1. Introduction
In 5G communication, millimeter wave (mmWave) communication is one of the most important technologies. Despite technical advantages, such as wide bandwidth and low latency, it suffers from low spectral efficiency, due to high sensitivity and low scattering and diffraction amounts, narrow coverage, and the unfavorable influence of non-line-of-sight (NLoS) propagation [
1]. Thus, mmWave path loss modeling acts as a crucial factor in determining the optimal placement and configuration of 5G base stations, which are directly related to the quality of user experience. To this end, it is important to design a robust and accurate path loss model even in a complex propagation environment, such as a dense urban scenario.
The existing path loss modeling methods are grouped into three categories: empirical methods [
2,
3], deterministic methods [
4,
5], and machine learning-based methods [
6,
7,
8,
9]. The empirical method builds a model based on curve fitting methods by using measurement data collected in a typical path loss environment. In empirical models, the carrier frequency, the distance between the transmitter (Tx) and the receiver (Rx), and the path loss factor (PLE) are included as key parameters. They are often unsuitable, though, for cell planning and optimization purposes, due to limited prediction accuracy [
2,
3].
Three-dimensional, 3D, ray-tracing is one of the most advanced deterministic mmWave path loss modeling methods. It simulates the behavior of physical propagation, based on geometric optics, including attenuation, reflection and scattering. The deterministic methods use a large number of computational resources, but can achieve higher accuracy than empirical methods. However, 3D models must be able to perform predictions precisely in propagation environments that are rarely used in deterministic methods in many deployment scenarios.
Path loss modeling, based on machine learning, is treated as a regression problem based on measured data. In this path loss modeling, the characteristics, extracted according to the measurement location and propagation environment data, are used as input, and the measured path loss value is used as the desired answer in training. The characteristics of machine learning-based models for path loss in urban scenarios include those associated with rooftop diffraction, T-R separation, obstacle penetration, reflection, and characteristics of the transmitting antenna, etc. This allows neural networks to learn the relationship between inputs and outputs and, thus, generally outperforms empirical models. However, machine learning-based modeling requires more than a certain amount of domain knowledge in parts such as input preprocessing, feature selection and extraction, and may require a large amount of computation.
Recently, a deep learning-based method for path loss modeling of mmWave in suburban and indoor environments has been proposed [
10,
11]. It uses a two-dimensional image generation algorithm called the Local Area Multi-Line Scan (LAMS) algorithm to transform the 2D map data between Tx and Rx into a two-dimensional image containing topographic information for training convolutional neural networks (CNNs). These methods have shown promising results with better prediction performance, in terms of accuracy, than empirical and deterministic methods.
However, 2D CNN-based modeling is not suitable for urban environments, where the heights and sizes of buildings are relatively irregular, because 2D images are disadvantageous in representing the different heights and detailed shapes of many buildings and complex networks of streets. Therefore, a three-dimensional LAMS image, which is advantageous for representing complex urban scenarios with many tall buildings, has been proposed to train 3D CNN, and the 3D CNN-based model has shown better performance, compared to the 2D CNN-based model [
12].
Although it has been shown that deep learning-based path loss models can outperform conventional models, their prediction accuracy in practice may be severely limited by the size of the measurement data set that is required for training, due to the sluggish growth rate of mmWave system deployment in urban areas. Few-shot learning methods have been introduced to address the issues of small training data sets [
13,
14,
15]. These methods, however, require a machine learning model to be trained on multiple tasks of disjoint support classes to be fine-tuned on a new set of classes. Measurement data sets that can be used as training data sets, however, cannot be organized into disjoint sets of multiple tasks, and hence the few-shot learning methods cannot be directly applied in mmWave path loss modeling.
In this paper, we propose a novel training method called multi-way local attentive learning which allows for learning from multiple perspectives on the same set of training samples with local attention paid to each subset of the entire dataset. Here, the entire data set is partitioned into multiple minibatches constructed by a data set partitioning scheme. Many different partitions can be made with respect to different attributes of the sample data such that a larger amount of knowledge is extracted from the same data set.
The main contributions of this paper can be summarized as follows:
We propose a 3D-LAMS algorithm that can generate 3D images that encode the radio propagation environment between a Tx and a Rx in dense urban areas.
We propose a 3D CNN path loss model that is expected to be able to extract more effectively the three-dimensional morphological information included in the 3D LAMS images which have a large impact on the amount of path loss.
Finally, we propose a novel learning method that addresses the overfitting issue due to the scarcity of measurement data for training a CNN model.
This paper is organized as follows.
Section 2 presents some of the previous works on mmWave path loss modeling based on deep learning. In
Section 3 the proposed methods are explained in detail, followed by experimental results with some analyses given in
Section 4. Finally, we conclude our discussion in
Section 5.
2. Related Works
Empirical methods try to build a model by using curve fitting techniques based on the measurement data collected in a representative path loss environment. They usually include carrier frequency, the distance between the transmitter (Tx) and receiver (Rx) (i.e., the TR-separation), and the path loss element as their main parameters. Although the simplicity of empirical methods has made them popular, their accuracy of prediction is often limited and not adequate for cell planning and optimization purposes [
16].
A CNN-based millimeter wave path loss model for suburban areas, where heights of buildings are generally low, was proposed in [
10]. Additionally, they proposed Enhanced Local Area Multi-Line Scan (E-LAMS) algorithms to extract topographic information within the path loss environment between Tx and Rx as an image, and to use it as input for 2D CNN. The proposed model has four subnetworks and feature-sharing layers, predicting path loss values for four directional antennae mounted on the receiver. The feature sharing layer used in this model shares common knowledge among subnetworks, and it allows generalization. As a result of comparing the path loss model proposed in [
10] with the state-of-the-art empirical path loss model, the path loss model proposed in [
10] proved to have better performance. However, since this was only considered in a suburban area, it is not clear that performance in urban areas, with varying heights of buildings, will be guaranteed.
A 3D CNN-based path loss model for urban areas, which convert and use tabular data converted into image was proposed in [
17]. In this paper, various feature data vectors of tabular data were spread to various pixels, and in the process, the importance of specific features was calculated and arranged to correspond. The generated image was fused to be a compound pseudo image to be used at the input of the CNN. Although this method of generating 3D CNN input images has been shown to achieve performance gain, there was a lack of explanation on how to extract features, such as tabular vectors.
FadeNet, which can predict large-scale fading from the base station to each location within the coverage area based on CNN, was proposed in [
18]. FadeNet mainly aims to plan and optimize 5G mmWave cellular networks. They collected and used measured data of mmWave cells in multiple sites. They were able to utilize parallel processing units of graphics processing units to reduce prediction time by 40×–1000×, compared to ray tracing methods. In terms of accuracy, the prediction accuracy of the proposed FadeNet was higher than distance dependent prediction and conditional least squares prediction.
The 3D CNN-based model proposed in [
12] aimed to achieve a similar level of performance as in suburban and indoor environment scenarios even in dense urban scenarios, with various morphological characteristics representing many high-rise buildings of various heights and complex street networks. As the input of the 3D CNN model, a 3D image, including building and terrain information, was used, and the RSRP data measured at seven base stations were used as the output. The use of 3D CNN model technique proved that 3D is more advantageous than 2D for CNN-based path loss prediction in complex urban environments.
CNN with Meta-learning is based on meta-learning, which performs well in few-shot learning scenarios with multiple tasks constituting meta-tasks [
19,
20,
21]. The CNN-based indoor and outdoor path loss model composed of multi-beam meta-tasks outperforms the CNN model, not only in the empirical model but also in the conventional training algorithm. Meta-learning, also known as “learning to learn”, means designing a model to learn new skills or quickly adapt to a new environment through several training tasks. The meta-learning techniques that motivated [
19,
20,
21] are Model-Agnostic Meta-Learning (MAML) and Reptile [
22,
23]. Both MAML and Reptile perform meta-optimization through gradient descent, and it enables the model to quickly learn new tasks with a small amount of data based on existing knowledge. Therefore, meta-learning was introduced to improve the learning performance of a model that accommodates different set values of each transmit antenna and different location characteristics of the receiver Rx, such as LoS/NLoS propagation.
Aster is a high-performance propagation model for Atoll that supports macro, micro, and small cell urban propagation scenarios. Aster is based on two major components: Vertical diffraction over rooftops, based on the Walfisch Ikegami model, and the multiple knife-edge Deygout method and horizontal diffraction, based on ray tracing [
4,
5,
24,
25]. In [
24], the Walfisch Ikegami model facilitates radio frequency (RF) path-loss predictions in typical suburban and urban environments, where the building heights are quasi-uniform. The method proposed in [
25] calculates multiple diffraction losses of VHF/UHF propagation for multiple sharp ridges or hills based on Deygout’s method and can yield very good estimates of the received signal level.
4. Experiments and Results
The field measurement dataset has a total of 750 measured RSRP values. Each piece of measured data has corresponding GPS-based location information (longitude, latitude, and height) and serving physical cell ID (PCI). This measured scenario consists of seven PCIs, which cover an area of approximately 300 m wide and 300 m long. The number of pieces of measurement data allocated for each PCI is different. This measured dataset was collected by driving vehicles equipped with GPS receivers and 5G mmWave RSRP measurement devices. The transmitter also consisted of different locations (longitude, latitude, and height) and different settings (Azimuth, Downtilt). The attributes of the measured data and transmitter data are in
Table 3, and the RSRP intensity of the measured data and the location plots of the PCI are in
Figure 4. We also found that two additional attributes, i.e., the distance (T-R separation) and the relative angle, affected the RSRP values the most through correlation analysis. As illustrated in
Figure 4, the two parameters, the horizontal relative angle and the distance from Tx to Rx, have a great influence on the RSRP value. We used these attributes mainly in multi-way partitioning.
The Line-of-Sight (LoS) is an important factor that greatly affects the path loss. Since it is difficult for a deep learning model to extract LoS/NLoS information directly from a 3D map, preprocessing is needed to provide an explicit LoS/NLoS value at each location. This can be done simply by calculating the ratio of virtual Tx-Rx line segment traversing through building structures. If the ratio is close to 0%, the Tx-Rx pair is determined as ‘LoS’.
The goal of this study was to predict the measured RSRP value by the proposed model when there were measured data and transmitter information which were not used for training. The dataset had 750 measured data mapped to 7 PCIs, respectively, and a scenario with a train-to-test ratio of 75:25 and an LoS environment ratio of nearly half could be selected, as shown in
Table 4. The finally selected scenario consisted of data corresponding to PCI 1 and 3 as test data and the remaining data as training data.
The structure of the 3D CNN model was the same as that mentioned in
Section 3.2, and the multi-way local attentive learning technique mentioned in
Section 3.3 was applied to the model. For comparison, prediction results of the basic 3D CNN, 3D CNN with meta-learning, and the Aster propagation model of Atoll were used in addition to the 3D CNN model with multi-way local attentive learning applied [
20].
The 3D CNN model with meta-learning was applied to 3D CNN models for generalization of a generic model that accommodated different set values of each transmitting antenna, and different location characteristics of the received Rx, such as LoS/NLoS propagation. The advantage of meta-learning is that, given a new environment, it can learn faster and produce good generalization performance compared to before, and it can learn efficiently with less data. In the case of path loss model learning, meta-learning-based learning consisting of a number of meta-learning tasks based on the actual measurement area (base station), base station operation morphology, and Tx-Rx distance could be applied [
22]. The Aster propagation model was based on advanced ray-tracing propagation techniques and combined high accuracy.
The single and multiple 3D CNN models with multi-way local attentive learning, the vanilla 3D CNN model, and the 3D CNN model with meta-learning were trained and tested for comparison. The Aster propagation model included in Atoll was also used to generate predicted path loss values.
Table 5 compares these models.
Table 6 shows the mean, minimum, and maximum values for the entire test data of various models mentioned above. Analysis of LoS in
Table 6 first shows that the Single 3D CNN model showed the best performance. Its minimum, mean and maximum were all lowest compared to other models, especially its mean, which was 4.38 dBm, with a difference of 0.47 dBm, compared to 4.85 dBm, the second lowest mean of Multiple 3D CNN model. The difference between its minimum and maximum was 4.86 dBm, the second smallest after 2.69 dBm of the Aster propagation model. This confirmed that 3D CNN with multi-way local attentive learning—single model had the second smallest variation among the five models. By comparing the minimum, mean, maximum, and variation of the aforementioned models, it could be seen that in LoS, the performance was good in the order of Single 3D CNN model, followed by Multiple 3D CNN model, 3D CNN with Meta-learning, basic 3D CNN, and Aster propagation model. Among them, the RMSE gap between the two 3D CNNs with multi-way local attentive learning was very small compared to the gap with other models. In the case of mean, it was very small, about 0.47 dBm.
Next, analyzing NLoS also shows that the Single 3D CNN model performed best. Its minimum, mean, and maximum all showed the lowest values compared to other models, but the difference from other models was smaller than in LoS. Its mean was 7.55 dBm, which was about 0.18 dBm different from 7.73 dBm, which was that of the Multiple 3D CNN model. In NLoS, the variation of 3D CNN with multi-way local attentive learning was also the smallest. Model performance was in the order of variation of Single 3D CNN model, multi model, basic 3D CNN, 3D CNN with Meta-learning, and Aster propagation model.
Through the analysis of
Table 6, it can be seen that 3D CNN with multi-way local attentive learning had improved both LoS and NLoS, compared to the basic 3D CNN, which was from a previous study. Of course, although the increase in performance improvement in NLoS was smaller than the increase in LoS, the improvement in performance in NLoS, from which it is more difficult to predict path loss, was meaningful.
Figure 5 is a graph that is expressed by sorting the receive points of the LoS test data set in order of distance, dividing the sections at intervals of 10 m, and averaging the absolute errors of various experiments included in the section. It helps enable more detailed analysis by comparing the measured errors for each section divided by distance.
Figure 5 shows that 3D CNN with multi-way local attentive learning—single model had a lower absolute error in sections in front of 150 m, compared to the 3D CNN and 3D Aster propagation models and in sections behind 150 m, compared to all the rest of the models. All the models, especially 3D CNN, tended to have lower absolute errors as the distance increased. In the case of the first section, the horizontal relative angle was small and the distance was close, but because the distance was small, the influence of the vertical relative angle increased, and it seemed that the absolute error occurred in the techniques that were not used for learning.
Figure 6 is the same as
Figure 5, except that NLoS was used instead of the LoS test dataset. Among the test data, NLoS did not have test data at 180 m to 190 m, 200 m to 240 m, so there were no dots on the graph.
Figure 6 shows that the results of all five models were similar, but this is because the number of data allocated for each section was different. As the distance was shorter, even if there were only a small number of buildings between Tx-Rx, the probability of being obscured by the buildings increased, so that a lot of data could be scattered in the short distance. However, the data we used for the test tended to be concentrated at 60–70 m, 120–130 m, and 170–180 m. In the 120–130 m and 170–180 m sections where the absolute error of 3D CNN with multi-way local attentive learning—single model was the lowest, there were many times more data than other sections, so, as in
Table 6, the Single 3D CNN model had the lowest error rate.
Table 7 shows the RMSE and the Cumulative distribution function (CDF) of absolute error based on 1, 3, and 10 dBm, respectively, for the entire test dataset, regardless of LoS/NLoS.
Figure 7 is a graph that expressed by sorting the receive points of the entire test data set in order of distance, dividing the sections at intervals of 10 m, and averaging the absolute errors of various experiments included in the section. When looking at each section of the T-R segment, the absolute error of the multi-way local attentive learning—single model in most sections was ranked low among the five path loss models. From
Table 7 and
Figure 7, it could be confirmed that the Single 3D CNN model had the lowest RMSE and absolute error among the five models.
Table 7 and
Figure 8 show the Cumulative Distribution Function for the absolute error of labels and predicted values for the path loss regression problem. First, as can be seen from
Figure 8, the absolute error distribution of the 3D CNN-based path loss model was generally lower than the absolute error distribution of the Aster propagation model. Also, it can be seen that the proposed model had a much higher probability of having a low absolute error compared to other comparative models. Specifically, the absolute error of the proposed model was 15.46% less than 1 dBm, and almost half of it was less than 3 dBm. Finally, this model could guarantee that the absolute error of more than 90% was less than 10 dBm. The result shows that the meta-learning based model achieved lower, or similar, performance compared to the model using only 3D CNN.
In addition, When the absolute error of less than 10 dBm was seen, the cumulative absolute error of multi-way local attentive learning with single model and multi model was lower than that of the other three models. However, in the case of using the multi model, the error larger than 10 dBm was higher than that of other models. It can be seen that in the combined process of multi-way local attentive learning using multi models, the learning of each model rather interfered with one another’s learning. However, in the case of using the single model, the absolute error tended to be lower than that of other models. The application of meta learning and multi model did not have much effect on the regression model learning for 5G mmWave path loss in urban areas, while the proposed multi-way local attentive learning with single model could be used.
Table 8,
Table 9 and
Table 10 present the partition-wise performance of path loss prediction in terms of the MAEs and their variances of different models. It can be clearly noticed the multi-way local attentive learning—single model performed the best in a most consistent way. This means that the proposed model gave a more robust performance than the other models.
5. Conclusions
This paper proposes a 5G mmWave path loss model to which a novel training method called multi-way Local Attentive Learning is applied. The 3D CNN-based path loss model is obtained by using 3D LAMS images which include three-dimensional morphological data. Since these data can provide important information about the radio propagation environment of dense urban scenarios, the 3D CNN model can give more accurate path loss prediction results. The proposed training method called multi-way Local Attentive Learning can further enhance the performance of the 3D CNN model, thanks to the improved mechanism of local attention provided by multi-way partitioning of a sample data set.
The path loss model performance is significantly improved by applying multi-way local attentive learning to the existing 3D CNN-based path loss model training. The experimental results shows that while the 3D CNN-based path loss model can guarantee performance in urban areas, applying the proposed multi-way local attentive learning can provide much better performance than using only basic learning methods, or meta-learning-based methods. In addition, we compared the prediction performance in LoS and NLoS environments for five models, including the proposed model. In all five models, the prediction performance in the NLoS environment was lower than the prediction performance in the LoS environment, which can be seen as being influenced by the characteristics of the mmWave with high straightness. Nevertheless, among the five compared models, the proposed model had high prediction accuracy in both LoS and NLoS environments.
The dataset partitioning method proposed in Algorithm 2 partitions the dataset and assigns a data attribute to each data partition. Data in these partitions are not guaranteed to be specific to the data attributes assigned to them. Therefore, in the follow-up study, for better learning, an algorithm that allows data specialized for a specific data attribute to form a partition in the data partitioning process will be studied.
In the future, it is expected that a path loss model that can be applied universally in urban areas could be provided through experiment with various hyperparameters, model fine-tuning, and training high-quality and quantity data. In addition, through deep learning model compression, it will be easier to use in the field, while maintaining, or increasing, model performance. We consider mixing a deterministic model, such as the 3D ray tracing method, and 3D CNN-based model with multi-way local attentive learning in a hybrid method in dense urban cases to increase prediction performance. Other state-of-the-art training methods and deep learning technologies should be considered regarding 5G path loss modeling.