This document provides an overview of signal processing techniques used in wireless systems, including diversity and equalization. It discusses various diversity techniques like spatial, temporal, frequency, angular, and polarization diversity as well as macro and micro diversity. It also explains different types of combining diversity including selection, maximal ratio combining, and equal gain combining. The document concludes with sections on linear equalizers such as zero forcing and MMSE, as well as nonlinear equalizers using algorithms like LMS and RLS.

1. Unit - 4
SIGNAL PROCESSING IN WIRELESS
SYSTEMS
Prepared by
JAI GANESH S
Asst.Professor - ECE

2. Syllabus
• Diversity
– Principles
– Macro Diversity
– Micro Diversity
– Signal Combining Techniques
– Transmit diversity
• Equalizer
– Linear feed back equalizers
– Decision feed back equalizers
• Coding techniques
– Channel Coding Techniques (Review)
– Speech Coding Techniques (Review)

3. Basic - Understanding
Dispersive
Channels

4. Diversity - Understanding
Dispersive
Channels

5. Diversity - Principle
• The principle of diversity is to ensure that the same
information reaches the receiver on a statistically
independent channels.

6. Diversity
• This is a technique implemented to improve the
channel quality and performance.
• This is achieved by placing the Tx signals in a
statistically independent channels.
• This reduces the over all fading of the received signals
at the receiver side.
• This technique mainly addresses the fading problems.

7. Correlation Coefficient
• Diversity is most efficient when the different
transmission channels carry independently faded copies
of the same signals.
• The correlation coefficient characterises the correlation
between signals on different diversity branches .
• Correlation can be done on different parameters such as
complex part of the signal, phase relations etc,
• Most important one is correlation between the signal
envelopes.

8. Lack of Correlation - Understanding
Dispersive
Channels

9. • The correlation coefficient is given by:
• Where x and y are the envelope of the signals.
• The signals are said to be “effectively” decorrelated if , ρ is
between a certain threshold value (typically 0.5 or 0.7)

10. Types of Diversity
• How to obtain the diversity in the signals ?
• Diversity are classified based on the fading methods.
–Small scale fading
• Microscopic diversity techniques are used.
–Large scale fading
• Macroscopic diversity techniques are used.

11. Micro diversity Techniques.
• There are 5 methods available.
– Spatial diversity
• Antenna elements separated by space
– Temporal diversity
• Transmission of signals at different time
– Frequency diversity
• Transmission of signals at different frequencies
– Angular diversity
• Multiple antennas with different antenna patterns
– Polarization diversity
• Multiple antenna with different polarizations

12. 1. Spatial diversity
• Signals are Transmitted / Received by more than one antenna and
the best signal is selected for processing.
• Oldest and simplest form of diversity
• Large correlation between the signals are undesirable, as it decreases
the effectiveness of diversity.
• Important factor is to establish the relation between the antenna
spacing (Different for Tr side and Different for the Rx side)
Transmitter Side
Receiver side 

13. Envelope Correlation Coefficient as a function of
antenna separation

14. 2.Temporal Diversity
• As the wireless propagation channels are time
variant, signals that are received at different times
are uncorrelated.
• Temporal diversity can be realized in 3 different
ways.
– Repetition coding
– Automatic repeat request
– Combination of interleaving and coding

15. • Repetition coding:
– The signal is repeated several times, where the repeat intervals
are sufficient for decorrelation of signals.
– This method is highly bandwidth inefficient
• Automatic Repeat ReQuest – (ARQ):
– Rx sends a message to transmitter to indicate weather it
received the data with sufficient quality.
– If not then transmission is repeated again.
– Efficiency is better than repetition coding.
– Retransmission occurs only at certain cases.
• Combination of interleaving and coding:
– The signals are interleaved and coded. Instead of sending the
actual data those code words are sent.
– The transmitted codeword can be reconstructed .

16. 3. Frequency Diversity
• Frequency diversity is implemented by transmitting
information on more than one carrier frequency.
• It does not mean that same messages are transmitted in
two different frequencies.
– When this is done then the signals undergoes different fading
levels.
• Instead, information is spread over a large bandwidth, so
the small parts of the information are conveyed by
different frequency components.
• Then the receiver averages over the different frequencies
to recover the original information.

17. Frequency Spreading

18. • The spreading is achieved by different methods:
– Compressing the information in time.(TDMA)
– Code division multiple access.(CDMA)
– Orthogonal frequency division multiplexing(OFDM)
– Frequency hopping in conjunction with coding.
Demerits:
- It requires large band width.
- More number of receivers are required.
- High cost.

19. 4. Angular Diversity
• It enhances the decorrelation of signals at closely
spaced antennas.
• Different antenna patterns can be achieved very
easily.
• This effect is due to Mutual Coupling.

20. Mutual Coupling
• Place 2 identical
antennas close to each
other
• Here antenna B acts as a
reflector for antenna A.
• Antenna A acts as a
reflector for Antenna B.
• Hence the pattern of
both the antennas are
skewed as shown in
figure.
• Of Course Antennas with
different radiation
pattern can also be used

21. • Mutual Coupling can also be increased by locating the
antenna at different parts of the casing.
• The various possibilities are shown in the figure.

22. 5. Polarization Diversity
• Signals are differentiated with the horizontally and vertically
polarizations.
• Reflection and the diffraction depends upon the polarizations.
• The fading levels at each polarization are independent. Thus the
diversity is achieved.

23. Macro Diversity
• Macro Diversity:
– To reduce the large scale fading these macro diversity is used.
– Large scale fading are generally caused by shadowing.
– If there is an hill between the BS and the MS then simply
increasing the Tx antenna and Rx antenna doesn’t make any
difference.
– Thus a intermediate BS (BS2) is placed in between the BS and MS
so that the hill does not lie in between the BS and BS2.
–Receive – Amplify – Retransmit.
Merits:
– Distance between BS and MS can be increased.
Demerits:
– It requires large bandwidth.
– frequency repeaters causes delay dispersion.

24. Diversity Achieved. How to Resolve?
Selection
Diversity
Combining
Diversity

25. Signal Combining Techniques
– Selection diversity
 Best signal is selected, and the rest are discarded.
• Selection
• Switched
• Feed back
– Combining diversity
All signals are combined together and then it is decoded.
• Maximal ratio combining
• Equal gain diversity

26. Selection Diversity
• There are 2 selection criteria:
– RSSI – Received Signal Strength Indication
– BER – Bit Error Rate
• The receiver selects the signal with the largest
instantaneous power

27. RSSI – Driven Selection Diversity

28. BER – Driven Selection Diversity
• Working…
– We first transmit the Training Sequence. (ie) Know signal
/ sequence.
– The Rx then demodulates the signal from each antenna
and compares / correlates it with the transmit signal.
– The antenna which received the smallest BER is chosen as
the best and that signal is processed further.

29. BER – Driven Selection Diversity

30. Merits and Demerits of RSSI and BER
• RSSI
– Merits:
• Only one RF Chain is used
• Process is done on only one signal
• Easy to implement
– Demerits:
• Waste of signal energy by discarding (n-1) received signals
• Not an optimum method
• BER
– Demerits:
• More number of Rx are used.
• Implementation is complex
• Training sequence is to be repeated again and again.
• Tradeoff between the duration of training and BER should be maintained.

31. Switched Selection Diversity
• The main drawback of the selection diversity is its
criteria.
• RSSSI and BER has to be monitored continuously
on all branches.
• Leads to complex designs and heavy hardware
requirements.
These drawbacks are eliminated by switched selection
diversity.

32. • In this method the selection criteria is monitored only in
the active branches.
• If it falls below a certain threshold value, then the
receiver switches to a different antenna.
• Case 1: All branches have equal power then the selection
of active branch is RANDOM.
• Case 2: All branches are below threshold level, then the
receiver just switches back and forth until an active line
is detected.
The performance of the switched diversity is worse than
the selection diversity. Hence it is not considered widely.

33. Feed Back Diversity
• Also called scanning diversity.
• This is a combination of selection and switched
diversity.
• All the available channels are scanned first in a fixed
sequence until one is found above the threshold level.
• The signal is received from that antenna until it falls
off the threshold value and scanning process is
initiated again.

34. 2. Combining Diversity
• It exploits all available copies of signals. Each signal
copy is multiplied by a (complex) weight and then
added up.
• Weight = phase correction + weight of amplitude
• Phase correction is done to make the signals coherent.
• Amplitude weighting has 2 methods:
– Maximal ratio combining (MRC).
– Equal gain combining (EGC).

35. Maximum Ratio Combining
• This method weighs all signal copies by their amplitude.
• They also does the phase correction for different antennas.
 Merits:
– Output are acceptable even when all the received signals are faded highly.

36. Equal Gain Combining
• This method weighs all the signals with equal amplitude and
performs phase correction to give equal gain diversity.

37. END
OF
DIVERSITY

38. EQUALISERS

39. Introduction
• Inter symbol interference is the major problem in
wireless communication which leads to the BIT
ERRORS at the receiver.
• Equalization is a technique used to reduce the inter
symbol interference.
• This device equalizes the dispersive effect of the
channel. (dispersion due to fading)
• Equalizers are mostly used at the receiver side.

40. Classification of equalizers.

41. • Linear equalizers:
– If the output is not used in the feed back path to adapt
the equalizer is called linear equalizer.
• Non linear equalizers:
– If the output is fed back to change the subsequent outputs
of the equalizer is called as non linear equalizers.

42. LINEAR EQUALIZERS
• They are simple and resembles the filter structures.
• The product of the transfer function of the channel
and equalizer must satisfy certain criteria.
• The criteria can be,
– Either, Achieving a completely flat transfer function of
the channel – filter concatenation.
– Or, Minimizing the mean square error at the filter output.
• The basic structure of the linear equalizer is shown in
the figure.

43. • Ci  Transmit Sequence sent over the channel.
• Ui  Sequence available at the Equalizer input.
• Now we have to convert the Ci to C^
i .
• The aim of this conversion is to produce ZERO Deviation.
OR
• To produce minimum mean square error.

44. Types of Linear Equalizers
• There are 2 types of linear equalizers, they are:
– Zero Forcing Equalizer (ZF)
– Minimum Mean Square Error Equalizer (MMSE)

45. Zero Forcing Equalizers Vs MMSE Equalizers

46. Merits and demerits
• Merits
– Simple and easy to implement
– It has faster convergence
– Unique structure
– When channel becomes more time dispersive, the length of the
equalizer can be increased.
• Demerits
– Structure is complicated than compared to a linear equalizer.
– Not suitable for severe distortion channels.

47. 2. MMSE Equalizers
• In mmse the ultimate aim is to reduce the BER but
not the ISI.
• This can be achieved by minimizing the mean square
error between the signals.
• For minimizing the error the coefficients are found
first.

48. ALGORITHMS FOR MMSE
• Least Mean Square - LMS
• Recursive Least Square - RLS

49. LMS Algorithm

50. RLS Algorithms
• No assumptions are made in general
• Each signal is received individually and then they are
analyzed for the type of dispersion.
• This is more advantageous than the LMS alg.

51. NON LINEAR EQUALISERS