DECISION FEED BACK EQUALIZER

OUTLINE

Inter Symbol Interference

Equalizers

Linear Equalizer

Non linear Equalizer

Decision Feed back Equalizer(DFE)

Predictive Decision Feed back Equalizer

Comparison of Predictive DFE and DFE

INTER SYMBOL INTERFERENCE

Inter symbol interference is a signal distortion in telecommunication. One or more symbols can interfere with other symbols causing noise or less reliable signal.

The main causes of inter symbol interference are multipath propagation or non-linear frequency in channels.

This has the effect of a blur or mixture of symbols, which can reduce signal clarity.

• To recover the information sequence that is corrupted by ISI, we considered two types of equalization methods,

The MLSE criterion that is efficiently implemented by the Viterbi algorithm.

A linear transversal filter.

EQUALIZERS• The process of compressing or reducing the effect of

ISI is termed as equalization which is performed by the equalizers.

• Equalization techniques can be classified into Linear Non linear

These are classified based on how the output of an adaptive equalizer is used for subsequent control of the equalizer.

LINEAR AND NON LINEAR PROCESS FOR EQUALIZATION OF TRANSMISSION

CHANNEL

Linear equalizer

In linear equalizer the output signal is not used in feedback path to adapt the equalizer.

There is no feedback path for linear equalizer. The current and the past values of the received signal are linearly weighted by equalizer coefficients and summed to produce the output.

c(z) =∑𝑘𝐶𝑘𝑍 −𝑘

Disadvantages of linear equalizers

• Do not perform well on channels which have deep spectral nulls in pass band.

• To compensate for distortions, linear equalizer places too much gain in vicinity of spectral nulls, and thus enhances noise present in those frequencies.

• So, nonlinear equalizer are used where channel distortion are too severe for a linear equalizer to handle.

Non linear equalizer

In non linear equalizer the output signal is fed back to change the subsequent outputs of the equalizer.

The three nonlinear equalizers can be either implemented using a transversal filter or a lattice filter or a transversal channel estimator.

These structures have the flexibility to use various kinds of algorithms to quickly update the weights.

Most of them are recursive algorithms, could either use the zero forcing or LMS least means square or RLS recursive least square or the variations thereof.

DECISION FEEDBACK EQUALIZER(DFE)

It is a nonlinear type of channel equalizer that uses the previous detector decision to eliminate the ISI(Inter Symbol Interference) on pulses that are currently being modulated.

Decision Feedback Equalization makes use of previous decisions in attempting to estimate the current symbol.

Its performance is generally better than the linear equalizer.

Basic idea :

Once an information symbol has been detected and decided upon, the ISI that it induces on future symbols can be estimated and subtracted out before detection of subsequent symbols.

In DFE, ISI the present symbol induces, is estimated and is subtracted out before detection of subsequent symbols.

The nonlinear equalizer of Decision Feedback Equalizer consists of two filters namely a feed forward filter and a feedback filter.

FEED FORWARD FILTER(FFF):

It which operates on the outputs of the chip matched filter, ICI cancellation on the transmitted symbols.

FEED BACK FILTER(FBF):

It operates on the past decisions of the desired users data as well as those of the interfering users data.

Operation of DFE

• Feed forward filter acts as a noise whitening (or) WMF filter.

• It sends the input to symbol to symbol detector which identify the errors between the symbols and the error value is loaded to the feedback filter.

• The feedback filter optimizes the coefficient values thereby generating a new sequence which is equal to the transmitted sequence.

Advantages:Performance comparable to the optimum

demodulator but with much lower computational complexity.

Low noise enhancement.Copes of larger ISI.

Disadvantages:Instability danger.

Predictive DFE

• proposed by Belfiore and Park in 1979.• Consists of an FFF and an FBF, the latter is called a

noise predictor.• Predictive DFE performs as well as conventional

DFE as the limit in the number of taps in FFF and the FBF approach infinity.

• The FBF in predictive DFE can also be realized as a lattice structure. The RLS algorithm can be used to yield fast convergence

Where,

B(w)=the frequency response of the infinite length feedback filter.

Et(w)=transmitted error and it denotes the power spectral density of the noise content and the ISI.

Ep(w) denotes predicted amount of error.

Comparison of predictive DFE and conventional DFE

• These two DFE structures result in equivalent performance if their lengths are infinite.

• The predictive DFE is suboptimum if the lengths of the two filters are finite.

• This suboptimum of the predictive DFE is suitable as an equalizer for trellis-coded signals, where the conventional DFE is not as suitable.

Reason for suboptimum:

In conventional DFE the optimization of its tap coefficients in the feed forward and feed back filters is done jointly. Hence, it yields the minimum MSE.

In predictive DFE the optimization of the feed forward filter and the feed back filter are done separately. Hence, its MSE is large than conventional DFE.

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