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7. Channel Models. 2. Medium Scale Fading : due to shadowing and obstacles. 3. Small Scale Fading : due to multipath. 1. Large Scale Fading : due to distance. Signal Losses due to three Effects:. Wireless Channel.

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7. Channel Models

2. Medium Scale Fading: due to shadowing and obstacles

3. Small Scale Fading: due to multipath

1. Large Scale Fading: due to distance

Signal Losses due to three Effects:

Wireless Channel

Frequencies of Interest: in the UHF (.3GHz – 3GHz) and SHF (3GHz – 30 GHz) bands;

  • Several Effects:

  • Path Loss due to dissipation of energy: it depends on distance only

  • Shadowing due to obstacles such as buildings, trees, walls. Is caused by absorption, reflection, scattering …

  • Self-Interference due to Multipath.

1.1. Large Scale Fading: Free Space

Path Loss due to Free Space Propagation:

For isotropic antennas:

Transmit antenna

Receive antenna


Path Loss in dB:

2. Medium Scale Fading: Losses due to Buildings, Trees, Hills, Walls …

The Power Loss in dB is random:

expected value

random, zero mean

approximately gaussian with

Values for Exponent : Hills, Walls …

Free Space 2

Urban 2.7-3.5

Indoors (LOS) 1.6-1.8

Indoors(NLOS) 4-6

Average Loss

Free space loss at reference distance


  • Reference distance

  • indoor 1-10m

  • outdoor 10-100m

Path loss exponent

Empirical Models for Propagation Losses to Environment Hills, Walls …

  • Okumura: urban macrocells 1-100km, frequencies 0.15-1.5GHz, BS antenna 30-100m high;

  • Hata: similar to Okumura, but simplified

  • COST 231: Hata model extended by European study to 2GHz

3. Small Scale Fading due to Multipath Hills, Walls ….

a. Spreading in Time: different paths have different lengths;




Example for 100m path difference we have a time delay

Typical values channel time spread: Hills, Walls …


b. Spreading in Frequency Hills, Walls …: motion causes frequency shift (Doppler)





for each path

Doppler Shift

Frequency (Hz)

Put everything together Hills, Walls …





Re{.} Hills, Walls …




Each path has …

…shift in time …

… attenuation…


…shift in frequency …

(this causes small scale time variations)

2.1 Statistical Models of Fading Channels Hills, Walls …

Several Reflectors:


average time delay Hills, Walls …

  • each time delay

  • each doppler shift

For each path with NO Line Of Sight (NOLOS):

Some mathematical manipulation … Hills, Walls …

Assume: bandwidth of signal <<

… leading to this:


random, time varying

Statistical Model for the time varying coefficients Hills, Walls …


By the CLT is gaussian, zero mean, with:

with the Doppler frequency shift.

Each coefficient is complex, gaussian, WSS with autocorrelation

and PSD

with maximum Doppler frequency.

This is called Jakes spectrum.

Bottom Line. This: autocorrelation




… can be modeled as:




For each path autocorrelation

  • unit power

  • time varying (from autocorrelation)

  • time invariant

  • from power distribution

Parameters for a Multipath Channel (No Line of Sight): autocorrelation

Time delays:



Power Attenuations:


Doppler Shift:

Summary of Channel Model:

WSS with Jakes PSD

Time delays

Power distribution

Maximum Doppler

2. Ricean (Line of Sight)

Same as Rayleigh, plus Ricean Factor

Power through LOS

Power through NOLOS

Simulink Example Channels

M-QAM Modulation

Rayleigh Fading Channel Parameters

Bit Rate

Set Numerical Values: Channels





carrier freq.

Recall the Doppler Frequency:

Easy to show that:

Channel Parameterization Channels

  • Time Spread and Frequency Coherence Bandwidth

  • Flat Fading vs Frequency Selective Fading

  • Doppler Frequency Spread and Time Coherence

  • Slow Fading vs Fast Fading

1. Time Spread and Frequency Coherence Bandwidth Channels


Try a number ofexperiments transmitting a narrow pulse at different random times

We obtain a number of received pulses

Received Power Channels


Take theaverage received powerat time

More realistically:

This defines the Coherence Bandwidth. Channels

Take a complex exponential signal with frequency . The response of the channel is:



i.e. the attenuation is not frequency dependent

Define the Frequency Coherence Bandwidth as

This means that the frequency response of the channel is “flat” within the coherence bandwidth:

Channel “Flat” up to the Coherence Bandwidth


Coherence Bandwidth

Flat Fading

Just attenuation, no distortion


Signal Bandwidth

Frequency Coherence


Frequency Selective Fading


Example: Flat Fading “flat” within the coherence bandwidth:

Channel :

Delays T=[0 10e-6 15e-6] sec

Power P=[0, -3, -8] dB

Symbol Rate Fs=10kHz

Doppler Fd=0.1Hz

Modulation QPSK

Very low Inter Symbol Interference (ISI)

Spectrum: fairly uniform

Example: Frequency Selective Fading “flat” within the coherence bandwidth:

Channel :

Delays T=[0 10e-6 15e-6] sec

Power P=[0, -3, -8] dB

Symbol Rate Fs=1MHz

Doppler Fd=0.1Hz

Modulation QPSK

Very high ISI

Spectrum with deep variations

transmitted “flat” within the coherence bandwidth:

3. Doppler Frequency Spread and Time Coherence

Back to the experiment of sending pulses. Take autocorrelations:


Take the FT of each one: “flat” within the coherence bandwidth:

This shows how the multipath characteristics change with time.

It defines the Time Coherence:

Within the Time Coherence the channel can be considered Time Invariant.

Summary of Time/Frequency spread of the channel “flat” within the coherence bandwidth:

Frequency Spread

Time Coherence

Time Spread

Frequency Coherence

Stanford University Interim (SUI) Channel Models “flat” within the coherence bandwidth:

Extension of Work done at AT&T Wireless and Erceg etal.

  • Three terrain types:

  • Category A: Hilly/Moderate to Heavy Tree density;

  • Category B: Hilly/ Light Tree density or Flat/Moderate to Heavy Tree density

  • Category C: Flat/Light Tree density

Six different Scenarios (SUI-1 – SUI-6).

Found in

IEEE 802.16.3c-01/29r4, “Channel Models for Wireless Applications,” http://wirelessman.org/tg3/contrib/802163c-01_29r4.pdf

V. Erceg etal, “An Empirical Based Path Loss Model for Wireless Channels in Suburban Environments,” IEEE Selected Areas in Communications, Vol 17, no 7, July 1999