--- title: "Coherence bandwidth/time and indoor propagation factors" subject: "Wireless Communication" chapter: 3 key: "semester_7/wireless_communication:coherence-indoor-propagation-factors" source: https://www.bctengineer.com/q/semester_7/wireless_communication/coherence-indoor-propagation-factors site: BCT Engineering --- # Coherence bandwidth/time and indoor propagation factors Wireless Communication · Chapter 3: Radio Wave Propagation in Mobile Networks - Asked in: 2082 Bhadra, 2+5 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/coherence-indoor-propagation-factors - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3 ## Question Define the terms coherence bandwidth and coherence time. What are the factors that influence indoor propagation model? Explain. ## Short answer Coherence bandwidth Bc is the flat-frequency range inversely related to delay spread; coherence time Tc is the unchanged-channel duration inversely related to Doppler shift. Indoor propagation depends on building layout, construction materials, building type, hard/soft partitions, floor attenuation, antenna placement, doors/windows and moving people. ## Answer #### Coherence bandwidth **Coherence bandwidth (Bc)** is the range of frequencies over which the channel gain is nearly constant, so that two frequency components in this range are strongly correlated. It is inversely related to rms delay spread: Bc ≈ 1/(50στ) for 0.9 correlation and Bc ≈ 1/(5στ) for 0.5 correlation. If signal bandwidth exceeds Bc, the signal suffers frequency-selective fading. #### Coherence time **Coherence time (Tc)** is the time over which the channel impulse response stays essentially unchanged. It is inversely related to maximum Doppler shift: Tc ≈ 9/(16πfm), or Tc ≈ 0.423/fm. If the symbol period exceeds Tc, the signal suffers fast fading. #### Factors influencing indoor propagation Indoor channels differ from outdoor ones: distances are short, path loss varies a lot over small distances, and the environment changes with layout and people. The main factors are: 1. **Building layout:** open-plan offices, corridors and rooms produce very different multipath. Corridors can act as waveguides. 2. **Construction materials:** concrete, brick, metal frames, glass and wood have different reflection and penetration losses. Metal-coated glass gives high loss. 3. **Building type:** offices, factories, homes, stores and stadiums have different clutter and ceiling heights, so the path loss exponent varies (about 1.6–1.8 for LOS in buildings, 4–6 when obstructed). 4. **Partition losses (same floor):** *hard partitions* (fixed walls) and *soft partitions* (movable panels, furniture) add loss per wall, e.g. a concrete wall can add 10–15 dB. 5. **Partition losses between floors (Floor Attenuation Factor):** loss depends on floor material, number of floors and reinforcement; the first floor gives the largest loss (often 10–20 dB), with less extra loss for each added floor. 6. **Antenna location and height:** whether the antenna is near the ceiling, in a corridor or outside affects coverage. 7. **Doors and windows, open or closed**, and movement of people, which change the multipath with time. A common indoor model is the log-distance model with partition terms: ```text PL(d) = PL(d0) + 10n log(d/d0) + Σ FAF + Σ PAF + Xσ ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Coherence bandwidth for 0.9 correlation is approximately: A. 1/(50 sigma) B. 50/sigma C. 1/(5 sigma) D. sigma/50 Answer: A. Bc = 1/(50 sigma_tau); 1/(5 sigma_tau) is for 0.5. (Key point: Bc rule) 2. A common coherence time rule is: A. Tc = 0.423/fm B. Tc = 4.23 fm C. Tc = 1/sigma D. Tc = fm Answer: A. Tc ~ 0.423/fm. (Key point: Tc rule) 3. Which statement about floor attenuation is right? A. Loss decreases for first floor B. Each floor adds equal loss C. Floors add no loss D. First floor gives the largest loss, with less extra for each additional floor Answer: D. Floor attenuation factor depends on material and number of floors. (Key point: Floor attenuation) 4. Which is a factor influencing indoor propagation? A. Building layout and construction materials B. Sunspot cycle C. Earth curvature D. Ionospheric layers Answer: A. Layout, materials, partitions, antenna placement, and people movement all matter. (Key point: Indoor factors) 5. The indoor log-distance model adds: A. Nothing B. Doppler terms C. FAF and PAF terms for floors and partitions D. Hata terms Answer: C. PL(d) = PL(d0) + 10n log(d/d0) + sum FAF + sum PAF + X. (Key point: Indoor model) ## Related in Wireless Communication - [Significance of coherence bandwidth and time](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acoherence-bandwidth-time-significance) — Wireless Communication, chapter 3, asked 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× - [Coherence bandwidth and delay spread relation](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afrequency-selective-coherence-delay) — Wireless Communication, chapter 3 - [Doppler spread, coherence bandwidth, fading classes](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adoppler-coherence-fading-classification) — Wireless Communication, chapter 3 - [Indoor propagation models (any two)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aindoor-propagation-models) — Wireless Communication, chapter 3 - [Short note: Doppler spread and coherence time](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adoppler-spread-coherence-time-note) — Wireless Communication, chapter 3 ## Related in other subjects - [Noise equivalent bandwidth; matched filter is time reversed](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aneb-matched-filter-reverse) — Communication Systems, chapter 9 - [Fuse vs MCB; HRC fuse time terms](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Afuse-vs-mcb-hrc-terms) — Switchgear and Protection, chapter 3 - [Embedded real-time software; model for project](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Aembedded-rt-software-model) — Instrumentation II, chapter 9 - [Model time scale, prototype day and moon](https://www.bctengineer.com/question.md?key=semester_3%2Ffluid_mechanics%3Amodel-time-scale-moon-gravity) — Fluid Mechanics, chapter 10