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Lecture3_small Scale Fading
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1
ENGG 5303/IERG 5100 Advanced Wireless Communications
Part III: Small Scale Fading
2
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