DPD Coefficient Estimator

Estimate memory-polynomial coefficients for digital predistortion

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Library:
Communications Toolbox / RF Impairments Correction

Description

Estimate memory-polynomial coefficients for digital predistortion (DPD) of a nonlinear power amplifier.

This icon shows the block with all ports enabled.

Ports

Input

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`PA In` — Power amplifier baseband-equivalent input
column vector

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

Data Types: double
Complex Number Support: Yes

`PA Out` — Power amplifier baseband-equivalent output
column vector

Power amplifier baseband-equivalent 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

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`Out` — Memory-polynomial coefficients
matrix

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

Parameters

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`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.

Tunable: Yes

Data Types: double

`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.

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

Memory-polynomial degree, specified as a positive integer.

Data Types: double

`Memory depth` — 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

`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.

Data Types: double

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

Dependencies

To enable this parameter, set Algorithm to Recursive least squares and set Forgetting factor source to Property.

Data Types: double

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

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

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 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 Algorithm to Recursive least squares.

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 Coefficient Estimator

Description