DPD

Digital predistorter

Library:
Communications Toolbox / RF Impairments Correction

Description

Apply digital predistortion (DPD) to a complex baseband signal using a memory polynomial to compensate for nonlinearities in a power amplifier. For more information, see Digital Predistortion.

This icon shows the block with all ports enabled.

Ports

Input

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`In` — Input baseband signal
column vector

Input baseband signal, specified as a column vector. This port is unnamed until the Coefficient source parameter is set to Input port.

Data Types: double
Complex Number Support: Yes

`Coef` — Memory-polynomial coefficients
matrix

Memory-polynomial coefficients, specified as a matrix. The number of rows in the matrix must equal the memory depth of the memory polynomial.

If the Polynomial type parameter is set to Memory polynomial, the number of columns in the matrix is the degree of the memory polynomial.
If Polynomial type is set to Cross-term memory polynomial, the number of columns in the matrix must equal m(n-1)+1. m is the memory depth of the polynomial, and n is the degree of the memory polynomial.

Example: complex([1 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0])

Dependencies

To enable this port, set the Coefficient source parameter to Input port.

Data Types: double
Complex Number Support: Yes

Output

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`Out` — Predistorted baseband signal
column vector

Predistorted baseband signal, returned as a column vector of the same length as the input signal.

Parameters

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`Polynomial type` — 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.

`Coefficient source` — Source of memory-polynomial coefficients
`Property` (default) | `Input port`

Source of the memory polynomial coefficients, specified as one of these values:

Property — Specify this value to use the Coefficients parameter to define the memory-polynomial coefficients
Input port — Specify this value to use the Coef input port to define the memory-polynomial coefficients

`Coefficients` — Memory-polynomial coefficients
`complex([1 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0])` (default) | matrix

Memory-polynomial coefficients, specified as a matrix. The number of rows must equal the memory depth of the memory polynomial.

If the Polynomial type is set to Memory polynomial, the number of columns is the degree of the memory polynomial.
If the Polynomial type is set to 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 parameter, set Coefficient source to Property.

Data Types: double
Complex Number Support: Yes

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

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.

Model Examples

Predistort Power Amplifier Input Signal in Simulink

Apply digital predistortion (DPD) to a 16-QAM signal of random symbols. The DPD Coefficient Estimator block uses a captured signal containing power amplifier (PA) input and output signals to determine the predistortion coefficient matrix. Digital predistortion of the signal preconditions is to correct impairments that the PA introduces. This model does not include a block representing the PA.

Block Characteristics

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

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

DPD

Description

Ports

Input

`In` — Input baseband signal
column vector

`Coef` — Memory-polynomial coefficients
matrix

Dependencies

Output

`Out` — Predistorted baseband signal
column vector

Parameters

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

`Coefficient source` — Source of memory-polynomial coefficients
`Property` (default) | `Input port`

`Coefficients` — Memory-polynomial coefficients
`complex([1 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0])` (default) | matrix

Dependencies

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

Model Examples

Predistort Power Amplifier Input Signal in Simulink

Block Characteristics

More About

Digital Predistortion

References

Extended Capabilities

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

See Also

Blocks

Objects

Topics

Communications Toolbox Documentation

Support

Documentation

DPD

Description

Ports

Input

In — Input baseband signal column vector

Coef — Memory-polynomial coefficients matrix

Dependencies

Output

Out — Predistorted baseband signal column vector

Parameters

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

Coefficient source — Source of memory-polynomial coefficients Property (default) | Input port

Coefficients — Memory-polynomial coefficients complex([1 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0]) (default) | matrix

Dependencies

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

Model Examples

Predistort Power Amplifier Input Signal in Simulink

Block Characteristics

More About

Digital Predistortion

References

Extended Capabilities

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

See Also

Blocks

Objects

Topics

Communications Toolbox Documentation

Support

`In` — Input baseband signal
column vector

`Coef` — Memory-polynomial coefficients
matrix

`Out` — Predistorted baseband signal
column vector

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

`Coefficient source` — Source of memory-polynomial coefficients
`Property` (default) | `Input port`

`Coefficients` — Memory-polynomial coefficients
`complex([1 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0])` (default) | matrix

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

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