce the most widely used deterministic path loss models. Reflection,
scattering and diffraction are modeled and calculated using ray tracing, and
the effects are combined as shown in Figure 1.

Figure 1. Ray tracing model.

The input to ray tracing models contains much more information about a
specific site than that of empirical models. GIS maps, often containing
building layers (specifying heights, shapes and locations of buildings),
terrain layers (altitude of ground) and clutter layers (categorized land use),
are typically used as input to ray tracing. Examples of these layers can be
found in Figure 2, where the values in each layer are typically normalized.

Antenna parameters such as location, height, azimuth, tilt and radiation
pattern are also required in ray tracing.

Ray tracing can calculate deterministic prediction of path loss at any
specified points. With site-specific and rich input information, it is usually
more accurate than empirical models. However, many factors affecting radio
propagation such as the material of building enclosure and density of
vegetation are not available in typical GIS maps, resulting in prediction
error (measured in RMSE) close to 10dB. Thus, to perform well for a specific
site in practice, ray tracing models require calibration which is essentially
over-fitting a few parameters to measurements from the same site using
expensive drive tests. Moreover, in a new site planning task, these
measurements are outright not available.

Ray tracing based radio propagation models are very complex and are
implemented as commercial softwares by several companies implementing their
proprietary technologies. They are usually very computationally intensive and
are often too slow for cellular network planning, which is essentially an
optimization process with thousands of steps and each step recalculates the
path loss of the whole area under consideration.

Another disadvantage of ray tracing models is that unconventional input
information such as satellite photos of areas cannot be easily incorporated
into the models. These new sources contain even richer information than
traditional GIS map layers.

##  3\. Proposed Neural Network Architecture and Training

In this section we present the details of proposed data driven propagation
model, including input tensor design, neural network architecture and training
methods.

###  3.1. Problem Formulation

We observe that the inputs to ray-tracing based propagation models include GIS
map layers, which are essentially numerical matrices and can be considered as
the channels of an image, as shown in Figure 2. Each pixel of the image here
is corresponding to a square area patch of $m$ by $m$ meters in the physical
world, where $m$ is the resolution of GIS map. Typical resolutions of an GIS
map are 5 meters, 10 meters and 20 meters.

Ray-tracing based models also utilize engineering parameters such as antenna
location (latitude, longitude and height), orientation and radiation pattern
as input information. These parameters are not in matrix format and cannot be
directly incorporated into input image tensors. There are two possible ways to
include these inputs into machine learning frameworks, e.g., neural network
architectures. We can keep the original format of these engineering parameters
and use as scalar inputs to a neural network in parallel to the image tensor
constructed with GIS map layers. By this design we are asking the neural
network to learn some underlying mechanisms on these parameters which we
already know with simple physics. We think a better approach is to translate
these parameters into additional channels of the input image tensor so that we
have a unified input in image format. By these translations, we are
essentially applying domain knowledge into the input tensor design, as will be
demonstrated in the next subsection.

Propagation models predict path loss values at each location in an area, which
can be gridded into square patches of $l$ by $l$ meters. If we assume the path
loss at any point within a patch to be the same (a common practice by field
engineers), the output can be formatted into a matrix of path loss values,
which can also be considered as an image with each pixel corresponding to a
small area patch of $l$ by $l$ meters. The intensity of a pixel is set to the
path loss value at the square patch representing the pixel. Note that in
practice $l$ is typically larger than or equal to $m$.

Thus the prediction process is essentially an image-to-image regression
problem, i.e., mapping from one image domain to another. Instead of using ray
tracing techniques to calculate the mapping, we propose to use an alternative
machine learning and data driven approach to learn the mapping. More
specifically we proposed to use a deep convolutional neural network (ConvNet)
as the propagation model and use simulated and real field data to train the
ConvNet. Details of the network architecture and training methodology will be
presented later in this section.

###  3.2. Input Tensor Design

One key aspect to use a ConvNet as propagation model is the design of input
tensor, such that all necessary information is organized in a format to be
utilized effectively by the neural network.

Figure 2. Channels of input tensor to PLNet.

We design the input to be a 3-dimensional tensor, with the shape of $C\times
W\times H$. $C$ is the number of channels defined below. $W$ and $H$ are the
width and height (in pixels) of the target area and they are design
parameters. For example, if the GIS map has a resolution of $m=5$ meters and
we would like to predict the path loss within an area of 1000 by 1000 meters,
the width and height of the patch are both 200 pixels.

As mentioned previously, layers (building, terrain and clutter) of GIS maps
are naturally image channels, while engineering parameters have to be
translated into extra channels of the input image tensor.

Instead of using extra channels to encode the latitude and longitude of the
antenna, we propose to use the 2-D location of the antenna as the center to
cut out a map patch (with all three layers) from the whole map. Subsequent
channels also use the same center.

In practice the antenna can be either installed on a small tower on top of a
building, or hang on the side. We encode the antenna height information in a
channel of the input tensor where each pixel has the same value representing
the antenna height in meters.

With the above intuition, we design the input tensor with 8 channels and
summarize each channel as follows:

  * •

Clutter channel contains the clutter layer of a GIS map, which categorizes
each pixel into one of the surface feature types, such as sea, forest, urban,
river, lake, village and other ground cover information. It is a categorical
value and usually numericalized as integers from 1 to 21.

  * •

Building channel contains the building layer of a GIS map, which describes the
general outline and height information of buildings. If there is building on a
pixel, the value of the pixel is the height of building at the pixel. If there
is no building on the pixel, the value is simply zero.

  * •

Terrain channel contains the terrain layer of a GIS map, describing the
altitude of each pixel, which is normalized by subtracting the lowest point in
the map patch.

  * •

Azimuth channel indicates the horizontal angle difference between the line of
sight from each pixel to the antenna and direction of main lobe.

  * •

Tilt channel indicates the vertical angle difference between the line of sight
from each pixel to the antenna and direction of main lobe.

  * •

Antenna height channel is designed to encode the height of antenna simply with
the height in meters at each pixel of the map patch.

  * •

Frequency channel describes the frequency of carrier signal. Signals with
different carrier frequencies usually have different attenuation, hence
different path losses. We simply copy the frequency value of a sample (the
carrier frequency of the base station) to each pixel.

  * •

Antenna Gain channel describes the antenna radiation pattern, i.e., how the
radio energy is distributed in the space around antenna. We assume the 3-D
radiation pattern is intercepted by the terrain surface below the antenna, and
the gain at each pixel on the surface is filled in this channel of the tensor.

Examples of the channels are shown in Figure 2. Note that in this framework,
the input tensor can be easily modified when new information is available. For
example, satellite photos of an area can be incorporated as an additional
channel for the input tensor.

Figure 3. Architecture of PLNet.

###  3.3. Network Architecture

Referring to the conventional propagation models, we observe that the path
loss at a specific location is determined by both the macro condition of the
environment such as the overall density of buildings in the area, and the
micro condition close to the receiver such as the number of walls nearby and
their specific locations.

To capture the above characteristics, a good neural network architecture for
path loss prediction should assemble different levels of abstraction inside a
neural network to form predictions. We propose to use a U-Net
(Ronneberger15_cnn, 18) type of architecture, which is also known as encoder-
decoder with skip connections. These skip connections are critical and serve
as the combinations of various abstraction levels. The detailed architecture
is shown in Figure 3.

In all the convolution and de-convolution layers, we use 3x3 kernel size and
set stride to 2. Padding is applied such that feature map size is only altered
by striding. Note that in Figure 3 the input tensor was designed to have the
same width and height as the output tensor (path loss matrix), i.e., the input
map layers has the same resolution as the path loss prediction. If they have
different resolution, it is easy to modify the architecture to up-sample/down-
sample the path loss matrix in the width and height dimensions. We dub our
neural network PLNet for easy reference later in this article.

###  3.4. Supervised Training

The most straight forward way to train PLNet is supervised training. The input
tensors are based on engineering parameters of base stations and GIS maps,
constructed according to Section 3.2. Corresponding labeled path loss matrices
are collected from field measurements or alternatively from commercial path
loss simulators. Details about data generation will be explained in Section 4.
With the labeled path loss matrices (supervisors) for all the training
samples, we can use mean absolute error (MAE) or mean square error (MSE) as
the loss function for training. MAE is defined as follows and MSE can be
defined similarly,

(5)
$\begin{split}\mathcal{J}_{L1}\left(\mathbf{\Theta}\right)&=\mathbb{E}_{\mathbf{(X,Y)}}\left\|\mathbf{Y}-\hat{\mathbf{Y}}\left(\mathbf{X},\mathbf{\Theta}\right)\right\|_{1}\\\
&\approx\frac{1}{NWH}\sum_{i=1}^{N}\sum_{j=1}^{W}\sum_{k=1}^{H}\left|\mathbf{Y}_{i}(j,k)-\hat{\mathbf{Y}}_{i}(j,k)\right|\end{split}$

where $\mathbf{\Theta}$ is the weights of PLNet and
$\mathbf{X}=\\{\mathbf{X}_{i}\\}_{i=1}^{N}$ are the input tensors as described
in Section 3.2. $\mathbf{Y}=\\{\mathbf{Y}_{i}\\}_{i=1}^{N}$ and
$\hat{\mathbf{Y}}=\\{\hat{\mathbf{Y}}_{i}\\}_{i=1}^{N}$ are the ground-truth
and predicted path loss matrices respectively. $N$ is the number of samples,
and $W$ and $H$ are the width and height of the path loss matrix.
$\mathbf{Y}_{i}(j,k)$ refers to path loss value at the $j^{th}$ row and
$k^{th}$ column of the ground truth path loss matrix of the $i^{th}$ sample.

Note that in field collected data not all pixels have valid measurements,
because it is not realistic to ask road testing equipment to traverse every
single pixel in the area. Actually it is not uncommon that only 5-10% of the
pixels in a path loss matrix have measured values. Pixels without valid
measurements should be excluded from the calculation of loss function, hence
will not affect the gradient back propagation. Just clamping the error from
these pixels at zero will effectively prevent them from interfering the
training process.

##  4\. Experiments

(a) Ground truth (simulated by ray tracing)

(b) Predicted by PLNet

Figure 4. Path loss matrices of ground truth calculated by commercial
simulator compared with PLNet prediction.

The proposed method is tested with both simulated data and real field data. We
use simulated data in addition to real field data for two reasons.

First, it takes time and effort to collect significant amount of field data to
train PLNet from scratch, and using simulated data to pre-train PLNet can
benefit prediction accuracy when only small amount of real data is available.
In our case, the pre-training is effective because, in both the simulated and
real data, the input tensors have the same distribution, i.e., they are both
constructed using GIS map layers, a set of know antenna radiation patterns,
and same ranges of antenna parameters. The only difference between the
simulated and real data is the path loss values (supervisors), so simulated
data are especially useful to train lower level representations in PLNet.

The second reason is that field data are usually proprietary and there is no
open data set for path loss prediction problem. For other researchers to test
our proposed method, GIS map layers and commercial path loss simulators (ray
tracing based) are available to the public (some may charge license fees). The
simulator we used in generating simulated data is the “Volcano propagation
model” developed by Siradel SAS (volcano_ray, 22).

(a) Building channel

(b) Terrian channel

Figure 5. Filters of the first convolution layer of PLNet. The weights of
filters corresponding to the building and terrain channels are plotted.

To generate simulated data, We use GIS maps of 40 cities around the world, and
randomly select suitable locations to “install” (virtual) antennas. Note that
the selected antenna locations need to be far enough from each other to ensure
independence among samples. We also select antenna radiation patterns randomly
from a set of known antennas, and set the antenna parameters such as azimuth,
tilt and transmitting power randomly. Given the GIS maps and antenna
parameters, Volcano simulator is used to calculate the corresponding path loss
matrices. We managed to generate more than 800,000 simulated samples.

We also collected about 400,000 field data samples using drive test or mobile
measurement report (contains GPS locations and received signal power) from
more than 50 cities worldwide. As pointed out in Section 3.4, not all pixels
have valid measurements, so we adjust the cost function and back propagation
accordingly as described in Section 3.4.

We increased the effective number of both simulated and field samples by data
augmentation techniques such as reflection and rotation.

Root-mean-square error (RMSE) is used as the metric for prediction accuracy
and it is calculated by averaging over all pixels and samples.

###  4.1. Results with Simulated Data

First we clarify that the results from this subsection, i.e., results using
simulated data (generated from ray tracing based models), are to demonstrate
that PLNet has the capacity to capture meaningful patterns from the input
tensor by ”learning from ray tracing”. In real application, PLNet will compete
with ray tracing based models, and we show in the next subsection that PLNet
trained by real field data outperformed ray tracing significantly.

We use the simulated data from 36 cities (728,574 samples) to train PLNet, and
data from the other 4 cities (96,724 samples) to test the performance of
PLNet.

It takes about 80 epochs for the training to converge, and we achieve test
performance of $\text{RMSE}=7.48\text{dB}$ using data from the 4 test cities.

Samples of predicted and ground truth (calculated by Volcano in this case)
path loss matrices are shown in Figure 4. The predicted path loss matrix
captures the overall patterns of the ground truth, but it is a little blurred
as a result of using MSE/MAE as loss function.

We also visualize the convolutional filters of the first layer in Figure 5.
The original PLNet has $3\times 3$ convolution filters for each channel and it
is hard to visualize such small filters, so we increase the filter size of the
first layer filters to $11\times 11$ just for visualization purpose. We can
see that the filters for building and terrain channels are indeed trained to
discover low level patterns of the corresponding map layers.

There are two interesting observations. First, the filter patterns of the
terrain channel is wider and smoother than those of the building channel. This
is because buildings have much sharper edge in map compared to smooth changing
terrains. Second, the filter patterns are similar to the ConvNets trained for
image recognition purpose, with the exception of some patterns having
distinctive highlighted pixels. When these filters convolve with the input
building or terrain channels, they search for higher buildings or terrains
near the current location. This is because protruding objects can reflect
electromagnetic waves and affect radio propagation.

From these results, we can see that the lower layers of PLNet are trained to
capture patterns of input map, even though it is trained with simulated data
generated by raytracing models. Thus it can be a good pre-training in the case
where real field data is limited.

###  4.2. Results with Field Data

Field collected data from 48 cities world-wide (319,350 samples) are utilized
to train our PLNet, and data collected from another 4 cities (8,316 samples)
are used to test the performance of PLNet against empirical and ray-tracing
based methods. The results are shown in Table 1, where PLNet ST stands for
PLNet by supervised training, and SPM is a widely applied empirical model in
industry. We can see the proposed PLNet out-perform the conventional methods
by a large margin in each test city.

Table 1. RMSE (in dB) of proposed methods compared with conventional methods using real data. Note that we anonymized the city names for privacy concerns. City | PLNet ST | Ray Tracing | SPM
---|---|---|---
City A | 8.44 | 11.84 | 16.56
City B | 9.54 | 12.87 | 17.15
City C | 9.04 | 12.28 | 16.88
City D | 8.81 | 12.02 | 17.02

We also plot samples of predicted path loss matrices by PLNet and conventional
methods in Figure 6. Note that only the center area of the ground truth path
loss matrix has valid values. PLNet predictions are more consistent with
ground truth and are less dramatic in the surrounding area.

|  |
---|---|---
|  |

(a) Field ground truth

(b) Prediction by PLNet

(c) Prediction by commercial ray tracing simulator

(d) Prediction by SPM

(e) Legend

Figure 6. Predicted path loss matrices by PLNet and conventional methods.

Because of the large errors, both empirical and ray-tracing based methods
recommend to “calibrate” their models before actual prediction. Basically
calibration is overfitting the conventional models to certain region of
consideration, for example a city. It is worth pointing out that in many cases
data required by calibration are not available, for example, in new
construction of cellular networks, where no base station has been constructed
yet. In other cases, data required by calibration has to be recorded through
expensive road test. So PLNet has considerable advantage here because it can
perform well without calibration.

But for the sake of completeness, we present the performance comparison after
calibration. A map of City D is shown in Figure 7, where the calibration data
is collected from the roads in blue color, and the data collected from roads
in red color are used for test after the calibration.

Figure 7. Map of City D where the calibration data is collected from the roads
in blue color, and the data collected from roads in red color are used for
test after the calibration.

Both SPM and Volcano use calibration data to fine-tune a few parameters
designed for calibration (volcano_ray, 22). For PLNet, we use the calibration
data to fine tune the neural network for a few epochs. The RMSE for SPM and
Volcano are 9.50dB and 8.53dB respectively, improved from the un-calibrated
performance. PLNet still has the best accuracy with
$\text{RMSE}=7.81\text{dB}$.

PLNet also has significant computation speed advantage over ray tracing based
method. To predict the path loss matrix of a single cell with $320\times 320$
pixels, Volcano needs 30 seconds (8-core Intel i7 CPU), while PLNet only needs
0.33 seconds (implemented in TensorFlow with one Nvidia Titan Xp GPU). Of
course PLNet benefits from GPU computation, but at this time we are not aware
of any ray tracing based path loss prediction software taking advantage of GPU
acceleration.

##  5\. Conclusions

In this paper we presented a new method to predict the radio propagation path
loss using a deep convolutional neural network, which we dub as PLNet. We
designed the input tensor to PLNet to include detailed GIS map layers and
antenna parameters. We also proposed network architecture of PLNet that are
tailored for this application. Using real field data, we showed that the
proposed method is significantly more accurate than conventional methods and
can also be computed much faster using modern GPUs.

###### Acknowledgements.

The authors would like to thank Dr. Jin Yang and Dr. Yan Xin for inspiring
discussions during the course of this work. The authors would also like to
thank the anonymous referees for their valuable comments and helpful
suggestions.

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