Linear Equalizer

情商ualize modulated signals using linear filtering

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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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`in`— Input signal
column vector

Input signal, specified as a column vector. The vector length ofinmust be equal to an integer multiple of theNumber of input samples per symbolparameter. For more information, seeSymbol Tap Spacing.

Data Types:double
Complex Number Support:Yes

`Desired`— Training symbols
column vector

Training symbols, specified as a column vector. The vector length ofDesiredmust be less than or equal to the length of inputin. TheDesired输入端口时被忽略Traininput port is0.

Dependencies

To enable this port, set theAdaptive algorithmparameter toLMSorRLS.

Data Types:double
Complex Number Support:Yes

`Train`— Train equalizer flag
`1`|`0`

Train equalizer flag, specified as1or0. The block starts training when this value changes from0to1(at the rising edge). The block trains until all symbols in theDesiredinput port are processed.

Dependencies

To enable this port, set theAdaptive algorithmparameter toLMSorRLSand select theEnable training control inputparameter.

Data Types:Boolean

`Update`— Update tap weights flag
`1`|`0`

Update tap weights flag, specified as1or0. The tap weights are updated when this value is1.

Dependencies

To enable this port, set theAdaptive algorithmparameter toCMAand the调整权重的旗帜parameter toInput port.

Data Types:Boolean

`Reset`— Reset equalizer flag
`1`|`0`

Reset equalizer flag, specified as1or0. IfResetis set to1, the block resets the tap weights before processing the incoming signal. The block performs initial training until all symbols in theDesiredinput port are processed.

Dependencies

To enable this port, select theEnable reset inputparameter.

Data Types:Boolean

Output

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`Out`— Equalized symbols
column vector

情商ualized symbols, returned as a column vector that has the same length as input signalin.

This port is unnamed until you select theOutput error signalorOutput taps weightsparameter.

`Err`— Error signal
column vector

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

`w`— Tap weights
column vector

Tap weights, returned as anN_Taps-by-1 vector, whereN_Tapsis the value of theNumber of Tapsparameter.wcontains the tap weights from the last tap weight update.

Parameters

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Structure parameters

`Number of taps`— Number of equalizer taps
`5`(default) | positive integer

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

`Signal constellation`— Signal constellation
`pskmod(0:3,4,pi/4)`(default) | vector

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`— Number of input samples per symbol
`1`(default) | positive integer

Number of input samples per symbol, specified as a positive integer. Setting this parameter to any number greater than1effectively creates a fractionally spaced equalizer. For more information, seeSymbol Tap Spacing.

Algorithm parameters

`Adaptive algorithm`— Adaptive algorithm
`LMS`(default) |`RLS`|`CMA`

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

LMS— Update the equalizer tap weights using theLeast Mean Square (LMS) Algorithm.
RLS— Update the equalizer tap weights using theRecursive Least Square (RLS) Algorithm.
CMA— Update the equalizer tap weights using theConstant Modulus Algorithm (CMA).

`Step size`— Step size
`0.01`(default) | positive scalar

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.

金枪鱼ble:Yes

Dependencies

To enable this parameter, setAdaptive algorithmtoLMSorCMA.

`Forgetting factor`— Forgetting factor
`0.99`(default) | scalar in the range (0, 1]

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.

金枪鱼ble:Yes

Dependencies

To enable this parameter, setAdaptive algorithmtoRLS.

`Initial inverse correlation matrix`— Initial inverse correlation matrix
`0.1`(default) | scalar | matrix

Initial inverse correlation matrix, specified as a scalar or anN_Taps-by-N_Tapsmatrix.N_Tapsis equal to theNumber of Tapsparameter value. If you specify this value as a scalar,a, the equalizer sets the initial inverse correlation matrix toatimes the identity matrix:a(eye(N_Taps)).

Dependencies

To enable this parameter, setAdaptive algorithmtoRLS.

Control parameters

`Reference tap`— Reference tap
`3`(default) | positive integer

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

`Input signal delay (samples)`— Input signal delay
`0`(default) | nonnegative integer

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 theResetinput port toggles to1.

Dependencies

To enable this parameter, setAdaptive algorithmtoLMSorRLS.

`调整权重的旗帜`— Source of adapt tap weights request
`Property`(default) |`Input port`

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

Property— Specify this value to use theAdaptive algorithmparameter to control when the block adapts tap weights.
Input port— Specify this value to use theUpdateinput port to control when the block adapts tap weights.

Dependencies

To enable this parameter, setAdaptive algorithmtoCMA.

`Adapt tap weights`— Adapt tap weights
`on`(default) |`off`

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, setAdaptive algorithmtoCMAand调整权重的旗帜toProperty.

`Initial tap weights source`——来源initial tap weights
`Auto`(default) |`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 theInitial weightsparameter.
Property— Initialize the tap weights using theInitial weightsparameter value.

`Initial weights`— Initial tap weights
`0`or`[0;0;1;0;0]`(default) | scalar | column vector

Initial tap weights used by the adaptive algorithm, specified as a scalar or anN_Taps-by-1 vector.N_Tapsis equal to theNumber of Tapsparameter value. The default is0when theAdaptive algorithmparameter is set toLMSorRLS. The default is[0;0;1;0;0]when theAdaptive algorithmparameter is set toCMA.

If you specifyInitial weightsas a vector, the vector length must be equal to theNumber of Tapsparameter value. If you specifyInitial weightsas a scalar, the equalizer uses scalar expansion to create a vector of lengthNumber of Tapswith all values set toInitial weights.

Dependencies

To enable this parameter, setInitial tap weights sourcetoProperty.

`Tap weight update period (symbols)`— Tap weight update period
`1`(default) | positive integer

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

`Enable training control input`— Enable training control input
`off`(default) |`on`

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

Dependencies

To enable this parameter, setAdaptive algorithmtoLMSorRLS.

`Update tap weights when not training`— Update tap weights when not training
`on`(default) |`off`

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, setAdaptive algorithmtoLMSorRLS.

`Enable reset input`— Enable reset input
`off`(default) |`on`

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

Diagnostic parameters

`Output error signal`— Enable error signal output
`off`(default) |`on`

Select this parameter to enable output portErrcontaining the equalizer error signal.

`Output taps weights`— Enable tap weights output
`off`(default) |`on`

Select this parameter to enable output portwcontaining tap weights from the last tap weight update.

`Simulate using`— Type of simulation to run
`Code generation`(default) |`Interpreted execution`

Type of simulation to run, specified asCode generationorInterpreted 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 thanInterpreted execution.
Interpreted execution–– Simulate the model by using the MATLAB^®interpreter. This option requires less startup time than theCode generationmethod, but the speed of subsequent simulations is slower. In this mode, you can debug the source code of the block.

Model Examples

Linearly Equalize QPSK-Modulated Signal in Simulink

应用线性均衡使用至少意味着汉堡ares (LMS) algorithm to recover QPSK symbols passed through an AWGN channel.

Adaptive Equalization with Filtering and Fading Channel

The behavior of the selected adaptive equalizer in a communication link that has a fading channel. The transmitter and receiver have root raised cosine pulse shaped filtering. A subsystem block enables you to select between linear or decision feedback equalizers that usie the least mean square (LMS) or recursive least square (RLS) adaptive algorithm.

Block Characteristics

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

More About

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Symbol Tap Spacing

You can configure the equalizer to operate as a symbol-spaced equalizer or as a fractional symbol-spaced equalizer.

To operate the equalizer at a symbol-spaced rate, specify the number of samples per symbol as1. Symbol-rate equalizers have taps spaced at the symbol duration. Symbol-rate equalizers are sensitive to timing phase.
To operate the equalizer at a fractional symbol-spaced rate, specify the number of input samples per symbol as an integer greater than1and provide an input signal oversampled at that sampling rate. Fractional symbol-spaced equalizers have taps spaced at an integer fraction of the input symbol duration. Fractional symbol-spaced equalizers are not sensitive to timing phase.

Algorithms

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Linear Equalizers

Linear equalizers can remove intersymbol interference (ISI) when the frequency response of a channel has no null. If a null exists in the frequency response of a channel, linear equalizers tend to enhance the noise. In this case, use decision feedback equalizers to avoid enhancing the noise.

A linear equalizer consists of a tapped delay line that stores samples from the input signal. Once per symbol period, the equalizer outputs a weighted sum of the values in the delay line and updates the weights to prepare for the next symbol period.

Linear equalizers can be symbol-spaced or fractional symbol-spaced.

For a symbol-spaced equalizer, the number of samples per symbol,K, is 1. The output sample rate equals the input sample rate.
For a fractional symbol-spaced equalizer, the number of samples per symbol,K, is an integer greater than 1. Typically,Kis 4 for fractionally spaced equalizers. The output sample rate is 1/Tand the input sample rate isK/T, whereTis the symbol period. Tap-weight updating occurs at the output rate.

This schematic shows a linear equalizer withLweights, a symbol period ofT, andKsamples per symbol. IfKis 1, the result is a symbol-spaced linear equalizer instead of a fractional symbol-spaced linear equalizer.

In each symbol period, the equalizer receivesKinput samples at the tapped delay line. The equalizer then outputs a weighted sum of the values in the tapped delay line and updates the weights to prepare for the next symbol period.

For more information, see情商ualization.

Least Mean Square (LMS) Algorithm

For the LMS algorithm, in the previous schematic,wis a vector of all weightsw_i, anduis a vector of all inputsu_i. Based on the current set of weights, the LMS algorithm creates the new set of weights as

w_new=w_current+ (StepSize)ue*.

The step size used by the adaptive algorithm is specified as a positive scalar. Increasing the step size reduces the equalizer convergence time but causes the equalized output signal to be less stable. To determine the maximum step size allowed when using the LMS adaptive algorithm, use themaxstepobject function. The * operator denotes the complex conjugate and the error calculatione=d-y.

Recursive Least Square (RLS) Algorithm

For the RLS algorithm, in the previous schematic,wis the vector of all weightsw_i, andu是所有输入的向量u_i. Based on the current set of inputs,u, and the inverse correlation matrix,P, the RLS algorithm first computes the Kalman gain vector,K, as

$K = \frac{P u}{(F o r g e t t i n g F a c t o r) + u^{H} P u} .$

The forgetting factor used by the adaptive algorithm is specified as a scalar in the range (0, 1]. Decreasing the forgetting factor reduces the equalizer convergence time but causes the equalized output signal to be less stable.Hdenotes the Hermitian transpose. Based on the current inverse correlation matrix, the new inverse correlation matrix is

$P_{new} = \frac{(1 - K u^{H}) P_{current}}{F o r g e t t i n g F a c t o r} .$

Based on the current set of weights, the RLS algorithm creates the new set of weights as

w_new=w_current+K*e.

The * operator denotes the complex conjugate and the error calculatione=d-y.

Constant Modulus Algorithm (CMA)

For the CMA adaptive algorithm, in the previous schematic,wis the vector of all weightsw_i, andu是所有输入的向量u_i. Based on the current set of weights, the CMA adaptive algorithm creates the new set of weights as

w_new=w_current+ (StepSize)u*e.

The step size used by the adaptive algorithm is specified as a positive scalar. Increasing the step size reduces the equalizer convergence time but causes the equalized output signal to be less stable. To determine the maximum step size allowed by the CMA adaptive algorithm, use themaxstepobject function. The * operator denotes the complex conjugate and the error calculatione=y(R- |y|²), whereRis a constant related to the signal constellation.

Linear Equalizer

Description

Ports

Input

in— Input signalcolumn vector

Desired— Training symbolscolumn vector

Dependencies

Train— Train equalizer flag1|0

Dependencies

Update— Update tap weights flag1|0

Dependencies

Reset— Reset equalizer flag1|0

Dependencies

Output

Out— Equalized symbolscolumn vector

Err— Error signalcolumn vector

w— Tap weightscolumn vector

Parameters

Number of taps— Number of equalizer taps5(default) | positive integer

Signal constellation— Signal constellationpskmod(0:3,4,pi/4)(default) | vector

Number of input samples per symbol— Number of input samples per symbol1(default) | positive integer

Adaptive algorithm— Adaptive algorithmLMS(default) |RLS|CMA

Step size— Step size0.01(default) | positive scalar

Dependencies

Forgetting factor— Forgetting factor0.99(default) | scalar in the range (0, 1]

Dependencies

Initial inverse correlation matrix— Initial inverse correlation matrix0.1(default) | scalar | matrix

Dependencies

Reference tap— Reference tap3(default) | positive integer

Input signal delay (samples)— Input signal delay0(default) | nonnegative integer

Dependencies

调整权重的旗帜— Source of adapt tap weights requestProperty(default) |Input port

Dependencies

Adapt tap weights— Adapt tap weightson(default) |off

Dependencies

Initial tap weights source——来源initial tap weightsAuto(default) |Property

Initial weights— Initial tap weights0or[0;0;1;0;0](default) | scalar | column vector

Dependencies

Tap weight update period (symbols)— Tap weight update period1(default) | positive integer

Enable training control input— Enable training control inputoff(default) |on

Dependencies

Update tap weights when not training— Update tap weights when not trainingon(default) |off

Dependencies

Enable reset input— Enable reset inputoff(default) |on

Output error signal— Enable error signal outputoff(default) |on

Output taps weights— Enable tap weights outputoff(default) |on

Simulate using— Type of simulation to runCode generation(default) |Interpreted execution

Model Examples

Linearly Equalize QPSK-Modulated Signal in Simulink

Adaptive Equalization with Filtering and Fading Channel

Block Characteristics

More About

Symbol Tap Spacing

Algorithms

Linear Equalizers

Least Mean Square (LMS) Algorithm

Recursive Least Square (RLS) Algorithm

Constant Modulus Algorithm (CMA)

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using Simulink® Coder™.

See Also

Blocks

Objects

Topics

Communications Toolbox Documentation

金宝app

Bridging Wireless Communications Design and Testing with MATLAB

`in`— Input signal
column vector

`Desired`— Training symbols
column vector

`Train`— Train equalizer flag
`1`|`0`

`Update`— Update tap weights flag
`1`|`0`

`Reset`— Reset equalizer flag
`1`|`0`

`Out`— Equalized symbols
column vector

`Err`— Error signal
column vector

`w`— Tap weights
column vector

`Number of taps`— Number of equalizer taps
`5`(default) | positive integer

`Signal constellation`— Signal constellation
`pskmod(0:3,4,pi/4)`(default) | vector

`Number of input samples per symbol`— Number of input samples per symbol
`1`(default) | positive integer

`Adaptive algorithm`— Adaptive algorithm
`LMS`(default) |`RLS`|`CMA`

`Step size`— Step size
`0.01`(default) | positive scalar

`Forgetting factor`— Forgetting factor
`0.99`(default) | scalar in the range (0, 1]

`Initial inverse correlation matrix`— Initial inverse correlation matrix
`0.1`(default) | scalar | matrix

`Reference tap`— Reference tap
`3`(default) | positive integer

`Input signal delay (samples)`— Input signal delay
`0`(default) | nonnegative integer

`调整权重的旗帜`— Source of adapt tap weights request
`Property`(default) |`Input port`

`Adapt tap weights`— Adapt tap weights
`on`(default) |`off`

`Initial tap weights source`——来源initial tap weights
`Auto`(default) |`Property`

`Initial weights`— Initial tap weights
`0`or`[0;0;1;0;0]`(default) | scalar | column vector

`Tap weight update period (symbols)`— Tap weight update period
`1`(default) | positive integer

`Enable training control input`— Enable training control input
`off`(default) |`on`

`Update tap weights when not training`— Update tap weights when not training
`on`(default) |`off`

`Enable reset input`— Enable reset input
`off`(default) |`on`

`Output error signal`— Enable error signal output
`off`(default) |`on`

`Output taps weights`— Enable tap weights output
`off`(default) |`on`

`Simulate using`— Type of simulation to run
`Code generation`(default) |`Interpreted execution`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.