Transcript No Slide Title

Techniques to control noise and fading
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Noise and fading are the primary sources of
distortion in communication channels
Techniques to reduce noise and fading are
usually implemented at the receiver
The most common mechanism is to have a
receiver filter that can cancel the effects of
noise and fading, at least partially
Digital technology has made it possible to
have adaptive filters
Principle of Equalization
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Equalization is the process of compensation
at the receiver, to reduce noise effects
The channel is treated as a filter with transfer
function
Equalization is the process of creating a filter
with an inverse transfer function of the
channel
Since the channel is a varying filter, equalizer
filter also has to change accordingly, hence
the term adaptive.
Equalization Model-Signal detection
Carrier
Transmitter
Channel
Receiver
Front End
IF Stage
Message signal x(t)
Detector
Detected signal y(t)
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Equalization model-Correction
Reconstructed
Signal
d(t)
y(t)
Decision
Maker
Equalizer
d(t)
heq (t)
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nb(t)
+
Equivalent
Noise
Equalizer System Equations
Detected signal
y(t) = x(t) * f(t) + nb(t)
=> Y(f) = X(f) F(f) + Nb(f)
Output of the Equalizer
^
d(t) = y(t) * heq(t)
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Equalizer System Equations
Desired output
^
D(f) = Y(f) Heq(f) = X(f)
=> Heq(f) X(f) F(f) = X(f)
=> Heq(f) F(f) = 1
Heq(f) = 1/ F(f) => Inverse filter
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System Equations
Error e(t)  d(t)  d(t)
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MSE Error = E[| e(t) | ]
Aim of equalizer: To minimize MSE error
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Equalizer Operating Modes
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Training
Tracking
Training and Tracking functions
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The Training sequence is a known pseudorandom signal or a fixed bit pattern sent by the
transmitter. The user data is sent immediately
after the training sequence
The equalizer uses training sequence to adjust
its frequency response Heq (f) and is optimally
ready for data sequence
Adjustment goes on dynamically, it is adaptable
equalizer
Block Diagram of Digital Equalizer
Z-1
w0k
y(k  2)
y(k  1)
y(k)
w1k
Z-1
y(k  N)
Z-1
w2k
wNk
d(k)
∑
Adaptive Algorithm
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e(k)
∑
+
d(k)
Digital Equalizer equations
• In discrete form, we sample signals at
interval of ‘T’ seconds : t = k T;
d(k)  y(k) * heq (k)
e(k)  d(k)  d(k)
•The output of Equalizer is:
d(k)  y(k) * heq (k)
N
  Wnk y(k  n)  Wok y(k) W1k y(k  1)...WNk y(k  N)
n 0
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Error minimization
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The adaptive algorithm is controlled by the
error signal,
e(k)  d(k)  d(k)
MinE[e(k)  e(k)*]  MinE[| e(k) |2 ]
Wnk1  Wnk  Kek1 * yn
The equalizer weights are varied until convergence
is reached.
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Types of equalizers
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Linear Equalizers.
Non Linear Equalizers.
Diversity techniques
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Powerful communications receiver
technique that provides wireless link
improvement at relatively low cost.
Unlike equalization, diversity requires no
training overhead.
Principle of diversity
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Small Scale fading causes deep and rapid
amplitude fluctuations as mobile moves
over a very small distances.
…Principle of diversity
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If we space 2 antennas at 0.5 m, one may
receive a null while the other receives a
strong signal. By selecting the best signal at
all times, a receiver can mitigate or reduce
small-scale fading. This concept is Antenna
Diversity.
Diversity Improvement
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Consider a fading channel (Rayleigh)
Channel
Input s(t)
• Input-output relation
r (t) =  (t) e
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-j q(t)
Output r(t)
s (t) + n (t)
Average value of signal to noise ratio
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SNR =  = (Eb / No)  2 (t)
Average SNR Improvement
Using Diversity
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p.d.f., p(γi) = (1 /  ) e – γi / 
where (γi  0 ) and γi = instantaneous
SNR
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Probability [γi  γ]  p(i)di
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0
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M diversity branches,
Probability [γi > γ]  1  (1  e /  )M
Average Snr Improvement
Using Diversity
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Average SNR improvement using
selection Diversity,
M
 /   1/ k
k 1
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Example : Assume that 5 antennas
are used to provide space diversity.
If average SNR is 20 dB, determine
the probability that the SNR will be  10 dB.
Compare this with the case of a single
receiver.
Solution :
 = 20 dB => 100.
Threshold γ = 10 dB = 10.
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…Example
Prob [γi > γ] = 1 – (1 – e – γ/  )M
For M = 5,
Prob = 1 – (1 – e
– 0.1 5
) = 0.9999
For M = 1(No Diversity),
Prob = 1 – (1 – e – 0.1 ) = 0.905
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Maximal Ratio Combining (MRC)
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MRC uses each of the M branches in
co-phased and weighted manner such
that highest achievable SNR is
available. If each branch has gain Gi,
rM = total signal envelope
M
=
Gr

i 1
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ii
…Maximal Ratio Combining (MRC)
… assuming each branch has some
average noise power N, total noise
power NT applied to the detector is,
M
NT  N Gi2
i 1
SNR  M  rM / 2NT
2
M
2
1
Max M  (ri )N   ri whenGi  ri /N
2
i1
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Average SNR Improvement
Average SNR  M  M
Pr obability( M   )  e
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 / 
k 1
(  / )

k 1 (k  1)!
M
EXAMPLE : Repeat earlier problem for
MRC case
Pr obability( M   )  e
 / 
 = 10, = 100, M = 5
k 1
(0.5)
Pr obability( M  10)  e 0.1 
k 1 (k  1)!
5
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k 1
(  / )

k 1 (k  1)!
M
…Example
= ee--0.1
0.1 [ 1 + 0.1 / 1 + 0.12 / 2 ! + 0.13 / 3 ! + 0.14 / 4 ! ]
= 0.905 [ 1.1051708 ]
= 0.9999998
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Types of diversity
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Space Diversity
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Either at the mobile or base station.
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At base station, separation on order of
several tens of wavelength are
required.
Polarization Diversity
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Orthogonal Polarization to exploit
diversity
…Types of diversity
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Frequency Diversity :
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More than one carrier frequency is
used
Time Diversity :
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Information is sent at time spacings
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Greater than the coherence time of
Channel, so multiple repetitions can be
resolved
Practical diversity receiver
– rake receiver
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CDMA system uses RAKE Receiver to
improve the signal to noise ratio at the
receiver.
Generally CDMA systems don’t require
equalization due to multi-path resolution.
Block Diagram Of Rake Receiver
M1 M2 M3
Correlator 1
Correlator 2
r(t)
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Correlator M
α1
α2
αM
Σ
Z’
 ()dt
Z
>
<
m’(t)
Principle Of Operation
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M Correlators – Correlator 1 is synchronized
to strongest multi-path M1. The correlator 2
is synchronized to next strongest multipath
M2 and so on.
The weights 1 , 2 ,……,M are based on
SNR from each correlator output. ( is
proportional to SNR of correlator.)
M
Z’ =  M ZM
m =1
…Principle Of Operation
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Demodulation and bit decisions are then
based on the weighted Outputs of M
Correlators.