1. Wireless Communication Technology
Chapter 5
Equalization and Diversity
Asst. Prof. Bijaya Shrestha
Department of Electronics & Communication Engineering
nec

2. Equalization
Intersymbol interference (ISI) caused by multipath in bandlimited (frequency selective) time dispersive channels distorts the transmitted signal, causing bit errors at the receiver.
ISI has been recognized as the major obstacle to high speed data transmission over wireless channels.
Equalization is a technique used to combat ISI.
Since the mobile fading channel is random and time varying, equalizers must track the time varying characteristics of the mobile channel, and thus are called adaptive equalizers.
By Asst. Prof. Bijaya Shrestha, nec, 2015

3. Adaptive Equalizer
The general operating modes of an adaptive equalizer include training and tracking.
First, a known, fixed-length training sequence for minimum bit error rate (BER) detection.
The training sequence is typically a pseudorandom binary signal or a fixed, prescribed bit pattern.
Immediately following this training sequence, the user data (which may or may not include coding bits) is sent, and the adaptive equalizer at the receiver utilizes a recursive algorithm to evaluate the channel and estimate filter coefficients to compensate for the distortion created by multipath in the channel.
By Asst. Prof. Bijaya Shrestha, nec, 2015

4. Adaptive Equalizer
The training sequence is designed to permit an equalizer at the receiver to acquire the proper filter coefficients in the worst possible channel conditions (e.g., fastest velocity, longest time delay spread, deepest fades, etc.) so that when the training sequence is finished, the filter coefficients are near the optimal values for reception of user data.
As user data are received, the adaptive algorithm of the equalizer tracks the changing channel.
As a consequence, the adaptive equalizer is continually changing its filter characteristics over time.
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5. Adaptive Equalizer
TDMA wireless systems are particularly well suited for equalizers.
An equalizer is usually implemented at baseband or at IF in a receiver.
From the figure, we see that the signal received by the equalizer is
If the impulse response of the equalizer is heq(t), then the output of the equalizer is
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6. Adaptive Equalizer
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7. Adaptive Equalizer
where g(t) is the combined impulse response of the transmitter, channel, RF/IF sections of the receiver, and the equalizer at the receiver.
The impulse response is given by
where cn are the filter coefficients
Assuming nb(t) = 0, in order to obtain the desired output as x(t), we must have
In frequency domain, we have
We find that an equalizer is an inverse filter of the channel such that if the channel is frequency slective, the equalizer enhances the frequency components with small amplitudes and attenuates the strong frequencies in the received frequency spectrum.
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8. Generic Adaptive Equalizer
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9. Generic Adaptive Equalizer
There is a single input yk into the equalizer at any time instant.
The adaptive equalizer structure shown in the figure is called a transversal filter.
There are N delay elements, N+1 taps, and N+1 tunable complex multipliers, called weights.
The adaptive algorithm is controlled by the error signal ek.
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10. Linear and Nonlinear Equalizers
If the reconstructed signal d(t) is not used in the feedback path to adapt the equalizer, the equalization is linear.
If d(t) is fedback to change the subsequent outputs of the equalizer, the equalizer is nonlinear.
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11. Linear Equalizers
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12. Linear Equalizers A linear transversal equalizer is shown in figure.
The current and past values of the received signal are linearly weighted by the filter coefficients and summed to produce the output.
Here,
where represent the complex filter coefficients or tap weights, is the output at time index k, yi is the input received signal at time t0+iT, t0 is the equalizer starting time, and N = N1 + N2 + 1 is the number of taps.
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13. Nonlinear Equalizers
Nonlinear equalizers are used in applications where the channel distortion is too severe for a linear equalizer to handle.
Decision feedback equalizer (DFE) is an example of a nonlinear equalizer.
In this equalizer, once an information symbol has been detected and decided upon, the ISI that it induces on future symbols can be estimated and subtracted before detection of subsequent symbols.
DFE structure consists of a feedforward filter (FFE) and a feedback filter (FBF).
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14. Nonlinear Equalizers
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15. Nonlinear Equalizers
The FBF is driven by decisions on the output of the detector, and its coefficients can be adjusted to cancel the ISI on the current symbol from past detected symbols.
The equalizer has N1 + N2 + 1 taps in the FFF and N3 taps in the FBF and its output can be expressed as
By Asst. Prof. Bijaya Shrestha, nec, 2015

16. Diversity and Diversity Techniques
Diversity is a powerful communication receiver technique that provides wireless link improvement at relatively low cost.
Diversity exploits the random nature of radio propagation by finding independent (or at least highly uncorrelated) signal paths for communication.
If one radio path undergoes a deep fade, another independent path may have a strong signal.
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17. Diversity and Diversity Techniques
Microscopic Diversity Technique
It is used to combat the effect of small-scale fading.
Example: If two antennas are separated by a fraction of a meter, one may receive a null while the other receives a strong signal.
By selecting the best signal at all times, a receiver can mitigate small-scale fading effects (this is called antenna diversity or space diversity).
Macroscopic Diversity Technique
It is the technique in which among different base stations, selecting a base station providing a strong signal, the mobile can improve substantially the average SNR on the forward link.
By using base station antennas that are sufficiently separated in space, the base station is able to improve the reverse link by selecting the antenna with the strongest signal from the mobile.
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18. Diversity and Diversity Techniques
The commonly used diversity techniques are
Space diversity
Polarization diversity
Frequency diversity
Time diversity
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19. Space Diversity
Space diversity, also known as antenna diversity, is one of the most popular forms of diversity used in wireless systems.
In space diversity, more than one spatially separated antennas are used in the receiver such that the signals received from those antennas are uncorrelated.
For mobile, the antenna separation is one half wavelength or more.
For base station, the antenna separation is in the order of several tens of wavelengths.
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20. Space Diversity
Space diversity reception methods can be classified into four categories
Selection diversity
Feedback diversity
Maximal ratio combining
Equal gain diversity
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21. Selection Diversity
Selection diversity is the simplest diversity technique.
m demodulators are used to provide m diversity branches whose gains are adjusted to provide the same average SNR for each branch.
The receiver branch having the highest instantaneous SNR is connected to the demodulator.
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22. Feedback or Scanning Diversity
Scanning diversity is very similar to selection diversity except that instead of always using the best of m signals, the m signals are scanned in a fixed sequence until one is found to be above a predermined threshold.
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23. Feedback or Scanning Diversity
This signal is then received until it falls below threshold and the scanning process is again initiated.
It is very simple to implement and only one receiver is required.
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24. Maximal Ratio Combining
The signals from all of the m branches are weighted according to their individual SNRs and then summed.
Here, the individual signals must be co-phased before being summed which generally requires an individual receiver and phasing circuit for each antenna element.
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25. Maximal Ratio Combining
Maximal ratio combining produces an output SNR equal to the sum of the individual SNRs.
Thus, it has the advantage of producing an output with an acceptable SNR even when none of the individual signals are themselves acceptable.
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26. Equal Gain Combining
In certain cases, it is not convenient to provide for the variable weighting capability required for true maximal ratio combining.
In such cases, the branch weights are all set to unity, but the signals from each branch are co-phased to provide equal gain combining diversity.
This allows the receiver to exploit signals that are simultaneously received on each branch.
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27. Polarization Diversity
At the base station, space diversity is considerably less practical than at the mobile because it requires large antenna spacings.
Polarization diversity provides two diversity branches allowing the antenna elements to be co-located.
Due to multiple reflections, horizontal and vertical polarization paths between a mobile and a base station are uncorrelated.
The reflection coefficient for each polarization is different, which results different amplitudes and phases for each.
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28. Frequency Diversity
Frequency diversity is implemented by transmitting information on more than one carrier frequency.
The frequencies separated by more than coherence bandwidth of the channel are uncorrelated and will thus not experience the same fades.
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29. Time Diversity
Time diversity repeatedly transmits information at time spacings that exceed the coherence time of the channel, so that multiple repetitions of the signal will be received with independent fading conditions, thereby providing for diversity.
One modern implementation of time diversity involves the use of the RAKE receiver for spread spectrum CDMA.
By demodulating several replicas of the transmitted CDMA signal, where each replica experiences a particular multipath delay, the RAKE receiver is able to align the replicas in time so that a better estimate of the original signal may be formed at the receiver.
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30. RAKE Receiver
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31. RAKE Receiver
In CDMA spread spectrum systems, the chip rate is typically much greater than the flat-fading bandwidth of the channel.
CDMA spreading codes are designed to provide very low correlation between successive chips.
Thus, propagation delay spread in the radio channel merely provides multiple versions of the transmitted signal at the receiver.
If these multipath components are delayed in time by more than a chip duration, they appear like uncorrelated noise at a CDMA reciever.
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32. RAKE Receiver
Since there is useful information in the multipath components, CDMA receivers may combine the time delayed versions of the original signal transmission in order to improve the SNR at the receiver.
A RAKE receiver attempts to collect the time-shifted versions of the original signal by providing a separate correlation receiver for each of the multipath signals.
Each correlation receiver may be adjusted in time delay.
The RAKE receiver is essentialy a diversity receiver designed specifically for CDMA, where the diversity is provided by the fact that the multipath components are practically uncorrelated from one another when their relative propagation delays exceed a chip period.
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33. RAKE Receiver
A RAKE Receiver utilizes multiple correlators to separately detect the M strongest multipath components.
The outputs of each correlator are then weighted to provide a better estimate of the transmitted signal than is provided by a single component.
Demodulation and bit decisions are then based on the weighted outputs of the M correlators.
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34. Interleaving
Interleaving is used to obtain time diversity in a digital communication system (2G and 3G) without adding any overhead.
The encoded data bits (called source bits) carry a great deal of information, and some source bits are more important than others and must be protected from errors.
The interleaver spreads out these important bits in time so that if there is a deep fade or noise burst, the important bits from a block of source data are not corrupted at the same time.
By Asst. Prof. Bijaya Shrestha, nec, 2015

35. Interleaving
By spreading the source bits over time, it becomes possible to make use of error control coding (called channel coding) which protects the source data from corruption by the channel.
An interleaver can be one of two forms: a block structure and a convolutional structure.
A block interleaver formats the encoded data into a rectangular array of m rows and n columns, and interleaves nm bits at a time.
Each row consists of a word of source having n bits.
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36. Interleaving
Source bits are placed into the interleaver by sequentially increasing the row number and filling the column.
The data from the matrix is read out sequentially increasing the column number and transmitted over the channel.
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37. References
Theodore S. Rappaport, Wireless Communications, second edition, Prentice Hall, 2012.
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