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# dfe

(To be removed) Construct decision-feedback equalizer object

dfe will be removed in a future release. Use `comm.DecisionFeedback` instead.

## Syntax

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

## Description

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 Equalization.

`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.

### Properties

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 Equalization.

### Note

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

PropertyDescription
`EqType`Fixed value, ```'Decision Feedback Equalizer'```
`AlgType`Name of the adaptive algorithm represented by `alg`
`nWeights`Number 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.
`nSampPerSym`Number of input samples per symbol (equivalent to `nsamp` input argument). This value relates to both the equalizer structure (see the use of K in Equalization) 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.
`SigConst`Signal constellation, a vector whose length is typically a power of 2.
`Weights`Vector that concatenates the complex coefficients from the forward filter and the feedback filter. This is the set of wi values in the schematic in Equalization.
`WeightInputs`Vector 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 Equalization.
`ResetBeforeFiltering`If `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.
`NumSamplesProcessed`Number 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 `alg`See 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
`Weights``zeros(1,sum(nWeights))`
`WeightInputs``zeros(1,sum(nWeights))`
`StepSize` (Variable-step-size LMS equalizers)`InitStep*ones(1,sum(nWeights))`
`InvCorrMatrix` (RLS equalizers)`InvCorrInit*eye(sum(nWeights))`

## Examples

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Equalize a signal using a decision feedback equalizer with least mean square (LMS) adaptation.

Set Up Transmitter

Create a QPSK modulated transmission signal containing random message data. Pass the signal through an arbitrary channel filter to add signal distortion.

```M = 4; % Alphabet size for modulation msg = randi([0 M-1],2500,1); % Random message hMod = comm.QPSKModulator('PhaseOffset',0); modmsg = hMod(msg); % Modulate using QPSK chan = [.986; .845; .237; .123+.31i]; % Channel coefficients filtmsg = filter(chan,1,modmsg); % Introduce channel distortion```

Set Up Equalizer

Create a DFE object that has 5 forward taps, 3 feedback taps. Specify the least mean square algorithm inline when creating the equalizer object. Initialize additional equalizer properties.

```dfeObj = dfe(5,3,lms(0.01)); % Set the signal constellation dfeObj.SigConst = hMod((0:M-1)')'; % Maintain continuity between calls to equalize dfeObj.ResetBeforeFiltering = 0; % Define initial coefficients to help convergence dfeObj.Weights = [0 1 0 0 0 0 0 0];```

Equalize Received Signal

`eqRxSig = equalize(dfeObj,filtmsg);`

Plot Results

Compare the first 200 equalized symbols (`initial`) to the remaining equalized signal (`final`).

```initial = eqRxSig(1:200); plot(real(initial),imag(initial),'+') hold on final = eqRxSig(end-200:end); plot(real(final),imag(final),'ro') legend('initial', 'final')```

Equalization of the received signal converges within approximately 200 samples.

Apply a decision feedback equalizer (DFE) to an 8-PSK modulated signal impaired by a frequency selective channel. The DFE uses 600 training symbols.

Create a PSK modulator System object™ and set the modulation order to 8.

`modulator = comm.PSKModulator('ModulationOrder',8);`

Create a column vector of 8-ary random integer symbols. Seed the random number generator, `rng`, to produce a predictable sequence of numbers.

```rng(12345); data = randi([0 7],5000,1);```

Use the `modulator` System object to modulate the random data.

`modData = modulator(data);`

Create a Rayleigh channel System object to define a static frequency selective channel with four taps. Pass the modulated data through the channel object.

```chan = comm.RayleighChannel('SampleRate',1000, ... 'PathDelays',[0 0.002 0.004 0.008],'AveragePathGains',[0 -3 -6 -9]); rxSig = chan(modData);```

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

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

Set the `SigConst` property of the DFE equalizer to match the 8-PSK modulator reference constellation. The reference constellation is determined by using the `constellation` method. For decision directed operation, the DFE must use the same signal constellation as the transmission scheme.

`equalizerDFE.SigConst = constellation(modulator).';`

Equalize the signal to remove the effects of channel distortion. Use the first 600 symbols to train the equalizer.

```trainlen = 600; [eqSig,detectedSig] = equalize(equalizerDFE,rxSig, ... modData(1:trainlen));```

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

```hScatter = scatterplot(rxSig,1,trainlen,'bx'); hold on scatterplot(eqSig,1,trainlen,'g.',hScatter); scatterplot(equalizerDFE.SigConst,1,0,'m*',hScatter); legend('Received signal','Equalized signal',... 'Ideal signal constellation'); hold off```

Create a PSK demodulator System object. Use the object to demodulate the received signal before and after equalization.

```demod = comm.PSKDemodulator('ModulationOrder',8); demodSig = demod(rxSig); demodEqualizedSig = demod(detectedSig);```

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

```errorCalc = comm.ErrorRate; nonEqualizedSER = errorCalc(data(trainlen+1:end), ... demodSig(trainlen+1:end)); reset(errorCalc) equalizedSER = errorCalc(data(trainlen+1:end), ... demodEqualizedSig(trainlen+1:end)); disp('Symbol error rates with and without equalizer:') disp([equalizedSER(1) nonEqualizedSER(1)])```

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

## Compatibility Considerations

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Not recommended starting in R2019a

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