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Algorithm of ITU-R P.526 and multi-edge peak diffraction analysis
Foreword
When an electromagnetic wave encounters an obstacle that is comparable in size to its wavelength during propagation, it bends around the obstacle and continues forward. This phenomenon is known as diffraction. In the TV and FM broadcasting frequency bands (30 MHz to 1000 MHz), where wavelengths range from meters to tens of meters, radio waves are highly susceptible to diffraction due to complex terrain features.
Traditional radio wave propagation prediction models such as ITU-R P.370 and ITU-R P.1546 are more suitable for open or low-lying hilly areas, but they tend to have significant errors in mountainous regions. To address this, the International Telecommunication Union (ITU) developed Recommendation ITU-R P.526, "Propagation by Diffraction," in 1978. This recommendation focuses on diffraction effects in signal propagation and provides methods for predicting field strength, while also considering terrain ruggedness. It includes diffraction effects caused by both the Earth’s curvature and natural obstacles. However, ITU-R P.526 only offers specific algorithms for single-edge, double-edge, and single-rounded peaks, without a general solution for complex terrains. This paper explores the calculation and practical application of ITU-R P.526 in multi-edge peak diffraction scenarios, using the Bullington and Epstein-Peterson methods.
Algorithm for ITU-R P.526
When dealing with a single complex-shaped obstacle, an exact analytical solution is difficult to achieve. However, for two specific shapes—knife-edge and cylindrical obstacles—a complete analytical solution can be derived. A knife-edge, which has negligible thickness, is shown in Figures 1 and 2, while a smooth cylindrical obstacle is illustrated in Figure 3.
In the case of a single-edge peak, only one obstacle on the propagation path causes signal loss. The effect of the obstacle can be calculated using the following formulas:
$$
\text{Loss} = \frac{2}{\pi} \int_{0}^{\infty} \frac{\sin(\theta)}{\theta} d\theta
$$
The parameters involved in these formulas are explained in Figures 1 and 2.
For a single circular peak, a correction factor is applied during loss calculations. This factor is given by:
$$
T(m,n) = k m b^3
$$
Where $k = 8.2 + 12.0n$ and $b = 0.73 + 0.27[1 - \exp(-1.43n)]$. The formula parameters are detailed in Figure 3.
Multimodal Diffraction
The simplest form of multi-peak diffraction is double-edge diffraction. While the Fresnel integral approach can be used, it involves heavy computation. The Bullington and Epstein-Peterson methods offer more efficient solutions through equivalent modeling.
In the Bullington method (see Figure 4), obstacles at points A, B, and C are replaced by an equivalent knife-edge at point D, where the influence of A and B becomes negligible.
In the Epstein-Peterson method (see Figure 5), segments a-b-h’1 and b-c-h’2 each represent a single-edge scenario. First, the diffraction loss L1 between a, b, and h’1 is calculated, followed by L2 between b, c, and h’2. A correction factor LC is then added:
$$
L_c = 10 \log_{10}(1 + 10^{(L_1 + L_2)/10})
$$
The total diffraction loss is:
$$
L = L_1 + L_2 + L_c
$$
In mountainous area propagation predictions, multiple obstacles often exist along the path. These must be simplified into either single or double-edge scenarios to calculate diffraction loss. The Bullington method allows sequential simplification of multiple edges into a single equivalent edge, while the Epstein-Peterson method can also be used. However, when the distance between obstacles is small, the Epstein-Peterson method may introduce larger errors. Therefore, it is important to limit the number of blade peaks considered and focus on those with the greatest impact on diffraction.
Practical Application
In the broadcasting industry, radio propagation models based on field strength predictions, primarily for television and FM radio, have historically relied on ITU-R P.370. Developed in 1951, this model provided VHF and UHF propagation curves for frequencies between 30 MHz and 1000 MHz. In 2001, ITU introduced the updated ITU-R P.1546, offering improved accuracy and broader applicability. Despite this, China's national standard still uses ITU-R P.370 for broadcast field strength predictions.
Although ITU-R P.1546 improves upon ITU-R P.370 in terms of accuracy and coverage, neither model accounts for diffraction effects caused by obstacles. As a result, in mountainous regions where diffraction plays a major role, the error rates in these models increase significantly. A typical example is the border region between Guangdong and Hong Kong.
To improve the accuracy of radio wave propagation predictions, researchers aim to find accurate analytical solutions to diffraction problems and also use real-world data to develop generalized propagation curves. These efforts are reflected in ITU-R P.526.
In practice, applying ITU-R P.526 for multi-edge diffraction requires integrating electronic maps to fully utilize its predictive capabilities. Extracting geographic parameters from these maps is a highly specialized task, involving the analysis of the first Fresnel zone, identification of blade peaks, and their equivalence. Real-world applications, such as frequency planning in the Guangdong-Hong Kong border area, show that ITU-R P.526 provides results closer to measured values when predicting radio wave propagation in complex mountainous regions.
It should be noted that when applying ITU-R P.526 in TV and FM broadcasting bands (30 MHz to 1000 MHz), the primary obstacles considered are natural terrain features like mountains and hills. The impact of tall buildings is generally not included. How to apply ITU-R P.526 to calculate diffraction effects from tall structures remains an ongoing area of research among industry experts.