1. Introduction

Wireless communication has become the backbone of modern technological advancement, enabling connectivity in areas such as telecommunications, autonomous systems, and smart cities. A critical component of wireless communication systems is radio wave propagation, which determines how signals travel between transmitters and receivers. Accurate propagation models are essential to predict signal behavior under varying environmental and operational conditions, ultimately ensuring reliable and efficient communication networks. This review focuses on the evolution, classification, and advancements of propagation models. By examining their development stages, from historical approaches to modern techniques, and exploring emerging trends such as 5G and 6G networks, the study provides a comprehensive understanding of the field. Additionally, this paper will explore the classification of propagation models based on signal fading characteristics during signal transmission. By identifying emerging trends and future directions, it aims to assist researchers and industry professionals in optimizing propagation models for 5G and 6G wireless communication networks.

2. Historical Development of Propagation Models

2.1. Early Stage

Radio wave transmission is rooted in James Clerk Maxwell's 1884 mathematical formulation, which clarified the relationship between electric and magnetic fields, laying the groundwork for electromagnetic wave theory. Heinrich Hertz validated Maxwell's predictions in 1888 by empirically demonstrating the generation and propagation of electromagnetic waves, confirming their travel at light speed. [1] After the invention of the first radio-wave telegraph by Guglielmo Marconi in 1896.[2] In 1900, Reginald Fessenden pioneered continuous radio wave transmission, achieving the first wireless voice communication on December 23. The 1906 inaugural radio broadcast marked the beginning of a "golden period" for radio, establishing foundational propagation models and communication system applications that facilitated future advancements.

2.2. Development Stage & Modern Stage

Mid-20th century advancements in propagation modeling were driven by radar technology from World War II and the rise of television broadcasting, highlighting the need for improved models. Empirical models, such as the Okumura-Hata model, emerged, utilizing field measurements and incorporating variables like terrain, frequency, and distance for enhanced signal predictions. The late 20th century marked the onset of modern propagation modeling with cellular communication technologies, where analytical and computational methods, including ray tracing and finite-difference time-domain (FDTD) techniques, became essential for modeling complex environments, including urban and indoor settings. Recently, machine learning approaches have further refined the accuracy and adaptability of these models.

3. Fundamentals and Classification of Propagation Models

3.1. Basic Principles of Propagation

In wireless communication, it is essential to consider the impact of reflection, diffraction, and scattering on signal propagation.[3] In fact, it would also be influenced by path loss, multipath effects, etc. Reflection occurs when signals encounter large obstacles, such as buildings or mountains. Diffraction enables signals to navigate around obstacles, whereas scattering occurs due to interactions with small objects like foliage or vehicles. Together with frequency, polarization, and environmental conditions, these phenomena influence wireless signal propagation characteristics.

3.2. Classification of Propagation Models

Propagation models can deliver precise mathematical representations of radio propagation for use in radio link and system simulations in system deployment modeling.[4] The objective is to comprehend and anticipate the propagation of wireless signals across various contexts. Propagation models can be classed in numerous ways based on characteristics such as distance, frequency, and environmental variables.[5] Common classification methods encompass fading scales (large-scale, medium-scale, and small-scale), environmental categories (urban, rural, or indoor), and particular signal characteristics such as multipath propagation.

However, this paper focuses on the classification of propagation models based on signal fading characteristics, as these directly reflect the primary influences encountered during signal transmission. These influences can be categorized as follows:

Signal propagation is influenced by three fading types: large-scale fading (path loss), medium-scale fading (shadowing), and small-scale fading (multipath). Large-scale fading involves gradual signal attenuation over long distances due to free-space propagation and environmental obstructions. Medium-scale fading, or shadowing, occurs when large obstacles like buildings or trees obstruct the signal path, leading to variations in signal strength. Small-scale fading, or multipath fading, results from the signal reaching the receiver via multiple paths due to reflections and scattering, causing amplitude and phase fluctuations. Models such as the Free Space Model, Ray Tracing Model, and Okumura-Hata Model address large-scale fading, while Rayleigh and Rician Fading Models focus on small-scale fading. This classification aids in understanding the key challenges in signal propagation, crucial for modern wireless communication systems where coverage, shadowing, and multipath effects significantly affect network performance.

3.3. Applications of Propagation Model

The modeling of propagation serves not only to precisely forecast signal strength at a distance from a source but also to delineate the spatial boundaries of a usage based on propagation.[6] Propagation models are widely used to address challenges in real-world communication systems. One significant application is in the base station layout.[7] Propagation models predict signal attenuation with distance, optimizing base station placement in urban and suburban areas to ensure stable coverage and minimize interference, crucial for reliable communication in dense environments.

Another key application is in satellite communication, where line-of-sight (LOS) propagation plays a critical role [8]. In satellite links, predicting signal behavior is vital for ensuring uninterrupted communication. Beyond rain attenuation, other factors such as ionospheric scintillation, tropospheric delays, and multipath fading must also be considered. These models aid in designing robust communication systems that can adapt to varying environmental and atmospheric conditions, such as heavy precipitation, solar activity, or temperature fluctuations.

4. Classic Propagation Models and Applications

4.1. Free Space Model

The Free Space Model describes the propagation of radio signals in an idealized environment where there are no obstacles, reflections, or interference. It assumes a line-of-sight (LOS) path between the transmitter and receiver, making it a fundamental model for analyzing signal attenuation over distance. The received signal power \( {P_{R}} \) ​ is calculated using the following equation:

\( {P_{R}}={P_{T}}{G_{T}}{G_{R}}{(\frac{λ}{4πd})^{2}} \) (1)

where \( {P_{T}} \) ​ is the transmitter power, \( {G_{T}} \) ​ and \( {G_{R}} \) are the transmitter and receiver antenna gains, \( d \) is the distance between the two antennas, and \( λ \) is the signal wavelength. The model demonstrates that the received power decreases proportionally to the square of the distance, which highlights the significant attenuation experienced as the signal travels further from the transmitter.

This model is extensively utilized in line-of-sight communication contexts, including satellite communication, microwave links, and short-range wireless systems. In satellite communication, the free space model effectively analyzes signal behavior between satellites and ground stations, as the lack of physical obstructions in space aligns with the model's assumptions. Microwave links, which operate over direct paths, leverage this model to evaluate signal loss and optimize performance. Similarly, short-range wireless technologies like Bluetooth and Wi-Fi employ the free space model to assess signal attenuation in open environments, ensuring effective communication within limited ranges. Recently, the application of free space models has expanded to optical communication, with Free Space Optical (FSO) technology utilizing light for data transmission in free space.[9]

Although the Free Space Model offers a coherent theoretical framework for comprehending signal propagation, it is constrained by its idealized premises.[10] In practical environments, factors such as reflections, diffraction, and obstructions significantly impact signal behavior, requiring more complex models to account for real-world conditions. Nonetheless, the Free Space Model remains a cornerstone for studying signal propagation in line-of-sight scenarios and serves as the basis for more advanced propagation models.

4.2. Ray Tracing Model

The ray tracing model is a sophisticated signal propagation framework that analyzes electromagnetic wave interactions with the environment. Unlike the free space model, it integrates environmental factors and considers wave behaviors such as reflection, refraction, scattering, and diffraction. This model excels in urban and densely populated indoor environments, where structures impact signal transmission. Utilizing detailed 3D environmental models, it offers precise predictions of signal strength and path loss, crucial for designing advanced wireless communication systems like 5G, where accuracy and coverage optimization are vital. However, its application demands substantial computational resources due to the reliance on 3D site modeling and extensive calculations. While it achieves remarkable accuracy, its practical implementation is often complemented by empirical models like the Okumura-Hata model, especially when computational efficiency is paramount.[11] By incorporating environmental details and accounting for multiple wave interactions, the ray tracing model bridges the gap between theoretical and real-world signal propagation, enabling engineers to design robust and reliable communication systems.

4.3. Okumura-Hata Model

The Okumura-Hata model is an empirical propagation model widely used for predicting path loss in urban, suburban, and rural environments.[12] It is an extension of Okumura’s measurements, providing a set of mathematical equations that simplify signal attenuation estimation over different terrains. This model is specifically designed for frequencies ranging from 150 MHz to 1500 MHz and is ideal for microcell environments, where the distances between transmitters and receivers range from 1 km to 20 km.

The path loss 𝑃𝐿 in the Okumura-Hata model is calculated using:

\( PL=A+B{log_{10}}{(d)}-C \) (2)

where \( A \) , \( B \) , and \( C \) are constants dependent on the frequency, base station height, and receiver height, and ddd is the distance between the transmitter and receiver. Separate formulations exist for urban, suburban, and open rural areas, allowing for adjustments based on environmental characteristics.

This model is particularly applicable to cellular network planning, where base stations need to be strategically placed to ensure consistent coverage. In urban environments, it accounts for signal loss due to buildings and dense structures. For suburban and rural areas, correction factors are introduced to accommodate fewer obstructions and larger open spaces.

The Okumura-Hata model's simplicity and reliability make it one of the most popular choices for large-scale wireless communication network design, such as 2G, 3G, and other early mobile systems. While it may lack the precision of newer models in complex environments, it remains a cornerstone for estimating signal propagation in diverse terrain conditions.

4.4. Shadowing Fading Model

Shadowing fading, also referred to as log-normal fading, causes variations in signal strength that are not directly proportional to the distance between the transmitter and the receiver. The signal attenuation in shadowing fading is modeled as a random process, where the received power follows a log-normal distribution on a logarithmic scale.[13] Mathematically, it can be expressed as:

\( PL(d)[dB] = PL (d0) [dB] + 10y lg d d 0+ Xσ[dB] \) \( (3) \)

In this equation, \( PL(d0) \) is the path loss at a reference distance \( {d_{0}} \) , \( y \) is the path loss exponent, and \( Xσ \) is a log-normally distributed variable that accounts for the randomness introduced by obstacles. The value of \( Xσ \) has a standard deviation \( σ \) which represents the fluctuation in dB caused by shadowing.

Shadowing fading is essential in mobile communication, particularly in urban environments where structures weaken signal strength. Accurate signal forecasting is critical for reliable communication in densely populated areas. This phenomenon also affects rural and forested wireless sensor networks, where natural barriers impede signal propagation, impacting connectivity and performance. Engineers utilize shadow fading models to create robust sensor networks. Designers of base stations and wireless infrastructure must account for terrain and potential obstructions to optimize coverage and minimize signal loss. Effective shadow fading modeling is crucial for enhancing base station placement, thereby improving the reliability and performance of wireless communication systems by anticipating the effects of large-scale obstacles.

4.5. Rayleigh and Rician Fading Models

The Rayleigh fading model describes signal behavior in multipath environments without a dominant line-of-sight (LOS) component, resulting in substantial random signal amplitude fluctuations. It posits that the received signal's amplitude follows a Rayleigh distribution, making it suitable for densely obstructed areas like urban environments. The lack of a strong direct path leads to highly variable signal strength and an unstable baseline. Conversely, the Rician fading model applies when a significant LOS component exists alongside multipath scattering. This model assumes the received signal amplitude adheres to a Rician distribution, featuring a higher baseline and reduced fluctuations compared to Rayleigh fading.[14] A dominant direct path enhances signal stability with minimal variation from scattered components. Rician fading occurs in environments with clear line-of-sight (LOS), like open rural areas, while Rayleigh fading is relevant in urban and indoor settings characterized by dense scattering and obstructions. Rician fading is preferable in partially obstructed scenarios, such as suburban regions, where a strong LOS component bolsters signal reliability. These models are crucial for understanding signal behavior across different propagation conditions, aiding engineers in optimizing wireless communication systems for both urban and rural contexts.

Table 1: Comparison of Propagation Models: Advantages, Disadvantages, and Application Scenarios

5. Conclusion

Propagation modeling has evolved significantly due to technological advancements and interdisciplinary approaches. Initially designed for simple environments, these models now address complex urban and indoor scenarios, driven by wireless technology demands. Interdisciplinary insights, particularly from geospatial data and Geographic Information Systems (GIS), have enhanced urban model accuracy. Computational electromagnetics and advanced simulation tools have further clarified wave behavior in intricate environments. The 6G era introduces new challenges and opportunities. Artificial intelligence (AI) is revolutionizing model optimization and real-time adaptability. Quantum communication's unique characteristics, like entanglement and superposition, require innovative modeling strategies. Additionally, the focus on sustainability is prompting the creation of energy-efficient models to reduce wireless networks' environmental impact. These trends highlight the evolving nature of propagation modeling, which remains essential for ensuring reliable, efficient, and sustainable connectivity in an interconnected world.