Modified REL-Based Piecewise Path Loss Modeling Approach for Shore-to-Ship Communication at 5.6 GHz

Abstract

The need for reliable and uninterrupted communication systems in the marine environment has become critically important with increasing maritime activities, environmental monitoring, and the spread of autonomous systems. However, the complex structure of electromagnetic wave propagation in a sea environment limits the accuracy of the existing propagation models. Thus, the Modified Round Earth Loss (REL) model was first developed in this study to estimate the path loss more accurately in shore-to-ship communication. Subsequently, a piecewise modeling approach based on the principle of two-segment data modeling was proposed. In the Modified REL model, unlike the traditional REL model, the paths and gains of the direct and reflected waves were not considered equal in the calculations. Moreover, unlike in the classical approach, the receiver height was not taken as a fixed value; the estimated best receiver height value for each measurement was included in the calculations as a representation of the effect of roughness in the sea environment. Thus, the model is better adapted to various environmental conditions. In addition, the proposed piecewise model divides the propagation medium into two regions using a break point calculated by Fresnel zone theory. The Modified REL model was used for the first region and the log-distance model was used for the second region. This method allows for more accurate modeling of signal behaviors, especially at different distances. Experimental measurements and performance evaluations conducted using four different shore-to-ship communication scenarios show that the Modified REL model shows an average improvement of up to 3% in Root Mean Square Error (RMSE) values compared to the classical REL model. Additionally, the proposed piecewise model improves the fitting error of the Modified REL model, which models the data as a single whole, by an average of 22.25%. These findings emphasize the necessity of propagation models that are sensitive and adaptable to environmental changes for maritime communication.

1. Introduction

The marine environment has become the focal point of economic, military, transportation, security, energy, and environmental activities, making the study and development of wireless communication systems, particularly radio wave propagation models crucial for all these activities, an increasingly important area of interest. Shore-to-ship communication technologies provide reliable connection between ships and coastal infrastructure for maritime and fishing applications. This is important for critical navigation, security, and real-time data exchange. Although such communication systems increase the operational efficiency of maritime activities, examining the marine environment as an electromagnetic wave propagation environment and correctly determining its effects are quite significant for reliable communication. Radio signals in the marine environment are affected by various factors such as sea state, salinity, water temperature, and differences in antenna heights, which change the propagation characteristics of the signals, such as reflection, diffraction, scattering, divergence, rain and atmospheric attenuations. Therefore, advanced propagation models that can adapt to environmental conditions are required to increase the reliability of shore-to-ship communication. Current research has focused on developing new propagation models to improve the performance of shore-to-ship and offshore communication systems. The need for broadband communication is of critical importance, especially in the exclusive economic zone (200 nautical miles), where states conduct their economic activities in the marine environment [1]. In addition to various activities such as oil and gas exploration, cargo and passenger transportation, and fish farms, the increase in autonomous systems and applications requiring remote control has increased the demand for reliable and efficient marine communication systems [2,3]. In addition, an uninterrupted communication infrastructure is required for environmental applications such as monitoring, control of offshore wind energy farms, flood warning systems, and water quality assessments [4,5,6]. Therefore, the introduction of new-generation communication technologies, such as 5G, in the marine environment necessitates the development of marine propagation models to meet such communication needs [7]. In the existing literature, various empirical models such as free space, log-distance, dual-slope, and ray-based models (2-ray and 3-ray) have been developed to estimate path loss in terrestrial environments and have also been used in shore-to-ship communication. However, models such as the Round Earth Loss (REL) model, which considers more complex environmental factors and provides a higher accuracy, have also been proposed. However, each of these models may be inadequate for adapting to variable conditions in the marine environment. In recent years, the 5 GHz frequency band has become prominent in maritime communication studies. The support of this frequency band with international regulations, allowing higher transmission power and providing wider coverage, increases the effectiveness of maritime communication [8,9]. In addition, organizations such as the European Telecommunications Standards Institute (ETSI) and the European Conference of Postal and Telecommunications Administrations (CEPT) recommend a frequency spectrum in the range of 5–8 GHz for maritime broadband radio communication [10].

In this context, to increase the accuracy and flexibility of path loss estimation in shore-to-ship communication, Modified REL and Proposed Piecewise models were developed for 5.6 GHz shore-to-ship communication in this study. In addition to the traditional REL model, the Modified REL model has additional parameters that consider the best receiver height ($h_{rbest}$) estimated according to the data pattern and the paths and gains of the direct and reflected waves. Therefore, it provides a better fit for the measured data in different sea scenarios. The Proposed Piecewise model, built on this model, divides the propagation environment into two different regions by determining the Fresnel distance, as in the double-slope model approach. The first region was modeled using a Modified REL, and the second region was modeled using the log-distance model. This approach provides a more accurate representation of complex propagation characteristics, and the advantages of modeling the measurement data in two parts instead of one are demonstrated in terms of accuracy and flexibility with a piecewise modeling method that considers environmental changes. For this purpose, comprehensive measurements and model evaluations were conducted for shore-to-ship communication in various scenarios. As a result, this research presents an innovative approach to increase the reliability and efficiency of shore-to-ship communication as an important step towards the development of propagation models that form the basis of maritime communication systems. It is believed that this study will make significant contributions to the existing literature on maritime propagation models and to other researchers in the field by drawing attention to the importance of new technological trends and international regulations in maritime communication, especially the use of the 5 GHz frequency band.

1.1. Related Works

In [11], experimental measurements were performed at 5.8 GHz for the shore-to-ship and ship-to-ship scenarios. The measurement data were modeled at large and small scales and the path loss exponent (n) and standard deviation ($\sigma$) values were found to be 5.6 and 6.4 dB for buoy-to-ship, 3.4 and 5.5 dB for boat-to-shore, and 2.7 and 4.9 dB for buoy-to-boat, respectively. Additionally, the Extreme Value Distribution (EVD) model provided the best fit for small-scale fading modeling. Shore-to-ship measurements at 2 GHz were performed in [1] for distances up to 45 km. The measurement data were modeled using an REL model that included parameters such as roughness, divergence, shadowing, and diffraction. Moreover, long-range measurement data were compared with the Plane Earth Loss (PEL), ITU-R, and REL models, and REL was found to be the best-fit model for the data. On the other hand, the variation in the shadowing coefficient with distance for different ${\beta }_0$ values is shown graphically. In [2], shore-to-ship measurement data at 2 GHz were compared with free space, Okumura-Hata, COST 231-Hata, and ITU-R models, and the ITU-R model was found to be the most suitable for cold open sea environments. In [12], it was emphasized that shore-to-ship measurements were performed at 5.8 GHz since a higher output power was allowed. Then, the data were divided into LOS and NLOS conditions by comparing the free space, log-distance, and 2-ray model performance. However, only the n and $\sigma$ parameters of the log-distance model were calculated as 4.58 and 3.49 dB for LOS, 2.08 and 5.12 dB for NLOS, and 4.3 and 7.15 dB for the combined LOS and NLOS scenarios. In [13], measurement data from another study were compared with the Irregular Terrain Methodology (ITM) and the proposed Improved ITM models by emphasizing that the 2-ray model was suitable for distances up to 1 km, whereas the proposed model performed better at long distances because of the consideration of the curvature of the earth. The work in [14] presented shore-to-sea environment measurements with three different antenna heights at 5.15 GHz by comparing them to free-space, 2-ray, and 3-ray models. Here, it was shown that the 2-ray model was suitable up to a certain distance calculated using the break point ($d_{break}$) formula, beyond which the 3-ray model was more successful. In [3], ship-to-anchored ship measurements were performed at 5.9 GHz for a distance of 2.6 km and modeled using the PEL, REL, and ITU-R models. The REL model was the most accurate in terms of the RMSE criterion, whereas for small-scale fading, the Distributed Power Two-Wave (TWDP) distribution provided the best results. On the other hand, [9] was a simulation study performed for ship-to-ship environments at 35 GHz and 94 GHz. It was stated that the 2-ray model could be used for short distances at high frequencies by emphasizing the importance of considering evaporation duct and sea surface roughness at millimeter-wave frequencies by proposing a 2-ray-based model including these parameters. In [15], to determine the sea-specific parameters, measurements were performed at 2.412 and 5.24 GHz, both on land and at sea, using the same measurement setup. A 2-3 dB difference between land and sea was observed at 2.4 GHz at a 2 m antenna height, while no significant difference was noted at 5.24 GHz at an antenna height of 5 m. Another ship-to-shore measurement campaign was performed at 5.2 GHz in [16], and a model was developed by combining the Karasawa model, which considers the scattering caused by sea surface roughness, with LOS conditions. The measurements were compared with this model and the ITU-R model, and it was concluded that the Karasawa model also performed well at 5.2 GHz. To determine the effect of the sea wave height on the received signal strength, 2.4 GHz ship-to-ship measurements were conducted in [17]. According to the results, longer links are sensitive to antenna gain fluctuations caused by sea movements, whereas shorter links are highly sensitive to path losses caused by effective elevation changes. In [8], shore-to-ship measurements were performed at 5.8 GHz under the IEEE 802.11n standard, as an alternative to costly wireless communication. According to the experiments, communication up to a distance of 7 km is possible at a data rate of 1 Mbit/s. Then, the effect of wave height (assumed to be 0.7 m) was analyzed using two different 2-ray models with antenna heights of 7.3 m and 8.7 m to account for the wave effects. The work in [18] presented shore-to-sea measurements at 2.4 GHz and 5 GHz at various antenna heights to investigate the tidal effects. It was observed that the roughness effect was more pronounced when approaching the shore. In addition, the measurement data were modeled by adding a tidal parameter to the 2-ray model. In [19], ship-to-ship measurements at 5.9 GHz were performed in calm seas, and mixed weather conditions were simulated using the Monte Carlo method. Based on these measurements, it was concluded that the REL model was suitable for calm seas. However, the simulation results showed that the free space model became more suitable as wind speed increased. The power delay profile, delay spread, and path loss were analyzed in [20] using ship-to-infrastructure and ship-to-ship measurements performed at 5.9 GHz. It was concluded that the channel capacity performed well up to 2500 m. Moreover, the REL model was found to fit the measurement data better than classical models such as ITU-R, free space, and single slope.

1.2. Motivation and Main Contributions

Shore-to-ship communication studies in the literature are comparatively summarized in terms of the models and carrier frequencies used in the studies, as shown in

Table 1. A comparative summary of shore-to-ship communication modeling studies.

Ref.	Freq. (GHz)	Models						Additional Parameters
		FSL	Log. Dis.	2-Ray	3-Ray	Pwise	Others	Div.	Refl.	Diff.	Shad.	Sea State
[1]	2	-	-	✓	-	-	ITU-R	✓	Effective	✓	✓	✓
[2]	2	✓	-	-	-	-	ITU-R Cost 231 Okum.	-	-	-	-	-
[3]	5.9	-	-	✓	-	-	ITU-R	✓	-	-	-	-
[8]	5.8	-	-	✓	-	-	-	-	-	-	-	-
[9]	35 94		-	✓	-	-	Sim. Study	✓	Fresnel Effective	✓	-	✓
[11]	5.8	-	✓	-	-	-	-	-	-	-	✓	-
[12]	5.8	✓	✓	✓	-	-	-	-	-	-	-	-
[13]	1.8	✓	-	✓	-	-	Imp. ITM	-	-	-	-	-
[14]	5.15	✓	-	✓	✓	✓	-	-	-	-	-	-
[15]	2.4 5.2	✓	-	✓	-	✓	-	-	Fresnel	-	-	✓
[16]	5.2	-	-	-	-	-	ITU-R Karasawa	-	Fresnel	-	-	-
[17]	2.4	-	-	✓	-	-	-	-	-	-	-	-
[18]	2.4 5	-	-	✓	-	-	-	-	-	-	-	-
[19]	5.9	-	-	✓	-	-	-	✓	Effective	✓	✓	✓
[20]	5.9	✓	-	✓	-	-	ITU-R	✓	Effective	✓	✓	✓
[21]	0.7	-	-	✓	-	-	ITM	-	-	-	-	-

FSL: Free Space Path Loss, Log. Dis.: Log-Distance Path Loss, Pwise: Piecewise Model, Div.: Divergence, Refl.: Reflection Coefficient, Diff.: Diffraction, Shad.: Shadowing.

. When shore-to-ship communication-specific measurement and modeling studies in the existing literature were examined, it was observed that free space (in [2,9,12,13,14,15,20]), log-distance (in [11,12]), simple 2-ray (in [8,12,13,14,15,17,18,21]), 3-ray (in [14]), 2-ray + additional parameters (REL) (in [1,3,9,19,20]), ITU-R (in [1,2,3,16,20]), Karasawa (in [16]), COST231 and Okumura-Hata models (in [2]) were used. However, the publications [1,2,9,13,17,21] were performed for different carrier frequencies than the 5.6 GHz band, which is within the scope of our study. On the other hand, [14,15] recommended the piecewise model approach and proposed 2-ray+3-ray and 2-segmented 2-ray models, respectively. In our study, experimental measurements were performed for four different environmental scenarios at 5.6 GHz carrier frequency for shore-to-ship communication, and the fit of the models used in the literature to the data was examined. Their performances were compared, and a path-loss model called Modified REL was developed. Subsequently, a Proposed Piecewise model, which uses the Modified REL and Log-distance models together, was developed by proposing a piecewise modeling approach for the data. The motivation of this proposal is to reduce the fitting errors between the measured data and the REL model, which shows a better fit than other models by considering the nature of the shore-to-ship propagation environments and providing a more generalizable modeling approach.

The main contributions of our work can be summarized as follows:

• A Modified REL model that represents environmental factors more flexibly and provides higher accuracy in shore-to-ship communication scenarios was proposed by considering the estimated $h_{rbest}$ and the varying paths and gains of the direct and reflected waves as additional parameters for each scenario unlike in the traditional REL model.
• A piecewise modeling approach based on dividing the propagation environment into two different regions based on the $d_{break}$ distance (calculated from the Fresnel zone theory) and modeling each region with appropriate models (Modified REL and log-distance) was proposed. This approach shows higher accuracy compared to the use of a single model.
• Comprehensive experimental data were collected at 5.6 GHz for four different shore-to-ship communication scenarios along the Black Sea coast in Trabzon, Türkiye.
• The proposed models were comprehensively evaluated in terms of fit to the experimental measurement data and compared with existing models in terms of fit performance (free space, log-distance, dual-slope, 2-ray, 3-ray, and REL).
• The Modified REL and proposed piecewise approach presented lower error rates (RMSE) and higher model fit (R²) than existing models, providing more reliable and accurate predictions for shore-to-ship communication.
• The findings were presented comprehensively, utilizing a combination of quantitative and qualitative outputs to substantiate the claims put forth in this paper.

2. Materials and Methods

2.1. Experimental Setup and Scenarios

Shore-to-ship measurements were carried out at 5.6 GHz by setting up two stations: one on land and the other at sea. The transmitter (Tx) setup was installed on a vehicle on land. The MK5 OBU device [22] and laptop were placed inside the vehicle, and the antenna of the device, with a magnetic base, was placed on the roof of the vehicle. The same measurement setup was used for the receiver (Rx) installed on a 12 m long boat. Here, the MK5 OBU device was placed inside the cabin of the boat, and the antenna of the device was placed on a metal rod made at the top front of the cabin. Figure 1 shows both the inside and outside views of the vehicle and boat used in the measurement setup and

Table 2. Experimental setup specifications [22].

Parameters	Values
Standard	IEEE 802.11p
Frequency Band	5.6 GHz
Data Rates	3–27 Mbps
Bandwidth	10 MHz
Max. Tx Power	23 dBm
Antenna Gains	5 dBi
GNSS	2.5 m Accuracy
Antenna type	Omnidirectional
Receiver Sensitivity	−99 dBm @ 3 Mbps

gives the technical specification of the experimental setup.

During the measurements, the Tx vehicle was parked on the shore, while the Rx boat moved away from the shore until communication was lost, and tried to return to the shore again following the same route. Throughout the experiment, the measurement data from both the Tx and Rx MK5 OBU devices were recorded on an SD card. These measurement data include the GPS location of the vehicle and the boat with the values of some parameters, such as the received signal strength, heading, and speed. The 5.6 GHz frequency band was selected for shore-to-ship measurements to comply with the Regulation on Short Range Radio Devices published by the Turkish Information Technologies and Communication Authority.

Four separate shore-to-ship measurements were carried out on different days. During the measurements, the Tx vehicle was kept stationary on the shore, while the Rx boat moved away until communication was interrupted and returned to the shore by following the same route. The boat speed was kept constant (approximately 10 knots) as long as weather conditions were allowed. Speed information was monitored using the GPS device of the boat. In the first scenario (M1), the weather was rainy, and the sea was relatively rough compared to the other scenarios. In the second scenario (M2), measurements were taken when the weather was cloudy, there was no rain, and the sea was rough. The third (M3) and fourth (M4) scenarios were carried out in a clearer and calmer sea environment than scenarios M1 and M2. Scenarios M3 and M4 were performed consecutively on the same day. The difference between these two scenarios is that the Tx antenna heights were different. In M3 scenario, the Tx antenna is positioned on the shore at 5.8 m, as in scenarios M1 and M2, while in the M4 scenario, the Tx is placed in the 3rd floor window of a building at 13.3 m. The comparative data for all scenarios, including weather, sea and wind conditions, as well as some parameter values of the measurements, are listed in

Table 3. Weather and sea conditions of the measurement scenarios.

	M1	M2	M3	M4
Weather state	Light rain shower	Mostly cloudy	Fair	Partly cloudy
Weather temp.	6.5–7 °C	8.6–10 °C	10 °C	7 °C
Sea water temp.	10.3 °C	9 °C	9.1 °C	9.1 °C
Wind speed	7 knots	6 knots	6 knots	6 knots
Sea state	3	3	2	2
$h_r$	3.5 m	3.5 m	3.5 m	3.5 m
$h_{rbest}$	3.61 m	3.43 m	3.55 m	3.47 m
$h_t$	5.8 m	5.8 m	5.8 m	13.3 m
${\beta }_0$	0.025	0.01	0.001	0.001
${\sigma }_h$	0.24 m	0.24 m	0.1 m	0.1 m

${\beta }_0$: Root Mean Square (RMS) surface slope, ${\sigma }_h$: RMS surface height (m).

.

In addition, the route followed by the Rx boat in the sea for all scenarios and an example of the coastal image taken from the boat during the measurement are shown in Figure 2. The red and blue lines in Figure 2 depict outbound and return routes, respectively. Additionally, in the red boxes labeled Tx, in the first three scenarios, there is a fixed-position Tx vehicle on the shore. In contrast, in the fourth scenario, a Tx device was fixed to a window on the third floor of a building. In all scenarios, the Rx boat was labeled with Rx.

2.2. Modified Rel Model and Proposed Piecewise Approach

This paper proposes a Modified REL model to accurately model reflections over ground and antenna gains based on the simplified REL model. While the REL model generally provides a structure that considers surface roughness and reflections, the inclusion of parameters, such as antenna gains and best Rx height, into the model significantly increases the estimation accuracy. The prediction of the reflections and losses of a signal on a rough surface considering the curvature of the Earth is the main purpose of the REL model. The most general expression for the pattern propagation (path gain) factor (F) in the REL model is as follows:

$$F=\left|1+{\Gamma }_{eff}·Div·S·{\displaystyle \frac{G_{ref}D}{G_{dir}R}}{e}^{-jk\Delta d}\right|$$

(1)

where $D=\sqrt{{(h_t-h_r)}^2+d^2}$ and $R=\sqrt{{(h_t+h_r)}^2+d^2}$ express direct and reflected wave paths, respectively. $h_t$ and $h_r$ are the Tx and Rx antenna heights, respectively, and the $\Delta d$ parameter represents the distance difference between the directly transmitted signal and the reflected signal ($R-D$), which plays a decisive role in the phase shifts and interference of the signals. $G_{ref}$ and $G_{dir}$ represent the angle-dependent gains of reflected and direct waves, respectively. The angle-dependent gains are expressed as $G_{ref}=G_{tr}{G}_{rr}$ and $G_{dir}=G_{td}{G}_{rd}$, where $G_{tr}$ and $G_{rr}$ represent the angle-dependent gains of the Tx and Rx antennas, respectively, for the reflected wave, and $G_{td}$ and $G_{rd}$ represent the angle-dependent gains for the direct wave.

${\Gamma }_{eff}$ refers to the effective (modified) reflection coefficient obtained by multiplying the Fresnel reflection coefficient ($\Gamma$) by the roughness coefficient (${\rho }_s$). ${\rho }_s$ is calculated by using the zero-order modified Bessel function ($I_0$) and the surface roughness (g) as follows:

$${\rho }_s=exp\left[-2{\left(2\pi g\right)}^2\right]·I_0\left(2{\left(2\pi g\right)}^2\right),g={\displaystyle \frac{{\sigma }_h·sin\psi }{\lambda }}$$

(2)

where ${\sigma }_h$ shows Root Mean Square (RMS) surface height, $\psi$ is grazing angle, and $\lambda$ is the wavelength of the signal. Divergence (Div.) considers the effects of the curvature of the Earth during the propagation of the signal over the surface, and helps model the deviations that the signal undergoes until it reaches the Rx as follows:

$$\begin{array}{c}\hfill Div={\displaystyle \frac{1}{\sqrt{1+\frac{2G_1{G}_2}{a_{e}Gsin\xi }}}},\xi ={sin}^{-1}\left({\displaystyle \frac{2a_e{h}_t+h_t^2-R_1^2}{2a_e{R}_1}}\right),{\varphi }_i={\displaystyle \frac{G_i}{a_e}},i=1,2\\ \hfill R_1=\sqrt{h_t^2+4a_e(a_e+h_t){sin}^2\left({\displaystyle \frac{{\varphi }_1}{2}}\right)},R_2=\sqrt{h_r^2+4a_e(a_e+h_r){sin}^2\left({\displaystyle \frac{{\varphi }_2}{2}}\right)}\end{array}$$

(3)

Here, $a_e$ = 6370 km represents the effective Earth radius, G represents the distance between the Rx and the Tx considering the curvature of the Earth, and $G_1=G/2+pcos((\pi +\alpha )/3)$ and $G_2=G-G_1$ represent the distances between the reflection point and the Tx and Rx, respectively. Here, the propagation distance was taken as $G\cong d$ since it is relatively short. p and $\alpha$ parameters are given as follows:

$$p={\displaystyle \frac{2}{\sqrt{3}}}\sqrt{a_e(h_t+h_r)+{\displaystyle \frac{G^2}{4}}},\alpha ={cos}^{-1}\left({\displaystyle \frac{2a_e(h_t-h_r)G}{p^3}}\right)$$

(4)

The S parameter reflects the shadowing effects of the signal, which becomes important, especially in environments with obstacles and surface roughness, compared to the wavelength, and is expressed as:

$$S={\displaystyle \frac{1-0.5\mathrm{erfc}\left(\frac{cot{\theta }_i}{\sqrt{2}{\beta }_0}\right)}{1+\Lambda ({\theta }_i,{\beta }_0)}},\Lambda ({\theta }_i,{\beta }_0)={\displaystyle \frac{1}{2}}\left[{\displaystyle \frac{\sqrt{2}{\beta }_0}{\sqrt{\pi }cot{\theta }_i}}exp\left(-{\displaystyle \frac{{cot}^2{\theta }_i}{2{\beta }_0^2}}\right)-\mathrm{erfc}\left({\displaystyle \frac{cot{\theta }_i}{\sqrt{2}{\beta }_0}}\right)\right]$$

(5)

where ${\theta }_i$ represents the incidence angle (90-$\psi$), and ${\beta }_0$ represents the RMS surface slope values.

The model obtained by adding the Div (divergence) parameter and $L_{Diff}$ (diffraction loss) to the free-space and 2-ray path loss models, which are generally accepted as PEL in the literature, and considering the curvature of the earth, is called the REL model [1]. However, in the existing studies, the assumptions $G_{ref}\cong G_{dir}$ and $D\cong R$ ($\Delta d\ne 0$) were generally made using the REL model in (1), and were simplified as $F_{REL}$:

$$F_{REL}=\left|1+{\Gamma }_{eff}·Div·S·e^{-jk\Delta d}\right|$$

(6)

Although the simplified REL model generally provides better results than other models in shore-to-ship communication environments, it may be insufficient to represent some effects that occur due to the marine environment’s nature. Therefore, instead of $F_{REL}$, which is widely used in the literature for a simplified REL model, a Modified REL model was proposed based on generalized F. Here, in addition to the roughness parameters, the total gains in the direct wave direction and reflected wave direction at the Tx and Rx ($G_{ref}\ne G_{dir}$) and the path taken by the direct wave and the path taken by the reflected wave ($D\ne R$) were not considered as equal, unlike $F_{REL}$. Consequently, the gain values that vary as a function of the antenna pattern which depends on the antenna height and grazing angle were also taken into account in calculations. In addition, instead of using a fixed $h_r$ value, the best $h_r$ value estimated for each measurement scenario was considered, $F_{modifiedREL}$ was developed, and a Modified REL model was obtained. Because rapid changes cannot be observed enough in the radio channel in an open-sea environment, one of the most important effects in this environment is the change in the sea wave height. When the propagation environment is considered, $h_r$ will be variable during the communication period depending on the changes in the ship movements caused by the sea wave [2]. These changes in antenna heights cause a horizontal shifting of the loss spikes of the RSSI signal obtained at the Rx [17]. Therefore, an examination was performed at the fixed Rx antenna height ($h_r$ = 3.5 m) determined in still water within the port relative to the sea surface and the change in the RSSI value at the Rx was observed. Because the Tx antenna assembly was on land and fixed, an evaluation was performed only for the Rx antenna height. To reveal the effect of the antenna change on the RSSI at the Rx and to increase the performance, the most suitable Rx antenna height value ($h_{rbest}$) corresponding to the lowest RMSE was calculated. Here, $h_r$ was optimized to increase the accuracy of the model. The $h_{rbest}$ value was determined for each scenario based on various tests and measurements. Optimizing $h_r$ minimizes signal loss and maximizes the power of the reflected signal. Thus, the antenna gains and reflection effects were calculated most accurately. Therefore, the model obtained by adding the $h_{rbest}$ parameter provided higher accuracy, particularly for highly reflective environments.

The final version of our proposed Modified REL model was developed to model the signal loss and reflection effects between the Tx and Rx more accurately as follows:

$$\begin{array}{c}\hfill RSS{I}_{modifiedREL}\left[dBm\right]=P_t\left[dBm\right]+G_{td}\left[dBi\right]+G_{rd}\left[dBi\right]-\\ \hfill L_{FSPL}\left[dB\right]+F_{modifiedREL}\left[dB\right]\pm L_{diff}\left[dB\right]-A\left[dB\right]\end{array}$$

(7)

where $P_t\left[dBm\right]$ is the Tx power, $G_{td}\left[dBi\right]$ and $G_{rd}\left[dBi\right]$ are the Tx and Rx antenna for the direct wave direction gains, respectively, $L_{FSPL}\left[dB\right]$ is the free space path loss, $F_{modifiedREL}\left[dB\right]$ is the improved pattern propagation factor, $A\left[dB\right]$ is the rain attenuation [23], and $L_{Diff}\left[dB\right]$ is the diffraction loss (can be positive or negative) caused by the bending of the signal around obstacles. In the calculations for the $L_{Diff}$ parameter according to all measurements, because the measurement distance (d) was smaller than the distance corresponding to 60% of the Fresnel zone ($D_{06}$), $L_{Diff}$ was taken as 0 dB in the calculations. Moreover, based on the meteorological data, the rain attenuation parameter $A\left[dB\right]$ was considered only for the M1 scenario.

The roughness coefficient ${\rho }_s$ used to determine the effective Fresnel reflection coefficient while calculating the $F_{modifiedREL}$ was calculated according to the ${\sigma }_h\left[m\right]$ (RMS surface height) value corresponding to the sea state according to the Beaufort scale [24]. ${\beta }_0$ (RMS surface slope), required for the calculation of the shadowing coefficient (S), was estimated according to the meteorological data of the measurement days and comments of the boat captain on the regional weather and sea conditions [11,12]. Considering the Beaufort scale, the wave heights and wind intensities specified in the meteorological data of the measurement days correspond to 2 and 3 sea states [25]. When the wave height—${\beta }_0$ graph created based on the measurements is examined, it is seen that ${\beta }_0$ varies between 0.04 and 0.07 for 1–4 m wave height [26]. For our study, the default ${\beta }_0$ values were taken into consideration as below 0.04 due to the wave height being at most 0.5 m in the scenarios, and the best ${\beta }_0$ estimation was performed for the lowest RMSE [1]. The obtained ${\beta }_0$ values were consistent with the meteorological data. As a result, using the above-defined parameters in the Modified REL model, the signal loss was estimated more accurately. This model provides a more accurate calculation of signal power both in free space and in environments with complex effects, such as reflection and diffraction. Optimization of the $h_{rbest}$ parameter and the addition of angle-dependent gains make the model more robust and show superior performance with lower error rates in different environments.

Finally, in this study, a piecewise modeling approach was also proposed that aims to represent the complex propagation characteristics more accurately by separating the signal propagation into two different regions. This model, which we call the Proposed Piecewise model, divides the propagation medium into two regions using the $d_{break}$ point, which is calculated from Fresnel zone theory, similar to the dual-slope model approach, using the Modified REL model for the first region and the log-distance model for the second region. The basis of the model is the use of different path loss models for both regions as follows:

$$ProposedPiecewise=\left\{\begin{array}{c}RSS{I}_{ModifiedREL}ford\le d_{break},\left(Region1\right)\hfill \\ RSS{I}_{log-distance}ford>d_{break},\left(Region2\right)\hfill \end{array}\right.$$

(8)

The breakpoint ($d_{break}={\displaystyle \frac{4h_t{h}_{rbest}}{\lambda }}$) determines the boundary between two different propagation regions and is calculated using the Fresnel zone theory that calculates the breakpoint using $h_t$, $h_{rbest}$, and $\lambda$. The $d_{break}$ distance indicates the point where the signal passes from complex effects such as reflection and diffraction to free-space propagation, and the signal propagation data are divided into two segments according to this distance. In Region1, the Modified REL model, which includes reflection and diffraction effects that we developed within the scope of this study, is used, whereas in Region2, the propagation data are represented more accurately by the log-distance model. The initial distance value of Region2 was taken as the $d_0$ value of the log-distance model, and the first RSSI value corresponding to the $d_{break}$ point of the Modified REL was taken as the $PL(d_0$) parameter. For Region2, n was estimated using these $d_0$ and $PL\left(d_0\right)$. Thus, Modified REL was used for Region1, and the log-distance model was used for Region2.

As a result, this approach provides a more accurate representation of complex propagation characteristics and shows that modeling the measurement data as two pieces instead of one yields more successful results. This piecewise modeling method provides higher agreement with the measurement data, especially when factors such as environmental changes, rough surfaces, and atmospheric conditions are considered.

3. Results and Discussion

In this study, propagation modeling was performed for shore-to-ship communication in the Black Sea, an inland sea in Türkiye, and as a result, a Modified REL and Piecewise path loss model was proposed. First, for the four different scenarios, shore-to-ship communication channel measurements were performed at 5.6 GHz along the Black Sea coast in Trabzon, Türkiye. These measurements were performed in four different scenarios, M1, M2, M3, and M4, according to the sea roughness, weather conditions, and Tx heights. While the M1, M2, and M3 scenarios represent changes in various weather and sea conditions, the M4 measurement was performed at different Tx heights under similar weather and sea conditions to the M3 measurement, focusing on the effect of this change on path loss. The maximum measurement distances vary in scenarios M1, M2, and M3 due to differences in weather and sea conditions, and in scenario M4 due to different transmitter antenna height.

In this context, first, the performances of the well-known free-space, log-distance, dual-slope, 2-ray, 3-ray, and REL models, which are frequently used in the literature for shore-to-ship communication, are presented comparatively for four different measurement scenarios, as shown qualitatively in Figure 3 and quantitatively in

Table 4. Performance comparisons of proposed model with existing models, RMSE in dB.

	M1		M2		M3		M4
Models	R2	RMSE	R2	RMSE	R2	RMSE	R2	RMSE
Free Space	0.88	3.11	0.90	3.50	0.88	5.72	0.82	5.72
Log-Distance	0.89	3.09	0.90	2.45	0.88	2.60	0.82	3.01
Dual-Slope	0.88	3.11	0.91	2.36	0.89	2.59	0.81	2.95
2-Ray	0.62	6.43	0.76	4.24	0.89	4.32	0.86	3.31
3-Ray	0.88	7.37	0.89	4.51	0.88	2.93	0.82	3.90
REL	0.91	2.79	0.95	2.34	0.94	3.97	0.93	2.62
Modified REL	0.92	2.72	0.95	2.26	0.97	3.87	0.95	2.54
Proposed Piecewise	0.92	2.68	0.95	1.92	0.93	2.42	0.95	1.65

. R² and RMSE metrics were used to evaluate the fit of the models to the measured data.

It can be seen that the proposed Modified REL and Piecewise models offer significant improvements compared to the existing models; in particular, the Proposed Piecewise model significantly reduced the error rates (RMSE) and increased the overall accuracy. The main contribution of this study is the development of a Modified REL model by adding the estimated best Rx height and the varying paths and gains of the direct and reflected waves as additional parameters according to the data to the calculation of the classical REL model, which provides more successful results than other models and a more realistic approach. Then, it was determined that the Modified REL represented the data well up to a certain distance ($d_{break}$ distance), but after this distance, it was in the log-distance pattern rather than the characteristic of this model. For this reason, a piecewise model based on a piecewise analysis of the data was proposed, and a performance comparison was made with other models for each scenario.

In this study, the performance results of our proposed Modified REL and Proposed Piecewise models were examined in detail, and both visual and numerical evaluations demonstrated the superiority and effectiveness of the proposed approaches. In scenario M1, the Modified REL and Proposed Piecewise models performed better than the other models. The Modified REL model provided a good fit to the measured data with an R² of 0.92 and an RMSE of 2.72. However, the Proposed Piecewise model exhibited the best performance with a lower RMSE value (2.68), despite achieving a similar R² value (0.92). In the M2 environment, both models showed significant improvements over the REL model, which had the best performance compared to the other models. The Modified REL model provided an R² of 0.95 and an RMSE of 2.26, whereas the Proposed Piecewise model maintained the same R² value and reduced the RMSE to 1.92. This implies a 15% error reduction and shows that the Proposed Piecewise model provides significant superiority in this scenario. In the M3 environment, the R² value of the Modified REL model was 0.97, and the RMSE value was 3.87, which shows considerably high accuracy compared to the other models. However, the R² value of the Proposed Piecewise model decreased slightly compared with that of the Modified REL and decreased to 0.93. However, the RMSE value decreased to 2.42, indicating a 37% error reduction. However, it has a similar R² value compared to the REL model and again improves the error by 39%. These results clearly show that the Proposed Piecewise model offers a significant advantage in reducing error rates in the M3 environment. These improvements provide superior overall performance despite some small decreases in R² values. Finally, in the M4 environment, the R² value of the Modified REL model is 0.95, and the RMSE value is 2.54. The Proposed Piecewise model provided a similar R² value (0.95) but reduced the RMSE value to 1.65, providing an improvement of approximately 35% over Modified REL and 37% over REL. This also implies that the Proposed Piecewise model provides a significant fitting performance with a low error rate in the M4 environment. Considering all the results, the piecewise modeling approach showed better performance than the other evaluated methods, because, according to the Rayleigh roughness criterion, it is stated that the roughness is a dominant effect at close distances to the Tx antenna and should be taken into account, while its effect can be neglected at longer distances [27]. Therefore, considering the data in a piecewise manner was a more accurate modeling approach.

If a qualitative evaluation is performed, the visual results presented in Figure 3 clearly demonstrate the performance superiority of the proposed models. It is observed that the REL model represents the data in each scenario better than the other models. However, owing to the parameters added to the Modified REL model, this model showed a higher fit to the measured data. Figure 3a (left side) indicates the fit of various existing models (free-space, log-distance, dual-slope, 2-ray, 3-ray, and REL) to the measured data for the M1 scenario and their comparison with the Modified REL model. In Figure 3a (right side), the Modified REL and the Proposed Piecewise model, which is based on a piecewise approach, are compared, and it is observed that the piecewise approach provides a superior fit to the entire data. The graphs in Figure 3b–d for the M2, M3, and M4 environments, respectively, make the improvements provided by the Proposed Piecewise model even more apparent. In the graph given for the M2 environment (Figure 3b), the Proposed Piecewise model, represented by the red line, shows the closest fit to the measured data and has a lower RMSE value than all other models. In the M3 and M4 environments, it was determined that this model successfully represented the data at short and long distances, significantly reduced the error rates in particular, and significantly increased the accuracy rate at both short and long distances. As a result, both numerical and visual evaluations show that the proposed Modified REL and Proposed Piecewise models provide significant advantages compared to other models used in shore-to-ship communication scenarios and offer high accuracy with lower error rates. In particular, the Proposed Piecewise model offers a more suitable solution for environments, such as shore-to-ship communication.

4. Conclusions

In this study, a Modified REL propagation model and a data modeling approach based on piecewise are proposed for shore-to-ship communication channels. Comprehensive performance evaluations demonstrated that the developed Modified REL model was better adapted to environmental variables and increased propagation accuracy compared to the simplified REL model. In particular, the Rx antenna height, which is not constant due to fluctuations in the sea environment, was optimized for each measurement and included in the calculations, and the adaptability of the model to environmental conditions increased. In addition, the Proposed Piecewise model successfully modeled more complex marine environment conditions by dividing the propagation environment into two regions according to the $d_{break}$ point calculated based on Fresnel zone theory. The first region is represented by the Modified REL model, and the second region is represented by the log-distance model, providing a higher accuracy that cannot be achieved with a single model. Tests conducted in four different shore-to-ship scenarios showed that the proposed models exhibited superior performance compared with existing models in terms of both accuracy and flexibility. In particular, the Modified REL model achieved an average decrease of up to 3% in RMSE values compared with the classical REL model and a significant increase in model fit (R²). In addition, the Proposed Piecewise model yielded more successful results than the Modified REL model, while R² did not change much for scenarios M1, M2, M3, and M4, the RMSE values decreased by 1.5%, 15%, 37.5%, and 35%, respectively, and an average improvement of 22.25% was achieved. These results reveal the importance of piecewise modeling strategies and approaches sensitive to environmental factors to increase the reliability and efficiency of shore-to-ship communication. In future studies, these models can be tested in a wider frequency range and different maritime environments, including the evaporation duct effect neglected in our proposed model. Thus, a more comprehensive performance evaluation and model recommendation can be made. This study contributes significantly to the development of advanced and adaptive propagation models in the field of marine communication.