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Material Type: Notes; Class: Wireless Communications; Subject: Electrical & Computer Engr; University: Villanova University; Term: Unknown 1989;
Typology: Study notes
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Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Yimin Zhang, Ph.D.
Department of Electrical & Computer Engineering
Villanova University
http://yiminzhang.com/ECE
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Outlines
Diversity Space Diversity
Selection Diversity Scanning Diversity Maximum Ratio Combining Equal Gain Combining
Polarization Diversity Frequency Diversity Time Diversity
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
DIVERSITY
diversity scheme
is a method that is used to develop information
from several signals transmitted over independent fading paths.
-^
It exploits the random nature of radio propagation by findingindependent (uncorrelated) signal paths for communication.
-^
Combining the multiple signals in such a fashion so as to reduce theeffects of excessive deep fades.
Yimin Zhang, Villanova University
Local scattering
Local scattering Same information,^ Same information,different copies.different copies.
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Diversity Methods
Diversity
Space Diversity Polarization DiversityFrequency Diversity
Time Diversity
Selection CombiningScanning Cobining
Maximum Ratio
Combining
Equal Gain Combining
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Space Diversity
A method of transmission or reception, or both, in which theeffects of
fading are minimized by the simultaneous use of two
or more physically separated antennas, ideally separated byone half or more wavelengths.
-^
Signals
received
from
spatially
separated
antennas
on
the
mobile
would have essentially uncorrelated envelopes for antenna separationsof one half wavelength or more.
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Selection Diversity
Consider a fading channel (Rayleigh)Input-output relationwhere
t ) is a Rayleigh random variable.
Average value of signal to noise ratio (SNR)The instantaneous SNR
is defined as i Fading channel
Output
r (
t )
Input
s (
t )
)(
t j^
−
θ
α
0
b^ α
Instantaneous signal power per branch
Mean noise power per branch
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
The
probability density function
for such a channel is
The pdf for a single branch that has SNR less than some threshold γ^ is
0
exp 1
) (^
i^
≥
⎞ ⎟ ⎠
⎛ ⎜ ⎝
Γ −
γ
γ
γ^
i
i
p
−^ Γ
∫
∫
γ
γ
γ
γ
γ
γ
γ
γ
γ^
i
i
i
i
i r^
0
0
Selection Diversity
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Cumulative distributioncurves
for output signals
from selection diversityfor various values of
The percentage of totaltime interval duringwhich a signal is belowany given level called“outage rate” at thatlevel.
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Compute the derivative of
γ )
The mean SNR iswhereEvaluating this equation the average SNR improvement using selection canbe found
1
) (
d d
) (
(^1) - M
−^ Γ
−Γ
⎤ ⎥ ⎦
⎡^ ⎢ ⎣
−
=
γ
γ
γ
γ
γ^
e
e
M
P
p^
M
M
dx
e
e
Mx
p^
x
x
M^
∞
−
−
∞
−
=
0
(^1) - M
0
1
)d (
x
Γ
M k^
k 1
1
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Selection Diversity: Summary
Selection diversity offers an average improvement in the link marginwithout requiring
additional transmitter power
or
sophisticated
receiver circuitry.
-^
Selection diversity is
easy to implement
because all that is needed
is a side monitoring station and an antenna switch at the receiver.
-^
However it is
not an optimal diversity technique
because it does not
use all of the possible branches simultaneously.
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
0
-40 -50 -60 -70 -80 -90 -
time (sec)
received signal (dBm)
Scanning Diversity
Scanning all the signals in a fixed sequence until the one with SNRmore than a predetermined threshold is identified. Also called switchand stay combining.
Presetthreshold
At someAt sometimetimeinstant, theinstant, thesignalsignalstrength ofstrength oftwotwobranchesbranchesare 1 and 2,are 1 and 2,the outputthe outputis either 1is either 1or 2.or 2.
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Scanning Diversity: Summary
This method is very simple to implement, requiring only onereceiver.
-^
The resulting fading statistics are somewhat inferior to thoseobtained by the other methods.
Yimin Zhang, Villanova University
ECE 8708 Wireless Communications :Equalization, Diversity, and Channel Coding
Maximal Ratio Combining
Combining all the signals in a co-phased and weighted manner soas to have the highest achievable SNR at the receiver at all times.
0
-40 -50 -60 -70 -80 -90 -
time (sec)
received signal (dBm)
At someAt sometimetimeinstant, theinstant, thesignalsignalstrength ofstrength oftwotwobranchesbranchesare 1 and 2,are 1 and 2,the outputthe outputisis(1x1+2x2)(1x1+2x2)/sqrt(5)/sqrt(5)=sqrt(5).=sqrt(5).
