Notes on Adaptive equalization

1. ADAPTIVE
EQUALIZATION
OLADAPO KAYODE

2. Outline
 Introduction
 Interference
 Inter-symbol interference
 Equalization
 Categories of equalization
 Adaptive Equalization
 Operating Modes of Adaptive Equalizer
 Block diagram of Adaptive Equalization
 Survey of Equalization Techniques
 Algorithm for Adaptive Equalization

3. Introduction
Interference
Wireless transmissions need to counter interference from a large kind of sources. There are
two main type of interference namely:
 Co-channel
 Adjacent Channel
Co-channel is also known as narrow band interference which is due to alternative closely
systems using an equivalent transmission frequency.
Adjacent channel interference case is caused when signals in nearby frequencies have
components outside their allocated range, and these components may interfere with on-
going transmission in the adjacent frequencies.
Inter-symbol interference
In addition to these two types is another type called Inter-symbol interference, which is a
form of twist of a signal in which one symbol interferes with subsequent symbols. This is an
unwanted development because the previous symbols have similar result as noise, therefore
creating less reliable communication.

4. Figure 1: Inter Symbol
Interference
Source: Chethan, Ravisimha & Kurian (2014)

5. Equalization
This is a commonly used strategy for resisting
inter symbol Interference. Since Inter-symbol
interference has been recognized as the main
blockage to high speed data transmission over
mobile radio channels. Equalization involves
the gathering of the dispersed symbol energy
into its original time interval.

6. Categories of Equalization
Equalizers are used in conquering the adverse effects of the channel and can be divided
into two broad categories:
 Maximum Likelihood Sequence Estimation (MLSE): This consist the making of channel
impulse response measurement and then giving a means for receiver adjustment to
the transmission area.
 Equalization with filters which make use of filters to reimburse the distorted pulses.
Depending on whether the timing is variant or invariant, equalizer can be categorize as
 Preset equalizer assume that the channel is time invariant; try to find H(f) and then
design an equalizer depending on H(f).
 Adaptive equalizer assume that the channel is time variant and also design an
equalizer filter with varying filter coefficients in time according to the change of channel
which try to eliminate ISS and additive noise at each time. This channel is assumed to
be slow.

7. Adaptive Equalization
As a mobile channel fades randomly and varied in time, the equalizer must track that the
time varying characteristics of the mobile channel, and thus are called adaptive
equalizers. It is an equalizer that automatically adapts to time-varying properties of the
mobile communication channel.
The following are the working principles of adaptive equalizers:
 Application of the received signal to receive filter. In this place, receive filter is not linked
filter. Because the channel impulse response is unknown. The receive filter in here is just
a low‐pass filter that refuse to accept all out of band noise.
 The output of the receiver filter is pictured at the symbol rate.
 Sampled signal is applied to adaptive transversal filter equalizer. Transversal filters are
actually FIR discrete time filters.
 The object is to adapt the coefficients to minimize the noise and inter-symbol interference
(depending on the type of equalizer) at the output.
 The adaptation of the equalizer is driven by an error signal

8. Operating Modes of Adaptive
Equalizer
Adaptive equalizer can operate in two modes:
 Decision Directed Mode which indicates that the receiver decisions are used to generate
error signal.
 Decision Directed Equalizer: This also indicates that adjustment is efficient in tracking slow
variations in the channel response.
Nevertheless, these approaches are not efficient during initial acquisition, which leads the
training and tracking mode.
 Training Mode
- Initially a known fixed length training sequence is sent by the transmitter, so that the
receiver’s equalizer adapt to a proper setting for minimum bit error rate (BER) detection.
- Training sequence is pseudo-random sequence or a fixed prescribed bit pattern. The training
sequence is designed to permit an equalizer at the receiver to acquire the proper filter
coefficients in the worst possible channel conditions.

9. Operating Modes of Adaptive
Equalizer
Therefore when the training sequence is finished, filter coefficients are near their optimal
values for reception of user data. An adaptive equalizer at the receiver uses a recursive
algorithm to evaluate the channel and estimate filter coefficients to compensate for the
channel.
- User data is sent immediately following the training sequence.
- The adaptive equalizer utilizes algorithm to estimate the filer coefficients (maximum delay,
deepest fades, maximum ISI etc.) near the optimum value to compensate for the distortion.
 Tracking Mode
- When user data is received, the adaptive algorithm tracks the changes in the channel.
- As a result, adaptive equalizer continuously changes the filter characteristics over time i.e.,
weight of the filter changes over time.
- When an equalizer is properly trained, it is said to be converged, equalizers are widely used
in TDMA system.

10. Block diagram of adaptive
equalizer
An adaptive equalizer is a time varying filter which is constantly tuned i.e. the weights
are updated continuously by the adaptive algorithm either by sample basis or block by
block basis. The adaptive algorithm is controlled by error signal, e(t), derived by
comparing the output of equalizer, d(t), with some signal d^(t), which is either exact
scaled replica of the transmitted signal x(t) or which represents a known property of
transmitted signal as shown in figure below:
Working Principle:
𝑦(𝑡) − 𝑥(𝑡) ∗ 𝑓(𝑡) + 𝑛𝑏 (𝑡)
𝑑(𝑡) = 𝑥(𝑡) ∗ 𝑓(𝑡) ∗ ℎ𝑒𝑞 (𝑡) + 𝑛𝑏 (𝑡) ∗ ℎ𝑒𝑞 (𝑡)
𝑑(𝑡) = 𝑥(𝑡) ∗ 𝑔(𝑡) + 𝑛𝑏 (𝑡) ∗ ℎ𝑒𝑞 (𝑡)
If, nb(t)=0; d(t) = x(t), such that g(t) = f(t) * heq(t)= (t)
which implies that the equalizer is an inverse filter of the channel

11. Figure 2: Block diagram of adaptive
equalizer
Source: SriKisna (2016)

12. Survey of Equalization
Techniques
Figure 3: Classification of equalization Source: SriKisna
(2016)

13. Survey of Equalization
Techniques
The classification of equalizer is determined by the usage of adaptive equalizer output
for subsequent control of the equalizer. Mostly, the decision make determines the value
of the digital data bit being received and applies threshold activity.
This technique can be classified into two broad categories:
 Linear equalizer which is generally the easiest to implement and have get the
concept involved though the techniques suffer from noise enhancement on
frequency-selective fading channels and are not applicable to wireless
communications. In linear equalization, the output signal d(t) is not used in feedback
path to adapt the equalizer and can be implemented as FIR filter.
 In Non-linear equalizer the most common is the decision-feedback equalization
because of its simplicity in implementing and does not suffer from noise
enhancement. But suffer from error propagation when binary digits (bits) are
decoded in error leading to poor performance on channels with low signal-to-noise
ratio (SNR). The best equalization technique to use is maximum likelihood sequence
estimation (MLSE).

14. Summary of Adaptive Equalization
Algorithm
There are three adaptive equalization algorithms namely:
 Zero Forcing Algorithm (ZF): aims to eliminate the inter-
symbol interference (ISI) at decision time instants (i.e. at the
centre of the bit/symbol interval).
 Least Mean Squares Algorithm (LMS): derived from “method
of steepest descent” and it is meant for convergence towards
minimum mean square error (MMSE)
 Recursive Least Squares Algorithm (RLS): offers faster
convergence, but is computationally more complex than LMS
(since matrix inversion is required).

15. Table 1: Comparison of various algorithms for
adaptive equalization
Source: Deepa (n.d)

16. Bibliography
Chethan B, Ravisimha B & Kurian (2014). The effects of Inter Symbol Interference (ISI) and
FIR Pulse Shaping Filters: A survey. International Journal of Advanced Research in
Electrical, Electronics and Instrumentation Engineering. Vol. 3, Issue 5, May 2014. 9412 -
9416
Deepa T. (n.d). Adaptive Equalization. SRM University. Retrieved from
http://www.srmuniv.ac.in/sites/default/files/files/adaptive_equalizer.pdf.
Goldsmith A. (2004). Wireless Communication. Stanford University.
Ranjan B. (n.d.). Equalization and Diversity Techniques for Wireless Communications: Lecture
Note 30. Department of Electrical Engineering, Indian Institute of Technology, Delhi.
Retrieved from http://textofvideo.nptel.ac.in/117102062/lec29.pdf
SriKisna E. (2016). A Notebook on Wireless Communication System. Retrieved from
https://www.researchgate.net/profile/Shree_Krishna_Khadka2/publication/306035050.

17. THANK
YOU