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MLSE Equalizer - Equalize using Viterbi algorithm

Library

Equalizers

Description

The MLSE Equalizer block uses the Viterbi algorithm to equalize a linearly modulated signal through a dispersive channel. The block receives a frame-based input signal and outputs the maximum likelihood sequence estimate (MLSE) of the signal, using an estimate of the channel modeled as a finite input response (FIR) filter.

This block supports single and double data types.

Channel Estimates

The channel estimate takes the form of a column vector containing the coefficients of an FIR filter in descending order of powers. The length of this vector is the channel memory, which must be a multiple of the block's Samples per input symbol parameter.

To specify the channel estimate vector, use one of these methods:

Set Specify channel via to Dialog and enter the vector in the Channel coefficients field.
Set Specify channel via to Input port. The block displays an additional input port, labeled Ch, that receives a frame-based vector.

Signal Constellation

The Signal constellation parameter specifies the constellation for the modulated signal, as determined by the modulator in your model. Signal constellation is a vector of complex numbers, where the kth complex number in the vector is the constellation point to which the modulator maps the integer k-1.

Note The sequence of constellation points must be consistent between the modulator in your model and the Signal constellation parameter in this block.

For example, to specify the constellation given by the mapping

set Constellation points to [1+i, -1+i, -1-i, 1-i]. Note that the sequence of numbers in the vector indicates how the modulator maps integers to the set of constellation points. The labeled constellation is shown below.

Preamble and Postamble

If your data is accompanied by a preamble (prefix) or postamble (suffix), then configure the block accordingly:

If you select Input contains preamble, then the Expected preamble parameter specifies the preamble that you expect to precede the data in the input signal.
If you check the Input contains postamble, then the Expected postamble parameter specifies the postamble that you expect to follow the data in the input signal.

The Expected preamble or Expected postamble parameter must be a vector of integers between 0 and M-1, where M is the number of constellation points. An integer value of k-1 in the vector corresponds to the kth entry in the Constellation points vector and, consequently, to a modulator input of k-1.

The preamble or postamble must already be included at the beginning or end, respectively, of the input signal to this block. If necessary, you can concatenate vectors in Simulink software using the Matrix Concatenation block.

To learn how the block uses the preamble and postamble, see "Reset Every Frame" Operation Mode below.

"Reset Every Frame" Operation Mode

One way that the Viterbi algorithm can transition between successive frames is called Reset every frame mode. You can choose this mode using the Operation mode parameter.

In Reset every frame mode, the block decodes each frame of data independently, resetting the state metric at the end of each frame. The traceback decoding always starts at the state with the minimum state metric.

The initialization of state metrics depends on whether you specify a preamble and/or postamble:

If you do not specify a preamble, the decoder initializes the metrics of all states to 0 at the beginning of each frame of data.
If you specify a preamble, the block uses it to initialize the state metrics at the beginning of each frame of data. More specifically, the block decodes the preamble and assigns a metric of 0 to the decoded state. If the preamble does not decode to a unique state -- that is, if the length of the preamble is less than the channel memory -- the decoder assigns a metric of 0 to all states that can be represented by the preamble. Whenever you specify a preamble, the traceback path ends at one of the states represented by the preamble.
If you do not specify a postamble, the traceback path starts at the state with the smallest metric.
If you specify a postamble, the traceback path begins at the state represented by the postamble. If the postamble does not decode to a unique state, the decoder identifies the smallest of all possible decoded states that are represented by the postamble and begins traceback decoding at that state.

Continuous Operation Mode

An alternative way that the Viterbi algorithm can transition between successive frames is called Continuous with reset option mode. You can choose this mode using the Operation mode parameter.

In Continuous with reset option mode, the block initializes the metrics of all states to 0 at the beginning of the simulation. At the end of each frame, the block saves the internal state metric for use in computing the traceback paths in the next frame.

If you select the Enable the reset input port check box, the block displays another input port, labeled Rst. In this case, the block resets the state metrics whenever the scalar value at the Rst port is nonzero.

Decoding Delay

The MLSE Equalizer block introduces an output delay equal to the Traceback depth in the Continuous with reset option mode, and no delay in the Reset every frame mode.

Dialog Box

Specify channel via: The method for specifying the channel estimate. If you select Input port, the block displays a second input port that receives the channel estimate. If you select Dialog, you can specify the channel estimate as a vector of coefficients for an FIR filter in the Channel coefficients field.
Channel coefficients: Vector containing the coefficients of the FIR filter that the block uses for the channel estimate. This field is visible only if you set Specify channel via to Dialog.
Signal constellation: Vector of complex numbers that specifies the constellation for the modulation.
Traceback depth: The number of trellis branches (equivalently, the number of symbols) the block uses in the Viterbi algorithm to construct each traceback path.
Operation mode: The operation mode of the Viterbi decoder. Choices are Continuous with reset option and Reset every frame.
Input contains preamble: When checked, you can set the preamble in the Expected preamble field. This option appears only if you set Operation mode to Reset every frame.
Expected preamble: Vector of integers between 0 and M-1 representing the preamble, where M is the size of the constellation. This field is visible and active only if you set Operation mode to Reset every frame and then select Input contains preamble.
Input contains postamble: When checked, you can set the postamble in the Expected postamble field. This option appears only if you set Operation mode to Reset every frame.
Expected postamble: Vector of integers between 0 and M-1 representing the postamble, where M is the size of the constellation. This field is visible and active only if you set Operation mode to Reset every frame and then select Input contains postamble.
Samples per input symbol: The number of input samples for each constellation point.
Enable the reset input port: When you check this box, the block has a second input port labeled Rst. Providing a nonzero input value to this port causes the block to set its internal memory to the initial state before processing the input data. This option appears only if you set Operation mode to Continuous with reset option.