1. Introduction
During the evolution of cellular networks, several systems have been developed without being standardized, which poses many problems, particularly in terms of electromagnetic compatibility (frequency distribution). As a solution, GSM (Global System for Mobile communication) is the first 2G cellular telephony standard to have been standardized, and is today the global benchmark for mobile radio systems. Given the apparent importance of the mobile channel, it is essential to master the design and densification methods of a mobile channel network. It is also necessary to study the physical behavior of the channel signals and evaluate the resulting losses.
The mobile system is based on electric radio links located inside the troposphere, the seat of many meteorological and climatic phenomena (rain, snow, fog, etc.), or above the ground with many obstacles (buildings, vegetation, etc.) inside buildings. The budgets study of such links requires considering the different attenuations (loss in free space, attenuation due to the different effects of the environment: hydrometeors, buildings, vegetation, etc.) and the different reinforcements of the signal between the transmitter and the receiver (antenna gains), where different propagation mechanisms come into play such as reflection, refraction, transmission, scattering, etc.
With the rapid growth and need for high-quality throughput and capacity of cellular networks, increasingly accurate modeling of the propagation channel under various environmental conditions, frequency ranges, and bandwidths have become extremely important. This modeling improves radio interfaces in terms of performance, optimizing networks during their deployment (determination of coverage, frequency allocation, power definition, antenna gains, etc.), and determining unavoidable disturbances. The models are of different types: deterministic, empirical, and semi-empirical models. Deterministic models are based on reference models represented in known physical processes. The computation time is relatively high [
1]. Experimental data only supports empirical models depending on frequency, distance, and antenna height (see
Table 1). They are powerful, fast, and do not require geographic databases [
1].
In the last decade, statistical learning algorithms have attracted much interest in academia and companies in various sectors. They have been successfully implemented to perform predictive tasks related to statistical processes. However, another approach to modeling a system is fascinating, namely artificial neural networks. They derive their modeling power from their ability to detect high-level interconnections, simultaneously involving several variables [
2]. Today, neural networks are well established in several fields: in the financial world for the prediction of market fluctuations, in the pharmaceutical field (analysis of organic molecules), in the banking field for the detection of credit card fraud, and in the calculation of credit ratings, in aeronautics for the programming of autopilots, etc.
The applications are numerous, and all share a common point essential to the usefulness of neural networks: the processes for which one wishes to make predictions have many explanatory variables and, above all, there are possibly nonlinear dependencies between these variables which, if discovered and exploited, can be used to increase the predictability of the process. From the point of view of process prediction, the main advantage of neural networks over traditional statistical models is that they can automate the discovery of essential links. The main interest of these networks is their ability to react automatically to a complex environment such as telecommunication systems. This study evaluates signal losses in a physical channel as an example.
The rest of the paper is organized as follows:
Section 2 discusses propagation models commonly used in path loss prediction. Related work is presented in
Section 3, while
Section 4 describes neural network architectures such as Multi-Layer Perceptron’s (MLP), selected neural network topologies and details of datasets processing.
Section 5 presents our contribution.
Section 6 presents the results obtained for loss prediction using neural network training, and compares the different neural network architectures.
Section 7 compares our contribution with some empirical models.
Section 8 is the conclusion.
2. Classification of Propagation Models
Propagation models design a radio interface to optimize performance and deploy systems in the field to determine radio coverage. The models will be used in engineering tools to predict various values that will benefit the deployment of radio telecommunications systems and radio coverage research (site selection, frequency allocation, power definition) and interference description. The models rely heavily on geographic datasets that include topography and land use types. This is because the way ultra-high frequency (UHF) radio waves propagate in a given space is intimately related to the obstacles (buildings, tree trunks, mountainsides, etc.) encountered along the propagation channel.
Therefore, the modeling of geographical objects is essential in any UHF wave propagation model [
3]. Propagation models are then used to provide a mathematical prediction of wave propagation between the origin and destination service area. This allows a system receiver to assess whether a planned radio system will sufficiently serve the desired service area. The following subsections present the fundamental models studied and their classification, data requirements, and coverage notes.
Table 1.
The empirical and semi-empirical model parameters.
Table 1.
The empirical and semi-empirical model parameters.
Models | Frequencies | Mobile Station Antenna Height | Base Station Antenna Height | Distance | The Scope of the Application |
---|
Okumura-Hata model [4]. | 200 to 1900 MHz | 30 to 200 m | 1 to 10 m | 1 km to 10 km | Weak Urban Dense Urban Rural
|
Free Space Path Loss (FSPL) model [5] | undefined | undefined | undefined | undefined | |
Cost 231-Hata [6]. | 1500–2000 MHz | 30 to 200 m | 1 to 10 m | 1 km to 20 km | |
Walfisch-Ikegami (WI) model [7,8]. | 800–2000 MHz | 1 to 3 m | 4 to 50 m | 0.02 to 5 km | |
ECC-33 or extended Hata-Okumura model [9,10]. | 200 to 3500 MHz | 30 to 200 m | 1 to 10 m | 1 km to 100 km | |
Stanford University Interim (SUI) model [11]. | To 11 GHz | 2 to 10 m | 10 to 80 m | 0.1 and 8 km | |
Ericsson model [12,13]. | 200 to 3.5 GHz | 30 to 200 m | 1 to 10 m | 1 km to 100 km | |
5. Our Contribution
This work introduces machine learning approaches to efficient path loss prediction to address the issues related to empirical and deterministic models. Considering a multi-transmitter situation, we developed and validated models for estimating path losses using MLP. The inputs to the machine learning algorithms change from one dataset to another. The parameters we used in the outdoor environment were: longitude and latitude extracted from payload, received signal strength indicator, signal-to-noise ratio, transmission frequency, spreading factor, packet sequence number, transmission bandwidth, distance between the gateway and the end-device, and power received at the gateway. Every parameter has an impact on signal propagation, e.g., the terrain causes attenuation in the signal. We used longitude and latitude to define the nature of the environment where the model can be applied. The essential indoor parameters were the number of floors and walls between the gateway and the end device. These parameters enable us to test the model in a building similar to the studied building. The output layer is the path loss in both environments.
5.1. General Description of the Designed System
In the MLP, neurons are put in layers that go from the input to the output. The output of each layer node is the weighted sum of its input over a particular activation function. We create three MLPs using path loss (PL) as the output layer for the experimental data gathered across fourteen base stations.
Figure 2 depicts the network topology of the MLP model with two hidden layers. We used this kind of network instead of a deep learning network because the aim was to achieve a higher computational speed.
Because it can be used for nonlinear functions and produces a smooth thresholding curve for the MLP, we chose the logistic sigmoid as the activation function. The standard output of the sigmoid function ranges from 0 to 1. When learning is performed in an MLP by repeatedly adjusting the weights, the feedforward approach comes first, followed by the backpropagation algorithm for excellent optimization. By updating MLP weights, the training aim is to minimize the loss function. The connections are joined together when the feedforward operation is finished. The backpropagation optimization approach is one of the essential hyperparameters for the MLP model. It starts by backpropagating to the weights of the first layer, moves on to the next iteration, and stops when the values of the weights reach a certain tolerance threshold.
5.2. Our Training Algorithm
The MLP training was carried out in a supervised manner using a backpropagation algorithm, whose objective is to adjust the weights and minimize the amount of quadrature error between the network output and the target result. The quadrature error is:
where
d(n) is the target value, and
is the value of the network output. The backpropagation algorithm defines the error gradient in aim to achieve a minimum.
The error gradient
E(x) is calculated for each weight as follows:
where
For the output layer i = L, the output error is denoted.
δLk is calculated as follows:
where
f(x) is the activation function.
For hidden layers, the error
is given by:
The modification of the weights
W(n) and the biases
b(n) is obtained by the following two equations:
0.7 is the learning step determining the convergence speed, and 0.6 is the momentum or inertia term that prevents the algorithm from getting stuck on a local minimum.
Ojo et al. [
32] designed the model with two hidden layers, while we tested three different architectures for the MLP models. However, their radial basis function (RBF) results were excellent. Isabona et al. [
33] focused on developing the networks in the urban areas while we conducted our models in three different areas. Additionally, they used several training algorithms, while we used the same training algorithm in all cases (
Figure 3).
5.3. Formatting of the Dataset Used in Training and Validation Sets
Network learning will be performed through a parallel learning model. It is necessary to build a learning base to develop network learning. Since the learning is supervised, the dataset must contain the network input and the desired output. To respond to the neural inputs and make the neural network training more efficient, the databases must go through a preprocessing step (
Figure 4). Preprocessing is a typical technique to remove spurious discontinuities in the input function space and reduce the question inputs to manageable data. This is followed by appropriate normalization, taking into account the magnitude of the acceptable network values.
5.4. Data Collection Procedure
5.5. MLP Network Learning
Fourteen datasets were used to optimize neuronal structures, which are composed of different numbers of samples. These datasets are further subdivided into a training set and a test set. The training datasets are composed of (60%), the test datasets are composed of (20%) items that are reserved for the final performance measurement, and the validation datasets of (20%) examples. The test, validation, and training samples must be different and be randomly selected from the original dataset.
The optimization process (learning, validation, and testing) was performed for many iterations for which error stabilization was obtained. The numbers of neurons in the first, second and third layers were changed, and the associated optimization error was recorded. In this study, the backpropagation algorithm was used. It is important to note that the end of the program can be caused by one of the following events:
5.6. Architecture Optimization
The optimization method chosen to solve a particular problem not only depends on the nature of the parameters to be optimized but also on the given problem. Therefore, only some general optimization methods can solve all problems, but many methods are adapted for each case. Therefore, we have designed the models with three different architectures (one, two, and three hidden layers).
As the network design grows, i.e., the number of layers and neurons increase, and the network will include more connections, which implies slower learning and processing. These topologies were chosen using an optimization procedure illustrated in
Figure 5. Once the neural network has been trained, it must be validated on a dataset that is not the same as the one used for the training. This validation allows us to evaluate the neural system’s performance and identify the data type that caused the problem. The network architecture will be modified if the performance is not achieved.
After testing several learning possibilities and measuring performance, we obtained the following architectures.
7. Comparison of our Models with Empirical Models
This section presents the results obtained for 14 different datasets with different path loss prediction techniques. The results obtained by our MLP were compared with those obtained by six empirical models: (Free Space Path Loss Model (FSPL), Walfisch-Ikegami model (WI), ECC-33 Model (ECC-33), COST 231-Hata model (PLCH), EricssonModel (PL999), Stanford University Interim Model (SUI)), and the type of model architecture. The results are shown in
Figure 10,
Figure 11,
Figure 12,
Figure 13,
Figure 14,
Figure 15,
Figure 16,
Figure 17,
Figure 18 and
Figure 19.
Analysis of the Simulation
Figure 10,
Figure 11,
Figure 12,
Figure 13,
Figure 14,
Figure 15,
Figure 16,
Figure 17,
Figure 18 and
Figure 19 shows that the MLP model has the lowest error when all measures are included. Still, the other six empirical models overestimated the path loss and are not suggested for use in the studied context. All observed datasets and alternative designs agree with the MLP model, which performs better than the empirical models.
The parameters were used in the simulation to improve the deployment of the MLP models outside the initial environment where they were built. Since the models were built outside the environment under consideration, these corrective variables were employed to estimate the empirical models. The parameters hr and hb represent the antenna height of the base station and the mobile station, respectively, which were also used in the experiment. These numerical values were obtained based on the taken measurements. We used different base station heights in our simulations and evaluations. The real data was obtained by controlling these correction variables and the specific properties of the model were used to design and test our models. We divided our datasets into four main environments (urban, suburban, rural, and indoor environments). Based on
Figure 10,
Figure 11,
Figure 12,
Figure 13,
Figure 14,
Figure 15,
Figure 16,
Figure 17,
Figure 18 and
Figure 19, the model proposed in this study gave the best performance compared to other empirical models:
The obtained result can be explained by the fact that these models were developed in a specific domain which was different from that of our datasets. To reach high accuracy, the path loss prediction should be close to the actual path loss value. Furthermore, these changes depend on the parameters of the dataset (distance, frequency, base station antenna height, mobile station antenna height). For example, in Datasets 11 to 14, the parameters were collected in an urban area with the same frequency, distance, and mobile station, but we noticed that the path loss value changed from one set to another because the height of the base station antenna changed; the longer the transmitter antenna, the lower the path loss. This also applies to Datasets 8 to 10, whose parameters were collected in the same situation, except for the base station antenna height.
On the other hand, the parameters of Dataset 4 were collected inside buildings. The path loss varies depending on the obstacles inside the building, such as wall thickness, room space, and number of windows. Our models showed to be the best in all cases because we used all possible parameters to make predictions almost identical to the actual path loss values.