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Hata model

The Hata model, also known as the Okumura–Hata model, is an empirical propagation model developed to predict the median for land services in urban areas, based on extensive field measurements conducted in , . Introduced by Masaharu Hata in 1980, it simplifies the graphical data from Yoshihisa Okumura's earlier work into a practical formula suitable for system planning in frequencies ranging from 150 MHz to 1500 MHz, with antenna heights of 30 m to 200 m, antenna heights of 1 m to 10 m, and link distances from 1 km to 20 km. The core of the model is a logarithmic equation for urban path loss L_p (in dB), expressed as: L_p = 69.55 + 26.16 \log_{10}(f) - 13.82 \log_{10}(h_b) - a(h_m) + [44.9 - 6.55 \log_{10}(h_b)] \log_{10}(d) where f is the in MHz, h_b is the height in meters, h_m is the height in meters, d is the distance in km, and a(h_m) is a correction factor dependent on f and h_m (e.g., a(h_m) = (1.1 \log_{10}(f) - 0.7) h_m - (1.56 \log_{10}(f) - 0.8) for small/medium cities). Adjustments are provided for non- environments: suburban areas subtract $2 [\log_{10}(f/28)]^2 - 5.4 dB, while open/rural areas subtract $4.78 [\log_{10}(f)]^2 + 18.33 \log_{10}(f) - 40.94 dB from the urban value. Due to its computational simplicity and reliance on easily obtainable parameters like and antenna heights—without needing detailed terrain data—the Hata model has become a foundational tool in the design of cellular , enabling efficient estimation of coverage, budgets, and signal strength for early generations of wireless systems. It remains influential in research and industry for validating more advanced models, though its predictions can vary in accuracy for specific suburban or obstructed environments. An extension, known as the , adapts the original for higher frequencies (1500–2000 MHz) relevant to personal communication systems (PCS), incorporating similar urban, suburban, and open-area corrections while maintaining the empirical approach for frequencies like MHz used in networks. This variant, developed under the COST 231 project, broadens applicability to modern urban planning but requires tuning for tropical or mountainous terrains where original assumptions may not hold.

History and Development

Okumura's Empirical Measurements

In the , Yoshihisa Okumura and his team at Public Corporation (now NTT) conducted pioneering field experiments to characterize in and suburban environments, focusing on land-mobile radio services. These measurements were primarily carried out in and around , , using mobile vans equipped with receiving equipment to simulate real-world cellular-like scenarios. The experiments spanned frequencies from 150 MHz to 1920 MHz, capturing data across VHF and UHF bands relevant to mobile communications at the time. The setup employed vertical antennas for both transmitting and receiving, with base stations elevated to heights between 30 m and 200 m to mimic rooftop or tower installations, and mobile antennas positioned at 1 m to 3 m above ground level to represent vehicle-mounted systems. Measurements were recorded along various routes covering distances from 1 km to 100 km, allowing for the analysis of both near-field and far-field behaviors in diverse terrains, including hilly areas and flat urban zones. This comprehensive , gathered over multiple campaigns in 1962, 1963, and 1965, provided the empirical foundation for understanding signal attenuation in cluttered environments. Key findings from these experiments demonstrated that median path loss increases systematically with greater transmitter-receiver separation, higher operating frequencies, and taller base station antennas, with urban clutter introducing additional losses compared to open areas—for instance, approximately 20 dB more attenuation in dense urban settings at 200 MHz over similar distances. Okumura's team generated graphical plots depicting median path loss as a function of distance for specific frequencies and antenna heights, differentiated by environmental categories such as quasi-smooth, average, and rugged terrain. These plots also illustrated variations due to location-specific factors, showing standard deviations in field strength typically ranging from 3 to 7 dB. The curves derived from these measurements implicitly accounted for terrain irregularities, such as hills and slopes, as well as building clutter and , by normalizing against free-space and applying empirical corrections based on observed median values across multiple test paths. Rather than using deterministic formulas, the approach relied on averaged readings from hundreds of measurement runs, enabling predictions that captured the probabilistic nature of in non-line-of-sight conditions without isolating individual or effects. This graphical methodology laid the groundwork for subsequent analytical models.

Hata's Formulation and Publication

In the late 1970s, Masaharu Hata, working at the Electrical Communication Laboratories of Public Corporation (NTT) in , developed a set of analytical equations to approximate the graphical propagation loss data compiled by Yoshihisa Okumura. This effort aimed to transform Okumura's empirical curves into computationally efficient regression-based formulas suitable for practical cellular radio system planning. By performing curve-fitting analyses on the median field strength versus distance plots, Hata derived simple logarithmic expressions that captured the essential dependencies on and antenna heights. Hata's formulation was detailed in his seminal paper titled "," published in the IEEE Transactions on Vehicular Technology. The paper appeared in volume VT-29, issue 3, in August 1980, spanning pages 317 to 325. In this work, Hata presented the model as an empirical tool derived directly from Okumura's experimental results, emphasizing its utility for VHF and UHF land mobile services. The model, commonly known as the Hata model in recognition of its primary developer, was initially designed for frequencies between 150 and 1500 MHz, with antenna heights ranging from 30 to 200 meters, mobile antenna heights from 1 to 10 meters, and effective distances from 1 to 20 kilometers. To address varying environments, Hata introduced correction factors applied to a fundamental , enabling adjustments for suburban and open-area scenarios without altering the core equation structure. These corrections, such as subtraction terms for non- settings, enhanced the model's versatility for early cellular deployments.

Model Fundamentals

Assumptions and Applicability

The Hata model is an empirical model that assumes operation beyond the immediate clutter zone surrounding the , starting from distances of 1 km, where local obstructions have less dominant influence on the signal. It does not require line-of-sight conditions between the transmitter and receiver, making it suitable for non-line-of-sight scenarios in macrocellular environments, and relies on knife-edge over buildings and terrain as a primary propagation mechanism. The model predicts the median , corresponding to 50% location coverage probability, by focusing on large-scale averaging and ignoring small-scale effects such as multipath . This empirical basis stems from the collaborative measurements by Okumura and Hata in urban settings around , , though it has been generalized for broader use. The model's applicability is limited to specific parameter ranges to ensure reliable predictions: frequencies between 150 MHz and 1500 MHz, effective antenna heights of 30 to 200 m, antenna heights of 1 to 10 m, and link distances of 1 to 20 km for and suburban environments. In open rural areas, the model can extend to distances up to 100 km, but with caveats regarding reduced accuracy due to varying smoothness and the need for additional . It performs best for frequencies below 2 GHz in macrocellular setups, where the environmental prerequisites include quasi-smooth with buildings or acting as diffractions sources, rather than highly irregular or forested landscapes. These conditions were derived from measurements in but have been validated and applied in diverse global contexts for land services.

Limitations and Accuracy Considerations

The Hata model exhibits several key limitations stemming from its empirical basis derived from specific measurement conditions. It is inherently restricted to carrier frequencies between 150 MHz and 1500 MHz, rendering it inaccurate for applications above this range without modifications like the COST-231 extension. The model is optimized for macrocellular deployments and performs poorly in microcellular or indoor environments, where antennas are typically below roof height or signals penetrate structures, as these scenarios introduce unmodeled and penetration losses. Additionally, it assumes relatively flat with uniform clutter distribution, such as consistent building heights and , which leads to degraded predictions in varied topographies including hilly or irregular landscapes. Accuracy assessments through validation against field measurements reveal typical root mean square () errors ranging from 4 to 10 across urban, suburban, and open areas. More specifically, studies report errors of 6 to 9 as standard for the model's predictions. Performance varies by environment: the model often overestimates in hilly terrain due to unaccounted elevation variations and clutter effects, while it tends to underestimate losses in dense urban settings with high-rise buildings, where increased multipath and shadowing are prominent. The Hata model focuses on median path loss and does not inherently incorporate shadow variance or fast components; shadow is addressed separately via a with a standard deviation of approximately 8 dB in areas, representing location-specific variations due to obstacles. Validation efforts against real-world measurements confirm a 50% of roughly ±8 dB, largely attributable to this shadowing effect. To mitigate these issues, practitioners recommend integrating the model with detailed terrain and clutter data adjustments, such as digital elevation models, for improved reliability in non-ideal conditions. However, it is unsuitable for 5G millimeter-wave bands (above 24 GHz), where higher frequencies demand more precise methods like ray-tracing to capture dominant line-of-sight and non-line-of-sight behaviors.

Environmental Propagation Models

Urban Model

The Urban Model in the Hata propagation framework predicts the median for cellular radio transmissions in dense environments, where buildings and other structures dominate the landscape, leading to significant multipath , , and effects. Derived empirically from field measurements in built-up areas, this model assumes the is elevated above the average rooftop level by approximately 4-50 meters to ensure line-of-sight over immediate obstacles while capturing urban clutter influences. It forms the core formulation upon which environmental corrections for suburban and open areas are applied, emphasizing over quasi-smooth terrain interspersed with urban features. The path loss L_{p,urban} is expressed in decibels (dB) by the following equation: L_{p,urban} = 69.55 + 26.16 \log_{10} f_c - 13.82 \log_{10} h_{te} - a(h_{re}) + (44.9 - 6.55 \log_{10} h_{te}) \log_{10} d Here, f_c represents the carrier frequency in MHz, h_{te} the effective base station antenna height in meters, h_{re} the effective mobile station antenna height in meters, and d the distance between the base and mobile stations in kilometers. The term a(h_{re}) is a correction factor that adjusts for the mobile antenna height, reflecting its reduced susceptibility to ground-level obstructions in urban settings. For small and medium-sized cities, this factor is computed as: a(h_{re}) = (1.1 \log_{10} f_c - 0.7) h_{re} - (1.56 \log_{10} f_c - 0.8) For large cities, alternative forms account for higher building densities and greater signal attenuation at street level: a(h_{re}) = 8.29 (\log_{10} (1.54 h_{re}))^2 - 1.1 when f_c \leq 200 MHz, and a(h_{re}) = 3.2 (\log_{10} (11.75 h_{re}))^2 - 4.97 when f_c \geq 400 MHz. This model is valid for frequencies between 150 and 1500 MHz, distances from 1 to 20 km, base station heights of 30 to 200 m, and mobile heights of 1 to 10 m, ensuring applicability to early cellular systems like those operating in the VHF and UHF bands. All terms in the equation yield values in dB, providing a straightforward computational tool for system planning in urban macrocell deployments where the base station overlooks typical building heights.

Suburban Model

The suburban model in the Hata propagation framework adjusts the urban path loss prediction to account for environments with lower building density, such as residential areas featuring scattered houses and reduced clutter compared to dense settings. This correction reflects decreased signal due to fewer obstructions, while maintaining similar height effects as in scenarios. The model is applicable to frequencies from 150 to 1500 MHz, heights of 30 to 200 m, heights of 1 to 10 m, and distances ranging from 1 to 20 km, ensuring avoidance of near-field effects within 1 km. The for suburban areas, L_{p,\text{suburban}}, is derived by subtracting a frequency-dependent correction from the L_{p,\text{urban}}: L_{p,\text{suburban}} (dB) = L_{p,\text{urban}} - 2 \left[ \log_{10} \left( \frac{f_c}{28} \right) \right]^2 - 5.4 where f_c is the in MHz. This formula, originally valid up to 1.5 GHz, has been extended in some applications to 2 GHz while retaining the core structure. The correction term typically reduces predicted by 2 to 7 across common bands, enhancing coverage estimates for semi-urban deployments. This suburban adjustment originates from empirical plots in Okumura's measurements, which highlighted the median differences between and suburban terrains; Hata approximated these disparities to yield the logarithmic correction, emphasizing less loss over rooftops and in suburban contexts. Unlike denser , the suburban variant assumes dominated by ground reflections and sparse multipath, leading to more predictable signal behavior in residential outskirts.

Open Model

The open model within the Hata propagation framework predicts in rural or open environments, specifically targeting flat open fields with minimal obstacles such as sparse . This model adjusts the base prediction to account for the reduced in unobstructed terrains, resulting in lower overall compared to suburban or settings. The formulation relies on empirical data from field measurements, incorporating adjustments for environmental factors like and effects to approximate behavior beyond simple free-space loss. The original model uses the small mobile station correction factor and applies to base station heights of 30-200 m. The path loss for open areas, denoted as L_{p,open}, is expressed relative to the urban path loss L_{p,urban} as follows: L_{p,open} = L_{p,urban} - 4.78 (\log_{10} f_c)^2 + 18.33 \log_{10} f_c - 40.94 where f_c is the carrier frequency in MHz. This equation applies for distances of 1-20 km, though extensions allow validity up to 100 km in open terrains. The model is based on empirical data from field measurements in open areas, providing estimates that account for ground reflections and terrain effects in rural deployments, with path losses lower than those in suburban environments (due to fewer buildings) but significantly higher than ideal free-space conditions, emphasizing the role of terrain and atmospheric influences.

Derivative and Extended Models

COST-231 Hata Model

The COST-231 Hata model represents a key extension of the original Hata model, developed during the 1990s under the European Union-funded COST 231 project (1986–1996) to facilitate predictions for emerging and higher-frequency bands relevant to and early deployments. This semi-empirical model linearly extrapolates parameters from the Hata formulation to address in the 1500–2000 MHz range, focusing on macrocellular environments with antenna heights exceeding surrounding structures. It maintains the core structure of distance-dependent and environmental corrections while updating coefficients for elevated frequencies, enabling more accurate planning for urban and suburban cellular networks. The model's path loss equation is: L_{p,\text{COST}} = 46.3 + 33.9 \log f_c - 13.82 \log h_{te} - a(h_{re}) + (44.9 - 6.55 \log h_{te}) \log d + C_m where f_c is the carrier frequency in MHz, h_{te} is the effective transmitter height in meters (typically 30–200 m), h_{re} is the effective height in meters (1–10 m), d is the transmitter-receiver separation in km (1–20 km), a(h_{re}) is the receiver correction in , and C_m is the environmental correction in . The model applies to line-of-sight and non-line-of-sight scenarios in built-up areas, with validity limited to the specified parameter ranges to ensure reliability in PCS applications. The receiver height correction a(h_{re}) is refined for urban settings: for metropolitan areas (population > 3 million), it is a(h_{re}) = 3.2 (\log (11.75 h_{re}))^2 - 4.97; for smaller cities, it adopts a(h_{re}) = (1.1 \log f_c - 0.7) h_{re} - (1.56 \log f_c - 0.8). The environmental factor C_m is 0 dB for areas (medium-sized /suburban centres) or +3 dB for centres; for suburban environments, the is the urban value minus [2 (\log (f_c / 28))^2 + 5.4] dB, while open/rural areas subtract [4.78 (\log (f_c))^2 - 18.33 \log (f_c) + 40.94] dB from the urban value. These adaptations reflect measured data from cities, prioritizing coverage predictions. Empirical validation of the COST-231 Hata model yields a (RMS) error of approximately 7 dB when compared against field measurements in urban and suburban settings, indicating good overall accuracy for planning though subject to local terrain variations. This error level supports its widespread adoption in standards bodies like for frequency bands up to 2 GHz, with the model's simplicity facilitating rapid computations in propagation tools.

Extended Hata Model

The Extended Hata (eHata) model, developed by the (NTIA) between 2015 and 2017, serves as an empirical propagation prediction tool specifically tailored for the (CBRS) and the 3.5 GHz band. It builds upon earlier empirical approaches by tuning parameters to accommodate frequencies ranging from 1500 MHz to 3000 MHz, enabling accurate estimates in diverse environments. This extension addresses the need for reliable modeling in spectrum sharing scenarios, particularly for protecting incumbent systems while facilitating commercial deployment. The eHata model for urban environments computes median relative to free space using a formulation that incorporates -dependent curves refitted from Okumura's data, with terms such as 97.62 + 3.19 \log f + 4.45 (\log f)^2 for the and corrections, combined with distance-dependent that transitions to a two-slope model beyond a distance. The full and environmental adjustments for clutter categories including urban, suburban, and open areas are detailed in the NTIA , allowing for morphology-specific refinements. It supports heights of 30–200 m and distances from 1 km to 100 km, reflecting contemporary cellular deployments with taller antennas and varied link spans. To handle extrapolations beyond the original Hata model's ranges, the eHata implementation employs for key parameters, ensuring smooth and reliable predictions at extended frequencies and distances. This approach, combined with and reliability factors, enhances applicability to modern scenarios. The model has been validated against U.S.-based measurements, achieving a error of less than 8 , which demonstrates its robustness for practical use in . An open-source C++ is publicly available, facilitating integration into simulation tools and further research by the wireless community.