| Rayleigh Fading (NLOS) | PDF: f(r) = (r/σ²)·exp(-r²/2σ²)
K-factor = 0 (no LOS) | Amplitude distribution when no dominant LOS component. Multiple reflections with similar power combine randomly. Envelope follows Rayleigh distribution. | NLOS indoor environments. Average of K=0 in TGn model A/B/C/E/F. Worst-case fading depth = -20 to -40 dB below mean. Affects cell-edge STAs most. | Proakis 5th Ed. Ch.14
IEEE 802.11 TGn |
| Rician Fading (LOS) | PDF: f(r) = (r/σ²)·exp(-(r²+A²)/2σ²)·I₀(Ar/σ²)
K = A²/2σ² (K-factor) | Amplitude distribution with dominant LOS component (amplitude A) plus scattered components (variance σ²). K-factor = ratio of LOS power to scatter power. | LOS in offices (TGn Model D: K=3 dB). Higher K = less fading = more reliable link. K→∞ = no fading (pure LOS). K=0 = Rayleigh. | Proakis 5th Ed. Ch.14
IEEE 802.11 TGax eval |
| Coherence Bandwidth | Bc ≈ 1/(5·στ)
(90% coherence)
Bc ≈ 1/(2π·στ)
(50% coherence) | Frequency range over which channel response is approximately constant (correlated). Above Bc: channel varies across frequency = frequency-selective fading. | OFDM subcarrier spacing must be << Bc for flat fading per subcarrier.
802.11ax: 78.125 kHz spacing. Indoor office στ=30-50 ns → Bc=4-6 MHz >> 78.125 kHz ✓
Outdoor στ=100-300 ns → Bc=0.6-2 MHz >> 78.125 kHz ✓ | ITU-R M.2135
Proakis Ch.14 |
| Coherence Time | Tc = 0.423/fD
where fD = v·fc/c (Doppler)
Example: v=3 km/h, fc=5 GHz:
fD = 0.83 Hz×5GHz/c ≈ 13.9 Hz
Tc ≈ 30 ms | Time over which channel impulse response is approximately constant. Above Tc: channel changes during packet = time-selective fading. | 802.11ax symbol = 16 µs. At walking speed (3 km/h), Tc ≈ 30 ms >> 16 µs → channel stable per symbol ✓
At vehicle speed (100 km/h): Tc ≈ 0.9 ms - channel may change during 64-symbol PPDU. 802.11bd (V2X) must handle this. | ITU-R M.2135
Proakis Ch.14 |
| Doppler Spread | fD_max = v·fc/c
ICI threshold: Δf << 1/Tc | Maximum frequency shift due to motion. Creates ICI (Inter-Carrier Interference) in OFDM when subcarrier spacing is comparable to Doppler spread. | 802.11ax: Δf = 78.125 kHz. fD at 100 km/h @ 5 GHz = 463 Hz. ICI ratio = 463/78125 = 0.006 = negligible.
802.11ah (sub-1 GHz): Δf = 31.25 kHz. Even lower Doppler spread due to lower fc. | IEEE 802.11ax D8.0 §27.3
ETSI TR 103 594 |
| RMS Delay Spread (στ) | στ = √(Σ(τk²·Pk)/ΣPk - (Στk·Pk/ΣPk)²)
where Pk = power of path k, τk = delay | Root Mean Square of the power-weighted delay of all multipath components. Key parameter for OFDM guard interval design. | CP must be ≥ στ to prevent ISI. 802.11ax CP options: 0.8/1.6/3.2 µs:
• 0.8 µs: indoor office (στ < 100 ns) ✓
• 1.6 µs: large office/warehouse ✓
• 3.2 µs: outdoor/stadium (στ < 500 ns) ✓ | IEEE 802.11 TGn channel models
ITU-R P.1238 |
| Fresnel Zone Clearance | r₁ = √(λd₁d₂/d)
60% clearance needed to avoid diffraction loss
Example: 802.11ac at 5 GHz, d=100m:
r₁ = √(0.06×50×50/100) = 1.7m | Ellipsoidal region around LOS path where reflected waves can constructively/destructively interfere. Obstruction of 1st Fresnel zone → significant diffraction loss. | Critical for outdoor point-to-point Wi-Fi links. 5 GHz at 100m needs 1.7m clearance above obstacles. At 2.4 GHz: 2.5m clearance. Taller obstacles or longer links = larger Fresnel zone. | ITU-R P.530
IEEE 802.11 outdoor deployment guides |
| Two-Ray Ground Reflection | PL = 40log(d) - 20log(hT) - 20log(hR)
Breakpoint: d_bp = 4·hT·hR/λ | Beyond breakpoint, both direct and ground-reflected rays combine. PL exponent increases from 2 to 4. Destructive interference at breakpoint. | Outdoor Wi-Fi: flat ground, AP at 3m, client at 1.5m, 5 GHz → d_bp = 4×3×1.5/0.06 = 300m. Beyond 300m: n=4. Important for outdoor campus/park coverage planning. | ITU-R P.1411
IEEE 802.11ah (long-range) |
| MIMO Channel Rank | H = U·Σ·V†
Rank = number of non-zero singular values
Capacity = Σ log₂(1 + λᵢ·SNR/Nt) | MIMO channel matrix H (Nr×Nt). SVD decomposition reveals independent spatial channels (eigenmodes). Rank = number of useful streams. | Rank < min(Nt,Nr) if paths are highly correlated (few independent scatterers). Corridor LOS: rank often = 1 (no MIMO gain). Rich scattering NLOS: rank ≈ min(Nt,Nr). Use cross-pol antennas + scattering to improve rank. | Foschini & Gans 1998
Telatar 1999
IEEE 802.11 TGn |
| PAPR of OFDM | PAPR = max|s(t)|² / E[|s(t)|²]
Theoretical max: 10·log₁₀(N) dB
802.11ax 20 MHz: 10·log₁₀(256) = 24 dB
Typical after clipping: 8-13 dB | Peak-to-Average Power Ratio. OFDM has high PAPR because N subcarriers can add constructively at peak. Power amplifier must handle peak without saturation (clipping = distortion = EVM degradation). | 6 dB IBO (Input Back-Off) typical. Limits effective TX power. DPD (Digital Pre-Distortion) reduces required IBO to 3 dB. Higher-order QAM (4096-QAM) more sensitive to PAPR clipping. | IEEE 802.11-2020 §27.3.14
ETSI EN 301 893 §4.2.3 |