Equalize using decision feedback equalizer that updates weights with RLS algorithm
The RLS Decision Feedback Equalizer block uses a decision feedback equalizer and the RLS algorithm to equalize a linearly modulated baseband signal through a dispersive channel. During the simulation, the block uses the RLS algorithm to update the weights, once per symbol. When you set the Number of samples per symbol parameter to 1, the block implements a symbol-spaced equalizer and updates the filter weights once for each symbol. When you set the Number of samples per symbol parameter to a value greater than 1, the weights are updated once every Nth sample, for a fractionally spaced equalizer.
The Input port accepts a column vector input signal. The Desired port receives a training sequence with a length that is less than or equal to the number of symbols in the Input signal. Valid training symbols are those symbols listed in the Signal constellation vector.
Set the Reference tap parameter so it is greater than zero and less than the value for the Number of forward taps parameter.
The port labeled Equalized outputs the result of the equalization process.
You can configure the block to have one or more of these extra ports:
Mode input, as described in Reference Signal and Operation Modes in Communications System Toolbox™User's Guide.
Err output for the error signal, which is the difference between the Equalized output and the reference signal. The reference signal consists of training symbols in training mode, and detected symbols otherwise.
Weights output, as described in Adaptive Algorithms in Communications System ToolboxUser's Guide.
To learn the conditions under which the equalizer operates in training or decision-directed mode, see Adaptive Algorithms in Communications System Toolbox User's Guide.
For proper equalization, you should set the Reference tap parameter so that it exceeds the delay, in symbols, between the transmitter's modulator output and the equalizer input. When this condition is satisfied, the total delay, in symbols, between the modulator output and the equalizer output is equal to
1+(Reference tap-1)/(Number of samples per symbol)
Because the channel delay is typically unknown, a common practice is to set the reference tap to the center tap of the forward filter.
The number of taps in the forward filter of the decision feedback equalizer.
The number of taps in the feedback filter of the decision feedback equalizer.
The number of input samples for each symbol.
A vector of complex numbers that specifies the constellation for the modulation.
A positive integer less than or equal to the number of forward taps in the equalizer.
The forgetting factor of the RLS algorithm, a number between 0 and 1.
The initial value for the inverse correlation matrix. The matrix must be N-by-N, where N is the total number of forward and feedback taps.
A vector that concatenates the initial weights for the forward and feedback taps.
When you select this check box, the block has an input port that allows you to toggle between training and decision-directed mode. For training, the mode input must be 1, and for decision directed, the mode must be 0. For every frame in which the mode input is 1 or not present, the equalizer trains at the beginning of the frame for the length of the desired signal.
When you select this check box, the block outputs the error signal, which is the difference between the equalized signal and the reference signal.
When you select this check box, the block outputs the current forward and feedback weights, concatenated into one vector.
 Farhang-Boroujeny, B., Adaptive Filters: Theory and Applications, Chichester, England, Wiley, 1998.
 Haykin, Simon, Adaptive Filter Theory, Third Ed., Upper Saddle River, N.J., Prentice-Hall, 1996.
 Kurzweil, Jack, An Introduction to Digital Communications, New York, Wiley, 2000.
 Proakis, John G., Digital Communications, Fourth Ed., New York, McGraw-Hill, 2001.