the presentation consists of a brief description about ADAPTIVE LINEAR EQUALIZER , its classification and the associated attributes of ZERO FORCING EQUALIZER and MMSE EQUALIZER

1. ADAPTIVE LINEAR
EQUALIZER
By
R.SOPHIA JEANNE
jrsophia@gmail.com

2. What is adaptive linear equalization?
The equalizers are designed to be adjustable to
the channel response and for time variant
channels to be adaptive to the time variations
in the channel response .
Typically employed in high-speed
communication systems, which do not use
differential modulation schemes or frequency
division multiplexing

3. Cont…
The equalizer is the most expensive
component of a data demodulator and can
consume over 80% of the total computations
needed to demodulate a given signal
Adaptive equalizers compensate for signal
distortion attributed to inter-symbol
interference (ISI), which is caused by
multipath within time-dispersive channels

4. Time nature of adaptive linear
equalizer
Adaptive filter assumes that the channel is time
variant and tries to design an equalizer filter
whose coefficients are also time variant
according to the change of the channel and also
try to eliminate ISI and additive noise at each
time . The implicit assumption of adaptive
equalizer is that the channel is varying slowly.

5. Linear vs. non-linear equalizer
techniques
Two general categories
linear
nonlinear equalization
Linear:
No feedback path to adapt the equalizer , the
equalization is linear.
Non linear
fed back to change the subsequent outputs of the
equalizer the equalization is non-linear.

6. Types of linear equalizers
Zero-forcing:
Designs E(z) so that the ISI is totally removed
Minimum mean square error:
designs E(z) to minimize mean square error
MSE = 𝑘 𝜀2
𝑘 = 𝑘(𝑐 𝑘 − 𝑐(𝑘))2

7. Basic idea: zero forcing equalizer
Raised cosine
spectrum
Transmitted
symbol spectrum
Channel frequency
response
(incl. T & R filters)
Equalizer
frequency
response
=
       Z f B f H f E f
0 ffs = 1/T
 B f
 H f
 E f
 Z f

8. Zero forcing equalizer

9. The overall response at the detector input must
satisfy Nyquist’s criterion for no ISI
Zero-Forcing Equalizer

10. Cont….
• Suppose the received pulse in a PAM system is
p(t), which suffers ISI
• This signal is sampled at times t=nT to give a
digital signal pn=p(nT)
• We wish to design a digital filter HE(z) which
operates on pn to eliminate ISI
• Zero ISI implies that the filter output is only
non-zero in response to pulse n at sample
instant n, i.e. the filter output is the unit pulse
dn in response to pn

11. MMSE equalizer

12. Basic idea: MMSE EQUALIZER
The aim is to minimise 2
kJ E e
ˆ ˆ
k k k k ke z b b z  (or
depending on source
EqualizerChannel
kz
ˆ
kb
ke
 r k s k
+
Estimate of
k:th symbol
Input to
decision
circuit
 z k  ˆb k
Error

13. Cont….
MMSE formulation
HE(z)
xn yn
an
- E[(.)2]
For a ‘fixed’ equaliser E[(.)2] is minimised by
adjusting the coefficients of HE(z). Effectively we
have a trade off between noise enhancement and
ISI.

14. Cont….
The solution has the form,
o
E
NzP
zH


)(
1
)(
– equaliser needs knowledge of the noise PSD
– If No=0, the solution is the same as the ZFE
– When noise is present the ZFE solution is modified to
make a trade-off between ISI and noise amplification
Where P(z) is the Z transform of the
channel pulse response and No is the noise

15. Advantages and disadvantages of
adaptive linear equalizer
Advantages:
Optimal approximation for the Channel- once
calculated it could feed the Equalizer taps.
Disadvantges:
Heavy processing( due to matrix inversion
which itself is a challenge)
Not adaptive ( calculated periodically which is
not good for varying channels)

16. Applications of adaptive equalizer
Noise cancellation
Hands- free earphones
Aircraft headphones