DPD

Digital predistorter

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Libraries:
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 and Optimizing Estimator Polynomial Degree and Memory Depth.

This icon shows the block with all ports enabled.

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 from input and output signals from a power amplifier (PA) 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.

Open Model

Ports

Input

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

Out — Predistorted baseband signal

column vector

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

Parameters

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.

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 model reuses the C code for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than with the Interpreted execution option.

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

For more information, see Simulation Modes (Simulink).

Block Characteristics

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

Algorithms

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

  $$x\text{(}n\text{)}=f\text{(}u\text{(}n\text{))}\triangleq {\displaystyle \sum _{m\text{=0}}^{M-1}{c}_m\times u\text{(}n\text{-}m\text{)}}+{\displaystyle \sum _{m\text{=0}}^{M-1}{\displaystyle \sum _{j\text{=0}}^{M-1}{\displaystyle \sum _{k\text{=0}}^{K-1}{a}_{mjk}\times u\text{(}n\text{-}m\text{)}\times |u\text{(}n\text{-}j\text{)}{|}^k}}}.$$

  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

  $$x\text{(}n\text{)}=f\text{(}u\text{(}n\text{))}\triangleq {\displaystyle \sum _{m\text{=0}}^{M-1}{\displaystyle \sum _{k\text{=0}}^{K-1}{a}_{mk}\times u\text{(}n\text{-}m\text{)}\times |u\text{(}n\text{-}m\text{)}{|}^k}}.$$

  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].

Optimizing Estimator Polynomial Degree and Memory Depth

The DPD coefficient estimator based on [1] offers one specific indirect learning architecture, and may not be an optimal estimator. Other estimators, such as those using a direct learning architecture, may achieve better DPD results.

With the indirect learning architecture coefficient estimator, choosing the optimal degree and memory depth for the DPD coefficient estimator is a manual and iterative process. Consider starting by using a DPD coefficient estimator that has the same degree and the memory depth as that of the PA model, and check the DPD results. Assuming the results look promising, try reducing the degree and the memory depth for the DPD coefficient estimator. If DPD results are roughly the same or better, consider using the smaller degree and a smaller memory depth for the DPD coefficient estimator because it will be less computationally intensive. You should also experiment with degrees and memory depths above the degree and the memory depth of the PA model. If DPD performance improves using a higher degree or a larger memory depth for the DPD coefficient estimator may be desirable.

Regardless of the polynomial degree used for the estimator, you must control the bandwidth of the DPD input signal to avoid aliasing due to nonlinearities. As a rule of thumb, set the oversampling ratio of the DPD input signal equal to or greater than the degree of the DPD memory polynomial.

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.

Extended Capabilities

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

Version History

Introduced in R2019a