--- title: "Large scale path loss and small scale fading" subject: "Wireless Communication" chapter: 3 key: "semester_7/wireless_communication:large-scale-loss-small-fading" source: https://www.bctengineer.com/q/semester_7/wireless_communication/large-scale-loss-small-fading site: BCT Engineering --- # Large scale path loss and small scale fading Wireless Communication · Chapter 3: Radio Wave Propagation in Mobile Networks - Asked in: 2072 Magh, 8 marks - Video: [Channel Models in Wireless Communication](https://www.youtube.com/watch?v=2yUZFxz5gts) — Wireless Explained - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/large-scale-loss-small-fading - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3 ## Question Explain the mobile radio propagation in terms of large scale path loss and small scale fading. ## Short answer Large-scale path loss gives the mean power over hundreds of metres, following a log-distance law with log-normal shadowing. Small-scale fading is the rapid amplitude and phase fluctuation over a few wavelengths, caused by multipath and Doppler. Their combination gives the total received signal variation. ## Answer Mobile radio propagation is described by two effects that act on very different distance scales: **large-scale path loss** (including shadowing) and **small-scale fading**. The received signal is their combination. ```text Pr (dBm) |\ /\/\ small-scale fading (fast ripples) | \/ \/\/\ | ---- \/\/\/\ local mean (shadowing) | ---- \/\/\/\ | - - - - - - - - - - mean path loss ~ 10n log d +----------------------------- log d ``` #### Large-scale path loss - Describes the **mean received power** averaged over 5λ–40λ, as a function of T–R distance. It changes slowly over hundreds of metres. - **Distance-dependent loss:** Pr ∝ 1/dⁿ; n = 2 in free space (Friis), 4 for two-ray at large d, 2.7–5 in urban areas. ```text PL(d) = PL(d0) + 10n log(d/d0) + Xσ ``` - **Shadowing (log-normal fading):** obstacles such as hills and buildings make the local mean vary randomly about the distance trend. Xσ is a zero-mean Gaussian in dB, with σ about 6–12 dB. - Models: free space, two-ray, log-distance, Okumura, Hata, and indoor partition models. - Used for coverage area, cell size, link budget and interference planning. #### Small-scale fading - Rapid change of amplitude and phase over a few wavelengths (fractions of a second), caused by **multipath** waves adding constructively and destructively. Signal may vary by 30–40 dB within half a wavelength. - Effects: rapid amplitude changes, random frequency modulation (Doppler) and time dispersion (echoes, ISI). - Factors: multipath, speed of the mobile, speed of surrounding objects, and signal bandwidth. - Types: flat or frequency selective (by delay spread στ vs Ts), fast or slow (by coherence time Tc vs Ts). - Statistics: **Rayleigh** envelope when there is no LOS path, **Ricean** when a strong LOS exists. - Countered by diversity, equalization, interleaving and coding. | Aspect | Large-scale path loss | Small-scale fading | |---|---|---| | Scale | 100s–1000s of m | ~λ/2 | | Cause | Distance, shadowing | Multipath, Doppler | | Distribution | Log-normal | Rayleigh / Ricean | | Design use | Coverage, cell planning | Receiver/modem design | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In PL(d) = PL(d0) + 10n log(d/d0) + X_sigma, what does X_sigma represent? A. Zero-mean Gaussian (in dB) shadowing about the distance trend B. Doppler shift in Hz C. Rayleigh fading envelope D. Antenna gain Answer: A. X_sigma is a zero-mean Gaussian random variable in dB with sigma about 6-12 dB, modelling log-normal shadowing. (Key point: Log-distance model) 2. Which set of path loss exponents n is correct? A. n = 4 in free space, 2 in two-ray B. n = 2 in free space, 4 for two-ray at large d C. n = 1 in free space, 2 for two-ray D. n = 2 everywhere Answer: B. Free space has n = 2 (Friis); the two-ray model at large distance gives n = 4; urban areas 2.7-5. (Key point: Path loss exponent) 3. Why can the signal vary by 30-40 dB within half a wavelength? A. The mobile leaves the cell B. Multipath waves add constructively and destructively C. Shadowing by hills D. The path loss exponent changes Answer: B. Small-scale fading arises from the vector sum of multipath waves with varying phases. (Key point: Cause of small-scale fading) 4. Which pairing of conditions and distributions is correct for small-scale fading envelope? A. Rayleigh with strong LOS, Ricean with no LOS B. Log-normal for both C. Rayleigh with no LOS, Ricean with a strong LOS path D. Gaussian with no LOS, Rayleigh with LOS Answer: C. Rayleigh models no-LOS multipath; Ricean applies when a strong dominant LOS component exists. (Key point: Envelope statistics) ## Related in Wireless Communication - [Large vs small scale models; propagation mechanisms](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Alarge-small-scale-propagation) — Wireless Communication, chapter 3 - [Small scale fading types and factors](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Asmall-scale-fading-types-factors) — Wireless Communication, chapter 3, asked 2× - [Small scale fading and influencing factors](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Asmall-scale-fading-factors) — Wireless Communication, chapter 3 - [Path loss vs fading; time dispersion fading](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Apath-loss-vs-fading-time-dispersion) — Wireless Communication, chapter 3 - [Doppler effect; cordless phone path loss](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adoppler-effect-cordless-phone) — Wireless Communication, chapter 3, asked 2× - [Path loss and multipath channel parameters](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Apath-loss-multipath-parameters) — Wireless Communication, chapter 3 ## Related in other subjects - [Path loss in radio wave propagation](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Apath-loss-derivation) — Propagation and Antenna, chapter 5, asked 2× - [Steps to establish small scale unit](https://www.bctengineer.com/question.md?key=semester_7%2Forganization_and_management%3Aentrepreneurship-small-scale-steps) — Organization and Management, chapter 8 - [Friis equation and free space path loss](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afriis-path-loss-free-space) — Propagation and Antenna, chapter 5, asked 2× - [Friis, path loss and LOS distance](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afriis-path-loss-los-distance) — Propagation and Antenna, chapter 5