A Novel Machine Learning Scheme for mmWave Path Loss Modeling for 5G Communications in Dense Urban Scenarios

Abstract

Accurate and efficient path loss prediction in mmWave communication plays an important role in large-scale deployment of the mmWave-based 5G mobile communication systems. Existing methods often present limitations in accuracy and efficiency and fail to fulfill the requirements of cell planning, especially in dense urban environments. 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. The sample data set can be partitioned in various ways with respect to different attributes, such that a larger amount of knowledge can be extracted from the same data set. The proposed scheme outperforms the existing schemes in terms of prediction accuracy at the average RMSE of 6.01 dBm.

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.

3. The Proposed Method

3.1. 3D-LAMS Algorithm

Dense urban scenarios require new approaches that consider large variations in the heights and shapes of buildings, which significantly affect path loss values, as opposed to the low and nearly identical average building heights in suburban scenarios. The first step of the new approach would be to design a new CNN image generation algorithm that can extract the 3D topographical information with a good representational power of the wave propagation environment. Our proposed algorithm is motivated by the LAMS algorithm designed to generate 2D CNN images for path loss modeling in suburban and indoor scenarios [10,11].

Based on Digital Elevation Map (DEM) data, the 3D-LAMS algorithm (Algorithm 1) generates 3D images which include the topographical information of the propagation environment between Tx-Rx pairs. As shown in Figure 1, 3D-LAMS algorithm collects 3D topographical information by placing a number of 2D scan planes (perpendicular to the ground) of the parallelepiped connecting a Tx and a Rx within a 3D map data. As shown in

Table 1. Grayscale value of class in 3D-LAMS.

Index	Class	Grayscale
1	Building	240
2	Terrain	200
3	Sky	0
4	Ground	255

, different kinds of topographical objects are encoded into different pixel values (color values) of the grayscale.

Algorithm 1 3D-LAMS Algorithm

Input:  GPS locations of Tx and Rx  Size of a 3D-LAMS image: $\left(w,h,d\right)$  Rasterized 3D map image MR Output:  A 3D-LAMS image Divide the interval between Tx and Rx by $d$,$P_{1 ~ d}$ Determine the slope $S$ of a straight line perpendicular to the line between Tx and Rx and parallel to the XY plane Make empty 3D-array, $C\left[w\right]\left[h\right]\left[d\right]$ for $i=1$ to $d$ do 4.1. Make scan plane $S{P}_i$(center: $P_i$, size: $w\times d$, slope: $S$ and perpendicular to the XY plane) considering MR 4.2. Copy $S{P}_i$ to $C[][]\left[i\right]$ end for Save $C$ as a 3D-LAMS image

The size and number of scan planes are the user-defined parameters and should be determined empirically.

3.2. CNN Architecture

A CNN typically consists of multiple convolutional layers that automatically extract features by using filters (or kernels). The filters are adjustable parameters that can be determined by training based on loss functions. A CNN usually includes pooling and fully connected (FC) layers in addition to the convolution layers. Pooling layers can reduce the size of an activation map. The activation maps are the output of the convolutional layer and are expected to contain the features extracted by the convolutional layer. Based on the features extracted by the upper convolutional layers, the FC layers can be trained to generate final output with the supervision of the label(s).

The proposed CNN model takes a LAMS image as its input and produces a predicted Reference Signal Received Power (RSRP) value as the output [12]. The 3D-LAMS algorithm extracts the topographical data between a Tx and a Rx from the 3D map data and generates a 3D image sampled at uniform intervals proportional to the distance. Since the image generated through this algorithm contains only the important topographical data that affect the predicted path loss value, the CNN model can learn the features of the path loss environment more easily. As the image passes through the convolution layers, useful latent features of path loss are expected to be extracted. Pooling layers are not included in the proposed model. In general, the pooling layers can speed up learning by reducing the number of parameters and preventing overfitting, but they can also cause the loss of information included in the feature maps. In this work, we consider that it is advantageous to keep the size of the feature map unchanged, since the 3D-LAMS image contains only simplified information about the shape of buildings. The Rectified Linear Unit (ReLU) function is used as the activation function in the proposed model. The CNN model includes three convolution layers, as illustrated in Figure 2. The FC layer consists of two scalar input values, i.e., the relative angle and the distance between a Tx and a Rx, taken as additional inputs of the flattened layer of two hidden layers of 10 and 5 neurons, respectively, with ReLU activation functions. Relative angle is the difference of the angle between the direction from Tx to Rx and that of the main lobe of each antenna (azimuth or downtilt of Tx). The detailed model parameters are summarized in

Table 2. 3D CNN Path Loss Model Parameters.

Convolution Layer	1st	2nd	3rd
Input size	20, 20, 20	9, 9, 9	5, 5, 5
Input channel	1	80	20
Output size	9, 9, 9	5, 5, 5	4, 4, 4
Output channel	80	20	5
Kernel size	4, 4, 4	2, 2, 2	2, 2, 2
Stride size	2	2	1

. The architecture is chosen to have the CNN model to approximate the highly nonlinear underlying path loss functions as closely as possible.

As shown in Figure 3, additional nodes receiving the relative angle and distance are concatenated and become the input of the FC Network.

Based on the assumption that path loss can be regarded as a function of variables representing a large number of environmental factors that affect signal propagation, we can take advantage of the universal approximation capability of neural networks [26]. Path loss modeling in dense urban scenarios, where the heights and construction materials of buildings have a large amount of influence, requires 3D morphological information between a Tx and a Rx. The 3D CNN takes this information as its input data, as generated by the 3D LAMS algorithm, and learns important latent features in order to update its parameters (weights) trying to best approximate the underlying path loss function. Unfortunately, it is extremely difficult to explain how a trained neural network approximate an underlying function although there is a large amount of research effort being conducted in the subject area of eXplainable AI (XAI) [27,28].

3.3. Multi-Way Local Attentive Learning

Deep learning models are trained to approximate the underlying probability distribution of sample input–output pairs (or the underlying function) by updating the values of model parameters repeatedly with sample exposure. The model parameters have no explicit bearing on the parameters of empirical path loss models. or their values cannot be explicitly determined. The parameters of empirical models for the path loss in urban scenarios include those associated with rooftop-to-street diffraction and scatter loss, T-R separation, and differences between building height, etc. The 3D LAMS images are proposed to represent these parameters implicitly, such that the 3D CNN model, trained with the multi-way partitioning scheme, can approximate the underlying path loss function. We propose the Multi-way Local Attentive Learning algorithm to enhance the performance of the basic training algorithm for the CNN, by presenting the training data in minibatches sampled according to the inherent organization, such as associated PCIs, distances and relative angles.

In conventional training approaches, such as stochastic gradient descent, the entire training data set is partitioned into multiple, possibly overlapping, subsets of samples called a minibatch $\mathit{ℬ}$ to evaluate the estimate of the gradient over the entire training set:

$$\mathit{g}=\frac{1}{m^{\prime }}{\nabla }_{\theta }{{\displaystyle \sum }}_{i=1}^{m^{\prime }}L\left(x^{\left(i\right)},y^{\left(i\right)},\theta \right)$$

(1)

where $\mathit{ℬ}=\left\{{\mathit{x}}^{\left(\mathbf{1}\right)}\mathbf{,}\mathbf{\dots }\mathbf{,}{\mathit{x}}^{\left({\mathit{m}}^{\mathbf{\prime }}\right)}\right\}$ is the minibatch of size ${\mathit{m}}^{\mathbf{\prime }}$ drawn uniformly. We generalize this notion of minibatch, such that the minibatches are not generated by random sampling but, instead, by some data set partitioning scheme based on the values of training data attributes, i.e., ${\mathit{ℬ}}_{\mathit{p}}=\left\{{{\mathit{x}}_{\mathit{p}}}^{\left(\mathbf{1}\right)}\mathbf{,}\mathbf{\dots }\mathbf{,}{{\mathit{x}}_{\mathit{p}}}^{\left({\mathit{m}}^{\mathbf{\prime }}\right)}\right\},\mathbf{1}\mathbf{\le }\mathit{p}\mathbf{\le }\mathit{P}$, where $\mathit{P}$ represents the number of minibatches generated by a particular partition scheme. If we can have $\mathit{L}$ partitioning schemes over the entire sample data set, the set of minibatches comprises ${\mathbb{B}}_{\mathit{l}}=\left\{{\mathit{ℬ}}_{{\mathbf{1}}_{\mathit{l}}}, {\mathcal{B}}_{2_{\mathit{l}}}, \mathbf{\dots }, {\mathit{ℬ}}_{{\mathit{P}}_{\mathit{l}}}\right\}$, $\mathbf{1}\le \mathit{l}\le \mathit{L}$. Since each minibatch is made up of sample data set within a range of values with respect to a particular attribute, a CNN is expected to pay higher attention on certain features during the training.

The gradient can be approximately estimated using the randomly sampled minibatch and the optimization process based on this estimation is called stochastic gradient descent. Although the stochastic gradient descent ensures unbiased and computationally efficient learning, it cannot exploit the inherent partitions which can help learning by providing additional information specific to each partition. Hence, we propose to take advantage of inherent partitions whenever available instead of using randomly sampled minibatches. One advantage of this approach is that these partitions can be obtained in multiple ways based on a number of attributes of the training data. The number of features learned can increase as the number of partitions increase. This idea can be explained by the human analogy where students learn not only by different courses (subjects) but also by different grades, even for the same subject.

In multi-way local attentive learning, the entire training data set is partitioned into minibatches by the multi-way partitioning schemes, based on different attributes, and model parameters are trained using these minibatches. Several variants of this approach can be implemented, for instance, with respect to the order of minibatches used. Either a single model can be trained on all partitions, or an individual model can be trained on each partitioning scheme and then combined into a single model in the final stage. The proposed method is summarized in Algorithm 2 in detail. To our best knowledge, this approach has never been discussed in the literature in the past.

Algorithm 2 Multi-Way Local Attentive Learning

Require:  Training dataset $D=\left\{x^{\left(i\right)},y^{\left(i\right)}\right\}, 1\le i\le m$  Number of partition scheme $P$  Set of minibatches $\mathbb{B}=\left\{{\mathcal{B}}_1, {\mathcal{B}}_2, \dots , {\mathcal{B}}_P\right\}$  Size of minibatch $m^{\prime }$  Data attributes $A=A_1, A_2, \dots , A_P$  Trainable weights $\theta$  Learning rate $\epsilon$ Dataset Partition: 1. Initialize partition set $\mathbb{B}$ 2. forpin$P$ 2.1. Partition the D into ${\mathcal{B}}_p$ 2.2. Assign $A_p$ to ${\mathcal{B}}_p$ 3.  end for Training: Randomly initialize trainable weights θ forepochinepochs 2.1. Assign q = epoch mod $P$ 2.2. Sample a minibatch of $m^{\prime }$ from ${\mathcal{B}}_q$ $\left\{x^{\left(1\right)},x^{\left(2\right)}, \dots ,x^{\left(m^{\prime }\right)}\right\}$ with corresponding target $\left\{y^{\left(1\right)},y^{\left(2\right)}, \dots ,y^{\left(m^{\prime }\right)}\right\}$ 2.3. Evaluate ${\nabla }_{\theta }{\displaystyle \sum }_{i=1}^{m^{\prime }}L\left(x^{\left(i\right)},y^{\left(i\right)},\theta \right)$ 2.4. Update $\theta =\theta -\mathsf{\epsilon }\frac{1}{m^{\prime }}{\nabla }_{\theta }{\displaystyle \sum }_{i=1}^{m^{\prime }}L\left(x^{\left(i\right)},y^{\left(i\right)},\theta \right)$ end for

In addition to the method using one model proposed in Algorithm 2, a learning method that uses the same partitioned data and three models with the same amount of partitioned data also can be proposed. Each model learns partitioned data, and the weight values of the trained models are combined into one model to derive a value. We decided that the learning technique using one model will be called multi-way local attentive learning—single model, and the learning technique using multiple models will be called multi-way local attentive learning—multi model. A performance comparison of the two models is discussed in detail in Section 4.

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. The organization of measurement data.

	Rx	Tx
Attributes	Date and Time	PCI
	Longitude	Longitude
	Latitude	Latitude
	GPS Height	Height
	GPS Speed	Azimuth
	GPS Satellite	Mechanical downtilt
	GPS Head
	NR Serving PCI
	RSRP (dBm)
count	750	7

, 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. Selected scenario information.

Index	Test PCI	TS Ratio (%)	LoS Ratio (%)
1	1, 2	30.80	68
2	1, 3	25.87	55
3	1, 4	31.33	60
4	2, 3	24.13	30
5	2, 4	29.60	39
6	3, 4	24.67	22
7	1, 6, 7	25.60	56
8	2, 6, 7	23.86	30
9	4, 6, 7	24.40	3

. 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. Comparison of the proposed work with previous related works.

Models	Minibatch Schemes
Single 3D CNN model	Attribute-Based
Multiple 3D CNN model	Attribute-Based
3D CNN	Random Sampling
3D CNN with Meta-learning	Task-Based
Aster propagation model	None

compares these models.

Table 6. Minimum, Mean, Maximum Comparison Root Mean Square Error of various methods (LoS/NLoS).

Models	LoS/NLoS	RMSE (dBm)
		Minimum	Mean	Maximum
Single 3D CNN model	LoS	3.15	4.38	8.01
	NLoS	4.06	7.55	9.45
Multiple 3D CNN model	LoS	3.11	4.85	11.23
	NLoS	4.10	7.73	14.08
3D CNN model	LoS	4.86	7.63	11.57
	NLoS	5.93	8.11	16.46
3D CNN with Meta-learning	LoS	3.98	7.25	9.62
	NLoS	4.52	8.85	22.12
Aster propagation model	LoS	7.23	8.89	9.92
	NLoS	9.43	11.04	14.71

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. Comparison Root Mean Square Error of various methods.

Model	RMSE (dBm)	Absolute Error CDF (%)
		<1 dBm	<3 dBm	<10 dBm
Single 3D CNN model	6.01	15.46	46.91	90.21
Multiple 3D CNN model	6.67	12.37	36.61	77.32
3D CNN	7.85	7.21	22.16	77.84
3D CNN with Meta-learning	8.01	11.34	27.84	78.87
Aster propagation model	9.91	9.28	30.41	70.62

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. Comparison of mean absolute error and error variance according to the horizontal relative angle section.

Relative Angle Section	Single 3D CNN Model	Multiple 3D CNN Model	3D CNN	3D CNN with Meta-Learning	Aster Propagation Model
1	2.68	2.48	6.73	5.61	2.88
2	3.18	4.39	5.41	5.37	7.2
3	8.65	9.29	9.09	9.95	10.63
4	6.02	5.62	5.32	7.01	8.65
5	4.34	10.51	8.66	5.25	5.15
6	1.66	6.51	6.8	4.51	8.49
7	4.23	8.87	5.13	5.53	12.2
8	3.82	12.38	5.75	3.97	7.4
9	2.61	3.08	1.43	7.93	8.19
10	7.14	4.08	9.49	16.35	16.69
Variance	4.37	10.25	5.1	12.19	13.05

,

Table 9. Comparison of mean absolute error and error variance according to the distance section.

Distance Section	Single 3D CNN Model	Multiple 3D CNN Model	3D CNN	3D CNN with Meta-Learning	Aster Propagation Model
1	4.88	3.58	5.46	12.14	12.44
2	3.15	3.17	6.43	4.92	4
3	3.64	4.77	4.71	6.25	3.63
4	7.15	3.1	8.5	10.99	5.81
5	6.37	1.89	6.4	9.83	6.55
6	3.97	6.66	5.78	5.22	6.07
7	4.11	9.7	7.48	5.55	7.68
8	3.63	5.19	5.69	5.08	6.58
9	1.15	1.16	5.26	3.02	1.75
10	6.05	8.09	10.07	6.54	3.65
11	4.63	7.43	7.99	6.6	6.26
12	2.89	4.06	3.49	3.86	7.44
13	2.65	5.23	3.01	2.04	8.47
14	6.09	8.57	7.01	8.48	17.2
Variance	2.58	6.21	3.39	8.08	14.2

and

Table 10. Comparison of mean absolute error and error variance according to the PCI section.

PCI Section	Single 3D CNN Model	Multiple 3D CNN Model	3D CNN	3D CNN with Meta-Learning	Aster Propagation Model
1	4.12	6.23	7.28	5.58	7.27
3	5.44	6.79	5.48	6.98	7.92
Variance	0.43	0.37	0.81	0.14	0.11

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.