Chapter Summary

Chapter 5 Summary: Large-Scale Propagation

Key Points

• 1.

  Electromagnetic Propagation Fundamentals. Radio waves propagate via reflection, diffraction, and scattering. The Friis transmission equation gives received power in free space as $P_r = P_t G_t G_r (\lambda / 4\pi d)^2$, establishing the inverse-square law baseline for all path-loss models.

• 2.

  Reflection, Diffraction, and Scattering. Fresnel coefficients govern reflection amplitude and phase for TE and TM polarisations. Knife-edge diffraction (Fresnel parameter $\nu$) predicts loss behind obstacles. These mechanisms explain how signals reach receivers even without line-of-sight.

• 3.

  Path-Loss Models. The two-ray model predicts a transition from $d^{-2}$ to $d^{-4}$ decay beyond the breakpoint distance $d_c = 4 h_t h_r / \lambda$. The log-distance model $PL(d) = PL(d_0) + 10n\log_{10}(d/d_0)$ captures environment-specific decay through the path-loss exponent $n$.

• 4.

  Empirical and Standardised Models. The Okumura--Hata model (150--1500 MHz) and its COST-231 extension (up to 2000 MHz) remain workhorses for macro-cell planning. 3GPP TR 38.901 models cover up to 100 GHz for 5G system-level simulations. Every model has a defined validity range that must be respected.

• 5.

  Shadowing and Coverage. Shadow fading adds a log-normal random variable $X_\sigma \sim \mathcal{N}(0, \sigma^2)$ (dB) to the mean path loss. Outage probability is $P_{\text{out}} = Q((\overline{P_r} - P_{\min})/\sigma)$. The fade margin $= Q^{-1}(1 - p/100) \cdot \sigma$ ensures the desired coverage percentage.

• 6.

  Ray Tracing and Site-Specific Models. Ray tracing provides deterministic, site-specific channel predictions (power, delay spread, angle of arrival) using 3D geometry. It is essential for mmWave planning and digital-twin network optimisation, though it requires detailed environment data and significant computation.