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The Wireless Channel. Lecture 3. Area 1. Area 2. Short- term fading. Log-normal shadowing. Transmitter. Large and Small Scale Propagation Models. Wireless Mulipath Channel. Channel varies at two spatial scales: large scale fading small scale fading. Large-scale fading.

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large and small scale propagation models

Area 1

Area 2






Large and Small Scale Propagation Models
wireless mulipath channel
Wireless Mulipath Channel

Channel varies at two spatial scales:

large scale fading

small scale fading

large scale fading
Large-scale fading
  • In free space, received power attenuates like 1/r2.
  • With reflections and obstructions, can attenuate even more rapidly with distance. Detailed modelling complicated.
  • Time constants associated with variations are very long as the mobile moves, many seconds or minutes.
  • More important for cell site planning, less for communication system design.
small scale multipath fading
Small-scale multipath fading
  • Wireless communication typically happens at very high carrier frequency. (eg. fc = 900 MHz or 1.9 GHz for cellular)
  • Multipath fading due to constructive and destructive interference of the transmitted waves.
  • Channel varies when mobile moves a distance of the order of the carrier wavelength. This is 0.3 m for Ghz cellular.
  • For vehicular speeds, this translates to channel variation of the order of 100 Hz.
  • We wish to understand how physical parameters such as carrier frequency, mobile speed, bandwidth, delay spread impact how a wireless channel behaves from the communication system point of view.
  • We start with deterministic physical model and progress towards statistical models, which are more useful for design and performance evaluation.
physical models
Physical Models
  • Wireless channels can be modeled as linear time-varying systems:

where ai(t) and i(t) are the gain and delay of path i.

  • The time-varying impulse response is:
  • Consider first the special case when the channel is time-invariant:
impulse r response c characterization

Time variations property





Time spreading property



Impulse Rresponse Ccharacterization
  • Impulse response: Time-spreading : multipath
  • and time-variations: time-varying environment
passband to baseband conversion
Passband to Baseband Conversion
  • Communication takes place at [fc-W/2, fc+ W/2].
  • Processing takes place at baseband [-W/2,W/2].
baseband equivalent channel
Baseband Equivalent Channel
  • The frequency response of the system
  • Each path is associated with a delay and a complex gain.
multipath propagation
Multipath propagation

Signal can take many different paths between sender and receiver

due to reflection, scattering, diffraction

  • Time dispersion: signal is dispersed over time
  • interference with “neighbor” symbols Inter Symbol Interference (ISI)
  • The signal reaches a receiver directly and phase shifted
  • distorted signal depending on the phases of the different parts
the effects of multipath propagation
The Effects of Multipath Propagation

• Due to the different paths taken by the multipath components, they may arrive at different times

• If the symbol period TS is smaller than the delay spread, i.e. TS< Tm, Inter-Symbol Interference (ISI) will occur

• The receiver cannot determine which symbol each multipath component belongs to:

delay spread
Delay Spread

The Delay Spread Tm is defined as the difference between times-of arrival

of the first and last multipath components Typical values are as follows:

coherence bandwidth
Coherence Bandwidth
  • The Coherence Bandwidth Bcis a statistical measure of the range of frequencies over which the attenuation of the channel is approximately constant
  • Two frequency components f1 and f2 will experience similar attenuation if (f1 – f2) << Bc
  • Coherence Bandwidth is approximately related to the Delay Spread by:
  • Bc(Hz) = 1/Tm
  • e.g. in a particular factory environment,
  • Tm= 120ns, Bc= 1/(120 x 10-9) = 8.33 MHz
coherence bandwidth 2
Coherence Bandwidth (2)
  • If the transmitted signal has a bandwidth (Bu) much smaller than the Coherence Bandwidth(Bc), i.e. Bu<< Bc, all frequency components will be attenuated similarly.
  • This is called Flat Fading
  • Else, it will undergo Frequency-selective fading, with different components attenuated differently. This causes distortion of the signal
channel classification
Channel Classification

Based on Time-Spreading

  • Flat Fading
  • BS < BCTm < Ts
  • Rayleigh, Ricean distrib.
  • Spectral chara. of transmitted
  • signal preserved
  • Frequency Selective
  • BS > BC Tm > Ts
  • Intersymbol Interference
  • Spectral chara. of transmitted
    • signal not preserved
  • Multipath components resolved











channel classification1
Channel Classification

Based on Time-Variations











statistical models1
Statistical Models
  • Design and performance analysis based on statistical ensemble of channels rather than specific physical channel.
  • Recall that:
additive gaussian noise
Additive Gaussian Noise
  • The discrete-time baseband-equivalent model
rayleigh model
Rayleigh Model
  • Rayleigh flat fading model: many small scattered paths

Complex circular symmetric Gaussian .

  • Rayleigh PDF:
rician model
Rician Model
  • Used when LOS or other dominant non fading path exist.
  • Characterized by Rician factor K that compare signal power of the non-fading path to variance of multipath.
nakagami model
Nakagami model
  • More practical model

Rayleigh fading

Rician fading

No fading, Constant power

inter symbol interference isi
Inter-symbol Interference (ISI)
  • Time domain: dispersion (delay spread Tm)
  • Frequency domain: non-flat response in the band of interest
  • One-tap filter: flat frequency response
  • Multi-tap filter: frequency selective response
  • When symbol time T >> Tm, no ISI (narrowband or low rate)
  • For higher rate, T comparable to Tm , we need to deal with ISI
  • Equalization, OFDM, CDMA with RAKE