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ENGG 5303/IERG 5100 Advanced Wireless Communications

Part III: Small Scale Fading

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Update

We have considered Large scale fading: Path loss and shadowing

We will now consider Small scale fading: multipath fading

Flat and frequency selective fading Rayleigh fading Doppler spread and coherence time Delay spread and coherence bandwidth

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Statistical Multipath Model

Random number of multipath components, each with Random amplitude Random phase Random Doppler shift Random delay

Random components change with time Leads to time-varying channel impulse response

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Measured Channel Impulse Response

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Time Varying Multipath Channel

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Baseband Representation of Digitally Modulated Passband Signals

TX passband signals

Complex Representation of passband signals

x x

x x 4-PSK

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Representation of Received Passband Signals

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Multipath channel

Random Amplitude

Random Phase

Impulse response of the channel at time t to the impulse input at time t-t

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Rayleigh fading

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Update

We have considered Large scale fading: Path loss and shadowing

We will now consider Small scale fading: multipath fading

Flat and frequency selective fading Rayleigh fading Delay spread and coherence bandwidth Doppler spread and coherence time The effects of fading on system performance

Flat Fading vs. Frequency Selective Fading

Flat fading: L=1, i.e., no delay spread Channel impulse response is one single impulse The frequency response is a constant (over the

communication bandwidth) Usually occurs for narrowband communication, i.e.,

low symbol rates

Flat Fading vs. Frequency Selective Fading

Frequency selective fading: L>1, i.e., with delay spread Channel impulse response consists of multiple

impulses The frequency response varies over the

communication bandwidth Usually occurs for wideband communication, i.e.,

high symbol rates

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Multipath Dispersion and Frequency Selectivity

Time dispersion parameters Mean excess delay

Root mean square delay spread

Maximum excess delay

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Multipath Dispersion and Frequency Selectivity

Delay spread ( ) Spread of delays in echo

Coherence bandwidth ( ) Minimum separation of frequency for uncorrelated

fading Typical values

Indoor: Bc ~ 1MHz Outdoor: Bc ~ 100 kHz.

t

Bc 15 t

Time Varying Nature of Channel Fading

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Time-Varying Nature of Wireless Channel Cause for time-varying nature

movements of mobile or objects in the environment

On each path, is a random process This random process is correlated in time The faster the autocorrelation function decays with the

time difference, the faster the channel varies To measure how fast the channel varies: Doppler spread

and coherence time.

I (t) or Q (t)

l

Doppler Shift A measure of how fast the channel fading varies The frequency of radio wave changes when the receiver

moves relative to the transmitter (source of the wave) The received frequency is higher compared to the emitted

frequency when the receiver approaches the transmitter, and lower when the receiver moves away from the transmitter

Doppler Shift

Doppler frequency shift

Doppler spread: the maximum Doppler shift

source

observer v

fd =

v

cos

fD = v

Doppler Shift

One second of Rayleigh fading with a Doppler spread of 10Hz

One second of Rayleigh fading with a Doppler spread of 100Hz

Autocorrelation

E (t)*(t + )

J0 2 fD( )

fD = 10Hz

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Doppler Spread and Coherence Time

Doppler spread ( ) Spread of frequency due to mobility

Coherence time ( for time correlation above 0.5) Minimum separation of time for uncorrelated fading Typical Values

Pedestrian (~ 5 km / hr) fd ~ 14 Hz (at 2.4 GHz) Vehicular (~ 100 km/hr) fd ~ 300 Hz (at 2.4 GHz)

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Fast and Slow Fading

Very Fast Fading (Very rare in practical systems) Coherence time < Symbol period Channel variations faster than baseband signal

variations

Fast Fading Coherence time ~ 10 to a few hundred symbol

periods

Slow Fading Coherence time ~ a thousand or more symbol

periods

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Wireless Channel

Input Output