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Multipath Propagation

Due to signal reflection, refraction, diffraction and dispersion at walls, ground and obstacles at the transmission path a receiver detects multiple duplicates of the original signal. These duplicates which are taking different routes arrive with different phases, delays and amplitudes and are being superimposed at the receiver which results in a frequency-selective fading process. A multipath channel impulse response can be modelled by a series of dirac impulses: $$ h(t) = \sum\limits_k^{} \alpha_k \delta(t-\tau_k)\exp{(-j\phi_k)} $$ where

  • $t$ denotes the time
  • $k$ denotes the path index
  • $\alpha_k$ denotes the path attenuation
  • $\tau_k$ is the path delay
  • $\phi_k$ is the path phase
through fourier transformation one can derive the frequency response with frequency $f$ [2]: $$ H(f)=\sum\limits_k^{} \alpha_k\left[\exp{(-j2\pi f\tau_k)}\exp{(-j\phi_k)}\right] $$

The 802.11n multipath model provides 6 impulse responses with different delay spreads (time difference between the first and last arriving signal portion with significant energy) distinctive to each scenario. These models are based mainly on measurements carried out in buildings in the 2.4 and 5.0 GHz frequency band. Following the work in [5] the duplicates are assumed to be arriving in clusters in time as well as in the angular domain. Each cluster is attributed a random angle of incidence generated from a uniform distributed random variable on [0,2$\pi$). The angle of incidences within each cluster is approximated by a laplacian distribution with variance $\sigma^2$ described by: $$ p(\omega) = \frac{1}{\sqrt{2}\sigma}\exp{(-|\sqrt{2}\omega/\sigma|)} $$ $\sigma$ represents the angular spread of duplicates arriving from one cluster and is derived from observing outdoor channels because they exhibit a high correlation between angular spread and delay spread. Elevation angular spread is not included in the multipath model due to having negligible impact compared to the horizontal spread [3].

Root-mean-square (RMS) delay spreads (DS) for every 802.11b scenario [3]
scenario RMS DS in ns
Flat-fading 0
Typical residential environment 15
Typical residential or small office environment 30
Typical office environment 50
Typical large open space and office environments 100
Large open space (indoor and outdoor) 150