Documentation Center

  • Trial Software
  • Product Updates


Construct decision-feedback equalizer object


eqobj = dfe(nfwdweights,nfbkweights,alg)
eqobj = dfe(nfwdweights,nfbkweights,alg,sigconst)
eqobj = dfe(nfwdweights,nfbkweights,alg,sigconst,nsamp)


The dfe function creates an equalizer object that you can use with the equalize function to equalize a signal. To learn more about the process for equalizing a signal, see Adaptive Algorithms.

eqobj = dfe(nfwdweights,nfbkweights,alg) constructs a decision feedback equalizer object. The equalizer's feedforward and feedback filters have nfwdweights and nfbkweights symbol-spaced complex weights, respectively, which are initially all zeros. alg describes the adaptive algorithm that the equalizer uses; you should create alg using any of these functions: lms, signlms, normlms, varlms, rls, or cma. The signal constellation of the desired output is [-1 1], which corresponds to binary phase shift keying (BPSK).

eqobj = dfe(nfwdweights,nfbkweights,alg,sigconst) specifies the signal constellation vector of the desired output.

eqobj = dfe(nfwdweights,nfbkweights,alg,sigconst,nsamp) constructs a DFE with a fractionally spaced forward filter. The forward filter has nfwdweights complex weights spaced at T/nsamp, where T is the symbol period and nsamp is a positive integer. nsamp = 1 corresponds to a symbol-spaced forward filter.


The table below describes the properties of the decision feedback equalizer object. To learn how to view or change the values of a decision feedback equalizer object, see Accessing Properties of an Equalizer.

    Note:   To initialize or reset the equalizer object eqobj, enter reset(eqobj).

EqTypeFixed value, 'Decision Feedback Equalizer'
AlgTypeName of the adaptive algorithm represented by alg
nWeightsNumber of weights in the forward filter and the feedback filter, in the format [nfwdweights, nfbkweights]. The number of weights in the forward filter must be at least 1.
nSampPerSymNumber of input samples per symbol (equivalent to nsamp input argument). This value relates to both the equalizer structure (see the use of K in Decision-Feedback Equalizers) and an assumption about the signal to be equalized.
RefTap (except for CMA equalizers)Reference tap index, between 1 and nfwdweights. Setting this to a value greater than 1 effectively delays the reference signal with respect to the equalizer's input signal.
SigConstSignal constellation, a vector whose length is typically a power of 2.
WeightsVector that concatenates the complex coefficients from the forward filter and the feedback filter. This is the set of wi values in the schematic in Decision-Feedback Equalizers.
WeightInputsVector that concatenates the tap weight inputs for the forward filter and the feedback filter. This is the set of ui values in the schematic in Decision-Feedback Equalizers.
ResetBeforeFilteringIf 1, each call to equalize resets the state of eqobj before equalizing. If 0, the equalization process maintains continuity from one call to the next.
NumSamplesProcessedNumber of samples the equalizer processed since the last reset. When you create or reset eqobj, this property value is 0.
Properties specific to the adaptive algorithm represented by algSee reference page for the adaptive algorithm function that created alg: lms, signlms, normlms, varlms, rls, or cma.

Relationships Among Properties

If you change nWeights, MATLAB maintains consistency in the equalizer object by adjusting the values of the properties listed below.

PropertyAdjusted Value
StepSize (Variable-step-size LMS equalizers)InitStep*ones(1,sum(nWeights))
InvCorrMatrix (RLS equalizers)InvCorrInit*eye(sum(nWeights))

An example illustrating relationships among properties is in Linked Properties of an Equalizer Object.


Apply a decision feedback equalizer (DFE) to an 8-PSK modulated signal

Apply a decision feedback equalizer (DFE) to an 8-PSK modulated signal impaired by a frequency selector channel. The DFE uses 400 training symbols.

Set the modulation order to define 8-PSK modulation, and create a PSK modulator System object™.

M = 8;
hMod = comm.PSKModulator(M);

Create a 1500-by-1 column vector of random message symbols.

msg = randi([0 M-1],1500,1);

Modulate the random message signal by calling the step method of the comm.PSKModulator System object.

modmsg = step(hMod,msg);

Define a frequency selective channel with four taps, and then pass the modulated signal through the channel, introducing channel distortion.

chan = [.986; .845; .237; .123+.31i];
filtmsg = filter(chan,1,modmsg);

Create a DFE equalizer that has 10 feed forward tabs and five feedback tabs. The equalizer uses the LMS update method with a step size of 0.01.

numFFTaps = 10; numFBTaps = 5;
eq1 = dfe(numFFTaps, numFBTaps, lms(0.01));

For decision directed operation, the DFE must use the same signal constellation as the transmission scheme. Set the SigConst property to the constellation the modulator System object uses.

eq1.SigConst = step(hMod,(0:M-1)')'; 

Equalize the signal to help remove the effects of channel distortion. Use the first 400 symbols to train the equalizer.

trainlen = 400;
[symbolest,yd] = equalize(eq1,filtmsg,modmsg(1:trainlen));

Plot the received signal, equalizer output after training, and the ideal signal constellation.

h = scatterplot(filtmsg,1,trainlen,'bx'); hold on;
legend('Filtered signal','Equalized signal',...
   'Ideal signal constellation');
hold off;

Demodulate the signal at the equalizer output, and the unequalized signal at the input of the equalizer.

hDemod = comm.PSKDemodulator(8);
demodmsg_noeq = step(hDemod,filtmsg);
demodmsg = step(hDemod,yd);

Compute the error rates for the two demodulated signals and compare the results.

hErrorCalc = comm.ErrorRate;
ser_noEq = step(hErrorCalc, ...
    msg(trainlen+1:end), demodmsg_noeq(trainlen+1:end));
ser_Eq = step(hErrorCalc, msg(trainlen+1:end),demodmsg(trainlen+1:end));
disp('Symbol error rates with and without equalizer:')
disp([ser_Eq(1) ser_noEq(1)])

The equalizer helps eliminate the distortion introduced by the frequency selective channel, and reduces the error rate.

More About

See Also

| | | | | | |

Was this topic helpful?