comm.DPDCoefficientEstimator

Estimate memory-polynomial coefficients for digital predistortion

Description

The comm.DPDCoefficientEstimator System object™ estimates the coefficients of a memory polynomial for digital pre-distortion (DPD) of a nonlinear power amplifier, given the baseband equivalent input and baseband equivalent output of the power amplifier. For more information, see Digital Predistortion.

To compute predistortion coefficients:

Create the comm.DPDCoefficientEstimator object and set its properties.
Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?.

Creation

Syntax

estimator = comm.DPDCoefficientEstimator

estimator = comm.DPDCoefficientEstimator(Name,Value)

Description

estimator = comm.DPDCoefficientEstimator creates a digital predistortion coefficient estimator System object to estimate the coefficients of a memory polynomial for digital predistortion (DPD) of a nonlinear power amplifier.

example

estimator = comm.DPDCoefficientEstimator(Name,Value) sets properties using one or more name-value pairs. For example, comm.DPDCoefficientEstimator('PolynomialType','Cross-term memory polynomial') configures the predistortion coefficient estimator System object to estimate the coefficients for a memory-polynomial with cross terms. Enclose each property name in quotes.

Properties

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Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`DesiredAmplitudeGaindB` — Desired amplitude gain
`10` (default) | scalar

Desired amplitude gain in dB, specified as a scalar. This property value expresses the desired signal gain at the compensated amplifier output.

Tunable: Yes

Data Types: double

`PolynomialType` — Polynomial type
`'Memory polynomial'` (default) | `'Cross-term memory polynomial'`

Polynomial type used for predistortion, specified as one of these values:

'Memory polynomial' — Computes predistortion coefficients by using a memory polynomial without cross terms
'Cross-term memory polynomial' — Computes predistortion coefficients by using a memory polynomial with cross terms

For more information, see Digital Predistortion.

`Degree` — Memory-polynomial degree
`5` (default) | positive integer

Memory-polynomial degree, specified as a positive integer.

Data Types: double

`MemoryDepth` — Memory-polynomial depth
`3` (default) | positive integer

Memory-polynomial depth in samples, specified as a positive integer.

Data Types: double

`Algorithm` — Estimation algorithm
`'Least squares'` (default) | `'Recursive least squares'`

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

'Least squares' — Estimate the memory polynomial coefficients by using a least squares algorithm
'Recursive least squares' — Estimate the memory polynomial coefficients by using a recursive least squares algorithm

For algorithm reference material, see the works listed in [1] and [2].

Data Types: char | string

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

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

Tunable: Yes

Dependencies

To enable this property, set Algorithm to 'Recursive least squares'.

Data Types: double

`InitialCoefficientEstimate` — Initial coefficient estimate
`[]` (default) | matrix

Initial coefficient estimate for the recursive least squares algorithm, specified as a matrix.

If InitialCoefficientEstimate is an empty matrix, the initial coefficient estimate for the recursive least squares algorithm is chosen automatically to correspond to a memory polynomial that is an identity function, so that the output is equal to input.
If InitialCoefficientEstimate is a nonempty matrix, the number of rows must be equal to MemoryDepth.
- If PolynomialType is 'Memory polynomial', the number of columns is the degree of the memory polynomial.
- If PolynomialType is 'Cross-term memory polynomial', the number of columns must equal m(n-1)+1. m is the memory depth of the polynomial, and n is the degree of the memory polynomial.

For more information, see Digital Predistortion.

Dependencies

To enable this property, set Algorithm to 'Recursive least squares'.

Data Types: double
Complex Number Support: Yes

Usage

Syntax

coef = estimator(paIn,paOut)

Description

example

coef = estimator(paIn,paOut) estimates the coefficients of a memory polynomial for use by the comm.DPD System object to predistort a complex baseband signal by using a memory-polynomial to compensate for nonlinearities in a power amplifier.

Input Arguments

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`paIn` — Power amplifier baseband equivalent input
column vector

Power amplifier baseband equivalent input, specified as a column vector.

Data Types: double
Complex Number Support: Yes

`paOut` — Power amplifier baseband equivalent output
column vector

Power amplifier baseband equivalent output, specified as a column vector of the same length as paIn.

Data Types: double
Complex Number Support: Yes

Output Arguments

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`coef` — Memory-polynomial coefficients
matrix

Memory-polynomial coefficients, returned as a matrix. For more information, see Digital Predistortion.

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

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Common to All System Objects

`step`	Run System object algorithm
`release`	Release resources and allow changes to System object property values and input characteristics
`reset`	Reset internal states of System object

Examples

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Predistort Power Amplifier Input Signal

Open Live Script

Apply digital predistortion (DPD) to a power amplifier input signal. The DPD coefficient estimator System object uses a captured signal containing power amplifier input and output signals to determine the predistortion coefficient matrix.

Load a file containing the input and output signals for the power amplifier.

load('commpowamp_dpd_data.mat','PA_input','PA_output')

Generate a DPD coefficient estimator System object and a raised cosine transmit filter System object.

estimator = comm.DPDCoefficientEstimator( ...
    'DesiredAmplitudeGaindB',10, ...
    'PolynomialType','Memory polynomial', ...
    'Degree',5,'MemoryDepth',3,'Algorithm','Least squares');

rctFilt = comm.RaisedCosineTransmitFilter('OutputSamplesPerSymbol',2);

Estimate the digital predistortion memory-polynomial coefficients.

coef = estimator(PA_input,PA_output);

Generate a DPD System object using coef, the estimated coefficients output from the DPD coefficient estimator, as for the coefficient matrix.

dpd = comm.DPD('PolynomialType','Memory polynomial', ...
    'Coefficients',coef);

Generate 2000 random symbols and apply 16-QAM modulation to the signal. Apply raised cosine transmit filtering to the modulated signal.

s = randi([0,15],2000,1);
u = qammod(s,16);
x = rctFilt(u);

Apply digital predistortion to the data. The DPD System object returns a predistorted signal to provide as input to the power amplifier.

y = dpd(x);

Format of Coefficient Matrix for Digital Predistortion Memory Polynomial

Open Live Script

This examples shows the format of the coefficient matrix for the DPD memory polynomial by using a randomly generated coefficient matrix. The example:

Creates a digital predistortion System object configured using a memory polynomial coefficient matrix with the memory depth set to 3 and the polynomial degree set to 5 consisting of random values.
Predistorts a signal using the memory-polynomial coefficient matrix.
Compares one predistorted output element to the corresponding input element that has been manually computed using the memory-polynomial coefficient matrix.

Create a coefficient matrix representing a predistorter with the output equal to the input by generating a 3-by-5 coefficient matrix of zeros and setting the coef(1,1) element to 1. Add small random complex nonlinear terms to the coefficient matrix.

coef = zeros(3,5);
coef(1,1) = 1;
coef = coef + 0.01*(randn(3,5)+1j*randn(3,5));

Create a DPD System object using the memory polynomial coefficient matrix, coef.

dpd = comm.DPD('PolynomialType','Memory polynomial','Coefficients',coef);

Generate an input signal and predistort it using the dpd System object.

x = randn(20,1) + 1j*randn(20,1);
y = dpd(x);

Compare the manually distorted output for an input corresponding output element y(18) to show how the coefficient matrix is used to calculate that particular output value.

u = x(18:-1:(18-3+1));
isequal(y(18),sum(sum(coef.*[u u.*abs(u) u.*(abs(u).^2) u.*(abs(u).^3) u.*(abs(u).^4)])))

ans = logical
   1

Format of Cross-Term Coefficient Matrix for Digital Predistortion Memory Polynomial

Open Live Script

This examples shows the format of the coefficient matrix for the DPD memory polynomial by using a randomly generated coefficient matrix. The example:

Creates a digital predistorter System object configured using a cross-term memory polynomial coefficient matrix with the memory depth set to 3 and the polynomial degree set to 5 consisting of random values.
Predistorts a signal using the cross-term memory polynomial coefficient matrix.
Compares one predistorted output element to the corresponding input element that has been manually computed using the cross-term memory polynomial coefficient matrix.

coef = zeros(3,3*(5-1)+1);
coef(1,1) = 1;
coef = coef + 0.01*(randn(3,13) + 1j*randn(3,13));

Create a DPD System object using the cross-term memory polynomial coefficient matrix, coef.

dpd = comm.DPD('PolynomialType','Cross-term memory polynomial','Coefficients',coef);

Generate an input signal and predistort it using the dpd System object.

x = randn(20,1) + 1j*randn(20,1);
y = dpd(x);

Compare the manually distorted output for an input corresponding output element y(18) to show how the coefficient matrix is used to calculate that particular output value.

u = x(18:-1:(18-3+1));
isequal(y(18),sum(sum(coef.*[u u*abs(u.') u*(abs(u.').^2) u*(abs(u.').^3) u*(abs(u.').^4)])))

ans = logical
   1

More About

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Digital Predistortion

Wireless communication transmissions commonly require wide bandwidth signal transmission over a wide signal dynamic range. To transmit signals over a wide dynamic range and achieve high efficiency, RF power amplifiers (PAs) commonly operate in their nonlinear region. As this constellation diagram shows, the nonlinear behavior of a PA causes signal constellation distortions that pinch the amplitude (AM-AM distortion) and twist phase (AM-PM distortion) of constellation points proportional to the amplitude of the constellation point.

The goal of digital predistortion is to find a nonlinear function that linearizes the net effect of the PA nonlinear behavior at the PA output across the PA operating range. When the PA input is x(n), and the predistortion function is f(u(n)), where u(n) is the true signal to be amplified, the PA output is approximately equal to G×u(n), where G is the desired amplitude gain of the PA.

The digital predistorter can be configured to use a memory polynomial with or without cross terms.

The memory polynomial with cross terms predistorts the input signal as

$x (n) = f (u (n)) ≜ \sum_{m =0}^{M - 1} c_{m} \times u (n - m) + \sum_{m =0}^{M - 1} \sum_{j =0}^{M - 1} \sum_{k =0}^{K - 1} a_{m j k} \times u (n - m) \times | u (n - j) |^{k} .$

The memory polynomial with cross terms has (M+M×M×(K-1)) coefficients for c_m and a_mjk.
The memory polynomial without cross terms predistorts the input signal as

$x (n) = f (u (n)) ≜ \sum_{m =0}^{M - 1} \sum_{k =0}^{K - 1} a_{m k} \times u (n - m) \times | u (n - m) |^{k} .$
The polynomial without cross terms has M×K coefficients for a_mk.

Estimating Predistortion Function and Coefficients

The DPD coefficient estimation uses an indirect learning architecture to find function f(u(n)) to predistort input signal u(n) which precedes the PA input.

The DPD coefficient estimation algorithm models nonlinear PA memory effects based on the work in reference papers by Morgan, et al [1], and by Schetzen [2], using the theoretical foundation developed for Volterra systems.

Specifically, the inverse mapping from the PA output normalized by the PA gain, {y(n)/G}, to the PA input, {x(n)}, provides a good approximation to the function f(u(n)), needed to predistort {u(n)} to produce {x(n)}.

Referring to the memory polynomial equations above, estimates are computed for the memory-polynomial coefficients:

c_m and a_mjk for a memory polynomial with cross terms
a_mk for a memory polynomial without cross terms

The memory-polynomial coefficients are estimated by using a least squares fit algorithm or a recursive least squares algorithm. The least squares fit algorithm or a recursive least squares algorithms use the memory polynomial equations above for a memory polynomial with or without cross terms, by replacing {u(n)} with {y(n)/G}. The function order and dimension of the coefficient matrix are defined by the degree and depth of the memory polynomial.

For an example that details the process of accurately estimating memory-polynomial coefficients and predistorting a PA input signal, see Digital Predistortion to Compensate for Power Amplifier Nonlinearities.

For background reference material, see the works listed in [1] and [2].

References

[1] Morgan, Dennis R., Zhengxiang Ma, Jaehyeong Kim, Michael G. Zierdt, and John Pastalan. "A Generalized Memory Polynomial Model for Digital Predistortion of Power Amplifiers." IEEE^® Transactions on Signal Processing. Vol. 54, Number 10, October 2006, pp. 3852–3860.

[2] M. Schetzen. The Volterra and Wiener Theories of Nonlinear Systems. New York: Wiley, 1980.

Documentation

comm.DPDCoefficientEstimator

Description

Creation

Syntax

Description

Properties

DesiredAmplitudeGaindB — Desired amplitude gain 10 (default) | scalar

PolynomialType — Polynomial type 'Memory polynomial' (default) | 'Cross-term memory polynomial'

Degree — Memory-polynomial degree 5 (default) | positive integer

MemoryDepth — Memory-polynomial depth 3 (default) | positive integer

Algorithm — Estimation algorithm 'Least squares' (default) | 'Recursive least squares'

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

Dependencies

InitialCoefficientEstimate — Initial coefficient estimate [] (default) | matrix

Dependencies

Usage

Syntax

Description

Input Arguments

paIn — Power amplifier baseband equivalent input column vector

paOut — Power amplifier baseband equivalent output column vector

Output Arguments

coef — Memory-polynomial coefficients matrix

Object Functions

Common to All System Objects

Examples

Predistort Power Amplifier Input Signal

Format of Coefficient Matrix for Digital Predistortion Memory Polynomial

Format of Cross-Term Coefficient Matrix for Digital Predistortion Memory Polynomial

More About

Digital Predistortion

References

Extended Capabilities

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

See Also

Objects

Blocks

Topics

Communications Toolbox Documentation

Support

`DesiredAmplitudeGaindB` — Desired amplitude gain
`10` (default) | scalar

`PolynomialType` — Polynomial type
`'Memory polynomial'` (default) | `'Cross-term memory polynomial'`

`Degree` — Memory-polynomial degree
`5` (default) | positive integer

`MemoryDepth` — Memory-polynomial depth
`3` (default) | positive integer

`Algorithm` — Estimation algorithm
`'Least squares'` (default) | `'Recursive least squares'`

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

`InitialCoefficientEstimate` — Initial coefficient estimate
`[]` (default) | matrix

`paIn` — Power amplifier baseband equivalent input
column vector

`paOut` — Power amplifier baseband equivalent output
column vector

`coef` — Memory-polynomial coefficients
matrix

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