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7. Channel Models

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**Signal Losses due to three Effects:**

1. Large Scale Fading: due to distance 2. Medium Scale Fading: due to shadowing and obstacles 3. Small Scale Fading: due to multipath

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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.

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**1.1. Large Scale Fading: Free Space**

Path Loss due to Free Space Propagation: For isotropic antennas: Transmit antenna Receive antenna wavelength Path Loss in dB:

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**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

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**Average Loss Free space loss at reference distance dB**

indoor 1-10m outdoor m Path loss exponent Values for Exponent : Free Space 2 Urban Indoors (LOS) Indoors(NLOS) 4-6

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**Empirical Models for Propagation Losses to Environment**

Okumura: urban macrocells 1-100km, frequencies GHz, BS antenna m high; Hata: similar to Okumura, but simplified COST 231: Hata model extended by European study to 2GHz

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**3. Small Scale Fading due to Multipath. **

a. Spreading in Time: different paths have different lengths; Receive Transmit time Example for 100m path difference we have a time delay

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**Typical values channel time spread:**

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**b. Spreading in Frequency: motion causes frequency shift (Doppler)**

Receive Transmit time time for each path Doppler Shift Frequency (Hz)

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**Put everything together**

Transmit Receive time time

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**Re{.} LPF channel Each path has … …shift in time … … attenuation…**

paths …shift in frequency … (this causes small scale time variations)

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**2.1 Statistical Models of Fading Channels**

Several Reflectors: Transmit

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

average time delay each time delay each doppler shift

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**Some mathematical manipulation …**

Assume: bandwidth of signal << … leading to this: with random, time varying

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**with the Doppler frequency shift.**

Statistical Model for the time varying coefficients random By the CLT is gaussian, zero mean, with: with the Doppler frequency shift.

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**Each coefficient is complex, gaussian, WSS with autocorrelation**

and PSD with maximum Doppler frequency. This is called Jakes spectrum.

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Bottom Line. This: time … can be modeled as: delays

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For each path unit power time varying (from autocorrelation) time invariant from power distribution

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

Time delays: sec dB Power Attenuations: Hz Doppler Shift: Summary of Channel Model: WSS with Jakes PSD

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**Non Line of Sight (NOLOS) and Line of Sight (LOS) Fading Channels**

Rayleigh (No Line of Sight). Specified by: Time delays Power distribution Maximum Doppler 2. Ricean (Line of Sight) Same as Rayleigh, plus Ricean Factor Power through LOS Power through NOLOS

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**Rayleigh Fading Channel Parameters**

Simulink Example Rayleigh Fading Channel Parameters M-QAM Modulation Bit Rate

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**Recall the Doppler Frequency:**

Set Numerical Values: velocity carrier freq. Recall the Doppler Frequency: Easy to show that: modulation power channel

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**Channel Parameterization**

Time Spread and Frequency Coherence Bandwidth Flat Fading vs Frequency Selective Fading Doppler Frequency Spread and Time Coherence Slow Fading vs Fast Fading

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**1. Time Spread and Frequency Coherence Bandwidth**

Try a number of experiments transmitting a narrow pulse at different random times We obtain a number of received pulses transmitted

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**Take the average received power at time**

More realistically: Received Power time

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**This defines the Coherence Bandwidth.**

Take a complex exponential signal with frequency The response of the channel is: If then i.e. the attenuation is not frequency dependent Define the Frequency Coherence Bandwidth as

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**Frequency Selective Fading**

This means that the frequency response of the channel is “flat” within the coherence bandwidth: Channel “Flat” up to the Coherence Bandwidth frequency Coherence Bandwidth Flat Fading Just attenuation, no distortion < Signal Bandwidth Frequency Coherence > Frequency Selective Fading Distortion!!!

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**Very low Inter Symbol Interference (ISI)**

Example: Flat Fading 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 Spectrum: fairly uniform Very low Inter Symbol Interference (ISI)

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**Example: Frequency Selective Fading**

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 Spectrum with deep variations Very high ISI

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**3. Doppler Frequency Spread and Time Coherence**

Back to the experiment of sending pulses. Take autocorrelations: transmitted Where:

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Take the FT of each one: 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.

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**Summary of Time/Frequency spread of the channel**

Time Coherence Time Spread Frequency Coherence

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**Stanford University Interim (SUI) Channel Models**

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 c-01/29r4, “Channel Models for Wireless Applications,” 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

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