An intelligent wireless communication model based on multi-feature fusion and quantile regression neural network

Abstract

Throughout the wireless communication network planning process, efficient signal reception power estimation is of great significance for accurate 5 G network deployment. The wireless propagation model predicts the radio wave propagation characteristics within the target communication coverage area, making it possible to estimate cell coverage, inter-cell network interference, and communication rates, etc. In this paper, we develop a series of features by considering various factors in the signal transmission process, including the shadow coefficient, absorption coefficient in test area and base station area, distance attenuation coefficient, density, azimuth angle, relative height and ground feature index coefficient. Then we design a quantile regression neural network to predict reference signal receiving power (RSRP) by feeding the above features. The network structure is specially constructed to be generalized on various complex real environments. To prove the effectiveness of proposed features and deep learning model, extensive comparative ablation experiments are applied. Finally, we have achieved the precision rate (PR), recall rate (RR), and inadequate coverage recognition rate (PCRR) of 84.3%, 78.4%, and 81.2% on the public dataset, respectively. The comparison with a series of state-of-the-art machine learning methods illustrates the superiority of the proposed method.

Keywords

RSRP prediction neural network correlation analysis shadowing effect information entropy

1 Introduction

As the development of new radio technology, the worldwide application of 5 G communication is also expanding [1]. During the process of establishing and deploying the 5 G communication network, operators need to select the suitable base station sites within a limited coverage area to meet the communication needs of users [2]. Due to the complex environment faced by radio wave propagation, transmitted signals are affected by various factors on the path, such as buildings, plains, mountains, lakes, atmosphere, and earth curvatures [3, 4]. Actually, the electromagnetic waves no longer propagate in a single way and path [5], but produce a complex transmission, diffraction, scattering, reflection, refraction, etc. Therefore, it is challenging to build an accurate and robust wireless communication model to predict the signal power in different regions and help select the appropriate base station location.

Currently, the most common wireless propagation models can be generally divided into three categories: the theoretical models [6, 7], empirical models [8, 9], and improved empirical models [10 –12]. Based on the electromagnetic wave propagation theory, the theoretical models can calculate the upper bound of the loss by considering the reflection, diffraction, and refraction in the space, and the most representative one is the Volcano model [6]. The establishment of empirical models is to obtain fixed fitting forms from the empirical data, such as the Cost 231-Hata [8] and the Okumura-Hata [9]. Further, improved empirical models can provide predictions for more fine-grained scenarios by introducing more parameters into the fitting equations, e.g. the standard propagation model (SPM) [10].

In practice, to obtain the wireless communication propagation model that conforms to real environment of the target area, a large amount of practical data, engineering parameters, and electronic maps need to be collected to calibrate the propagation model. With the popularity of wireless LTE networks worldwide, billions of users around the world are generating numerous data at all times. Thus, how to reasonably use these data to assist the construction of wireless networks has become an important topic. In recent years, the big data driven machine learning technique has made significant progress and been successfully applied in the many fields like image processing [13] and speech analysis [14]. The availability of parallel architecture [15] enables machine learning models to achieve efficient computing and allows them closely integrated with wireless communication applications. The machine learning based methods can utilize the massive data to establish the wireless propagation model. Then it can be employed to predict the RSRP values of wireless communication signals covered in a new environment, thereby incredibly reducing the construction costs of base stations and improving communication efficiency.

Nevertheless, building the machine learning based mapping models between engineering parameters, geographic environment factors, and RSRP of test areas in the complex real-world situations still faces the following challenges:

There are a lot of strong interference sources in the practical communication environment, including welding machines, trams, and high-voltage power transformers. Therefore, even with the same transmit power and receiver sensitivity, it is difficult to ensure a consistent and effective communication distance [16].

In free space or ideal conditions, distance is the only factor that affects signal attenuation. In the real world, signal transmissions are susceptible to the interference from complex and changeable physical environments, such as terrain fluctuations, building distribution, and climate effects [17]. Obstacles including walls, trees, and hills can cause severe signal loss; the metal objects reflecting radio waves lead to multipath interferences; the moisture in the air (i.e., the humidity) can absorb radio frequency (RF) energy.

Machine learning models can easily fall into the “overfitting” problem if the data is insufficient or underrepresented. In other words, the models can accurately predict the RSRP of training samples, but cannot successfully generalize their excellent prediction ability to the test area in the new environment [18].

Based on the above facts, it is crucial to extract effective and stable features that reflect attenuation characteristics of the wireless communication signal, and construct the robust machine learning models to establish the potential relationship between features and signal receiving power. Features determine the upper limit of prediction performance, while a good machine learning model can approach this limit as much as possible.

In this paper, we develop a series of features by considering various factors in the signal transmission process, including the shadow coefficient, distance attenuation coefficient, absorption coefficient in test area and base station area, density, azimuth angle, relative height, and ground feature index coefficient. First of all, we consider that the signals are disturbed by obstacles in the propagation path, which cause the reflection, refraction, and diffraction, resulting in the signal attenuation. Hence we determine the shadow coefficient according to the propagation distance of the signal, the building height, and the ground object type in the propagation path. Secondly, we calculate the absorption coefficients of the base station and the target area based on building heights and the types of ground objects within the range of 10 m near the target by considering signal absorptions in different environments. In addition, according to the Cost 231-Hata model, we also define the distance attenuation coefficient, relative height coefficient, and ground feature type coefficient. Moreover, in view of the impact of buildings during the signal propagation, the density coefficients of test areas are determined by searching the number of buildings within the radius of 200 m. Finally, we design a quantile regression neural network to predict RSRP by feeding the above features. Experiments on the public dataset [19] show that our proposed method has achieved the highest PR, RR, and PCRR of 84.3%, 78.4%, and 81.2%, respectively. The extensive comparisons with state-of-the-art methods also illustrate its superiority.

The rest of the paper is organized as follows. In Section 2, we briefly describe the related work in the field. In Section 3, we introduce the proposed eight kinds of features in detail. Section 4 presents the specific architecture, training process, and hyper-parameters setting of the quantile regression neural network. Experimental results and analysis are given in Section 5. Finally, the conclusion and future directions are summarized in Section 6.

2 Related work

In this section, we introduce the related work of RSRP prediction methods to help construct the base station location map.

2.1 Theoretical models

Bai et al. [7] proposed a future RSRP prediction method based on past channel measurement results. Based on the general geometric channel model, the RSRP prediction error of the linear minimum mean square error (MMSE) predictor can be calculated and linked to the key parameters of the system, such as maximum Doppler spread and channel measurement periodicity. The flower pollination algorithm (FPA) [20] is developed to use the mapping technology to meta-heuristically deal with the binary optimizations, such as NP-hard binary problems in advanced cellular networks, i.e. antenna positioning problem (APP). M. Radmard et al. [21] designed a Neyman-Pearson detector in the Rayleigh scattering model and used it to establish the antenna placement criteria for transmitters and receivers. Yang et al. [22] considered the complex objective function and high dimensionality of antenna placement problems and proposed a two-part solution, which consists of the low-complexity objective function simplification method and the particle swarm algorithm based (PSO) high-dimensional layout algorithm. S. Bi et al. [23] studied the optimal layout of energy nodes (ENs) at a given fixed access points (APs) position and adopted a greedy method to solve the non-convexity problem. The proposed solution can effectively reduce the costs of network deployment while meeting the performance requirements. Actually, the positions of base stations in the wireless network can be modelled by a repulsive random process, and its regularity is adjustable between the triangular lattice and the homogeneous Poisson point process. Lagum et al. [24] analyzed three regularity measures based on the coefficient of variation (CoV) of geometric properties of the point process and took the CoV of the nearest neighbor distance as the most sensitive measure.

2.2 Empirical models

Akande et al. [8] illustrated that the Cost 231-Hata model trained by ordinary least squares method could be applied to the prediction of path loss in suburban areas more accurately. Singh [9] discussed the impact of key parameters under various channel models on the prediction of signal coverage, achievable data rate, bit error rate (BER) and antenna gain. F. Sohrabi and E. Kuehn [25] proposed a two-step method for generating RSRP maps, including regression clustering and RSRP estimation. Compared with the existing environment-based regression and inverse distance weighted interpolation methods, the average absolute errors of the predicted RSRP map have been greatly reduced. Y. Liu et al. [26] found that ignoring the geometric distribution of candidate locations would have a negative influence on the performance of the traditional meta-heuristic algorithm and proposed a geometric induction genetic algorithm based on local coverage evaluation and local geometric site pattern retention. Abdelkhalek et al. [27] proposed a novel multi-objective node placement model, which simultaneously optimized the four objectives of communication coverage maximization, active structure cost minimization, total capacity bandwidth maximization, and network noise level minimization. S. Wang and C. Ran [28] developed a dynamic cellular network planning framework that divided a service area into multiple sub regions with almost equal traffic loads. However, in practice, the path loss usually contains anisotropy due to the influence of terrain and obstacles. K. Sato et al. [29] extended the Kriging method to distributed wireless networks with arbitrary transmitters, such as mobile ad hoc networks (MANETs) and vehicular ad hoc networks (VANETs). Furthermore, M. Pesko et al. [30] took into account the characteristics to estimate transmitter parameters, including the transmitter location, antenna pattern, antenna azimuth, transmission power and propagation model parameters, and obtain the best match between the available measurement value and the predicted signal level.

2.3 Improved empirical models

Improved empirical models usually have a higher structural complexity and require more training data to improve their generalization ability. Thrane et al. [11] compared various traditional and deep learning based channel models under the condition of simple path loss and demonstrated the well adaptability of deep learning models to different cases. Parera et al. [12] proposed a transfer learning framework to reconstruct the wireless environment map corresponding to the target antenna tilt configuration by transferring the knowledge obtained from another tilt configuration of the same antenna when the target has limited measurements. Rufaida et al. [31] conducted the experimental evaluation of RSRP prediction on XGBoost and light gradient boosting machine under various configurations. Results validated the superior performance of the two approaches against k-nearest neighbor (KNN) and support vector machine (SVM). M. Ayadi et al. [32] fed into the built neural network model with features such as frequency, environment type, land use distribution, diffraction loss, etc., and obtained the absolute average error of 0.235 dB, the standard deviation of 6.850 dB, and the correlation coefficient of 85%. S. Sotiroudis et al. [33] compared the results of two neural networks with those of the ray tracing models and proved the excellence of deep learning methods. H. Yilmaz and T. Tugcu [34] used the classical least square method to estimate the additional information about channel parameters. By improving the ability of network management and coordination, the machine learning method will play an important role in dealing with the complexity of future mobile wireless networks.

3 Multi-feature design and integration

In this part, we introduce eight features in detail to characterize the properties of signal transmission.

3.1 Shadow coefficient

For the shadow effect, we consider the building interference in the area within 100 m of maximum path of transmitter and receiver, that is, the spindle-shaped area in the r (r = 20 m) coordinate range, as shown in Fig. 1. We first define a spindle-shaped shadow region constrained by functions g₁(·) and g₂(·). Any points (s_x, s_y) in the shadow area should satisfy the following conditions:

$g_{1} (s_{x}) ⩾ s_{y} and g_{2} (s_{x}) ⩽ s_{y}$ (1)

Fig. 1

Schematic diagram of shadow area.

The expressions of two functions g₁(·) and g₂(·) are determined according to the base station coordinates (e₂, e₃), the target test area coordinates (e₁₃, e₁₄), and the farthest area coordinates (s_{x_1}, s_{y_1}) and (s_{x_2}, s_{y_2}), as given by

$\begin{matrix} (x + \frac{c_{4} c_{5} - c_{2} c_{6}}{c_{2} c_{3} - c_{1} c_{4}})^{2} + (g_{1} (x) + \frac{c_{1} c_{6} - c_{3} c_{5}}{c_{2} c_{3} - c_{1} c_{4}})^{2} \\ = (e_{2} + \frac{c_{4} c_{5} - c_{2} c_{6}}{c_{2} c_{3} - c_{1} c_{4}})^{2} + (e_{3} + \frac{c_{1} c_{6} - c_{3} c_{5}}{c_{2} c_{3} - c_{1} c_{4}})^{2}, \\ e_{3} ⩽ x ⩽ e_{13} \end{matrix}$ (2)

$\begin{matrix} (x + \frac{c_{4} c_{5}^{'} - c_{2}^{'} c_{6}}{c_{2}^{'} c_{3} - c_{1}^{'} c_{4}})^{2} + (g_{2} (x) + \frac{c_{1}^{'} c_{6} - c_{3} c_{5}^{'}}{c_{2}^{'} c_{3} - c_{1}^{'} c_{4}})^{2} \\ = (e_{2} + \frac{c_{4} c_{5}^{'} - c_{2}^{'} c_{6}}{c_{2}^{'} c_{3} - c_{1}^{'} c_{4}})^{2} + (e_{3} + \frac{c_{1}^{'} c_{6} - c_{3} c_{5}^{'}}{c_{2}^{'} c_{3} - c_{1}^{'} c_{4}})^{2}, \\ e_{3} ⩽ x ⩽ e_{13} \end{matrix}$ (3) where $\begin{matrix} \begin{matrix} c_{1} = e_{2} - s_{x_1} \\ c_{2} = e_{3} - s_{y_1} \\ c_{3} = e_{2} - e_{13} \\ c_{4} = e_{3} - e_{14} \\ c_{5} = \frac{(e_{2}^{2} - s_{x_1}^{2}) - (s_{y_1}^{2} - e_{3}^{2})}{2} \\ c_{6} = \frac{(e_{2}^{2} - e_{13}^{2}) - (e_{14}^{2} - e_{3}^{2})}{2} \\ c_{1}^{'} = e_{2} - s_{x_2} \\ c_{2}^{'} = e_{3} - s_{y_2} \\ c_{5}^{'} = \frac{(e_{2}^{2} - s_{x_2}^{2}) - (s_{y_1}^{2} - e_{3}^{2})}{2} \end{matrix} \end{matrix}$

The coordinates of the farthest areas in the above equations, i.e. (s_{x_1}, s_{y_1}) and (s_{x_2}, s_{y_2}), can be obtained by:

${\begin{matrix} (s_{x} - e_{2})^{2} + (s_{y} - e_{3})^{2} = (s_{x} - e_{13})^{2} + (s_{y} - e_{14})^{2} \\ (s_{x} - \frac{e_{13} - e_{2}}{2})^{2} + (s_{y} - \frac{e_{14} - e_{3}}{2})^{2} = r^{2} \end{matrix}$ (4)

Then we traverse all the samples ${a_{i}^{1}, a_{i}^{2}, \dots, a_{i}^{M_{i}}}$ in the cell to extract their distance to the base station and form the shadow coefficient ξ₁:

$\begin{matrix} ξ_{1} = [\sqrt{{(e_{13}^{1} - e_{2}^{1})}^{2} + {(e_{14}^{1} - e_{3}^{1})}^{2}}, \\ \dots, \sqrt{{(e_{13}^{s} - e_{2}^{s})}^{2} + {(e_{14}^{s} - e_{3}^{s})}^{2}}] \end{matrix}$ (5) where S represents the number of block test areas in the shaded area. All feature values of the ideal area are set to 0 to ensure that the shadow coefficients of all test areas have the same dimensions.

3.2 Absorption coefficient in test areas

For multipath signal interference, we only consider that buildings within 10 m will cause reflection and refraction of signals at test points, and result in the frequency selective fading of signals, as shown in Fig. 2(a). In this case, the building height $e_{15}^{i}$ , elevation $e_{16}^{i}$ , index type $e_{17}^{i}$ , and relative distance d ⁱ of the surrounding test area are aggregated into the one-dimensional vector to represent the signal attenuation effect of the target test area, as given by

$ξ_{2} = [e_{15}^{1}, e_{16}^{1}, e_{17}^{1}, d^{1}, . . ., e_{15}^{X}, e_{16}^{X}, e_{17}^{X}, d^{X}]$ (6) where X = 10 represents the number of test areas within 10 m around the target test area.

Fig. 2

Schematic diagram of multipath interference range in test area and base station area.

3.3 Absorption coefficient in base station areas

For absorption coefficient in base station areas, we also only consider that the buildings within 10 m will cause reflection, refraction and other multipath interference to the signal of the test point, as shown in Fig. 2(b). At this time, the relative height $e_{15}^{i} + e_{16}^{i} - e_{4}^{i} - h$ (h is the altitude of the base station area), index type $e_{17}^{i}$ , and relative distance d ⁱ of surrounding test areas are saved into a one-dimensional vector to represent the signal attenuation effect of the target test area, i.e.,

$\begin{matrix} ξ_{3} = & [e_{15}^{1} + e_{16}^{1} - e_{4}^{1} - h, e_{17}^{1}, d^{1}, . . ., e_{15}^{X} \\ + e_{16}^{X} - e_{4}^{X} - h, e_{17}^{X}, d^{X}] \end{matrix}$ (7) where X = 10 also reflects the effective range.

3.4 Distance attenuation coefficient

According to the item (44.9 - 6.55 log ₁₀h_u) log ₁₀d of the Cost 231-Hata model [8], the distance between the receiver in the test area and the base station is positively related to the path loss. The greater the distance is, the greater the loss and the weaker the signal strength will be, which is consistent with our common sense. Therefore, we define the Euclidean distance between the receiver and the base station as the distance attenuation coefficient:

$ξ_{4} = \sqrt{(e_{13} - e_{2})^{2} + (e_{14} - e_{3})^{2}}$ (8)

3.5 Density

Considering that there may be many building clusters near the target, we use the number of building clusters within a radius of 200 meters as the density coefficient ξ₅ in test area. Since the number of test areas in different cells is different, the test area density coefficient needs to be normalized based on the data in the respective cells.

3.6 Azimuth angle

The base stations need to transmit corresponding signals to all directions when it works. However, due to the horizontal angle, the transmitted signals cannot be guaranteed to face the target antenna directly and results in a certain “blind field of vision” in the base station. Therefore, for the base stations with different horizontal transmitting angles, the signal strength of the surrounding targets will also be affected. In view of this, we introduce the azimuth between the receiver and the base station as a prediction basis for the coverage signal strength. as given by

$ξ_{6} = arctan (e_{13} - e_{2}) / (e_{14} - e_{3})$ (9)

Then we can calculate the azimuth between each target grid and the site grid.

3.7 Relative height

The relative height formed by difference between the base station antenna, the target antenna and the height of buildings around the target antenna make the signal have the shadow attenuation effect. Therefore, the relative height factors should include the height of base station, the altitude of the grid where the base station is located, the altitude of the target grid and the height of the building where the target grid is located, as given by

$ξ_{7} = e_{4} + e_{10} - e_{15} - e_{16}$ (10)

3.8 Ground feature

The ground feature type at the grid where the receiving antenna is located causes the received signal to produce the effect of amplitude reduction or enhancement. For example, open areas such as plain and flat land lead to the corresponding lower attenuation of the received signal strength, while the targets in the building cluster are subject to more interference, which makes the received signal weaker or even shielded. In the Cost 231-Hata model, there are scene correction constants as compensation for propagation models in different scenes, but it is often inaccurate. Due to some other characteristics of the test area (for example, the base station is generally placed near the urban areas and far from the suburbs) are inconsistent, the clutter index of each sample are extracted as the ground feature.

Finally, all the features are grouped into the one-dimensional vector of size 1 × 243. We visualize the distribution of RSRP values and features in two test areas, as shown in Fig. 3. By observing the intensity of the received signal in different positions of the test area, we can analyze the correlation between features and the RSRP values.

Fig. 3

Visualization results of RSRP values and features of two sample test areas.

4 Quantile regression neural network

4.1 Architecture

Given multiple test areas in a cell V_i (i = 1, 2, ..., 4000) with different environments [19], our goal is to build the quantile regression neural network f (·) to estimate the RSRP values ${y_{i}^{1}, y_{i}^{2}, . . ., y_{i}^{M_{i}}}$ of M_i test areas in the target cell.

The specific architecture of the quantile regression neural network consists of the following layers: an input layer I; three convolutional layers H₁, H₂, and H₃; three batch normalization layers BN₁, BN₂, and BN₃; a max-pooling layer P; a global pooling layer G; two fully connected layers, i.e. FC₁ with Dropout and FC₂ with identity mapping; and an output layer O, as shown in Fig. 4. The number of neurons in the input layer is consistent with dimensions of input feature vectors, i.e. 1 × 243. The convolutional layers are used to encode input features, characterize the association between features and the mapping relationship with the output results. The number of convolution kernels in H₁, H₂, and H₃ is set to 64, 64, and 32, and the corresponding convolution kernel sizes are 1 × 4, 1 × 3, and 1 × 2, respectively. The max-pooling layer helps to reduce the impact of the relative position of features, and further improve the robustness of convolutional layers to the position of key information. Each hidden layer is followed by the activation function PReLU [35] to complete the non-linear transformation of the output of this layer, as defined by

$υ (I) = {\begin{matrix} I, & I ⩾ 0 \\ τ I, & I < 0 \end{matrix}$ (11) where I represents the input of current layer and τ is a trainable parameter to prevent neuronal necrosis.

Fig. 4

Specific architecture of quantile regression neural network.

After the feature map of each convolutional layer, a BN layer [36] is added to speed up the convergence of the quantile regression neural network model. The inconsistency of the output distributions of each layer makes the network difficult to converge, therefore the BN layer unifies the output distribution of each layer through the following equations:

${\begin{matrix} {BN}_{γ, τ} = γ {\hat{υ}}_{i} + τ \\ {\hat{υ}}_{i} = \frac{υ_{i} - μ_{D_{t}}}{\sqrt{σ_{D_{t}}^{2} + ɛ}} \\ σ_{D_{t}}^{2} = \frac{1}{M} \sum_{i = 1}^{M} (υ_{i} - μ_{D_{t}})^{2} \\ μ_{D_{t}} = \frac{1}{M} \sum_{i = 1}^{M} υ_{i} \end{matrix}$ (12)

where γ and τ are two trainable parameters, and ɛ is a small constant to avoid the denominator being 0. D_t represents the mini-batch set at t-th training iterations and M is the batch size.

After the last convolutional layer, a global pooling layer is used to regularize the structure of deep neural network. Each feature map of the upper convolutional layer is averaged to a value and then fed into the fully connected layer, in which Dropout [37] is designed to randomly remove neurons with a certain probability. Finally, the predicted RSRP values are output through last FC layer with identity mapping.

4.2 Training process

The network can be trained by iteratively optimizing the loss function L, i.e., the root mean square error (RSME) between true values and the predicted values, as given by

$\begin{matrix} L (x, y) = min \\ \sqrt{\frac{\sum_{i = 1}^{4000} \sum_{j = 1}^{M_{i}} {f ([x_{1}, x_{2}, . . ., x_{n}]_{i}^{j}; θ) - y_{i}^{j}}^{2}}{\sum_{k = 1}^{4000} M_{k}}} \end{matrix}$ (12) where θ represents the network parameters.

Given an initialized neural network f₀ (x ; θ₀), the parameters (i.e., weights and biases) in k-th layer at the t-th training iteration can be updated through gradient back propagation with the Adam [38]:

$θ_{t} = θ_{t - 1} - α_{t} \cdot \frac{{\hat{s}}_{t}}{\sqrt{{\hat{r}}_{t}} + ɛ}$ (13) where α _t denotes the learning rate at the t-th training iteration, ɛ is a small constant for numerical stability. ${\hat{s}}_{t}$ and ${\hat{r}}_{t}$ represent the modified first and second moment estimates respectively, and can be calculated according to

${\hat{s}}_{t} = \frac{s_{t}}{1 - β_{1}^{t}}$ (14)

${\hat{r}}_{t} = \frac{r_{t}}{1 - β_{2}^{t}}$ (15) where $\begin{matrix} \begin{matrix} s_{t} = β_{1} s_{t - 1} + (1 - β_{1}) \nabla_{t} \\ r_{t} = β_{2} r_{t - 1} + (1 - β_{2}) \nabla_{t}^{2} \\ \nabla_{t} = \frac{1}{M} \sum_{i = 1}^{M} \frac{\partial L (x_{i}, y_{i})}{\partial θ_{t - 1}} \end{matrix} \end{matrix}$

In the above equations, β₁ and β₂ are exponential decay rates of first and second moment estimations respectively, and belong to the interval of [0, 1). Δ _t denotes the batch gradient to determine the descent direction at l-th training iteration. Finally, the convergent network model f_* (x ; θ_*) can be obtained by continuously iterating through the above steps, i.e. from Equation (13) to Equation (18). In the testing phase, the deep neural network model is evaluated on the test set to observe its actual prediction performance.

4.3 Hyper-parameters initialization

During the whole training process, a large number of hyper-parameters are introduced and need to be set manually, as summarized in Table 1. The learning rate is set to 0.005 and reduced exponentially with a parameter of 0.9; batch size M = 128 determines the direction of gradient descent, so its selection needs to consider the degree of information redundancy of all samples; exponential decay rates β₁ and β₂ are set to 0.9 and 0.999 respectively, so that the deviation of the moment estimations is close to 0; small constants ɛ and ɛ are both set to 10^–8 for numerical stability; Dropout rate is chosen as 0.4 to reduce the model’s dependence on certain neurons; L2-regularization (i.e. weight decay) is used to reduce the structural risk of the model and improve its generalization capability, and the weight decay rate is set to 0.0001.

Table 1
Hyper-parameters setting in the training process of quantile regression neural network

Hyper -parameters values

Learning rate α 0.005

Batch size M 128

Exponential decay rate β₁ 0.9

Exponential decay rate β₂ 0.999

Small constant ɛ 10^–8

Small constant ɛ 10^–8

Dropout rate 0.4

Weight decay rate 0.0001

Hyper -parameters	values
Learning rate α	0.005
Batch size M	128
Exponential decay rate β₁	0.9
Exponential decay rate β₂	0.999
Small constant ɛ	10^–8
Small constant ɛ	10^–8
Dropout rate	0.4
Weight decay rate	0.0001

5 Experimental results and analysis

5.1 Experimental dataset and evaluation methods

We conduct the experiments on the public dataset [19], which contains a total of 4000 training areas with various engineering parameters, location information, and RSRP values. Then we use PR, RR, and PCRR as metrics to evaluate the performance of the proposed method, which can be calculated by:

$PR = \frac{TP}{TP + FP}$ (16)

$RR = \frac{TP}{TP + FN}$ (17)

$PCRR = 2 \times \frac{PR \times RR}{PR + RR}$ (18) where TP, FP, and FN represent true positive, false positive, and false negative predictions, respectively. PR and RR values can measure the PSRP prediction accuracy of the quantile regression neural network. In other words, the effective identification of weak coverage area, i.e. high PCRR values, can better help operators plan and optimize wireless communication networks accurately.

5.2 Prediction results

We first present the fitting results of training, validation, and testing samples in Fig. 5. It can be seen that the RSRP values of training samples can be predicted well, except for some special cases with high bias. In fact, these samples can also be well fitted but it is not necessary. We have stopped the training of the quantile regression neural network in advance to prevent the “overfitting” problem. On the other hand, the prediction variance of the validation and testing samples is obviously smaller than that of the training samples, which means that the distribution of prediction errors become more uniform.

Fig. 5

Prediction results of RSRP values on the training, validation, and test sets.

The RSME values of training, validation, and test sets are also reported in Table 2. We have achieved the RSME values of 0.2443, 0.4502, and 0.5133 on three sets, respectively. The PR, RR, and PCRR values are then presented in Table 3. Although the performance gap still exists between the training set and the test set, the proposed method can achieve the PR, RR, and PCRR values of 84.3%, 78.4%, and 81.2% on the test set, respectively. According to the results, the network performs a good accuracy, but the recall rate is somewhat unsatisfactory, which is due to the “imbalanced learning problem” caused by the small number of samples in the weak coverage area. The model has a higher deviation and is more inclined to predict a higher RSRP value.

Table 2

RSME values of the quantile regression neural network

Performance	Training set	Validation set	Test set
RSME	0.2443	0.4502	0.5133

Table 3

The PR, RR, and PCRR results of the quantile regression neural network

Performance	PR (%)	RR (%)	PCRR (%)
Training set	93.2	87.5	90.3
Validation set	87.1	80.2	83.5
Test set	84.3	78.4	81.2

5.3 Sensitivity to features and classifiers

To observe the influence of the combination of a series of features and classifiers, the ablation study results are presented in Table 4. A total of three kinds of regression models, i.e. the logistic regression (LR), the polynomial regression (PR), and neural network (NN), are used to verify the effectiveness of designed features and the superiority of the proposed model in this paper. Seven feature combinations are used to judge the dependence and sensitivity of the model on particular features, including ξ₁, ξ₂, ξ₁+ξ₃, ξ₁+ξ₂+ξ₅, ξ₁+ξ₃+ξ₄, ξ₁+ξ₂+ξ₄+ξ₈, and ξ₃+ξ₅+ξ₆+ξ₇. It can be seen that as the number of features increases under a same regression model, all the evaluation indicators have improved. Moreover, when more than three features are used to predict RSRP values, the performance gap between different feature combinations is small, which proves the robustness of the designed features. On the other hand, comparing the prediction performance of different classifiers also proves the superiority of the designed neural network model

Table 4
Ablation study of a series of features with various classifiers

Combinations PR (%) RR (%) PCRR (%) RSME

LR ξ ₁ 65.1 60.2 62.6 0.7595

ξ ₂ 60.0 55.9 57.9 0.8107

ξ₁+ξ₃ 69.8 65.1 67.4 0.7436

ξ₁+ξ₂+ξ₅ 78.4 72.2 75.2 0.6749

ξ₁+ξ₃+ξ₄ 79.7 71.8 75.5 0.6539

ξ₁+ξ₂+ξ₄+ξ₈ 80.1 73.1 76.4 0.6028

ξ₃+ξ₅+ξ₆+ξ₇ 80.2 74.9 77.5 0.5293

PR ξ ₁ 64.0 59.8 61.8 0.7602

ξ ₂ 58.0 55.8 56.9 0.8048

ξ₁+ξ₃ 71.2 67.3 69.2 0.7370

ξ₁+ξ₂+ξ₅ 76.8 71.3 73.9 0.6601

ξ₁+ξ₃+ξ₄ 77.4 73.6 75.5 0.6454

ξ₁+ξ₂+ξ₄+ξ₈ 77.8 75.2 76.5 0.5991

ξ₃+ξ₅+ξ₆+ξ₇ 80.3 73.8 76.9 0.5625

NN ξ ₁ 66.2 62.2 64.1 0.7451

ξ ₂ 60.2 57.3 58.7 0.7900

ξ₁+ξ₃ 71.4 67.8 69.6 0.7204

ξ₁+ξ₂+ξ₅ 79.4 72.5 75.8 0.6367

ξ₁+ξ₃+ξ₄ 80.2 74.0 77.0 0.6130

ξ₁+ξ₂+ξ₄+ξ₈ 80.7 75.3 77.9 0.5978

ξ₃+ξ₅+ξ₆+ξ₇ 82.9 76.6 79.6 0.5204

	Combinations	PR (%)	RR (%)	PCRR (%)	RSME
LR	ξ ₁	65.1	60.2	62.6	0.7595
	ξ ₂	60.0	55.9	57.9	0.8107
	ξ₁+ξ₃	69.8	65.1	67.4	0.7436
	ξ₁+ξ₂+ξ₅	78.4	72.2	75.2	0.6749
	ξ₁+ξ₃+ξ₄	79.7	71.8	75.5	0.6539
	ξ₁+ξ₂+ξ₄+ξ₈	80.1	73.1	76.4	0.6028
	ξ₃+ξ₅+ξ₆+ξ₇	80.2	74.9	77.5	0.5293
PR	ξ ₁	64.0	59.8	61.8	0.7602
	ξ ₂	58.0	55.8	56.9	0.8048
	ξ₁+ξ₃	71.2	67.3	69.2	0.7370
	ξ₁+ξ₂+ξ₅	76.8	71.3	73.9	0.6601
	ξ₁+ξ₃+ξ₄	77.4	73.6	75.5	0.6454
	ξ₁+ξ₂+ξ₄+ξ₈	77.8	75.2	76.5	0.5991
	ξ₃+ξ₅+ξ₆+ξ₇	80.3	73.8	76.9	0.5625
NN	ξ ₁	66.2	62.2	64.1	0.7451
	ξ ₂	60.2	57.3	58.7	0.7900
	ξ₁+ξ₃	71.4	67.8	69.6	0.7204
	ξ₁+ξ₂+ξ₅	79.4	72.5	75.8	0.6367
	ξ₁+ξ₃+ξ₄	80.2	74.0	77.0	0.6130
	ξ₁+ξ₂+ξ₄+ξ₈	80.7	75.3	77.9	0.5978
	ξ₃+ξ₅+ξ₆+ξ₇	82.9	76.6	79.6	0.5204

5.4 Comparison of various prediction methods

In this part, we compare several RSRP prediction methods like regression clustering (RC) [25], KNN [31], SVM [31], XGBoost [31], and the corresponding results have been reported in Table 5. Our proposed method achieves the highest PR (84.3%), RR (78.4%), and PCRR (81.2%) values, and the lowest RSME (0.5133) on the RSRP prediction task, which improved the state-of-the-art performance by 4.1%, 3.7%, 3.8%, and 0.1172, respectively. The results also illustrate the good characterization of designed features for RSRP values and the nonlinear mapping ability of proposed neural network.

Table 5
Comparison results of various RSRP prediction methods

Methods PR (%) RR (%) PCRR (%) RSME

RC [25] 74.0 70.2 72.0 0.6807

KNN [31] 70.8 66.3 68.5 0.7238

SVM [31] 77.4 72.9 75.1 0.6760

XGBoost [31] 80.2 74.7 77.4 0.6305

Proposed method 84.3 78.4 81.2 0.5133

Methods	PR (%)	RR (%)	PCRR (%)	RSME
RC [25]	74.0	70.2	72.0	0.6807
KNN [31]	70.8	66.3	68.5	0.7238
SVM [31]	77.4	72.9	75.1	0.6760
XGBoost [31]	80.2	74.7	77.4	0.6305
Proposed method	84.3	78.4	81.2	0.5133

6 Conclusion

Wireless environment maps cover the performance information of communication system, so it is one of the key techniques to realize the self-organizing network. Among them, signal intensity maps are critical for network planning and operation of cellular operators, but their acquisition costs are high and may be limited or inaccurate in some locations. In this paper, we designed a variety of features to reflect the factors affecting RSRP, and then build a quantile regression neural network model to predict the RSRP values of multiple test areas. The visualization results show the strong correlation between these features and RSRP values. Finally, experimental verification on a public dataset indicates the effectiveness and superiority of the proposed method.

In the future, we plan to apply more types of machine learning regression models, such as Lasso and ElasticNet, to verify the effects of designed features on RSRP prediction.

Footnotes

Acknowledgments

This work was partially supported by Fundamental Research Funds of Shandong University (Grant No. 2018JC040), National Natural Science Foundation of China (Grant No. 61571275), and National Key R&D Program of China (Grant No. 2018YFC0831503).

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An intelligent wireless communication model based on multi-feature fusion and quantile regression neural network

Abstract

Keywords

1 Introduction

2 Related work

2.1 Theoretical models

2.2 Empirical models

2.3 Improved empirical models

3 Multi-feature design and integration

3.1 Shadow coefficient

3.6 Azimuth angle

4.1 Architecture

5.1 Experimental dataset and evaluation methods

Table 5 Comparison results of various RSRP prediction methods Methods PR (%) RR (%) PCRR (%) RSME RC [25] 74.0 70.2 72.0 0.6807 KNN [31] 70.8 66.3 68.5 0.7238 SVM [31] 77.4 72.9 75.1 0.6760 XGBoost [31] 80.2 74.7 77.4 0.6305 Proposed method 84.3 78.4 81.2 0.5133

Footnotes

Acknowledgments

References

Table 5
Comparison results of various RSRP prediction methods

Methods PR (%) RR (%) PCRR (%) RSME

RC [25] 74.0 70.2 72.0 0.6807

KNN [31] 70.8 66.3 68.5 0.7238

SVM [31] 77.4 72.9 75.1 0.6760

XGBoost [31] 80.2 74.7 77.4 0.6305

Proposed method 84.3 78.4 81.2 0.5133