LTE wireless network coverage optimisation based on corrected propagation model

As an important part of information transmission, communication technology has attracted more and more attention and has been studied extensively [1]. With the rapid development of mobile communication technology, the data transmission rate provided by the communication system is also getting faster and faster [2]. The upgrade of communication service technology provides more convenience for people's life and work [3]. However, with the large-scale application of LTE technology, we have to face more and more challenges while carrying out large-scale communication network business construction [4]. The high-speed integration of the wireless mobile network and Internet makes the broadband development of the mobile communication network more urgent [5], and the planning and coverage optimisation of the wireless network has become the most urgent task to be solved today [6].

The wireless network propagation model is a mathematical model based on the comparison between the theoretical calculation and measured data [7]. It is also an expression related to the measured data obtained from the environment, such as frequency, distance, height and other factors. It is a simulation and prediction of the information loss of the propagation path between the receiver and transmitter [8]. This is an important prerequisite for communication network planning and coverage optimisation [9]. Due to the difference in the signal transmission environment, different network communication structures, uneven spatial distribution of users and uncertain use behaviour, wireless network transmission is always a dynamic network [10]. Due to different environments and parts of the city landscape, the communication model is different [11] and must adapt to the environment of the real response through the spread of the actual environment model testing and calibration [12]. The spread of the wireless propagation model provides better coverage for the wireless network system construction, larger channel capacity and more high-quality and efficient communications [13]. This is particularly important for the current LTE communication system [14].

At present, researchers at home and abroad have conducted a large number of theoretical studies and practical tests on wireless network propagation models [15], and they concluded various classical network propagation models, including deterministic model, empirical model and semi-deterministic semi-empirical model [16]. The deterministic model is based on the theory of electromagnetic field and is directly calculated to obtain the actual environmental conditions, such as signal ray tracking and signal geometric diffraction [17]. The empirical model is also called the statistical model based on test results, and the expression obtained after the statistical analysis of a large number of test results is called the path loss formula [18]. The formula of the empirical model usually involves only the height of the communication antenna, the distance between sending and receiving information, frequency and other factors; and these variable pieces of information can be easily obtained by equipment; its calculation process is simple, so the empirical model is widely used in reality [19]. Famous empirical models include Okumura–Hata [20], Cost 231–Hata [21] CCIR and Cost 231–Walfisch–Ikegami model [22]. For example, based on the principle of reverse ray tracing, Villaluz et al. [23] proposed a diffraction algorithm of arbitrary wedge on the basis of the urban scene model and established an urban multipath prediction model by tracking all possible paths of signal from the source point to the field point. Mardeni and Priya [24] summarised the prediction model based on the ray tracing algorithm applied to high-speed railway tunnel scenarios through comparative analysis of the application of the mirror method, bounce ray method and ray density normalisation. Jimoh et al. [25] compared the prediction effects of nine empirical models in Nigeria, including Hart model, Davidson model, CCIR model and Ericsson model, and verified the accuracy of CCIR. Lee and Lee [26] integrated the models of different prediction radii in Lee's model and proposed an improved model for deploying and optimising the comprehensive prediction of skin cells, microcells and macrocells with different cell types. Jain and Shrivastava [27], on the basis of Cost 231–Hart model, tested data in a multi-scene environment based on a nonlinear least square method and proposed the correction factor of this model in a multi-geomorphic environment.

On the other hand, in the study of the propagation model, the propagation model of the wireless communication network can be divided into two types: one is a large-scale propagation model and the other is a small-scale propagation model. The large-scale propagation model mainly describes the changes in the size of the signal received by the transmitting and receiving devices within a certain distance (several hundred metres or longer). Such changes are due to the influence of various obstacles encountered on the wireless propagation path between the receiver and receiving antennas on the wireless signals. Major large-scale propagation models include SPM universal model, Cost 231–Hata model, Lee model, Walfisch–Ikegami model and Okumura–Hata model [28]. The small-scale propagation model mainly describes the model in which the intensity of the received signal changes rapidly within a short time (second level) or a short distance (several wavelengths). The main small-scale propagation models include Raleigh time-varying channel model, AGWN model [29] and Roentgen fading model. The two models mentioned here can coexist with each other. In the actual communication environment, there exists both large-scale signal attenuation and small-scale signal attenuation in the same wireless communication system. Under the current situation of very limited signal spectrum resources, propagation characteristics of the two wireless networks should be based on. The quality of communication transmission channel and information utilisation rate can be improved in targeted and effective ways [30]. However, in wireless network planning and design, it is usually only necessary to consider the fading of the large-scale model mainly because of the mean value of the signal field intensity received by the receiving device in unit time [31]. However, small-scale fading is usually used in theoretical research for the design of digital receiving equipment and the selection of signal transmission technology, which is generally not considered in the planning stage of the wireless communication network.

Additionally, in the current mobile communication network planning, the wireless network propagation model is an important factor affecting the efficiency and accuracy of planning schemes [32]. However, the classical wireless propagation model is usually calculated through statistics and fitting of a large amount of test data in the actual network environment. The empirical model uses statistical methods to conduct statistical analysis of all environmental factors, but the empirical model has a large error in specific physical area scenarios [33]. Additionally, the traditional transmission model mainly considers the influence of signal coverage distance and antenna relative height on signal path loss, and the rational application scenario is relatively simple and only applicable to flat areas such as rural areas and plains [34]. At present, the communication model widely used in the communication network is an improved experiential communication model with more detailed classification. Each classification has a fixed fitting formula, which makes the communication model suitable for the actual complex environment. Among them, typical propagation models include standard propagation model [35]. At present, the classical propagation model is widely adopted in the 4G (4th generation) propagation model in China, and the SPM model is optimised on the basis of the Cost 231–Hata model.

Based on a variety of different types of typical problems of signal propagation (e.g., area coverage, low coverage, interference serious and overlapping coverage). To ask questions that corresponds to the wireless network communication model solutions (e.g., By adjusting the antenna azimuth, hanging high, dip Angle, base station transmission power and other related parameters), and optimization is the typical problem to solve, It is necessary to compare the measured data and verify the error range between the simulated prediction data and the actual test data again after the solution implementation. The propagation model obtained from these works is helpful for the subsequent simulation prediction data so as to accurately judge the areas with various practical problems in the current network, such as over-coverage, weak coverage, overlapping coverage, high interference and low rate. Thus, it can effectively and accurately guide and reference the existing network coverage planning and communication quality optimisation, and improve the efficiency of communication network construction.

Propagation model correction is a curve fitting process in essence, that is, by adjusting the coefficients of the propagation model, the error between the path loss calculated by the propagation model and the measured path loss is minimised. In free space, the propagation model between the receiver and receiver antennas is the simplest. Suppose that the power density of radio wave on the sphere of non-directional point source radiation is S, which can be expressed as follows: (1) S=Pt4πd2Gt S = {{{P_t}} \over {4\pi {d^2}}}{G_t}

The power received by the receiving antenna at the sphere is as follows: (2) Pr=SAr {P_r} = S{A_r}

The effective receiving area of the receiving antenna is as follows: (3) At=λ24πGr {A_t} = {{{\lambda ^2}} \over {4\pi}}{G_r}

In Eqs (1)–(3), G_t and G_r are the gain of transmitting antenna and receiving antenna, respectively, and λ is the wavelength. According to the previous formula, the received power is as follows: (4) Pr=Pt(λ4πd)2GtGr {P_r} = {P_t}{\left({{\lambda \over {4\pi d}}} \right)^2}{G_t}{G_r}

In engineering, the ratio of P_t to P_r is defined as propagation loss L. The expression of propagation loss can be obtained from Eq. (4): (5) L=PtPr=(4πdλ)21GtGr L = {{{P_t}} \over {{P_r}}} = {\left({{{4\pi d} \over \lambda}} \right)^2}{1 \over {{G_t}{G_r}}}

In free space, only the loss caused by the energy diffusion of electromagnetic wave exists, which is called path loss. When G_t = G_r = 1, that is, the receiver and receiving antennas are both two ideal point source antennas in free space, and the free space path loss in dB can be expressed as follows: (6) L=lg(4πdλ)2=32.45+20lgf+20lgd L = \lg {\left({{{4\pi d} \over \lambda}} \right)^2} = 32.45 + 20\lg f + 20\lg d

It can be seen from Eq. (6) that the factors affecting path loss are transmission frequency and transmitting distance. In other words, if f or d are doubled, then L is increased by 6 dB. If G_t and G_r are not 1, that is, the gain of the transmitting and receiving antennas is not 1, the gain of the antennas can be considered in the link budget.

If the working frequency of the LTE system is 2.6 GHz, the path loss formula of free-space propagation model is as follows: (7) L=40.75+20lgd L = 40.75 + 20\lg d

Okumura, a Japanese scientist, proposed a signal strength prediction model based on a large amount of propagation loss test data, but the prediction model has to query all kinds of curve charts to predict, which is not conducive to computer processing. Hata was improved on the basis of the Okumura model, and the Okumura–Hata model was obtained by setting restrictions on curve fitting. Almost all the empirical propagation models proposed in the later period are modified and improved on this basis. The model is mainly used for a quasi-flat terrain macrocellular system with a frequency of 150–1500 MHz and a cell radius of >1 km. The effective antenna heights of the base station and mobile station are set as 30–200 m and 1–10 m, respectively. The empirical formula of the Okumura–Hata model is as follows: (8) L=69.55+26.16logfc−13.82loghte−a(hre)+(44.9−6.55loghte)logd+Ccell+Cterrain L = 69.55 + 26.16\log {f_c} - 13.82\log {h_{te}} - a({h_{re}}) + (44.9 - 6.55\log {h_{te}})\log d + {C_{cell}} + {C_{terrain}}

Here, a(h_re) is the height correction factor of the mobile station antenna, h_te is the effective height of the base station antenna (m), h_re is the effective height of the mobile station antenna and C_cell and C_terrain are cell type correction factor and terrain correction factor, respectively. The effective height is calculated by subtracting the average altitude from the antenna to the ground and superimposing the altitude of the ground. The expression form of antenna height correction factor h_re of the mobile station will change with the size and frequency of different cities, which is expressed as follows: (9) a(hre)={(1.11logfc)hre−(1.56log(fc)−0.8)8.29(log1.54hre)2−1.1(fc≤300 MHz)3.2(log11.75hre)2−4.97(fc≥300 MHz) a({h_{re}}) = \left\{{\matrix{{(1.11\log {f_c}){h_{re}} - (1.56\log ({f_c}) - 0.8)} \hfill \cr {8.29(\log 1.54{h_{re}}{)^2} - 1.1({f_c} \le 300\;{\rm{MHz}})} \hfill \cr {3.2(\log 11.75{h_{re}}{)^2} - 4.97({f_c} \ge 300\;{\rm{MHz}})} \hfill \cr}} \right.

The expressions of cell correction factors in different transmission environments will be different, which can be expressed as follows: (10) Ccell={0−2[log(fc28)]2−4.78(logfc)2−18.33logfc−40.98 {C_{cell}} = \left\{{\matrix{0 \hfill \cr {- 2{{\left[{\log \left({{{{f_c}} \over {28}}} \right)} \right]}^2}} \hfill \cr {- 4.78(\log {f_c}{)^2} - 18.33\log {f_c} - 40.98} \hfill \cr}} \right.

The topographic correction factor C_terrain can reflect the influence of important environmental topographic factors such as water area, trees and buildings on propagation loss.

The Okumura–Hata model is only suitable for a low-frequency band, so the European Association for Scientific and Technological Research proposed the Cost 231–Hata model. This model is an extension of the Hata model, which is suitable for urban landforms and suburban wireless network planning. It is generally used in macrocell base stations with a radius of >1 km and an application frequency of up to 2000 MHz. The path loss expression of this model is as follows: (11) L=46.3+33.9logfc−13.82loghte−a(hre)+(44.9−6.55loghte)logd+Ccell+Cterrain+CM L = 46.3 + 33.9\log {f_c} - 13.82\log {h_{te}} - a({h_{re}}) + (44.9 - 6.55\log {h_{te}})\log d + {C_{cell}} + {C_{terrain}} + {C_M}

Here, f_c represents frequency and unit MHz; d represents the distance between the transmitter and receiver; h_re and h_te are correction factors of base station height and receiver height, respectively.

From the form of Eqs (1) and (4), the two Hata models are almost the same, and the factors taken into consideration are completely the same. The main differences lie in the coefficients of various factors, including the constant term, frequency, correction factor a(h_re) and metropolitan centre correction factor C_M. C_M has a value of 0 in rural and suburban settings and 3 in urban areas. a(h_re) function of the urban area is defined as follows: (12) a(hre)=3.2[log(11.75hre)]2−4.97 a({h_{re}}) = 3.2{\left[{\log \left({11.75{h_{re}}} \right)} \right]^2} - 4.97 a(h_re) function in rural and suburban environments is defined as follows: (13) a(hre)=(1.22log(fc)−0.7)hre−(1.56log(fc)−0.8) a({h_{re}}) = (1.22\log ({f_c}) - 0.7){h_{re}} - (1.56\log ({f_c}) - 0.8)

The Cost 231–Walfisch–Ikegami model is an extension of the Cost–Hata model on the basis of the Walfisch–Bertoni model and Ikegami model. The model takes into account the loss of free path, the loss from roof to street and the loss affected by the angle between the antenna and street and can be used to calculate the loss of all kinds of conditions >2000 MHz. When there is a line of sight (LOS) propagation between the transmitter and receiver, the path loss formula is as follows: (14) L=42.6+logd+20logf L = 42.6 + \log d + 20\log f

When there is non-line-of-sight (NLOS) transmission between the transmitter and receiver, as shown in Figure 1, the path loss formula is as follows: (15) L=L0+L1+L2 L = {L_0} + {L_1} + {L_2} where L₀ is attenuation of free space and L₁ represents diffraction from the roof to the street, denoted as follows: (16) L1=−16.9−10logw+10logf+20log(hR−hm)+L11(ϕ) {L_1} = - 16.9 - 10\log w + 10\log f + 20\log ({h_R} - {h_m}) + {L_{11}}(\phi)

Fig. 1

In the formula, w is the width of the street where the receiver is located (m), h_R is the average height of the building (m), h_m is the height of the receiving antenna, ϕ is the incident angle of the connection of the receiver and receiving antenna relative to the street, and the function L₁₁(ϕ) is defined as follows: (17) L11(ϕ)={−10+0.3571ϕ0<ϕ<35∘2.5+0.075(ϕ−35∘)35∘≤ϕ<55∘4−0.1114(ϕ−55∘)55∘≤ϕ≤90∘ {L_{11}}(\phi) = \left\{ {\matrix{{ - 10 + 0.3571\phi } \hfill & {0 < \phi {{ < 35}^ \circ }} \hfill \cr {2.5 + 0.075(\phi - {{35}^ \circ })} \hfill & {{{35}^ \circ } \le \phi {{ < 55}^ \circ }} \hfill \cr {4 - 0.1114(\phi - {{55}^ \circ })} \hfill & {{{55}^ \circ } \le \phi \le {{90}^ \circ }} \hfill \cr } } \right.

Here, L₂ represents the loss caused by diffraction due to multiple obstacles, which can be expressed as follows: (18) L2=L21+ka+kdlogf−9logb {L_2} = {L_{21}} + {k_a} + {k_d}\log f - 9\log b

The success of model correction is usually achieved by comparing the predicted value of the model with the measured value of the environment and statistical analysis of the error.

Assume that the prediction error of point i is as follows: (19) E(i)[dB]=Pmeasured(i)[dBm]−Ppredicted(i)[dBm] {{E(i)} \over {[dB]}} = {{{P_{measured}}(i)} \over {[dBm]}} - {{{P_{predicted}}(i)} \over {[dBm]}}

Each parameter of judgement is represented by Eqs (20)–(22).

The mean square deviation (RMS) is as follows: (20) ERMS[dB]=1n∑i=1nE(i)[dB] {{{E_{RMS}}} \over {[dB]}} = \sqrt {{1 \over n}\sum\limits_{i = 1}^n {{E(i)} \over {[dB]}}}

Mean error is as follows: (21) E¯[dB]=1n∑i=1nE(i)[dB] {{\bar E} \over {[dB]}} = {1 \over n}\sum\limits_{i = 1}^n {{E(i)} \over {[dB]}}

The standard deviation (Std Dev) error is as follows: (22) σE[dB]=1n∑i=1n(E(i)[dB]−E¯[dB])2

In this study, the wireless propagation model of LTE system is corrected, and its coverage is predicted through the combination of the neural network algorithm and the particle swarm optimisation algorithm, and the correction method and correction results are verified. Based on the LTE network planning project of a big city in China, the research and application of LTE system wireless propagation model correction are carried out on the basis of classical outdoor propagation model and existing model correction algorithm. The correction results are applied to the actual project, and the actual problems such as over-coverage, weak coverage, overlapping coverage, high interference and low rate can be accurately judged through the prediction data of simulation software. Thus, it can effectively and accurately guide and reference the planning and optimisation of the live network. The main results are as follows:

Use simulation software to simulate the classical correction propagation models such as Okumura–Hata, Cost 231–Hata, Cost 231–Walfisch–Ikegami and SPM. Simulation results show that the SPM model can adapt to a wider range of frequency bands, take more comprehensive loss factors into account and achieve more accurate results. Therefore, the SPM model is selected as the basic model of LTE wireless propagation model correction. Combined with the LTE project of this study, site selection and related equipment of CW test, path planning of the data collection process and data processing steps are given.