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PULSE SHAPING AND EQUALIZATIONREMYA RM TECH ECE FIRST YEARREG NO: 15304019

CONTENTSINTRODUCTIONCHARACTERISATION OF BAND LIMITED SIGNALSIGNAL DESIGN FOR BAND LIMITED SIGNALEYE DIAGRAMINTERPRETATION OF EYE DIAGRAMDESIGN OF BAND LIMITED SIGNAL FOR NO ISI-THE NYQUIST CRITERIA

CONTENTSDESIGN OF BAND LIMITED SIGNAL WITH CONTROLLED ISI- THE PARTIAL RESPONSELINEAR EQUALIZATIONDECISION FEEDBACK EQUALIZATIONMLSE EQUALIZATIONTURBO EQUALIZATIONBLIND EQUALIZATION

INTRODUCTIONAll physical channels are bandlimited, with C(f) = 0 for |f| > W Nondistorting (ideal) channel: |C(f)| = const. for | f | < W and is linear

All other channels are nonideal (distort the signal in amplitude, phase or both)

INTRODUCTIONPulse shaping and equalization is taken into account when the channel is bandlimited to some specified bandwidth of W HzUnder this condition, the channel may be modeled as a linear filter having an equivalent low pass frequency response C(f), that is zero for lfl >W HzFor pulse shaping process, consider the design of the signal pulse g(t) in a linearly modulated signal represented as

that efficiently utilizes the total available channel bandwidth W

INTRODUCTIONWhen the channel is ideal for | f | W, a signal pulse can be designed that allows us to transmit at symbol rates comparable to or exceeding the channel bandwidth W.

When the channel is not ideal, signal transmission at a symbol rate equal to or exceeding W results in inter-symbol interference (ISI) among a number of 2 adjacent symbols.

Telephone channels are such channels that are characterized by as band limited linear filters

CHARACTERISATION OF BAND LIMITED CHANNELSConsider a band limited channel which is characterized as linear filter with the low pass frequency response C(f) and the impulse response as C(t). Then a signal of the form ] is transmitted over a bandpass telephone channel, the equivalent low pass received signal is

SIGNAL DESIGN FOR BAND LIMITED SIGNALConsider a lowpass transmitted signal which is common for most of the modulation techniques is represented as

Consequently, the received signal can be represented where

and z(t) reprsents the additive white Guassian noise

SIGNAL DESIGN FOR BAND LIMITED SIGNALFrom the sampled data the required information sequence is obtained is given by

where desired information signal ISI additive white gaussian noise variable at the kth sampling instant

SIGNAL DESIGN FOR BAND LIMITED SIGNALThe output of the receiving filter is

After filtering operation, signal is sampled at at times t=kT+ , k=0,1,2....

EYE DIAGRAMThe amount of ISI and noise in a digital communication system can be viewed on an oscilloscope.For PAM signals, we can display the received signal y(t) on the vertical input with the horizontal sweep rate set at 1/T. The resulting oscilloscope display is called an eye pattern.

Eye diagram is a means of evaluating the quality of a received digital waveform

By quality is meant the ability to correctly recover symbols and timingThe received signal could be examined at the input to a digital receiver or at some stage within the receiver before the decision stage

INTERPRETATION OF EYE DIAGRAM

The effect of ISI is to cause the eye to closeThereby reducing the margin for additive noise to cause errorsEye diagram can also give an estimate of achievable BERCheck eye diagrams at the end of class for participationAn eye diagram is a periodic depiction of a digital waveform. It helps to visualize the behavior of the system, presence of ISI, etc.

EYE DIAGRAM

DESIGN OF BAND LIMITED SIGNAL FOR NO ISI-THE NYQUIST CRITERIAAssuming that the band-limited channel has ideal frequency response, i.e., C( f ) = 1 for | f | W,then the pulse x(t) has a spectral characteristic where

The output of the receiver is given by

DESIGN OF BAND LIMITED SIGNAL FOR NO ISI-THE NYQUIST CRITERIAThe condition for zero ISI is

This condition is also termed as Nyquist criteria for zero ISI or Nyquist criteria for pulse shaping.

The necessary and sufficient condition for x(t) to satisfy is that its fourier transform x(f)

satisfy

DESIGN OF BAND LIMITED SIGNAL FOR NO ISI-THE NYQUIST CRITERIAAssuming that the band-limited channel has ideal frequencyresponse, i.e., C( f ) = 1 for | f | W, then the pulse x(t) has a spectral characteristic Where

We are interested in determining the spectral properties of the pulse x(t), that results in no inter-symbol interference

DESIGN OF BAND LIMITED SIGNAL FOR NO ISI-THE NYQUIST CRITERIAThe condition for no ISI This condition is also termed as Nyquist criteria for zero ISI or Nyquist criteria for pulse shaping

The necessary and sufficient condition for x(t) to satisfy

is that its fourier transform x(f) satisfies

DESIGN OF BAND LIMITED SIGNAL WITH CONTROLLED ISI-PARTIAL RESPONSEThe condition of achieving zero ISI , so that the data can be transferred at maximum possible rate ( R=1/T=2W).Instead of achieving zero ISI, this method introduces controlled amount of ISI in the transmitted signal and counteracts it upon receiving it. The transmit filter is designed to introduce deterministic or controlled amount of ISI and is counteracted in the receiver side. Methods like duobinary signaling, modified duobinary signaling are employed under this category. The resulting signals are called partial response signals which are transmitted at Nyquist rate of 2W symbols/second. This method is also called Correlative Coding

LINEAR EQUALISATIONThe linear equalizers are simple to implement and: Rely on the principle of inverting H (f ). Cancel ISI at the cost of possibly enhancing noise (ZFE), or provide a tradeoff between noise enhancement and ISI removal (MMSE).

In non-blind mode, H (f ) is estimated by feeding an impulse. Equalization is performed digitally, so h [n] is what usually matters.

In blind mode, the system uses known training sequences.

heq [n] is implemented as a FIR (finite impulse response) filter.

LINEAR EQUALISATION

FIR transversal filter

A transveral FIR filter can equalize the worst-case ISI only when the peak distortion is small.In presence of noise, the peak distortion grows.

The MMSE gives the filter coefficients to keep a minimum mean square error between the output of the equalizer and the desired signal. The MMSE equalizer requires training sequences (d(t)). y(t) and v(t) are signals affected by noise.LINEAR EQUALIZATION

Linear equalizers are simple to implement, but they have severe limitations in wireless channels.

Linear equalizers are not good in compensating for the appearance of spectral zeros.

The decision feedback equalizer (DFE) can help in counteracting these effects.

DECISION FEEDBACK EQUALIZATION

DECISION FEEDBACK EQUALIZATION

Structure of a DFE

The DFE works by first estimating the ISI indirectly, in the feedbackpath.The ISI affected signal is reconstructed by using previously decided symbols, and the result is subtracted from the output of the feedforward part of the equalizer. This feedforward part is responsible for compensating the remaining ISI.The estimated error is used to calculate the forward filter and the feedback filter coefficients. They can be jointly estimated with a minimum mean square error strategy.DECISION FEEDBACK EQUALIZATION

AdvantagesThe system works better in presence of spectral nulls, because the channel is not inverted. It is inherently adaptive.Drawbacks When a symbol is incorrectly decided, this error propagates during some symbol periods, depending on the memory of the system.

DECISION FEEDBACK EQUALIZATION

MLSE EQUALIZERA maximum likelihood sequence estimation (MLSE) equalizer works over different principles. The channel is considered as a system with memory described by a trellis.The state of the system is built by considering the number of successive symbols matching the length of the channel response.The symbols at the input of the channel drive the transitions.

MLSE EQUALIZER

MLSE equalizer structure for GSM (source: http://cnx.org/content)

MLSE EQUALIZERThe MLSE equalizer requires training sequences, as in the case of the DFE or the MMSE.

It has to build metrics that indicate the likelihood of a possible transition over the trellis.

The optimal algorithm to implement the MLSE criterion is the Viterbi algorithm.

Advantages It is optimal from the sequence estimation point of view. It can provide the lowest frame error rate.

Disadvantages It is difficult to implement.It becomes quickly unfeasible when the channel memory grows. The sequence has to be buffered in blocks, adding delay to the operation of the system.

MLSE EQUALIZER

TURBO EQUALIZATION

Turbo-equalizer principle

TURBO EQUALIZATIONConventional solutions generally involve both equalizationand channel coding which are done separately. In what follows,we introduce a new receiver scheme, called a turbo equalizer,where adaptive equalization and channel decoding are jointly optimized in order to improve the global performanceA turbo equalizer allows the receiver to benefit from channel decoder gain thanks to an iterative process applied to the same data block

TURBO EQUALIZATIONIn fact, the turbo-equalizer performance depends on channel selectivity and/or its time variation. For a large number of time-invariant channels, the turbo equalizer succeeds in completely removing the ISI and exhibits the same performance as the coded additive white Gaussian noise channels (AWGN).For time-varying channels, the turbo equalizer eliminates ISI and leads to a diversity gain.

BLIND EQUALIZATIONBlind channel equalization is also known as a self-recovering equalization. The objective of blind equalization is to recover the unknown input sequence to the unknown channel based solely on the probabilistic and statistical properties of the input sequence. The receiver can synchronize to the received signal and to adjust the equalizer without the training sequence.

BLIND EQUALIZATIONThe term blind is used in this equalizer because it performs the equalization on the data without a reference signal

Instead, the blind equalizer relies on knowledge of the signal structure and its statistic to perform the equalization.Blind signal is the unknown signal which would be identified in output signal with accommodated noise signal at receiver.

BLIND EQUALIZATIONChannel equalization uses the idea & knowledge of training sequences for channel estimation where as Blind channel equalization doesnt utilizes the characteristics of training sequences for frequency and impulse response analysis of channel.Blind Channel Equalization differs from channel equalization and without knowing the channel characteristics like transfer function & SNR it efficiently estimate the channel and reduces the ISI by blind signal separation at receiver side by suppressing noise in the received signal.

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