(To be removed) Construct constant modulus algorithm (CMA) object
alg = cma(stepsize)
alg = cma(stepsize,leakagefactor)
cma function creates an adaptive algorithm object that you
can use with the
lineareq function or
dfe function to create an equalizer object. You can then use the
equalizer object with the
equalize function to equalize a
signal. To learn more about the process for equalizing a signal, see Equalization.
After you use either
create a CMA equalizer object, you should initialize the equalizer object's
Weights property with a nonzero vector. Typically, CMA is
used with differential modulation; otherwise, the initial weights are very
important. A typical vector of initial weights has a 1 corresponding to the center
tap and 0s elsewhere.
alg = cma(stepsize) constructs an adaptive
algorithm object based on the constant modulus algorithm (CMA) with a step size of
alg = cma(stepsize,leakagefactor) sets the
leakage factor of the CMA.
leakagefactor must be between 0 and 1. A
value of 1 corresponds to a conventional weight update algorithm, while a value of 0
corresponds to a memoryless update algorithm.
The table below describes the properties of the CMA adaptive algorithm object. To learn how to view or change the values of an adaptive algorithm object, see Equalization.
|Fixed value, |
|CMA step size parameter, a nonnegative real number|
|CMA leakage factor, a real number between 0 and 1|
Use the constant modulus algorithm (CMA) to create an adaptive equalizer object.
Set the number of weights and the step size for the equalizer.
nWeights = 1; stepSize = 0.1;
Create an adaptive algorithm object using the
alg = cma(stepSize);
Construct a linear equalizer using the algorithm object.
eqObj = lineareq(nWeights,alg)
eqObj = EqType: 'Linear Equalizer' AlgType: 'Constant Modulus' nWeights: 1 nSampPerSym: 1 SigConst: [-1 1] StepSize: 0.1000 LeakageFactor: 1 Weights: 0 WeightInputs: 0 ResetBeforeFiltering: 1 NumSamplesProcessed: 0
Referring to the schematics in Equalization, define w as the vector of all weights wi and define u as the vector of all inputs ui. Based on the current set of weights, w, this adaptive algorithm creates the new set of weights given by
LeakageFactor) w + (
where the * operator denotes the complex conjugate.
 Haykin, Simon, Adaptive Filter Theory, Third Ed., Upper Saddle River, NJ, Prentice-Hall, 1996.
 Johnson, Richard C., Jr., Philip Schniter, Thomas. J. Endres, et al., “Blind Equalization Using the Constant Modulus Criterion: A Review,” Proceedings of the IEEE, Vol. 86, October 1998, pp. 1927–1950.