# Path Loss Channel Model for Inland River Radio Propagation at 1.4 GHz

Authors: Junyi Yu; Wei Chen; Kun Yang; Changzhen Li; Fang Li; Yishui Shui
Journal: International Journal of Antennas and Propagation
 (2017)

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## Abstract

In this paper, a propagation path loss model for inland river is proposed by three improvements compared with the Round Earth Loss (REL) model for open-sea environment. Specifically, parameters optimization uses Okumura-Hata model in dB scale to replace the equation transformed from the free space loss in REL model; secondly, diffraction loss caused by the obstacles (e.g., large buildings, bridges, or some other facilities near the river bank) is also taken into account; mixed-path methodology as another improvement is used for Inland River (IR) model because the actual propagation environment between transmitter (TX) antenna and receiver (RX) antenna contains both land part and water part. The paper presents a set of 1.4 GHz measurements conducted along the Yangtze River in Wuhan. According to the comparison between path loss models and experimental results, IR model shows a good matching degree. After that, Root Mean Square Error (RMSE), Grey Relation Grade and Mean Absolute Percentage Error (GRG-MAPE), Pearson Correlation Coefficient, and Mean Absolute Percentage Error (PCC-MAPE) are employed to implement quantitative analysis. The results prove that IR model with consideration of mixed path and deterministic information is more accurate than other classic empirical propagation models for these scenarios.


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## Body

## 1. Introduction

As the third longest river of the world, Yangtze River plays an important role in Chinese water transportation. Our investigation in Changjiang Maritime Safety Administration showed that the whole basin navigation mileage of Yangtze River was up to 80000 kilometers (including main-stream and tributaries), accounting for about 65 percent of China inland waterways navigation mileage. In 2015, large-scale ports along the trunk line of the Yangtze River completed cargo throughput 2.118 billion tons. Thus, it is essential to provide high data rate and reliable communication service between ship to ship and ship to shore to ensure the safety of navigation. However, the performance of present broadband communication systems have not been optimized for the maritime applications due to lack of a comprehensive Inland River channel model, which is indispensable to the system design and optimization. To solve the above challenge, we propose a dedicated IR model in this article.The inland river terrain profile contains both land and water regions. For the land area, various measurement campaigns have been performed to develop the radio channel models (e.g., Okumura-Hata empirical model [1–4]). The COST-231 Hata model [5] extending frequency adaption of Okumura-Hata is valid in frequency range from 1.5 to 2.0 GHz. However, some of key propagation phenomena have not been considered by either of them, including scattering, divergence, and shadowing. REL model derived from Two-Ray theory is proposed in [6] for the open-sea scenario, which has taken effective reflection and shadowing effect due to the roughness of sea surface as well as divergence and diffraction phenomena caused by earth curvature into account. But unlike the case of open-sea, the influence of the obstacles near the inland river (e.g., diffraction loss caused by some large bridges) and mixed-path effect cannot be neglected. Paper [7] provided a methodology of field strength estimation in distance ranged from 1 km to 1000 km, and frequency ranged from 30 MHz to 3000 MHz. It is applied for land-path, sea-path, and mixed-path scenarios. However, propagation effects including scattering, divergence, and earth curvature still have not been included either. Consequently, the IR model will take these effect factors into account and make some quantitative analysis to improve the effectiveness and accuracy.The rest of paper is organized as below: In Section2, our new IR model is proposed based on REL model. Three typical measurement campaigns are introduced in detail in Section 3. Section 4 mainly includes analysis on finite dimensions diffraction loss as well as study on other key propagation phenomena such as effective reflection, shadowing effect on the reflected ray, divergence, and earth curvature effect. Afterward, the parameters estimation of IR model and two simulation verifications are given in Section 5. In Section 6, path loss models’ effectiveness and adaptability are evaluated by using RMSE, GRG-MAPE, and PCC-MAPE algorithms, respectively. Finally, conclusions are drawn in Section 7.


## 2. Path Loss Model for Inland River

### 2.1. Round Earth Loss Model

Plain Earth Loss (PEL) model based on Two-Ray propagation path is commonly used for cellular communication [1]. However, the earth cannot be regarded as a “plane” when the TX-RX distance exceeds several kilometers. By accounting for scattering, divergence, shadowing, and earth curvature effects, REL model is proposed for open-sea environment [6] and its geometrical model is given in Figure 1.Figure 1
Round Earth Loss model.ThehTX and hRX are corresponding to the height of TX and RX antennas, respectively. RE which is assumed as an approximate value 6731 km, denotes earth radius. Propagation path loss PLe is given by(1)PLe=λ4πD2·1+R·ej2π/λDdiff2,where (2π/λ)·Ddiff represents the phase difference between reflected wave and line of sight (LOS) wave. D is equal to D_LOS which denotes the length of LOS path. R is the specular reflection coefficient [2, 8](2)Ddiff=DR_X1+DR_X2-D,where D is calculated by(3)D2=RE+hTX2+RE+hRX2-2RE+hTXRE+hRXcos⁡dRE.The angles α, β in Figure 1 are obtained by using(4)α+β=dRE=D_1+D_2RE,arccos⁡RE+hTX-RE·cos⁡αDR_X1+α=arccos⁡RE+hRX-RE·cos⁡βDR_X2+β.Here, the lengths of DR_X1 and DR_X2 are as follows:(5)DR_X12=RE+hTX2+RE2-2RE+hTX·RE·cos⁡α,DR_X22=RE+hRX2+RE2-2RE+hRX·RE·cos⁡β.Finally, the REL model [6] for open-sea radio propagation can be further expressed as follows:(6)PLe=20lg⁡λ4πD+20lg⁡η+Le_diff,η=1+Rrough·Sc·Diveff·ej2π/λDdiff,where Rrough represents effective reflection coefficient. Sc and Diveff are corresponding to shadowing coefficient, and divergence coefficient, respectively. Considering the case of long TX-RX distance, Le_diff denotes the diffraction loss derived from earth curvature effect. On the basis of (6), the structure of this propagation path loss model is divided into two parts (shown in Figure 2).Figure 2
The structure of REL model.Free space model (Part-1) estimates the path loss derived from LOS ray between TX and RX. Also, this model can be transformed to a linear function oflg⁡(D) [9]. For reflected signal, various effect factors such as effective reflection, shadowing, divergence, and earth curvature will increase the propagation path loss especially for the case at large TX-RX distances for the open sea [6]. Thus, Part-2 is an integration of them to make REL model applicable for the open sea environment.


### 2.2. Inland River Model

There are common features between sea surface and river surface. Therefore, scattering, shadowing, and divergence still need to be taken into consideration. With an increase of TX-RX distance, the diffraction loss caused by earth curvature will also occur. More details will be given in Section4. However, inland river area which contains both land region and water region is different from the open-sea, for example, buildings or bridges on the river bank may influence signal transmission. In addition, the conductivity of fresh water (σc=0.001) is also different from sea water (σc=4) [8]. In summary, compared to the REL model, there are three improvements in the IR model.


#### 2.2.1. Parameters Optimization

Low matching degree of the REL model and free space model by comparing with the measurement data proves inefficiency of these classic models [10, 11], which indicate the necessity of model optimization. Since the inland river region is a combination of all-land region and all-water region, the corresponding radio propagation path loss for these single scenarios PLL and PLW are defined as the upper and lower bounds of the IR model. According to the Two-Ray theory, environmental correction factors Ml and Ms are employed to optimize IR model to obtain the PLL and PLW, respectively. Assuming that both Ml and Ms in dB can also be depicted by linear format dependence with the logarithmic length of LOS path (shown in Figure 3), the parameters αL, βL for all-land region and the parameters αW, βW for all-water region are obtained by(7)αL=20lg⁡λ4π+αl,βL=βl-2;αW=20lg⁡λ4π+αs,βW=βs-2,where αl, βl, αs, and βs are empirical parameters. More details about these parameters’ estimation will be given in Section 5.Figure 3
The structure of Inland River model.


#### 2.2.2. Diffraction Loss Caused by Obstacles near the River

Watercourse is narrow and sinuous. The buildings located at the river bank or some other facilities (e.g., bridges) may cause an additional diffraction lossOblm which is ignorable in open-sea environment. Thus, IR model includes this part shown in Figure 3. The calculation of this parameter can be found in Section 4.


#### 2.2.3. Mixed-Path Methodology

Mixed-path feature for the inland river environment makes it necessary to combine the path losses of land regionPLL and water region PLW (shown in Figure 3). To resolve this problem, a proper method which is proposed by [7] is expressed as follows:(8)PLIR=1-A·PLL+A·PLW.Here,PLIR expresses the propagation path loss for inland river. “A” is a mixed-path interpolation factor, which is given in (9). The percentage of the water path Friver and the land path Fland can be obtained from GPS position information in the route which is also recorded in our measurement data(9)A=1-1-Friver2/3V,(10)V=max⁡1.0,1.0+Δ40.0,(11)Δ=ElandD-EriverD.In (11), Eland and Eriver correspond to the equivalent field strength (dB) for all-land and all-water paths, respectively:(12)ElandD=139.3-PLL+20lg⁡f,EriverD=139.3-PLW+20lg⁡f.Here, f denotes the carrier frequency in MHz.


## 2.1. Round Earth Loss Model

Plain Earth Loss (PEL) model based on Two-Ray propagation path is commonly used for cellular communication [1]. However, the earth cannot be regarded as a “plane” when the TX-RX distance exceeds several kilometers. By accounting for scattering, divergence, shadowing, and earth curvature effects, REL model is proposed for open-sea environment [6] and its geometrical model is given in Figure 1.Figure 1
Round Earth Loss model.ThehTX and hRX are corresponding to the height of TX and RX antennas, respectively. RE which is assumed as an approximate value 6731 km, denotes earth radius. Propagation path loss PLe is given by(1)PLe=λ4πD2·1+R·ej2π/λDdiff2,where (2π/λ)·Ddiff represents the phase difference between reflected wave and line of sight (LOS) wave. D is equal to D_LOS which denotes the length of LOS path. R is the specular reflection coefficient [2, 8](2)Ddiff=DR_X1+DR_X2-D,where D is calculated by(3)D2=RE+hTX2+RE+hRX2-2RE+hTXRE+hRXcos⁡dRE.The angles α, β in Figure 1 are obtained by using(4)α+β=dRE=D_1+D_2RE,arccos⁡RE+hTX-RE·cos⁡αDR_X1+α=arccos⁡RE+hRX-RE·cos⁡βDR_X2+β.Here, the lengths of DR_X1 and DR_X2 are as follows:(5)DR_X12=RE+hTX2+RE2-2RE+hTX·RE·cos⁡α,DR_X22=RE+hRX2+RE2-2RE+hRX·RE·cos⁡β.Finally, the REL model [6] for open-sea radio propagation can be further expressed as follows:(6)PLe=20lg⁡λ4πD+20lg⁡η+Le_diff,η=1+Rrough·Sc·Diveff·ej2π/λDdiff,where Rrough represents effective reflection coefficient. Sc and Diveff are corresponding to shadowing coefficient, and divergence coefficient, respectively. Considering the case of long TX-RX distance, Le_diff denotes the diffraction loss derived from earth curvature effect. On the basis of (6), the structure of this propagation path loss model is divided into two parts (shown in Figure 2).Figure 2
The structure of REL model.Free space model (Part-1) estimates the path loss derived from LOS ray between TX and RX. Also, this model can be transformed to a linear function oflg⁡(D) [9]. For reflected signal, various effect factors such as effective reflection, shadowing, divergence, and earth curvature will increase the propagation path loss especially for the case at large TX-RX distances for the open sea [6]. Thus, Part-2 is an integration of them to make REL model applicable for the open sea environment.


## 2.2. Inland River Model

There are common features between sea surface and river surface. Therefore, scattering, shadowing, and divergence still need to be taken into consideration. With an increase of TX-RX distance, the diffraction loss caused by earth curvature will also occur. More details will be given in Section4. However, inland river area which contains both land region and water region is different from the open-sea, for example, buildings or bridges on the river bank may influence signal transmission. In addition, the conductivity of fresh water (σc=0.001) is also different from sea water (σc=4) [8]. In summary, compared to the REL model, there are three improvements in the IR model.


### 2.2.1. Parameters Optimization

Low matching degree of the REL model and free space model by comparing with the measurement data proves inefficiency of these classic models [10, 11], which indicate the necessity of model optimization. Since the inland river region is a combination of all-land region and all-water region, the corresponding radio propagation path loss for these single scenarios PLL and PLW are defined as the upper and lower bounds of the IR model. According to the Two-Ray theory, environmental correction factors Ml and Ms are employed to optimize IR model to obtain the PLL and PLW, respectively. Assuming that both Ml and Ms in dB can also be depicted by linear format dependence with the logarithmic length of LOS path (shown in Figure 3), the parameters αL, βL for all-land region and the parameters αW, βW for all-water region are obtained by(7)αL=20lg⁡λ4π+αl,βL=βl-2;αW=20lg⁡λ4π+αs,βW=βs-2,where αl, βl, αs, and βs are empirical parameters. More details about these parameters’ estimation will be given in Section 5.Figure 3
The structure of Inland River model.


### 2.2.2. Diffraction Loss Caused by Obstacles near the River

Watercourse is narrow and sinuous. The buildings located at the river bank or some other facilities (e.g., bridges) may cause an additional diffraction lossOblm which is ignorable in open-sea environment. Thus, IR model includes this part shown in Figure 3. The calculation of this parameter can be found in Section 4.


### 2.2.3. Mixed-Path Methodology

Mixed-path feature for the inland river environment makes it necessary to combine the path losses of land regionPLL and water region PLW (shown in Figure 3). To resolve this problem, a proper method which is proposed by [7] is expressed as follows:(8)PLIR=1-A·PLL+A·PLW.Here,PLIR expresses the propagation path loss for inland river. “A” is a mixed-path interpolation factor, which is given in (9). The percentage of the water path Friver and the land path Fland can be obtained from GPS position information in the route which is also recorded in our measurement data(9)A=1-1-Friver2/3V,(10)V=max⁡1.0,1.0+Δ40.0,(11)Δ=ElandD-EriverD.In (11), Eland and Eriver correspond to the equivalent field strength (dB) for all-land and all-water paths, respectively:(12)ElandD=139.3-PLL+20lg⁡f,EriverD=139.3-PLW+20lg⁡f.Here, f denotes the carrier frequency in MHz.


## 2.2.1. Parameters Optimization

Low matching degree of the REL model and free space model by comparing with the measurement data proves inefficiency of these classic models [10, 11], which indicate the necessity of model optimization. Since the inland river region is a combination of all-land region and all-water region, the corresponding radio propagation path loss for these single scenarios PLL and PLW are defined as the upper and lower bounds of the IR model. According to the Two-Ray theory, environmental correction factors Ml and Ms are employed to optimize IR model to obtain the PLL and PLW, respectively. Assuming that both Ml and Ms in dB can also be depicted by linear format dependence with the logarithmic length of LOS path (shown in Figure 3), the parameters αL, βL for all-land region and the parameters αW, βW for all-water region are obtained by(7)αL=20lg⁡λ4π+αl,βL=βl-2;αW=20lg⁡λ4π+αs,βW=βs-2,where αl, βl, αs, and βs are empirical parameters. More details about these parameters’ estimation will be given in Section 5.Figure 3
The structure of Inland River model.


## 2.2.2. Diffraction Loss Caused by Obstacles near the River

Watercourse is narrow and sinuous. The buildings located at the river bank or some other facilities (e.g., bridges) may cause an additional diffraction lossOblm which is ignorable in open-sea environment. Thus, IR model includes this part shown in Figure 3. The calculation of this parameter can be found in Section 4.


## 2.2.3. Mixed-Path Methodology

Mixed-path feature for the inland river environment makes it necessary to combine the path losses of land regionPLL and water region PLW (shown in Figure 3). To resolve this problem, a proper method which is proposed by [7] is expressed as follows:(8)PLIR=1-A·PLL+A·PLW.Here,PLIR expresses the propagation path loss for inland river. “A” is a mixed-path interpolation factor, which is given in (9). The percentage of the water path Friver and the land path Fland can be obtained from GPS position information in the route which is also recorded in our measurement data(9)A=1-1-Friver2/3V,(10)V=max⁡1.0,1.0+Δ40.0,(11)Δ=ElandD-EriverD.In (11), Eland and Eriver correspond to the equivalent field strength (dB) for all-land and all-water paths, respectively:(12)ElandD=139.3-PLL+20lg⁡f,EriverD=139.3-PLW+20lg⁡f.Here, f denotes the carrier frequency in MHz.


## 3. Measurement Campaigns

In our project, measurement campaigns were performed for three different scenarios described as follows:(i)
Urban watercourse environment with few obstacles between TX and RX(ii)
Urban watercourse environment with huge buildings between TX and RX(iii)
Suburban watercourse environmentIn all of these measurement campaigns, Zhongxing Telecommunication Equipment Corporation (ZTE) provided most of apparatuses, which contain cross-polarized base station (BS) antenna (TX), Customer Premise Equipment (CPE), Building Baseband Unit (BBU), and Remote Radio Unit (RRU), which operate in the frequency range from 1447 MHz to 1467 MHz. The transmitter end emitted 4G signal with 20 MHz bandwidth. Considering the case of long distance transmission, uplink-downlink and special subframe were set to configuration 1 and configuration 7 [12] during the whole tests, respectively. In addition, both GPS position data and the information of vessel speed were collected and saved through a Motorola mobile phone (ME525).


### 3.1. Urban Environment Measurement Campaign Description

Figure4(a) shows that RRU and transmitter antenna (15 dBi gain, 65∘ (Az.) and 8∘ (El.)) were placed on the iron tower which was located at the roof of a tall building near the river. Therefore, the height of BS antenna is equal to 79.55 m (including the height of iron tower: 68.30 m, the length of TX antenna: 1.50 m, and the height of shore: 9.75 m) above the river level after ignoring the influence of season tide. At the receiver side (Figure 4(b)), the CPE connected to the PC via RJ45 port can both transmit and receive the radio signals through two omnidirectional antennas (3.5 dBi gain). After that, our urban measurement campaigns can be divided into downstream part and upstream part as follows.Figure 4
Transmitter antenna and receiver antenna.
(a)
Transmitter antenna on the iron tower in Jianghan district (b)
Receiver antenna at the patrol boat


#### 3.1.1. Downstream Part

The patrol boat sailed from a wharf beside our base station to the Tianxingzhou Yangtze River Bridge with the average speed of 14 knots. There was no obstacle higher than TX in this direction. Moreover, two bridges (shown in Figure5) which can be found between the BS and terminal point were the Second Wuhan Yangtze River Bridge (3.511 km away from the TX) and Erqi Yangtze River Bridge (6.8 km away from the TX), respectively.Figure 5
The route of measurement campaign 1 with few obstacles between TX and RX.


#### 3.1.2. Upstream Part

Using the same BS and ship, we completed a 15.01 km measurement campaign in the upstream direction (shown in Figure6). The average speed was approximately 13 knots during the whole process. It was different from the downstream environment since there were some huge buildings (average height: 157 m) at the distance of 700 m from our base station.Figure 6
The route of measurement campaign 2 with large buildings between TX and RX.


### 3.2. Suburban Environment Measurement Campaign Description

As shown in Figure7, this measurement campaign was conducted in a suburban area which was positioned at Dengjiakou Town. The effective height of our BS antenna (TX) was 53.00 m (including the height of iron tower: 50.00 m, the length of TX antenna: 1.50 m and the height of shore: 1.50 m) above river level. Due to the supervision region limitation, our patrol boat with the CPE sailed only 3 km for this scenario.Figure 7
The route of suburban measurement campaign.Ultimately, all of the measurement information is summarized in Table1.Table 1
The measurement parameters.
Parameters Data_1 Data_2 Data_3 Carrier frequency 1457 MHz 1457 MHz 1457 MHz Bandwidth 20 MHz 20 MHz 20 MHz TX power 49.8 dBm 49.8 dBm 49.8 dBm TX beam width (65∘Az.,8∘El.)∗ (65∘Az.,8∘El.)∗ (65∘Az.,8∘El.)∗ RX beam width Omni Omni Omni TX height 79.55 m 79.55 m 53.00 m RX height 3.4 m 3.4 m 3.4 m TX gain 15 dBi 15 dBi 15 dBi RX gain 3.5 dBi 3.5 dBi 3.5 dBi Max.distance 11.06 km 15.01 km 7.778 km Temperature 8–18∘C 8–18∘C 11–21∘C File size 6.204 GB 6.204 GB 6.204 GB ∗Sector antenna.


## 3.1. Urban Environment Measurement Campaign Description

Figure4(a) shows that RRU and transmitter antenna (15 dBi gain, 65∘ (Az.) and 8∘ (El.)) were placed on the iron tower which was located at the roof of a tall building near the river. Therefore, the height of BS antenna is equal to 79.55 m (including the height of iron tower: 68.30 m, the length of TX antenna: 1.50 m, and the height of shore: 9.75 m) above the river level after ignoring the influence of season tide. At the receiver side (Figure 4(b)), the CPE connected to the PC via RJ45 port can both transmit and receive the radio signals through two omnidirectional antennas (3.5 dBi gain). After that, our urban measurement campaigns can be divided into downstream part and upstream part as follows.Figure 4
Transmitter antenna and receiver antenna.
(a)
Transmitter antenna on the iron tower in Jianghan district (b)
Receiver antenna at the patrol boat


### 3.1.1. Downstream Part

The patrol boat sailed from a wharf beside our base station to the Tianxingzhou Yangtze River Bridge with the average speed of 14 knots. There was no obstacle higher than TX in this direction. Moreover, two bridges (shown in Figure5) which can be found between the BS and terminal point were the Second Wuhan Yangtze River Bridge (3.511 km away from the TX) and Erqi Yangtze River Bridge (6.8 km away from the TX), respectively.Figure 5
The route of measurement campaign 1 with few obstacles between TX and RX.


### 3.1.2. Upstream Part

Using the same BS and ship, we completed a 15.01 km measurement campaign in the upstream direction (shown in Figure6). The average speed was approximately 13 knots during the whole process. It was different from the downstream environment since there were some huge buildings (average height: 157 m) at the distance of 700 m from our base station.Figure 6
The route of measurement campaign 2 with large buildings between TX and RX.


## 3.1.1. Downstream Part

The patrol boat sailed from a wharf beside our base station to the Tianxingzhou Yangtze River Bridge with the average speed of 14 knots. There was no obstacle higher than TX in this direction. Moreover, two bridges (shown in Figure5) which can be found between the BS and terminal point were the Second Wuhan Yangtze River Bridge (3.511 km away from the TX) and Erqi Yangtze River Bridge (6.8 km away from the TX), respectively.Figure 5
The route of measurement campaign 1 with few obstacles between TX and RX.


## 3.1.2. Upstream Part

Using the same BS and ship, we completed a 15.01 km measurement campaign in the upstream direction (shown in Figure6). The average speed was approximately 13 knots during the whole process. It was different from the downstream environment since there were some huge buildings (average height: 157 m) at the distance of 700 m from our base station.Figure 6
The route of measurement campaign 2 with large buildings between TX and RX.


## 3.2. Suburban Environment Measurement Campaign Description

As shown in Figure7, this measurement campaign was conducted in a suburban area which was positioned at Dengjiakou Town. The effective height of our BS antenna (TX) was 53.00 m (including the height of iron tower: 50.00 m, the length of TX antenna: 1.50 m and the height of shore: 1.50 m) above river level. Due to the supervision region limitation, our patrol boat with the CPE sailed only 3 km for this scenario.Figure 7
The route of suburban measurement campaign.Ultimately, all of the measurement information is summarized in Table1.Table 1
The measurement parameters.
Parameters Data_1 Data_2 Data_3 Carrier frequency 1457 MHz 1457 MHz 1457 MHz Bandwidth 20 MHz 20 MHz 20 MHz TX power 49.8 dBm 49.8 dBm 49.8 dBm TX beam width (65∘Az.,8∘El.)∗ (65∘Az.,8∘El.)∗ (65∘Az.,8∘El.)∗ RX beam width Omni Omni Omni TX height 79.55 m 79.55 m 53.00 m RX height 3.4 m 3.4 m 3.4 m TX gain 15 dBi 15 dBi 15 dBi RX gain 3.5 dBi 3.5 dBi 3.5 dBi Max.distance 11.06 km 15.01 km 7.778 km Temperature 8–18∘C 8–18∘C 11–21∘C File size 6.204 GB 6.204 GB 6.204 GB ∗Sector antenna.


## 4. Effect Factors Analysis

As mentioned above, the IR model contains some effect factors which will be analyzed in the following contents.


### 4.1. Finite Dimensions Diffraction Loss

The diffraction loss caused by obstacles (such as huge buildings and bridges) along the river is an important effect factor. Many approximate methods based on multiple knife-edges diffraction have been proposed to calculate its loss value (e.g., Bullington method [2], Epstein-Petersen method [13], Deygout method [14], ITU-R method [15], etc.). To make such calculations, an assumption that the two sides of an obstacle are regarded as two thin screens of negligible thickness is necessary [15]. In addition, Professor Molisch [1] provided a comparison of these different methods. According to measurement campaigns, Deygout method is an appropriate one due to inland river environment fulfills its requirement: “small number of screens of different height.”In Figure8(a), each building is simplified as two infinite-width screens which corresponds its two sides. However, the idealized infinite-width screen will increase the diffraction loss in most instances because the width of obstacles actually is finite. Thus, the finite-width screen diffraction given by paper [15–17] for analyzing finite dimensions obstacles will be employed in this paper. The approach can be regarded as a combination of multiple knife-edges diffraction in several directions (e.g., three-knife-edges diffraction consists of top, left side, and right side, as shown in Figure 8(b)) [15].Figure 8
Obstacles approximation and finite dimensions obstacle diffraction.
(a)
Obstacles approximation (b)
Finite dimensions obstacle diffractionAccording to the description of Section3.1, there is a bridge which is 3.511 km away from the base station. The corresponding special finite-width obstacle diffraction can be simulated in Figure 9. Two parts diffraction loss should be calculated in this case.Figure 9
Finite dimensions bridge diffraction.


#### 4.1.1. The Diffraction above the Bridge

Figure10 provides the geometrical information based on measurement 1. After that, diffraction loss Lon is given by(13)Lon=-20lg⁡12-ej·π/42·Fνf_up+L02,Fνf_up=∫0νf_upe-j·πt2/2dt,where νf_up is the Fresnel parameter. According to [1], the screen 02 (shown in Figure 10) is regarded as “main screen” due to a higher single knife-edge diffraction loss L02:(14)νf_up=θon2λ·dt2ob1-1+Wb-1,θon=arctan⁡hb+hbth-hTXdt2ob1+arctan⁡hb+hbth-hb+hbthWb.Figure 10
Diffraction over the bridge.In (14), θon denotes the diffraction angle of screen 01. hbth is the thickness of obstacle. hb, Wb, dt2ob1, and hTX represent bridge’s height, bridge’s width, and distance from TX to screen 01 and the height of TX, respectively.


#### 4.1.2. The Diffraction Loss under the Bridge

The diffraction loss under the bridgeLdown is calculated by using(15)Ldown=-20lg⁡12-ej·π/42·Fνf_down+l01,Fνf_down=∫0νf_downe-j·πt2/2dt,where νf_down is the Fresnel parameter in this case, which can be obtained by using (16). Unlike the diffraction part above the bridge, the screen 01 (shown in Figure 11) results in a larger diffraction loss l01 than the screen 02:(16)νf_down=θunder2λ·dob2_2r-1+Wb-1.Here, dob2_2r denotes the distance between screen 02 to RX. The θunder is given by(17)θunder=arctan⁡hTX-hb-hTX-hbWb+arctan⁡hTX-hb-hTX-hRXdob2_2r.The hRX which can be found in Figure 11 denotes the RX antenna height. According to [15], the total bridge diffraction loss is expressed as(18)ξonϑ=10Lon/20,ξdownϑ=10Ldown/20,Difmeanϑ=-10·lg⁡ξon-2ϑ+ξdown-2ϑ,where ξon and ξdown are the loss factors. Difmean denotes the average diffraction loss of the bridge. Since the Second Yangtze River Bridge is a suspension bridge, the constructions on it cannot be ignored. Therefore, screen 01 and screen 02 shown in Figures 10 and 11 should also include the height of obstacles. On the basis of measurement data, the diffraction loss caused by this bridge is shown in Figure 12.Figure 11
Diffraction under the bridge.Figure 12
Diffraction loss caused by bridge in measurement 1.The results indicate that there is a large increase of diffraction up to 18 dB loss between 4 km and 6 km. Its maximum value occurs at a TX-RX distance of 6.5 km away from the BS. The corresponding diffraction loss maintains within[0, 5 dB] when the TX-RX distance is longer than 9 km.In measurement campaign 2, there are some high buildings with an average height of 157 m at a TX-RX distance of 700 m. The finite dimensions obstacles’ diffraction for this scenario can be approximated as an equivalent structure in Figure13. Similar estimation approach is used to acquire their diffraction loss.Figure 13
Finite dimensions buildings diffraction.As shown in Figures14 and 15, obstacle 1 will influence the measurement route ranging from 3 km to 10 km while obstacle 2 will bring additional diffraction loss between 10 km and 15 km. Thus, a diffraction loss dip should be found at the distance of 10 km, which is caused by a 40.1 m space between obstacle 1 and obstacle 2.Figure 14
Diffraction loss caused by obstacle 1 in measurement 2.Figure 15
Diffraction loss caused by obstacle 2 in measurement 2.For measurement campaign 3 in suburban environment, the diffraction loss can be neglected (Oblm = 0 dB) because the height of base station is much higher than the other buildings nearby.


### 4.2. Other Effect Factors

IR model inherits some effect factors from the REL model due to their similarity of environment. All of them will be described in detail as follows.


#### 4.2.1. Effective Reflection from River Surface

The inland river surface is rarely smooth due to the water roughness (shown in Figure16). As a result, the scattering leads to an energy reduction compared with the idealize specular reflection [6]. Assuming the height distribution of the water surface in inland river is similar with the sea wave surface which agrees with a Gaussian distribution [18]. The effective reflection coefficient Rrough is given by(19)Rrough=R·e-2·2π/λσhsin⁡π/2-θIN2,EffTX=hTX-0.5·RE·α2,EffRX=hRX-0.5·RE·β2,where θIN denotes the incident angle in Figure 1. EffTX and EffRX correspond to the effective height of TX and RX antennas, respectively. σh represents the standard deviation of surface height distribution. With increasing distance of TX and RX, the grazing angle ϕ (ϕ=π/2-θIN) reduces accordingly and approaches to zero when the radio link is tangent to the horizon. In this situation, the effective reflection coefficient Rrough will approximate to the specular reflection coefficient R. According to [8], the value of R is determined by permittivity εs and conductivity σc for various terrain types. Thus, the specular reflection coefficient of the sea water (εs=80, σc=4) is different from fresh water (εs=80, σc=0.001) of inland river (shown in Figure 17).Figure 16
Scattering and effective reflection.Figure 17
R as a function of the TX-RX distance (hTX=79.55m, hRX=3.4m).


#### 4.2.2. Shadowing Effect on the Reflected Ray

Although Kirchhoff Theory assumes that any point on the surface does not block others [1], the shadowing may still occur during the measurement campaigns, especially when the incident angle θIN is large enough (shown in Figure 18). According to [19], this phenomenon should be considered when the elevation angle θtca (shown in Figure 1) is less than 0.5 degrees. Afterwards, the shadowing coefficient Sc based on the assumption that the sea surface and its slope can be modeled by using a two-dimensional Gaussian process is calculated by(20)Sc=1-0.5·erfc⁡cot⁡θIN/2w0Λ+1,Λ=122π·w0cot⁡θIN·e-cot2⁡θIN/2·w02-erfc⁡cot⁡θIN2w0,where erfc is an error function and w02 denotes the mean-square surface slope [20]. The shadowing coefficient with different w02 can be found in Figure 19. The figure illustrates that a larger value of w0 will lead to a smaller shadowing coefficient. Moreover, all of Sc are equal to zero because reflected rays are totally shadowed when the TX-RX distance exceeds 38.3895 km.Figure 18
Shadowing effect on the reflected ray.Figure 19
S c as a function of the TX-RX distance (hTX=79.55m, hRX=3.4m).


#### 4.2.3. Divergence

The earth curvature can decrease the power densityρE carried by the reflected ray as shown in Figure 20. The reduction of ρE will lead to a lower received signal level (RSL) [6]. Consequently, the divergence coefficient Diveff also should be taken into account for long-distance inland river path loss model:(21)Diveff=11+2·D_1D_2/REEH1+EH2;EH1>0,EH2>00;otherwise,where D_1 and D_2 are shown in Figure 1. EH1 and EH2 represent EffTX and EffRX, respectively. Figure 21 indicates that the influence of Diveff will become bigger with the increasing distance d. Ultimately, divergence coefficient also turns to zero beyond the distance 38.3895 km.Figure 20
Divergence effect.Figure 21
Divergence coefficient as a function of the TX-RX distance (hTX=79.55m, hRX=3.4m).


#### 4.2.4. Earth Curvature Effect

For the long-distance scenario, the surface of earth can be regarded as an obstacle which will block 0.6 First Fresnel Zone (FFZ)D06(f,hTX,hRX) between TX and RX antennas:(22)D06=Df·DhDf+Dhkm,Df=3.89·10-5·fhTXhRX,Dh=4.1hTX+hRX.References [21, 22] propose a theory of ground-wave propagation over a smooth spherical earth (shown in Figure 22), which is able to analyze the diffraction loss caused by earth curvature effect. The dTXh denotes the distance between TX and the horizon while dRXh represents the distance between RX and the horizon. Both of them can be obtained by(23)Dis_1=dTXh=2keRE·hTX,Dis_2=dRXh=2keRE·hRX,dsum=Dis_1+Dis_2,where ke is equal to 1 [19]. The TX-RX distance d can be divided into Dis_1, Dis_2, and Dis_3 shown in Figure 22. Then the corresponding diffraction loss of each part is given as follows [6]:(24)L1=20lg⁡N15.656πζ1,L2=20lg⁡N2,20lg⁡Nn=-0.5+35lg⁡ζn+10lg⁡Fs,ζn=2π·Dis_n/λ2π·ke·RE/λ2/3;n=1,2,3,20lg⁡Fs=-0.048ζn3+1.0875ζn2+4.0782ζn-0.8806,L3=0.0086ζ33+0.2063ζ32+11.0997ζ3-0.8934.Figure 22
Ground-wave propagation over a smooth spherical earth.Here,Fs and L3 are given by approximated polynomial functions from [6]. After that, the total path loss Le_diff is represented as follows.Ifd≥dsum, L3 will be treated as a loss because Dis_3 is more than 0 [6]. Thus, Le_diff is obtained as(25)Le_diff=L1+L2-L3.Ifd<D06, the diffraction loss Le_diff will be equal to 0 because the radio link is over the horizon(26)Le_diff=0.In this case, the earth curvature can be ignored.IfD06≤d<dsum, L3 will be regarded as a gain owing to the fact that d is shorter than (Dis_1+Dis_2) [6]. Thus, the Le_diff can be represented by(27)Le_diff=L1+L2+L3.Last but not least, limited by the law of conservation of energy,Le_diff also should be set to zero when L3 is bigger than L1+L2 in this situation.Based on the above-mentioned three measurement campaigns,D06 are equal to 11.3590 km, 11.3590 km, and 8.0229 km, respectively. Therefore, measurement data 1 with Max.distance 11.06 km and measurement data 3 with Max.distance 7.778 km fulfill the condition: d<D06. However, in measurement 2, some positions are between D06 (11.3590 km) and dsum (38.3895 km), which can be found in Figure 23. It means that the diffraction loss derived from earth curvature effect will appear from 11.3590 km to 15.01 km.Figure 23
Diffraction loss caused by earth curvature in the case of measurement data_2.


## 4.1. Finite Dimensions Diffraction Loss

The diffraction loss caused by obstacles (such as huge buildings and bridges) along the river is an important effect factor. Many approximate methods based on multiple knife-edges diffraction have been proposed to calculate its loss value (e.g., Bullington method [2], Epstein-Petersen method [13], Deygout method [14], ITU-R method [15], etc.). To make such calculations, an assumption that the two sides of an obstacle are regarded as two thin screens of negligible thickness is necessary [15]. In addition, Professor Molisch [1] provided a comparison of these different methods. According to measurement campaigns, Deygout method is an appropriate one due to inland river environment fulfills its requirement: “small number of screens of different height.”In Figure8(a), each building is simplified as two infinite-width screens which corresponds its two sides. However, the idealized infinite-width screen will increase the diffraction loss in most instances because the width of obstacles actually is finite. Thus, the finite-width screen diffraction given by paper [15–17] for analyzing finite dimensions obstacles will be employed in this paper. The approach can be regarded as a combination of multiple knife-edges diffraction in several directions (e.g., three-knife-edges diffraction consists of top, left side, and right side, as shown in Figure 8(b)) [15].Figure 8
Obstacles approximation and finite dimensions obstacle diffraction.
(a)
Obstacles approximation (b)
Finite dimensions obstacle diffractionAccording to the description of Section3.1, there is a bridge which is 3.511 km away from the base station. The corresponding special finite-width obstacle diffraction can be simulated in Figure 9. Two parts diffraction loss should be calculated in this case.Figure 9
Finite dimensions bridge diffraction.


### 4.1.1. The Diffraction above the Bridge

Figure10 provides the geometrical information based on measurement 1. After that, diffraction loss Lon is given by(13)Lon=-20lg⁡12-ej·π/42·Fνf_up+L02,Fνf_up=∫0νf_upe-j·πt2/2dt,where νf_up is the Fresnel parameter. According to [1], the screen 02 (shown in Figure 10) is regarded as “main screen” due to a higher single knife-edge diffraction loss L02:(14)νf_up=θon2λ·dt2ob1-1+Wb-1,θon=arctan⁡hb+hbth-hTXdt2ob1+arctan⁡hb+hbth-hb+hbthWb.Figure 10
Diffraction over the bridge.In (14), θon denotes the diffraction angle of screen 01. hbth is the thickness of obstacle. hb, Wb, dt2ob1, and hTX represent bridge’s height, bridge’s width, and distance from TX to screen 01 and the height of TX, respectively.


### 4.1.2. The Diffraction Loss under the Bridge

The diffraction loss under the bridgeLdown is calculated by using(15)Ldown=-20lg⁡12-ej·π/42·Fνf_down+l01,Fνf_down=∫0νf_downe-j·πt2/2dt,where νf_down is the Fresnel parameter in this case, which can be obtained by using (16). Unlike the diffraction part above the bridge, the screen 01 (shown in Figure 11) results in a larger diffraction loss l01 than the screen 02:(16)νf_down=θunder2λ·dob2_2r-1+Wb-1.Here, dob2_2r denotes the distance between screen 02 to RX. The θunder is given by(17)θunder=arctan⁡hTX-hb-hTX-hbWb+arctan⁡hTX-hb-hTX-hRXdob2_2r.The hRX which can be found in Figure 11 denotes the RX antenna height. According to [15], the total bridge diffraction loss is expressed as(18)ξonϑ=10Lon/20,ξdownϑ=10Ldown/20,Difmeanϑ=-10·lg⁡ξon-2ϑ+ξdown-2ϑ,where ξon and ξdown are the loss factors. Difmean denotes the average diffraction loss of the bridge. Since the Second Yangtze River Bridge is a suspension bridge, the constructions on it cannot be ignored. Therefore, screen 01 and screen 02 shown in Figures 10 and 11 should also include the height of obstacles. On the basis of measurement data, the diffraction loss caused by this bridge is shown in Figure 12.Figure 11
Diffraction under the bridge.Figure 12
Diffraction loss caused by bridge in measurement 1.The results indicate that there is a large increase of diffraction up to 18 dB loss between 4 km and 6 km. Its maximum value occurs at a TX-RX distance of 6.5 km away from the BS. The corresponding diffraction loss maintains within[0, 5 dB] when the TX-RX distance is longer than 9 km.In measurement campaign 2, there are some high buildings with an average height of 157 m at a TX-RX distance of 700 m. The finite dimensions obstacles’ diffraction for this scenario can be approximated as an equivalent structure in Figure13. Similar estimation approach is used to acquire their diffraction loss.Figure 13
Finite dimensions buildings diffraction.As shown in Figures14 and 15, obstacle 1 will influence the measurement route ranging from 3 km to 10 km while obstacle 2 will bring additional diffraction loss between 10 km and 15 km. Thus, a diffraction loss dip should be found at the distance of 10 km, which is caused by a 40.1 m space between obstacle 1 and obstacle 2.Figure 14
Diffraction loss caused by obstacle 1 in measurement 2.Figure 15
Diffraction loss caused by obstacle 2 in measurement 2.For measurement campaign 3 in suburban environment, the diffraction loss can be neglected (Oblm = 0 dB) because the height of base station is much higher than the other buildings nearby.


## 4.1.1. The Diffraction above the Bridge

Figure10 provides the geometrical information based on measurement 1. After that, diffraction loss Lon is given by(13)Lon=-20lg⁡12-ej·π/42·Fνf_up+L02,Fνf_up=∫0νf_upe-j·πt2/2dt,where νf_up is the Fresnel parameter. According to [1], the screen 02 (shown in Figure 10) is regarded as “main screen” due to a higher single knife-edge diffraction loss L02:(14)νf_up=θon2λ·dt2ob1-1+Wb-1,θon=arctan⁡hb+hbth-hTXdt2ob1+arctan⁡hb+hbth-hb+hbthWb.Figure 10
Diffraction over the bridge.In (14), θon denotes the diffraction angle of screen 01. hbth is the thickness of obstacle. hb, Wb, dt2ob1, and hTX represent bridge’s height, bridge’s width, and distance from TX to screen 01 and the height of TX, respectively.


## 4.1.2. The Diffraction Loss under the Bridge

The diffraction loss under the bridgeLdown is calculated by using(15)Ldown=-20lg⁡12-ej·π/42·Fνf_down+l01,Fνf_down=∫0νf_downe-j·πt2/2dt,where νf_down is the Fresnel parameter in this case, which can be obtained by using (16). Unlike the diffraction part above the bridge, the screen 01 (shown in Figure 11) results in a larger diffraction loss l01 than the screen 02:(16)νf_down=θunder2λ·dob2_2r-1+Wb-1.Here, dob2_2r denotes the distance between screen 02 to RX. The θunder is given by(17)θunder=arctan⁡hTX-hb-hTX-hbWb+arctan⁡hTX-hb-hTX-hRXdob2_2r.The hRX which can be found in Figure 11 denotes the RX antenna height. According to [15], the total bridge diffraction loss is expressed as(18)ξonϑ=10Lon/20,ξdownϑ=10Ldown/20,Difmeanϑ=-10·lg⁡ξon-2ϑ+ξdown-2ϑ,where ξon and ξdown are the loss factors. Difmean denotes the average diffraction loss of the bridge. Since the Second Yangtze River Bridge is a suspension bridge, the constructions on it cannot be ignored. Therefore, screen 01 and screen 02 shown in Figures 10 and 11 should also include the height of obstacles. On the basis of measurement data, the diffraction loss caused by this bridge is shown in Figure 12.Figure 11
Diffraction under the bridge.Figure 12
Diffraction loss caused by bridge in measurement 1.The results indicate that there is a large increase of diffraction up to 18 dB loss between 4 km and 6 km. Its maximum value occurs at a TX-RX distance of 6.5 km away from the BS. The corresponding diffraction loss maintains within[0, 5 dB] when the TX-RX distance is longer than 9 km.In measurement campaign 2, there are some high buildings with an average height of 157 m at a TX-RX distance of 700 m. The finite dimensions obstacles’ diffraction for this scenario can be approximated as an equivalent structure in Figure13. Similar estimation approach is used to acquire their diffraction loss.Figure 13
Finite dimensions buildings diffraction.As shown in Figures14 and 15, obstacle 1 will influence the measurement route ranging from 3 km to 10 km while obstacle 2 will bring additional diffraction loss between 10 km and 15 km. Thus, a diffraction loss dip should be found at the distance of 10 km, which is caused by a 40.1 m space between obstacle 1 and obstacle 2.Figure 14
Diffraction loss caused by obstacle 1 in measurement 2.Figure 15
Diffraction loss caused by obstacle 2 in measurement 2.For measurement campaign 3 in suburban environment, the diffraction loss can be neglected (Oblm = 0 dB) because the height of base station is much higher than the other buildings nearby.


## 4.2. Other Effect Factors

IR model inherits some effect factors from the REL model due to their similarity of environment. All of them will be described in detail as follows.


### 4.2.1. Effective Reflection from River Surface

The inland river surface is rarely smooth due to the water roughness (shown in Figure16). As a result, the scattering leads to an energy reduction compared with the idealize specular reflection [6]. Assuming the height distribution of the water surface in inland river is similar with the sea wave surface which agrees with a Gaussian distribution [18]. The effective reflection coefficient Rrough is given by(19)Rrough=R·e-2·2π/λσhsin⁡π/2-θIN2,EffTX=hTX-0.5·RE·α2,EffRX=hRX-0.5·RE·β2,where θIN denotes the incident angle in Figure 1. EffTX and EffRX correspond to the effective height of TX and RX antennas, respectively. σh represents the standard deviation of surface height distribution. With increasing distance of TX and RX, the grazing angle ϕ (ϕ=π/2-θIN) reduces accordingly and approaches to zero when the radio link is tangent to the horizon. In this situation, the effective reflection coefficient Rrough will approximate to the specular reflection coefficient R. According to [8], the value of R is determined by permittivity εs and conductivity σc for various terrain types. Thus, the specular reflection coefficient of the sea water (εs=80, σc=4) is different from fresh water (εs=80, σc=0.001) of inland river (shown in Figure 17).Figure 16
Scattering and effective reflection.Figure 17
R as a function of the TX-RX distance (hTX=79.55m, hRX=3.4m).


### 4.2.2. Shadowing Effect on the Reflected Ray

Although Kirchhoff Theory assumes that any point on the surface does not block others [1], the shadowing may still occur during the measurement campaigns, especially when the incident angle θIN is large enough (shown in Figure 18). According to [19], this phenomenon should be considered when the elevation angle θtca (shown in Figure 1) is less than 0.5 degrees. Afterwards, the shadowing coefficient Sc based on the assumption that the sea surface and its slope can be modeled by using a two-dimensional Gaussian process is calculated by(20)Sc=1-0.5·erfc⁡cot⁡θIN/2w0Λ+1,Λ=122π·w0cot⁡θIN·e-cot2⁡θIN/2·w02-erfc⁡cot⁡θIN2w0,where erfc is an error function and w02 denotes the mean-square surface slope [20]. The shadowing coefficient with different w02 can be found in Figure 19. The figure illustrates that a larger value of w0 will lead to a smaller shadowing coefficient. Moreover, all of Sc are equal to zero because reflected rays are totally shadowed when the TX-RX distance exceeds 38.3895 km.Figure 18
Shadowing effect on the reflected ray.Figure 19
S c as a function of the TX-RX distance (hTX=79.55m, hRX=3.4m).


### 4.2.3. Divergence

The earth curvature can decrease the power densityρE carried by the reflected ray as shown in Figure 20. The reduction of ρE will lead to a lower received signal level (RSL) [6]. Consequently, the divergence coefficient Diveff also should be taken into account for long-distance inland river path loss model:(21)Diveff=11+2·D_1D_2/REEH1+EH2;EH1>0,EH2>00;otherwise,where D_1 and D_2 are shown in Figure 1. EH1 and EH2 represent EffTX and EffRX, respectively. Figure 21 indicates that the influence of Diveff will become bigger with the increasing distance d. Ultimately, divergence coefficient also turns to zero beyond the distance 38.3895 km.Figure 20
Divergence effect.Figure 21
Divergence coefficient as a function of the TX-RX distance (hTX=79.55m, hRX=3.4m).


### 4.2.4. Earth Curvature Effect

For the long-distance scenario, the surface of earth can be regarded as an obstacle which will block 0.6 First Fresnel Zone (FFZ)D06(f,hTX,hRX) between TX and RX antennas:(22)D06=Df·DhDf+Dhkm,Df=3.89·10-5·fhTXhRX,Dh=4.1hTX+hRX.References [21, 22] propose a theory of ground-wave propagation over a smooth spherical earth (shown in Figure 22), which is able to analyze the diffraction loss caused by earth curvature effect. The dTXh denotes the distance between TX and the horizon while dRXh represents the distance between RX and the horizon. Both of them can be obtained by(23)Dis_1=dTXh=2keRE·hTX,Dis_2=dRXh=2keRE·hRX,dsum=Dis_1+Dis_2,where ke is equal to 1 [19]. The TX-RX distance d can be divided into Dis_1, Dis_2, and Dis_3 shown in Figure 22. Then the corresponding diffraction loss of each part is given as follows [6]:(24)L1=20lg⁡N15.656πζ1,L2=20lg⁡N2,20lg⁡Nn=-0.5+35lg⁡ζn+10lg⁡Fs,ζn=2π·Dis_n/λ2π·ke·RE/λ2/3;n=1,2,3,20lg⁡Fs=-0.048ζn3+1.0875ζn2+4.0782ζn-0.8806,L3=0.0086ζ33+0.2063ζ32+11.0997ζ3-0.8934.Figure 22
Ground-wave propagation over a smooth spherical earth.Here,Fs and L3 are given by approximated polynomial functions from [6]. After that, the total path loss Le_diff is represented as follows.Ifd≥dsum, L3 will be treated as a loss because Dis_3 is more than 0 [6]. Thus, Le_diff is obtained as(25)Le_diff=L1+L2-L3.Ifd<D06, the diffraction loss Le_diff will be equal to 0 because the radio link is over the horizon(26)Le_diff=0.In this case, the earth curvature can be ignored.IfD06≤d<dsum, L3 will be regarded as a gain owing to the fact that d is shorter than (Dis_1+Dis_2) [6]. Thus, the Le_diff can be represented by(27)Le_diff=L1+L2+L3.Last but not least, limited by the law of conservation of energy,Le_diff also should be set to zero when L3 is bigger than L1+L2 in this situation.Based on the above-mentioned three measurement campaigns,D06 are equal to 11.3590 km, 11.3590 km, and 8.0229 km, respectively. Therefore, measurement data 1 with Max.distance 11.06 km and measurement data 3 with Max.distance 7.778 km fulfill the condition: d<D06. However, in measurement 2, some positions are between D06 (11.3590 km) and dsum (38.3895 km), which can be found in Figure 23. It means that the diffraction loss derived from earth curvature effect will appear from 11.3590 km to 15.01 km.Figure 23
Diffraction loss caused by earth curvature in the case of measurement data_2.


## 4.2.1. Effective Reflection from River Surface

The inland river surface is rarely smooth due to the water roughness (shown in Figure16). As a result, the scattering leads to an energy reduction compared with the idealize specular reflection [6]. Assuming the height distribution of the water surface in inland river is similar with the sea wave surface which agrees with a Gaussian distribution [18]. The effective reflection coefficient Rrough is given by(19)Rrough=R·e-2·2π/λσhsin⁡π/2-θIN2,EffTX=hTX-0.5·RE·α2,EffRX=hRX-0.5·RE·β2,where θIN denotes the incident angle in Figure 1. EffTX and EffRX correspond to the effective height of TX and RX antennas, respectively. σh represents the standard deviation of surface height distribution. With increasing distance of TX and RX, the grazing angle ϕ (ϕ=π/2-θIN) reduces accordingly and approaches to zero when the radio link is tangent to the horizon. In this situation, the effective reflection coefficient Rrough will approximate to the specular reflection coefficient R. According to [8], the value of R is determined by permittivity εs and conductivity σc for various terrain types. Thus, the specular reflection coefficient of the sea water (εs=80, σc=4) is different from fresh water (εs=80, σc=0.001) of inland river (shown in Figure 17).Figure 16
Scattering and effective reflection.Figure 17
R as a function of the TX-RX distance (hTX=79.55m, hRX=3.4m).


## 4.2.2. Shadowing Effect on the Reflected Ray

Although Kirchhoff Theory assumes that any point on the surface does not block others [1], the shadowing may still occur during the measurement campaigns, especially when the incident angle θIN is large enough (shown in Figure 18). According to [19], this phenomenon should be considered when the elevation angle θtca (shown in Figure 1) is less than 0.5 degrees. Afterwards, the shadowing coefficient Sc based on the assumption that the sea surface and its slope can be modeled by using a two-dimensional Gaussian process is calculated by(20)Sc=1-0.5·erfc⁡cot⁡θIN/2w0Λ+1,Λ=122π·w0cot⁡θIN·e-cot2⁡θIN/2·w02-erfc⁡cot⁡θIN2w0,where erfc is an error function and w02 denotes the mean-square surface slope [20]. The shadowing coefficient with different w02 can be found in Figure 19. The figure illustrates that a larger value of w0 will lead to a smaller shadowing coefficient. Moreover, all of Sc are equal to zero because reflected rays are totally shadowed when the TX-RX distance exceeds 38.3895 km.Figure 18
Shadowing effect on the reflected ray.Figure 19
S c as a function of the TX-RX distance (hTX=79.55m, hRX=3.4m).


## 4.2.3. Divergence

The earth curvature can decrease the power densityρE carried by the reflected ray as shown in Figure 20. The reduction of ρE will lead to a lower received signal level (RSL) [6]. Consequently, the divergence coefficient Diveff also should be taken into account for long-distance inland river path loss model:(21)Diveff=11+2·D_1D_2/REEH1+EH2;EH1>0,EH2>00;otherwise,where D_1 and D_2 are shown in Figure 1. EH1 and EH2 represent EffTX and EffRX, respectively. Figure 21 indicates that the influence of Diveff will become bigger with the increasing distance d. Ultimately, divergence coefficient also turns to zero beyond the distance 38.3895 km.Figure 20
Divergence effect.Figure 21
Divergence coefficient as a function of the TX-RX distance (hTX=79.55m, hRX=3.4m).


## 4.2.4. Earth Curvature Effect

For the long-distance scenario, the surface of earth can be regarded as an obstacle which will block 0.6 First Fresnel Zone (FFZ)D06(f,hTX,hRX) between TX and RX antennas:(22)D06=Df·DhDf+Dhkm,Df=3.89·10-5·fhTXhRX,Dh=4.1hTX+hRX.References [21, 22] propose a theory of ground-wave propagation over a smooth spherical earth (shown in Figure 22), which is able to analyze the diffraction loss caused by earth curvature effect. The dTXh denotes the distance between TX and the horizon while dRXh represents the distance between RX and the horizon. Both of them can be obtained by(23)Dis_1=dTXh=2keRE·hTX,Dis_2=dRXh=2keRE·hRX,dsum=Dis_1+Dis_2,where ke is equal to 1 [19]. The TX-RX distance d can be divided into Dis_1, Dis_2, and Dis_3 shown in Figure 22. Then the corresponding diffraction loss of each part is given as follows [6]:(24)L1=20lg⁡N15.656πζ1,L2=20lg⁡N2,20lg⁡Nn=-0.5+35lg⁡ζn+10lg⁡Fs,ζn=2π·Dis_n/λ2π·ke·RE/λ2/3;n=1,2,3,20lg⁡Fs=-0.048ζn3+1.0875ζn2+4.0782ζn-0.8806,L3=0.0086ζ33+0.2063ζ32+11.0997ζ3-0.8934.Figure 22
Ground-wave propagation over a smooth spherical earth.Here,Fs and L3 are given by approximated polynomial functions from [6]. After that, the total path loss Le_diff is represented as follows.Ifd≥dsum, L3 will be treated as a loss because Dis_3 is more than 0 [6]. Thus, Le_diff is obtained as(25)Le_diff=L1+L2-L3.Ifd<D06, the diffraction loss Le_diff will be equal to 0 because the radio link is over the horizon(26)Le_diff=0.In this case, the earth curvature can be ignored.IfD06≤d<dsum, L3 will be regarded as a gain owing to the fact that d is shorter than (Dis_1+Dis_2) [6]. Thus, the Le_diff can be represented by(27)Le_diff=L1+L2+L3.Last but not least, limited by the law of conservation of energy,Le_diff also should be set to zero when L3 is bigger than L1+L2 in this situation.Based on the above-mentioned three measurement campaigns,D06 are equal to 11.3590 km, 11.3590 km, and 8.0229 km, respectively. Therefore, measurement data 1 with Max.distance 11.06 km and measurement data 3 with Max.distance 7.778 km fulfill the condition: d<D06. However, in measurement 2, some positions are between D06 (11.3590 km) and dsum (38.3895 km), which can be found in Figure 23. It means that the diffraction loss derived from earth curvature effect will appear from 11.3590 km to 15.01 km.Figure 23
Diffraction loss caused by earth curvature in the case of measurement data_2.


## 5. Parameters Estimation and Simulation Verification

As mentioned in Section2, IR model has four empirical parameters αl, βl, αs, and βs. Figure 24 shows a series of classic radio propagation path loss models which are widely used in wireless communication such as free space model, REL model, Okumura-Hata model, and ITU-R models. The simulation outcomes indicate that measurement results which are between ITU-R land-path model and sea-path model show obvious mixed-path characteristics. However, ITU-R mixed-path models do not have a good fitting degree, which is displayed in Figure 24. Compared with other models, Okumura-Hata urban model and suburban model match better with the raw data. In addition, both of them are able to be expressed in logarithmic scale [3, 4]. We assume that the environmental correction factor (shown in Section 2.2 and Figure 3) for all-water regions Ms can be depicted by (28):(28)Ms=αsub-20lg⁡λ4π+βsub+210lg⁡D,(29)αs=αsub-20lg⁡λ4π,βs=βsub+2.Figure 24
The simulation of classic radio propagation path loss models based on measurement data_1.Here,αsub and βsub are derived from Okumura-Hata suburban model [3, 4]. For all-land regions, the Okumura-Hata urban model and suburban model are employed to calculate the corresponding correction factors Ml (urban or suburban).In the case of urban environment,(30)Ml=αurb-20lg⁡λ4π+βurb+210lg⁡D;αl=αurb-20lg⁡λ4π,βl=βurb+2.In the case of suburban environment,(31)Ml=Ms.Here,αurb and βurb can be acquired from the Okumura-Hata model for urban scenario [3, 4]. After that, the IR model with different standard deviation of surface height distribution σh and mean-square surface slope w02 (the values of other variables are the same) are described in Figures 25 and 26, respectively. It can be found that the smaller w02 and σh will lead to the higher loss peaks derived from reflection effect. On the basis of the comparison outcomes, IR model chooses 0.002 and 0.2 as the values of w02 and σh, which also confirms that the surface of river is smoother than open-sea (w02=0.25, σh=0.008 in [6]). Moreover, a good matching degree of diffraction loss proves that the finite dimensions bridge diffraction in IR model are applicable for this scenario.Figure 25
IR model with differentw02.Figure 26
IR model with differentσh.To verify the universal applicability of IR model, measurement data_2 and measurement data_3 are employed as reference sequences. Figure27 shows that IR model agrees well with the reflection phenomenon and the diffraction loss caused by huge buildings near the river which have great effect on signal transmission. In addition, as mentioned in Section 4.1, the dip occurring around the 10 km is due to a 40.1 m space between the two buildings. In Figure 28, both the Okumura-Hata (suburban) model and the IR model match well with the measurement data. In conclusion, these comparisons for the three scenarios prove that the inland river scenario can be approximated as a mixed-path Two-Ray geometric model. Secondly, the assumptions of parameters optimization in Section 2 and parameters estimation in Section 5 are reasonable. Thirdly, the finite dimensions method is verified to be an effective way to calculate the diffraction loss caused by bridges, huge buildings, and some other facilities near the river. As shown in Figures 25, 26, and 27, reflection phenomenon is the dominant influence factor from 1 km to 3 km, which will bring a loss within the scope of [0, 15] dB. On the basis of quantitative analysis in Section 3, diffraction phenomenon is more obvious than other phenomena in 4 km~6 km of measurement 1 and 3 km~15 km of measurement 2.Figure 27
Simulation verification based on measurement data_2. Region 1 denotes the diffraction loss caused by obstacle 1. The dip in Region 2 is derived from space between the two buildings. Region 3 represents diffraction loss caused by obstacle 2.Figure 28
Simulation verification based on measurement data_3.


## 6. Performance Evaluation

In order to quantify the practicability of these models, three kinds of model selection algorithms are employed. RMSE criteria is a commonly used methodology to evaluate the difference between the theoretical model and measurement data [11, 23, 24] due to low complexity. By defining the model selection as an “track association problem” in automation and traffic field, [10] provides two new methods (GRG-MAPE and PCC-MAPE) based on Uncertainty-Mathematical Theory, which have been proven more accurate than RMSE.On the basis of the three methodologies mentioned above, Tables2, 3, and 4 list the performance evaluation results of path loss models, respectively.Table 2
The RMSE model selection results.
Models Measurements Data_1∗ D a t a _ 2 ∗ D a t a _ 3 ∗ ITU-R land-path 1% 13.7119 9.3384 7.5479 ITU-R land-path 10% 14.3341 9.3848 9.1265 ITU-R land-path 50% 14.6268 9.4386 9.7505 ITU-R sea-path 1% 21.0225 30.3053 26.2342 ITU-R sea-path 10% 19.6629 28.7838 25.0719 ITU-R sea-path 50% 18.7016 27.7185 24.146 ITU-R mixed-path 1% 14.4477 15.1869 15.0571 ITU-R mixed-path 10% 13.2697 14.1991 13.6386 ITU-R mixed-path 50% 12.5827 13.7837 12.9074 Free space model 30.4055 42.5521 25.4202 Okumura-Hata (suburban) 9.2825 18.8068 1.8525 Okumura-Hata (urban) 7.8181 8.0515 12.9709 REL model 33.3084 44.2648 28.2632 IR model 4.6159 6.3594 1.8310 ∗The smaller RMSE value means better matching degree.Table 3
The GRG-MAPE model selection results.
Models Measurements Data_1∗ D a t a _ 2 ∗ D a t a _ 3 ∗ ITU-R land-path 1% 0.8833 0.9315 0.9264 ITU-R land-path 10% 0.8795 0.9318 0.9138 ITU-R land-path 50% 0.8774 0.9317 0.9094 ITU-R sea-path 1% 0.8648 0.8090 0.8064 ITU-R sea-path 10% 0.8725 0.8175 0.8137 ITU-R sea-path 50% 0.8779 0.8235 0.8193 ITU-R mixed-path 1% 0.9136 0.8976 0.8778 ITU-R mixed-path 10% 0.9201 0.9030 0.8892 ITU-R mixed-path 50% 0.9240 0.9054 0.8944 Free space model 0.7865 0.7360 0.8123 Okumura-Hata (suburban) 0.9296 0.8774 0.9570 Okumura-Hata (urban) 0.9303 0.9378 0.8934 REL model 0.7659 0.7206 0.7853 IR model 0.9574 0.9522 0.9582 ∗The larger GRG-MAPE value means better matching degree.Table 4
The PCC-MAPE model selection results.
Models Measurements D a t a _ 1 ∗ D a t a _ 2 ∗ D a t a _ 3 ∗ ITU-R land-path 1% 0.8891 0.9321 0.9419 ITU-R land-path 10% 0.8848 0.9324 0.9317 ITU-R land-path 50% 0.8832 0.9329 0.9276 ITU-R sea-path 1% 0.8773 0.8165 0.8195 ITU-R sea-path 10% 0.8838 0.8246 0.8271 ITU-R sea-path 50% 0.8884 0.8305 0.8329 ITU-R mixed-path 1% 0.9263 0.9046 0.8932 ITU-R mixed-path 10% 0.9318 0.9102 0.9024 ITU-R mixed-path 50% 0.9352 0.9127 0.9070 Free space model 0.7967 0.7447 0.8242 Okumura-Hata (suburban) 0.9390 0.8851 0.9797 Okumura-Hata (urban) 0.9398 0.9458 0.9058 REL model 0.7581 0.7173 0.8058 IR model 0.9688 0.9612 0.9822 ∗The larger PCC-MAPE value means better matching degree.In Table2, RMSE values denote the error levels of the estimation sequences. Thus, both free space model and REL model are not appropriate for all of these three scenarios due to high RMSE values. As shown in Data_1 and Data_2, Okumura-Hata (urban) model shows smaller RMSE values (7.8181 and 8.0515) than the suburban model and the ITU-R models apart from the IR model (4.6159 and 6.3594). For suburban watercourse scenario (Data_3), IR model and Okumura-Hata (suburban) model are the optimal model and the suboptimal model, respectively. The values in Tables 3 and 4 describe the matching degrees of corresponding path loss models. Afterwards, all of comparison results indicate that IR model performs most effectively for these environments, whereas the Okumura-Hata (suburban) model also matches well with our measurement data in suburban scenario.For the computational complexity of these path loss models, free space model [1], Okumura-Hata suburban model, and its urban model [3, 4] are much simpler than others due to lack of sufficient effect factors analysis. ITU-R models [7] own many corrections to the prediction results, including terrain clearance angle correction, antenna height, mixed-path, and tropospheric scattering. However, these commonly used classic empirical models do not analyze deterministic information which is calculated in IR model such as diffraction loss caused by bridges or buildings. Moreover, IR model has three improvements compared with original REL model [6], which can be found in Section 2. Consequently, IR model is more complex than ITU-R models and REL model.


## 7. Conclusion

In this paper, a new propagation path loss model based on the REL model is proposed for inland river environment. Compared with the REL model, this model shows three improvements derived from differences between open-sea and inland river. In the aspect of parameters optimization, the formula in dB scale transformed from the free space model is replaced by the Okumura-Hata model. Secondly, an additional diffraction loss caused by the obstacles near the river has been included. Then, the mixed-path feature is taken into consideration by using the methodology from Recommendation ITU-R P.1546-5. To acquire reference groups and perform parameters estimation, three measurement campaigns have been conducted for different scenarios. According to effect factors analysis and simulation results, the high matching degree of IR model indicates that the radio channel of inland river scenario can be simplified by using Two-Ray geometric model and the method of linear parameters optimization as well as the calculation of finite dimensions diffraction loss are effective. Besides, the comparison between the measurement results and classical path loss models suggests that propagation path without mixture of land and water path is not appropriate for inland river owing to its special mixed-path characteristics. In order to better evaluate the model’s effectiveness, RMSE, GRG-MAPE, and PCC-MAPE are used for model selection. The corresponding outcomes also prove that our IR model which considers mixed path and some deterministic information matches best with the measurement results.



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*Source: 5853724-2017-01-16.xml*