--- title: "Path loss vs fading; time dispersion fading" subject: "Wireless Communication" chapter: 3 key: "semester_7/wireless_communication:path-loss-vs-fading-time-dispersion" source: https://www.bctengineer.com/q/semester_7/wireless_communication/path-loss-vs-fading-time-dispersion site: BCT Engineering --- # Path loss vs fading; time dispersion fading Wireless Communication · Chapter 3: Radio Wave Propagation in Mobile Networks - Asked in: 2071 Bhadra, 2+6 marks - Video: [Fading in Wireless Communication Channels | Simplified | Antenna and Wave Propagation Module 6 |](https://www.youtube.com/watch?v=nIata4K7egE) — THE BACKBENCH ENGINEERING COMMUNITY - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/path-loss-vs-fading-time-dispersion - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3 ## Question What is the difference between path loss and fading of signal? Explain time dispersion fading and its types. ## Short answer Path loss is the average power reduction with distance, while fading is the rapid random fluctuation around that average. Time dispersion spreads the received pulse and is described by delay spread and coherence bandwidth. Its types are flat fading, where all frequencies fade together, and frequency selective fading, which causes intersymbol interference. ## Answer #### Path loss vs fading **Path loss** is the average drop in signal power as the distance from the transmitter grows. **Fading** is the quick change of the received signal around that average, caused by multipath and motion. | Point | Path loss | Fading | |---|---|---| | Cause | Spreading of wave with distance, terrain | Multipath interference, Doppler | | Scale | Large scale (hundreds of metres to km) | Small scale (a few λ, short time) | | Nature | Slow, predictable, mean value | Rapid, random fluctuation | | Models | Free space, log-distance, Okumura, Hata | Rayleigh, Rician, delay/Doppler models | | Counter-measure | Power control, cell planning | Diversity, equalization, coding | #### Time dispersion fading **Time dispersion** happens because multipath copies of a symbol arrive at different delays, so the received pulse is spread out in time. It is described by the **rms delay spread** σ_τ in time, or the **coherence bandwidth** B_c ≈ 1/(5σ_τ) in frequency. Depending on how the signal compares with these, there are two types. **1. Flat fading** - Condition: B_s ≪ B_c and T_s ≫ σ_τ. - The channel has constant gain and linear phase over the full signal bandwidth, so all spectral parts of the signal fade together. - The shape of the spectrum is kept but the received amplitude goes up and down (deep fades). Little or no ISI. - Amplitude usually follows a Rayleigh distribution. Called a narrowband channel. - Example: AMPS 30 kHz channel in a typical urban area. **2. Frequency selective fading** - Condition: B_s > B_c and T_s < σ_τ (a common rule is T_s < 10σ_τ). - Different frequency components of the signal get different gains and phases. - Received signal contains several delayed, attenuated versions of the symbol, so the pulse is spread in time and causes **inter-symbol interference (ISI)**. - Called a wideband channel; needs equalizers, RAKE receivers or OFDM. ```text Flat fading Freq. selective fading |H(f)| |H(f)| |~~~~~~~~~~~~~ | /\ /\ /\ | [signal] |/ \/\/ [signal]\ +------------- f +------------------ f B_s << B_c B_s > B_c ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which statement distinguishes path loss from fading? A. Path loss is rapid and random, fading is slow B. Path loss is the slow mean drop with distance, fading is rapid fluctuation about it C. Both have the same scale D. Fading is only caused by distance Answer: B. Path loss is large-scale and predictable; fading is small-scale and caused by multipath and Doppler. (Key point: Path loss vs fading) 2. Which condition describes flat fading? A. B_s > B_c and T_s < sigma_tau B. B_s << B_c and T_s >> sigma_tau C. B_s >> B_D D. T_s < sigma_tau Answer: B. Flat fading needs signal bandwidth well below coherence bandwidth and symbol period much longer than rms delay spread. (Key point: Flat fading condition) 3. Why does frequency selective fading cause ISI? A. Doppler shift is large B. Delayed copies of a symbol spread the pulse in time C. All frequencies fade equally D. Amplitude is Rayleigh Answer: B. With B_s > B_c, delayed attenuated versions overlap into neighbouring symbols, causing ISI. (Key point: ISI in frequency selective fading) 4. The coherence bandwidth in the 50% case is approximately: A. 1/(50 sigma_tau) B. 5 sigma_tau C. 1/(5 sigma_tau) D. sigma_tau Answer: C. B_c is inversely related to rms delay spread: about 1/(5 sigma_tau) for 0.5 correlation. (Key point: Coherence bandwidth) ## Related in Wireless Communication - [Large scale path loss and small scale fading](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Alarge-scale-loss-small-fading) — Wireless Communication, chapter 3 - [Numerical: two-ray vs free-space path loss at 800 MHz](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Atwo-ray-path-loss-800mhz) — 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 - [Coherence bandwidth/time and types of fading](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acoherence-significance-fading-types) — Wireless Communication, chapter 3, asked 3× - [Two-ray model path and phase difference](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Atwo-ray-path-phase-difference) — Wireless Communication, chapter 3, asked 2× ## Related in other subjects - [Central tendency vs dispersion; mode 58](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Acentral-tendency-vs-dispersion-mode-58) — Probability and Statistics, chapter 1 - [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× - [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× - [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