Power Amplifier
Narrowband power amplifier with internal memory.
blockType: PowerAmplifier
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Path in the library: |
Description
The Power Amplifier block models a two-port power amplifier using a polynomial expression with memory derived from Volterra series. Volterra series models the non-linear relationship between input and output signals. This block includes memory effects: the output response depends on the current input signal and the input signal at previous points in time. Use this block when transmitting narrowband signals in an RF system.
The mask icons of the Power Amplifier block are dynamic and display the model specified in the parameters Model.
Model: Memory polynomial
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Model: Cross-term memory
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Ports
Input
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IN
—
time-dependent input signal
column
Details
A time-dependent input signal specified as a column. The column represents consecutive points in time.
| Data types |
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| Complex numbers support |
No |
Output
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OUT
—
time-dependent output signal
`complex column
Details
A time-dependent output signal returned as a complex column. The output signal is equal in size to the input signal.
| Data types |
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| Complex numbers support |
Yes |
Parameters
Main
#
Model —
amplifier model
Memory Polynomial | Cross-Term Memory
Details
A power amplifier model specified as a polynomial model with memory or a cross-memory model. The following table summarises the characteristics of these two models.
| Parameter value Model | Parameters | Characteristics Type of coefficients | In-band spectral growth | Out-of-band harmonic generation Out-of-band harmonic generation |
|---|---|---|---|---|
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Bandwidth (I,Q) |
Two-dimensional complex matrix |
Yes |
No |
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Bandwidth (I,Q) |
Two-dimensional complex matrix |
Yes |
No |
| Values |
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| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
No |
#
Coefficient matrix —
coefficient matrix
Scalar / array of real and/or complex numbers
Details
A coefficient matrix given as a two-dimensional complex matrix.
For models Memory Polynomial и Cross-Term Memory you can determine the complex coefficient matrix from the measured complex (I,Q) output and input characteristics of the amplifier.
The size of the matrix depends on the number of delays and the degree of nonlinearity of the system.
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For the model
Memory Polynomialthe matrix has dimension . -
For the model
Cross-Term Memorythe matrix has dimension .
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
#
Measured interval of PA data (s) —
sampling time of measured I/O data
Real number
Details
The sampling time of the input-output data that the block uses to construct the coefficient matrix.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
Optional
Algorithms
*Model type in the power amplifier block.
The Power Amplifier block supports two types of models.
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Memory Polynomial- The narrowband implementation of the memory polynomial (equation (19) from [1]) used in this model operates on the envelope of the input signal, generates no new frequency components, and captures in-band spectral growth. Use this model to design a narrowband amplifier operating at high frequency.The output signal at any time is the sum of all elements of a complex matrix of dimension :
In the matrix, the number of rows equals the number of memory members and the number of columns equals the degree of nonlinearity. The subscript of the signal indicates the amount of delay.
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Cross-Term Memory- The narrowband polynomial implementation with memory (equation (23) from [1]) used in this model also operates on the envelope of the input signal, generates no new frequency components, and captures in-band spectral growth. Use this model to build a narrowband amplifier operating at high frequency. This model includes leading and lagging memory terms and is a generalised implementation of the polynomial memory model.The output signal at any given time is the sum of all elements of a matrix given by the element-by-element product:
where is a matrix of complex coefficients of dimension and
In the matrix, the number of rows is equal to the number of memory members, and the number of columns is proportional to the degree of nonlinearity and the number of memory members. The subscript of the signal indicates the amount of delay. Additional columns that do not appear in the model Memory Polynomial, represent cross terms.
*Calculation of the coefficient matrix.
To compute the coefficient matrices, the block solves a redefined linear system of equations. Let’s consider the polynomial model Memory Polynomial for the case when the memory length is equal to 2 and the nonlinearity of the system is of the third degree.
The matrix describing the system has the form:
and the sum of its elements is equivalent to the inner product of
If a five-sample signal [x(1) x(2) x(3) x(4) x(5)] is applied to the input of an amplifier and the corresponding output is [y(1) y(2) y(3) y(4) y(5)], then the solution to k and the sum of its elements are equivalent to the inner product:
The matrix for the model is calculated in the same way Cross-Term Memory. The matrix describing this system has the form:
and the sum of its elements is equivalent to the inner product:
If a five-sample signal [x(1) x(2) x(3) x(4) x(5)] is applied to the input of the amplifier, and the corresponding output is [y(1) y(2) y(3) y(4) y(5)], the solution is
gives an estimate of the coefficient matrix.
Literature
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Morgan, Dennis R., Zhengxiang Ma, Jaehyeong Kim, Michael G. Zierdt, and John Pastalan. "A Generalised Memory Polynomial Model for Digital Predistortion of Power Amplifiers." IEEE Transactions on Signal Processing. Vol. 54, No. 10, October 2006, pp. 3852-3860.
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Gan, Li, and Emad Abd-Elrady. "Digital Predistortion of Memory Polynomial Systems using Direct and Indirect Learning Architectures". Proceedings of the Eleventh IASTED International Conference on Signal and Image Processing (SIP) (F. Cruz-Roldán and N. B. Smith, eds.), No. 654-802. Calgary, AB: ACTA Press, 2009.