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Equalizers
The Variable Step LMS Decision Feedback Equalizer block uses a decision feedback equalizer and the variable-step-size LMS algorithm to equalize a linearly modulated baseband signal through a dispersive channel. During the simulation, the block uses the variable-step-size LMS algorithm to update the weights, once per symbol. If the Number of samples per symbol parameter is 1, then the block implements a symbol-spaced equalizer; otherwise, the block implements a fractionally spaced equalizer.
The port labeled Input receives the signal you want to equalize, as a scalar or a frame-based column vector. The port labeled Desired receives a training sequence whose length is less than or equal to the number of symbols in the Input signal. Valid training symbols are those listed in the Signal constellation vector.
This block accepts only frame-based signals. If the value of Reference tap is equal to or greater than the frame size, the block will not work properly.
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 Controlling the Use of Training or Decision-Directed Mode in Communications Blockset 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 Retrieving the Weights and Error Signal in Communications Blockset User's Guide.
To learn the conditions under which the equalizer operates in training or decision-directed mode, see Using Adaptive Equalizers in Communications Blockset 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 step size that the variable-step-size LMS algorithm uses at the beginning of the simulation.
The increment by which the step size changes from iteration to iteration
The smallest value that the step size can assume.
The largest value that the step size can assume.
The leakage factor of the variable-step-size LMS algorithm, a number between 0 and 1. A value of 1 corresponds to a conventional weight update algorithm, and a value of 0 corresponds to a memoryless update algorithm.
A vector that concatenates the initial weights for the forward and feedback taps.
If you check this box, the block has an input port that enables you to toggle between training and decision-directed mode.
If you check this box, the block outputs the error signal, which is the difference between the equalized signal and the reference signal.
If you check this box, the block outputs the current forward and feedback weights, concatenated into one vector.
[1] Farhang-Boroujeny, B., Adaptive Filters: Theory and Applications, Chichester, England, Wiley, 1998.
Variable Step LMS Linear Equalizer, LMS Decision Feedback Equalizer
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