Power Amplifier
A narrow-band power amplifier with internal memory.
blockType: PowerAmplifier
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Path in the library: |
Description
Block Power Amplifier simulates a two-port power amplifier using a memory polynomial expression derived from the Volterra series. The Volterra series models the nonlinear 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 time points. Use this block when transmitting narrowband signals in an RF system.
Block Mask Icons Power Amplifier they are dynamic and display the model specified in the parameter 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
The time-dependent input signal is specified as a column. The column represents consecutive points in time.
| Data types |
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| Complex numbers support |
I don’t |
Output
#
OUT
—
time-dependent output signal
complex column
Details
The time-dependent output is 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 memory model or a cross-memory model. The following table shows the characteristics of these two models.
| Value of the Model parameter | Features | Type of coefficients | In-band spectral growth | Generation of out-of-band harmonics |
|---|---|---|---|---|
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Bandwidth (I,Q) |
Two-dimensional complex matrix |
Yes |
I don’t |
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Bandwidth (I,Q) |
Two-dimensional complex matrix |
Yes |
I don’t |
| Values |
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| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
No |
#
Coefficient matrix —
matrix of coefficients
Scalar / array of real and/or complex numbers
Details
The matrix of coefficients, given as a two-dimensional complex matrix.
For models Memory Polynomial and Cross-Term Memory You can define a complex coefficient matrix based on 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 a matrix of coefficients.
| Default value |
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| Program usage name |
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| Tunable |
No |
| Evaluatable |
Yes |
Additional Info
Algorithms
The type of model in the power amplifier unit
Block Power Amplifier supports two types of models.
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Memory Polynomial– the narrow-band implementation of the memory polynomial (equation (19) from [1]) used in this model operates on the envelope of the input signal, does not generate new frequency components and captures the in-band spectral growth. Use this model to create a narrowband amplifier operating at a high frequency.The output signal at any given time is the sum of all the elements of a complex matrix of dimension :
In a matrix, the number of rows is equal to the number of memory terms, and the number of columns is equal to the degree of non–linearity. The subscript of the signal indicates the amount of delay.
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Cross-Term Memory– the narrow-band polynomial implementation with memory (equation (23) from [1]) used in this model also operates on the envelope of the input signal, does not generate new frequency components and captures the in-band spectral growth. Use this model to create a narrowband amplifier operating at a high frequency. This model includes leading and lagging memory terms and is a generalized implementation of the polynomial memory model.The output signal at any given time is the sum of all the elements of the matrix given by the element-wise product:
where – a matrix of complex coefficients of dimension and
In a matrix, the number of rows is equal to the number of memory terms, and the number of columns is proportional to the degree of non-linearity and the number of memory terms. The subscript of the signal indicates the amount of delay. Additional columns that do not appear in the model Memory Polynomial, represent the cross terms.
Calculation of the coefficient matrix
To calculate the coefficient matrices, the block solves an overridden linear system of equations. Consider the polynomial model Memory Polynomial for the case when the memory length is 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
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)], then the solution to and the sum of its elements is 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)], then 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 Generalized 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.