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lineareq

(To be removed) Construct linear equalizer object

lineareq will be removed in a future release. Use comm.LinearEqualizer instead.

Syntax

eqobj = lineareq(nweights,alg)
eqobj = lineareq(nweights,alg,sigconst)
eqobj = lineareq(nweights,alg,sigconst,nsamp)

Description

The lineareq 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 = lineareq(nweights,alg) constructs a symbol-spaced linear equalizer object. The equalizer has nweights complex weights, 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 = lineareq(nweights,alg,sigconst) specifies the signal constellation vector of the desired output.

eqobj = lineareq(nweights,alg,sigconst,nsamp) constructs a fractionally spaced linear equalizer object. The equalizer has nweights 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 equalizer.

Properties

The table below describes the properties of the linear equalizer object. To learn how to view or change the values of a linear equalizer object, see Equalization.

Tip

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

PropertyDescription
EqTypeFixed value, 'Linear Equalizer'
AlgTypeName of the adaptive algorithm represented by alg
nWeightsNumber of weights
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 Equalization) and an assumption about the signal to be equalized.
RefTap (except for CMA equalizers)Reference tap index, between 1 and nWeights. Setting this to a value greater than 1 effectively delays the reference signal and the output signal by RefTap-1 with respect to the equalizer's input signal.
SigConstSignal constellation, a vector whose length is typically a power of 2
WeightsVector of complex coefficients. This is the set of wi values in the schematic in Equalization.
WeightInputsVector of tap weight inputs. This is the set of ui values in the schematic in Equalization.
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
Weightszeros(1,nWeights)
WeightInputszeros(1,nWeights)
StepSize (Variable-step-size LMS equalizers)InitStep*ones(1,nWeights)
InvCorrMatrix (RLS equalizers)InvCorrInit*eye(nWeights)

Examples

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This example configures the recommended comm.LinearEqualizer System object™ and the legacy lineareq feature with comparable settings.

Initialize Variables and Supporting Objects

d = randi([0 3],1000,1);
x = pskmod(d,4,pi/4);
r = awgn(x,25);
sps = 2; %samples per symbol for oversampled cases
nTaps = 6;
txFilter = comm.RaisedCosineTransmitFilter('FilterSpanInSymbols',nTaps, ...
    'OutputSamplesPerSymbol',4);
rxFilter = comm.RaisedCosineReceiveFilter('FilterSpanInSymbols',nTaps, ...
    'InputSamplesPerSymbol',4,'DecimationFactor',2);
x2 = txFilter(x);
r2 = rxFilter(awgn(x2,25,0.5));
filterDelay = txFilter.FilterSpanInSymbols/2 + ...
    rxFilter.FilterSpanInSymbols/2; % Total filter delay in symbols

To compare the equalized output, plot the constellations using code such as:

% plot(yNew,'*')
% hold on
% plot(yOld,'o')
% hold off; legend('New Eq','Old Eq'); grid on

Use LMS Algorithm with Linear Equalizer

Configure lineareq and comm.LinearEqualizer objects with comparable settings. The LeakageFactor property has been removed from LMS algorithm. The comm.LinearEqualizer System object™ assumes that leakage factor is always 1.

eqOld = lineareq(5,lms(0.05),pskmod(0:3,4,pi/4))
eqOld =
  EqType: 'Linear Equalizer'
  AlgType: 'LMS'
  nWeights: 5
  nSampPerSym: 1
  RefTap: 1
  SigConst: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  StepSize: 0.0500
  LeakageFactor: 1
  Weights: [0 0 0 0 0]
  WeightInputs: [0 0 0 0 0]
  ResetBeforeFiltering: 1
  NumSamplesProcessed: 0
eqNew = comm.LinearEqualizer('NumTaps',5,'Algorithm','LMS','StepSize',0.05, ...
    'Constellation',pskmod(0:3,4,pi/4),'ReferenceTap',1)
eqNew = comm.LinearEqualizer with properties:
  Algorithm: 'LMS'
  NumTaps: 5
  StepSize: 0.0500
  Constellation: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  ReferenceTap: 1
  InputDelay: 0
  InputSamplesPerSymbol: 1
  TrainingFlagInputPort: false
  AdaptAfterTraining: true
  InitialWeightsSource: 'Auto'
  WeightUpdatePeriod: 1

Call the equalizers.

yOld = equalize(eqOld,r,x(1:100));
yNew = eqNew(r,x(1:100));

Use RLS Algorithm with Linear Equalizer

Configure lineareq and comm.LinearEqualizer objects with comparable settings.

eqOld = lineareq(5,rls(0.95),pskmod(0:3,4,pi/4))
eqOld =
  EqType: 'Linear Equalizer'
  AlgType: 'RLS'
  nWeights: 5
  nSampPerSym: 1
  RefTap: 1
  SigConst: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  InvCorrInit: 0.1000
  InvCorrMatrix: [5×5 double]
  Weights: [0 0 0 0 0]
  WeightInputs: [0 0 0 0 0]
  ResetBeforeFiltering: 1
  NumSamplesProcessed: 0
eqNew = comm.LinearEqualizer('NumTaps',5,'Algorithm','RLS', ...
    'ForgettingFactor',0.95,'Constellation',pskmod(0:3,4,pi/4),'ReferenceTap',1)
eqNew = comm.LinearEqualizer with properties:
  Algorithm: 'RLS'
  NumTaps: 5
  ForgettingFactor: 0.9500
  InitialInverseCorrelationMatrix: 0.1000
  Constellation: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  ReferenceTap: 1
  InputDelay: 0
  InputSamplesPerSymbol: 1
  TrainingFlagInputPort: false
  AdaptAfterTraining: true
  InitialWeightsSource: 'Auto'
  WeightUpdatePeriod: 1

Call the equalizers. When ResetBeforeFiltering is set to true, each call of the equalize object resets the equalizer. To get the equivalent behavior call reset after each call of the comm.LinearEqualizer object.

yOld1 = equalize(eqOld,r,x(1:100));
yOld2 = equalize(eqOld,r,x(1:100));

yNew1 = eqNew(r,x(1:100));
reset(eqNew)
yNew2 = eqNew(r,x(1:100));

Configure lineareq and comm.LinearEqualizer objects with comparable settings. For the comm.LinearEqualizer object, set the initial inverse correlation matrix to eye(5)*0.2.

eqOld = lineareq(5,rls(0.95),pskmod(0:3,4,pi/4))
eqOld =
  EqType: 'Linear Equalizer'
  AlgType: 'RLS'
  nWeights: 5
  nSampPerSym: 1
  RefTap: 1
  SigConst: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  ForgetFactor: 0.9500
  InvCorrInit: 0.1000
  InvCorrMatrix: [5×5 double]
  Weights: [0 0 0 0 0]
  WeightInputs: [0 0 0 0 0]
  ResetBeforeFiltering: 1
  NumSamplesProcessed: 0
eqNew = comm.LinearEqualizer('NumTaps',5,'Algorithm','RLS', ...
    'ForgettingFactor',0.95,'Constellation',pskmod(0:3,4,pi/4),'ReferenceTap',1, ...
    'InitialInverseCorrelationMatrix',eye(5)*0.2)
eqNew = comm.LinearEqualizer with properties:
  Algorithm: 'RLS'
  NumTaps: 5
  ForgettingFactor: 0.9500
  InitialInverseCorrelationMatrix: [5×5 double]
  Constellation: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  ReferenceTap: 1
  InputDelay: 0
  InputSamplesPerSymbol: 1
  TrainingFlagInputPort: false
  AdaptAfterTraining: true
  InitialWeightsSource: 'Auto'
  WeightUpdatePeriod: 1

Call the equalizers. When ResetBeforeFiltering is set to true, each call of the equalize object resets the equalizer. To get the equivalent behavior call reset after each call of the comm.LinearEqualizer object.

yOld1 = equalize(eqOld,r,x(1:100));
yOld2 = equalize(eqOld,r,x(1:100));

yNew1 = eqNew(r,x(1:100));
reset(eqNew)
yNew2 = eqNew(r,x(1:100));

Use CMA Algorithm with Linear Equalizer

Configure lineareq and comm.LinearEqualizer objects with comparable settings. The LeakageFactor property has been removed from CMA algorithm. The comm.LinearEqualizer System object™ assumes that leakage factor is always 1.

eqOld = lineareq(5,cma(0.05),pskmod(0:3,4,pi/4))
eqOld =
  EqType: 'Linear Equalizer'
  AlgType: 'Constant Modulus'
  nWeights: 5
  nSampPerSym: 1
  SigConst: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  StepSize: 0.0500
  LeakageFactor: 1
  Weights: [1 0 0 0 0]
  WeightInputs: [0 0 0 0 0]
  ResetBeforeFiltering: 1
  NumSamplesProcessed: 0
eqNew = comm.LinearEqualizer('NumTaps',5,'Algorithm','CMA','StepSize',0.05, ...
    'Constellation',pskmod(0:3,4,pi/4),'ReferenceTap',1)
eqNew = comm.LinearEqualizer with properties:
  Algorithm: 'CMA'
  NumTaps: 5
  StepSize: 0.0500
  Constellation: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  ReferenceTap: 1
  InputSamplesPerSymbol: 1
  AdaptWeightsSource: 'Property'
  AdaptWeights: true
  InitialWeightsSource: 'Auto'
  WeightUpdatePeriod: 1

Call the equalizers.

yOld = equalize(eqOld,r);
yNew = eqNew(r);

Use Linear Equalizers Considering Signal Delays

Configure lineareq and comm.LinearEqualizer objects with comparable settings. The transmit and receive filters result in a signal delay between the transit and receive signals. Account for this delay by setting the RefTap property of the lineareq to a value close to the delay value in samples. Additionally, nWeights must be set to a value greater than RefTap.

eqOld = lineareq(filterDelay*sps+4,lms(0.01),pskmod(0:3,4,pi/4),sps);
eqOld.RefTap = filterDelay*sps+1 % Adjust to synchronize with delayed signal 
eqOld =
  EqType: 'Linear Equalizer'
  AlgType: 'LMS'
  nWeights: 16
  nSampPerSym: 2
  RefTap: 13
  SigConst: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  StepSize: 0.0100
  LeakageFactor: 1
  Weights: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  WeightInputs: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
  ResetBeforeFiltering: 1
  NumSamplesProcessed: 0

eqNew = comm.LinearEqualizer('NumTaps',16,'Algorithm','LMS','StepSize',0.01, ...
    'Constellation',pskmod(0:3,4,pi/4),'InputSamplesPerSymbol',sps, ...
    'ReferenceTap',filterDelay*sps+1,'InputDelay',0)
eqNew = comm.LinearEqualizer with properties:
  Algorithm: 'LMS'
  NumTaps: 16
  StepSize: 0.0100
  Constellation: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  ReferenceTap: 13
  InputDelay: 0
  InputSamplesPerSymbol: 2
  TrainingFlagInputPort: false
  AdaptAfterTraining: true
  InitialWeightsSource: 'Auto'
  WeightUpdatePeriod: 1

Call the equalizers. When ResetBeforeFiltering is set to true, each call of the equalize object resets the equalizer. To get the equivalent behavior call reset after each call of the comm.LinearEqualizer object.

yOld1 = equalize(eqOld,r,x(1:100));
yOld2 = equalize(eqOld,r,x(1:100));

yNew1 = eqNew(r,x(1:100));
reset(eqNew)
yNew2 = eqNew(r,x(1:100));

In the comm.LinearEqualizer object, InputDelay is used to synchronize with the delayed signal. NumTaps and ReferenceTap are independent of delay value. We can reduce the number of taps by utilizing the InputDelay to synchronize instead of reference tap. Reducing the number of taps also reduces equalizer self noise.

eqNew = comm.LinearEqualizer('NumTaps',11,'Algorithm','LMS','StepSize',0.01, ...
    'Constellation',pskmod(0:3,4,pi/4),'InputSamplesPerSymbol',sps, ...
    'ReferenceTap',6,'InputDelay',filterDelay*sps)
eqNew = comm.LinearEqualizer with properties:
  Algorithm: 'LMS'
  NumTaps: 11
  StepSize: 0.0100
  Constellation: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i]
  ReferenceTap: 6
  InputDelay: 12
  InputSamplesPerSymbol: 2
  TrainingFlagInputPort: false
  AdaptAfterTraining: true
  InitialWeightsSource: 'Auto'
  WeightUpdatePeriod: 1

yNew1 = eqNew(r2,x(1:100));
reset(eqNew)
yNew2 = eqNew(r2,x(1:100));

Compatibility Considerations

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Warns starting in R2020a

Introduced before R2006a