DPD Coefficient Estimator
Estimate memorypolynomial coefficients for digital predistortion
Libraries:
Communications Toolbox /
RF Impairments Correction
Description
Estimate the coefficients of a memory polynomial for digital predistortion (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 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 16QAM 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.
The PreLoadFcn
callback initializes model parameters, and also loads workspace variables PA_Input
and PA_Output
from the file commpowamp_dpd_data.mat
. For more information, see Model Callbacks (Simulink).
The PA_Input
and PA_Output
variables are basebandequivalent signals captured at the input and output of a PA. PA_Input
and PA_Output
are used by the DPD Coefficient Estimator block to estimate the memorypolynomial coefficients. The memorypolynomial coefficients are input to the DPD block to predistort the PA input signal.
The input signal path of the model generates a random symbol stream, applies 16QAM modulation, and then applies raisedcosine transmit filtering to the modulated signal.
The input signal is digitally predistorted in the DPD block using the memorypolynomial coefficients generated in the DPD Coefficient Estimator block. The DPD block returns the predistorted input signal for the PA that produced the distorted PA output signal.
Ports
Input
PA In — Power amplifier basebandequivalent input
column vector
Power amplifier basebandequivalent input, specified as a column vector.
Data Types: double
Complex Number Support: Yes
PA Out — Power amplifier basebandequivalent output
column vector
Power amplifier basebandequivalent output, specified as a column vector of the same length as PA In.
Data Types: double
Complex Number Support: Yes
Forgetting Factor — Forgetting factor
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.
Dependencies
To enable this port, set Algorithm to Recursive
least squares
and set Forgetting factor source to
Input port
.
Data Types: double
Output
Out — Memorypolynomial coefficients
matrix
Memorypolynomial coefficients, returned as a matrix. For more information, see Digital Predistortion.
Parameters
To edit block parameters interactively, use the Property Inspector. From the Simulink^{®} Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.
Desired amplitude gain (dB) — Desired amplitude gain
10
(default)  scalar
Desired amplitude gain in dB, specified as a scalar. This parameter value expresses the desired signal gain at the compensated amplifier output.
In addition to linearization, the DPD should make the combined gain between the DPD input and the power amplifier output as close as possible to the expected gain. Therefore, set this parameter based on the expected gain of the power amplifier that you obtain during PA characterization.
Tunable: Yes
Polynomial type — Polynomial type
Memory polynomial
(default)  Crossterm 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 termsCrossterm memory polynomial
— Computes predistortion coefficients by using a memory polynomial with cross terms
For more information, see Digital Predistortion.
Degree — Memorypolynomial degree
5
(default)  positive integer
Memorypolynomial degree, specified as a positive integer.
Memory depth — Memorypolynomial depth
3
(default)  positive integer
Memorypolynomial depth in samples, specified as a positive integer.
Algorithm — Estimation algorithm
Least squares
(default)  Recursive least squares
Adaptive algorithm used for equalization, specified as one of these values:
Least squares
— Estimate the memorypolynomial coefficients by using a least squares algorithmRecursive least squares
— Estimate the memorypolynomial coefficients by using a recursive least squares algorithm
For algorithm reference material, see the works listed in [1] and [2].
Forgetting factor source — Source of forgetting factor
Property
(default)  Input port
Source of the forgetting factor, specified as one of these values:
Property
— Specify this value to use the Forgetting factor parameter to specify the forgetting factor.Input port
— Specify this value to use the Forgetting Factor input port to specify the forgetting factor.
Dependencies
To enable this parameter, set Algorithm to Recursive
least squares
.
Forgetting factor — 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.
Dependencies
To enable this parameter, set Algorithm to Recursive
least squares
and set Forgetting factor source to
Property
.
Initial coefficient estimate — Initial coefficient estimate
[]
(default)  matrix
Initial coefficient estimate for the recursive least squares algorithm, specified as a matrix of real or complex values.
If you specify this value as 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 you specify this value as a nonempty matrix, the number of rows must be equal to the Memory depth parameter value.
If the Polynomial type parameter is set to
Memory polynomial
, the number of columns is the degree of the memory polynomial.If the Polynomial type parameter is set to
Crossterm memory polynomial
, the number of columns must equal m(n1)+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 Algorithm to Recursive
least squares
.
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 theInterpreted 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 theCode generation
option. In this mode, you can debug the source code of the block.
For more information, see Interpreted Execution vs. Code Generation (Simulink).
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

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 (AMAM distortion) and twist phase (AMPM 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
$$x\text{(}n\text{)}=f\text{(}u\text{(}n\text{))}\triangleq {\displaystyle \sum _{m\text{=0}}^{M1}{c}_{m}\times u\text{(}n\text{}m\text{)}}+{\displaystyle \sum _{m\text{=0}}^{M1}{\displaystyle \sum _{j\text{=0}}^{M1}{\displaystyle \sum _{k\text{=0}}^{K1}{a}_{mjk}\times u\text{(}n\text{}m\text{)}\times u\text{(}n\text{}j\text{)}{}^{k}}}}.$$
The memory polynomial with cross terms has (M+M×M×(K1)) coefficients for c_{m} and a_{mjk}.
The memory polynomial without cross terms predistorts the input signal as
$$x\text{(}n\text{)}=f\text{(}u\text{(}n\text{))}\triangleq {\displaystyle \sum _{m\text{=0}}^{M1}{\displaystyle \sum _{k\text{=0}}^{K1}{a}_{mk}\times u\text{(}n\text{}m\text{)}\times u\text{(}n\text{}m\text{)}{}^{k}}}.$$
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 memorypolynomial coefficients:
c_{m} and a_{mjk} for a memory polynomial with cross terms
a_{mk} for a memory polynomial without cross terms
The memorypolynomial 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 memorypolynomial 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
See Also
Blocks
Objects
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