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Coherence bandwidth/time and indoor propagation factors

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.

Define the terms coherence bandwidth and coherence time. What are the factors that influence indoor propagation model? Explain.

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:

PL(d) = PL(d0) + 10n log(d/d0) + Σ FAF + Σ PAF + Xσ

✓ Answer checked by Claude Opus 5.5 (high effort)

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