# Linear Equalizer

Equalize modulated signals using linear filtering

• Library:
• Communications Toolbox / Equalizers

## Description

The Linear Equalizer block uses a tapped delay line filter to equalize a linearly modulated signal through a dispersive channel. Using an estimate of the channel modeled as a finite input response (FIR) filter, the block processes input frames and outputs the estimated signal.

This icon shows the block with all ports enabled for configurations that use the LMS or RLS adaptive algorithm.

This icon shows the block with all ports enabled for configurations that use the CMA adaptive algorithm.

## Ports

### Input

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Input signal, specified as a column vector. The vector length of in must be equal to an integer multiple of the Number of input samples per symbol parameter. For more information, see Symbol Tap Spacing.

Data Types: double
Complex Number Support: Yes

Training symbols, specified as a column vector. The vector length of Desired must be less than or equal to the length of input in. The Desired input port is ignored when the Train input port is 0.

#### Dependencies

To enable this port, set the Adaptive algorithm parameter to LMS or RLS.

Data Types: double
Complex Number Support: Yes

Train equalizer flag, specified as 1 or 0. The block starts training when this value changes from 0 to 1 (at the rising edge). The block trains until all symbols in the Desired input port are processed.

#### Dependencies

To enable this port, set the Adaptive algorithm parameter to LMS or RLS and select the Enable training control input parameter.

Data Types: Boolean

Update tap weights flag, specified as 1 or 0. The tap weights are updated when this value is 1.

#### Dependencies

To enable this port, set the Adaptive algorithm parameter to CMA and the Source of adapt weights flag parameter to Input port.

Data Types: Boolean

Reset equalizer flag, specified as 1 or 0. If Reset is set to 1, the block resets the tap weights before processing the incoming signal. The block performs initial training until all symbols in the Desired input port are processed.

#### Dependencies

To enable this port, select the Enable reset input parameter.

Data Types: Boolean

### Output

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Equalized symbols, returned as a column vector that has the same length as input signal in.

This port is unnamed until you select the Output error signal or Output taps weights parameter.

Error signal, returned as a column vector that has the same length as input signal in.

Tap weights, returned as an NTaps-by-1 vector, where NTaps is the value of the Number of Taps parameter. w contains the tap weights from the last tap weight update.

## Parameters

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Structure parameters

Number of equalizer taps, specified as a positive integer. The number of equalizer taps must be greater than or equal to the value of the Number of input samples per symbol parameter.

Signal constellation, specified as a vector. The default value is a QPSK constellation generated using this code: pskmod(0:3,4,pi/4).

Number of input samples per symbol, specified as a positive integer. Setting this parameter to any number greater than 1 effectively creates a fractionally spaced equalizer. For more information, see Symbol Tap Spacing.

Algorithm parameters

Adaptive algorithm used for equalization, specified as one of these values:

Step size used by the adaptive algorithm, specified as a positive scalar. Increasing the step size reduces the equalizer convergence time but causes the equalizer output estimates to be less stable.

Tunable: Yes

#### Dependencies

To enable this parameter, set Adaptive algorithm to LMS or CMA.

Forgetting factor used by the adaptive algorithm, specified as a scalar in the range (0, 1]. Decreasing the forgetting factor reduces the equalizer convergence time but causes the equalizer output estimates to be less stable.

Tunable: Yes

#### Dependencies

To enable this parameter, set Adaptive algorithm to RLS.

Initial inverse correlation matrix, specified as a scalar or an NTaps-by-NTaps matrix. NTaps is equal to the Number of Taps parameter value. If you specify this value as a scalar, a, the equalizer sets the initial inverse correlation matrix to a times the identity matrix: a(eye(NTaps)).

#### Dependencies

To enable this parameter, set Adaptive algorithm to RLS.

Control parameters

Reference tap, specified as a positive integer less than or equal to the Number of Taps parameter value. The equalizer uses the reference tap location to track the main energy of the channel.

Input signal delay in samples relative to the reset time of the equalizer, specified as a nonnegative integer. If the input signal is a vector of length greater than 1, then the input delay is relative to the start of the input vector. If the input signal is a scalar, then the input delay is relative to the first call of the block and to the first call of the block after the Reset input port toggles to 1.

#### Dependencies

To enable this parameter, set Adaptive algorithm to LMS or RLS.

Source of the adapt tap weights request, specified as one of these values:

• Property — Specify this value to use the Adaptive algorithm parameter to control when the block adapts tap weights.

• Input port — Specify this value to use the Update input port to control when the block adapts tap weights.

#### Dependencies

To enable this parameter, set Adaptive algorithm to CMA.

Select this parameter to adaptively update the equalizer tap weights. If this parameter is cleared, the block keeps the equalizer tap weights unchanged.

#### Dependencies

To enable this parameter, set Adaptive algorithm to CMA and Source of adapt weights flag to Property.

Source for initial tap weights, specified as one of these values:

• Auto — Initialize the tap weights to the algorithm-specific default values, as described in the Initial weights parameter.

• Property — Initialize the tap weights using the Initial weights parameter value.

Initial tap weights used by the adaptive algorithm, specified as a scalar or an NTaps-by-1 vector. NTaps is equal to the Number of Taps parameter value. The default is 0 when the Adaptive algorithm parameter is set to LMS or RLS. The default is [0;0;1;0;0] when the Adaptive algorithm parameter is set to CMA.

If you specify Initial weights as a vector, the vector length must be equal to the Number of Taps parameter value. If you specify Initial weights as a scalar, the equalizer uses scalar expansion to create a vector of length Number of Taps with all values set to Initial weights.

#### Dependencies

To enable this parameter, set Initial tap weights source to Property.

Tap weight update period in symbols, specified as a positive integer. The equalizer updates the tap weights after processing this number of symbols.

Select this parameter to enable input port Train. If this parameter is cleared, the block does not reenter training mode after the initial tap training.

#### Dependencies

To enable this parameter, set Adaptive algorithm to LMS or RLS.

Select this parameter to use decision directed mode to update equalizer tap weights. If this parameter is cleared, the block keeps the equalizer tap weights unchanged after training.

#### Dependencies

To enable this parameter, set Adaptive algorithm to LMS or RLS.

Select this parameter to enable input port Train. If this parameter is cleared, the block does not reenter training mode after the initial tap training.

Diagnostic parameters

Select this parameter to enable output port Err containing the equalizer error signal.

Select this parameter to enable output port w containing tap weights from the last tap weight update.

Type of simulation to run, specified as Code generation or Interpreted execution.

• Code generation –– Simulate the model by using generated C code. The first time you run a simulation, Simulink® generates C code for the block. The C code is reused for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than Interpreted execution.

• Interpreted execution –– Simulate the model by using the MATLAB® interpreter. This option requires less startup time than the Code generation method, but the speed of subsequent simulations is slower. In this mode, you can debug the source code of the block.

## Block Characteristics

 Data Types double | single Multidimensional Signals no Variable-Size Signals yes

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## Version History

Introduced in R2019a