{blockLibraryPP_blocksPP_FF_RFSS_BlocksetFF_IdealizedSS_BasebandFF_PowerSS_AmplifierPP_label}
Narrowband power amplifier with internal memory.
blockType: PowerAmplifier
|
Path in the library: |
Description
The {blockLibraryPP_blocksPP_FF_RFSS_BlocksetFF_IdealizedSS_BasebandFF_PowerSS_AmplifierPP_label} 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 {blockLibraryPP_blocksPP_FF_RFSS_BlocksetFF_IdealizedSS_BasebandFF_PowerSS_AmplifierPP_label} block are dynamic and display the model specified in the parameters Model.
Model: Memory polynomial
|
|
Model: Cross-term memory
|
|
Optional
Algorithms
*Model type in the power amplifier block.
The {blockLibraryPP_blocksPP_FF_RFSS_BlocksetFF_IdealizedSS_BasebandFF_PowerSS_AmplifierPP_label} block supports two types of models.
-
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.
-
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
-
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.
-
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.