Memoryless Nonlinearity
Apply memoryless nonlinearity to complex baseband signal
- Library:
Communications Toolbox / RF Impairments
Description
The Memoryless Nonlinearity block applies memoryless nonlinear impairments to a complex baseband signal. Use this block to model memoryless nonlinear impairments caused by signal amplification in the radio frequency (RF) transmitter or receiver. For more information, see Memoryless Nonlinear Impairments.
Note
All values of power assume a nominal impedance of 1 ohm.
Ports
Input
Output
Parameters
Model Examples
Block Characteristics
Data Types |
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Multidimensional Signals |
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Variable-Size Signals |
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More About
Memoryless Nonlinear Impairments
Memoryless nonlinear impairments distort the input signal amplitude and phase. The amplitude distortion is amplitude-to-amplitude modulation (AM/AM) and the phase distortion is amplitude-to-phase modulation (AM/PM).
| Model Method | Memoryless Nonlinear Impairment |
|---|---|
Cubic polynomial | AM/AM and AM/PM |
Hyperbolic tangent | |
Saleh model | |
Ghorbani model | |
Rapp model | AM/AM only |
The modeled impairments apply the AM/AM and AM/PM distortions differently, according to the model method you specify. The models apply the memoryless nonlinear impairment to the input signal by following these steps.
Multiply the signal by an input gain factor.
Note
You can normalize the signal to 1 by setting the input scaling gain to the inverse of the input signal amplitude.
Split the complex signal into its magnitude and angle components.
Apply an AM/AM distortion to the magnitude of the signal, according to the selected model method, to produce the magnitude of the output signal.
Apply an AM/PM distortion to the phase of the signal, according to the selected model method, to produce the angle of the output signal.
Note
This step does not apply for the Rapp model.
Combine the new magnitude and angle components into a complex signal. Then, multiply the result by an output gain factor.
The first four model methods (cubic polynomial, hyperbolic tangent, Saleh model, and Ghorbani model) apply AM/AM and AM/PM impairments as shown in this figure.
The Rapp model method applies AM/AM distortion as shown in this figure.
Cubic Polynomial and Hyperbolic Tangent Model Methods
This figure shows the AM/PM conversion behavior for the cubic polynomial and hyperbolic tangent model methods.
The AM/PM conversion scales linearly with an input power value between the lower and upper limits of the input power level. Outside this range, the AM/PM conversion is constant at the values corresponding to the lower and upper input power limits, which are zero and (AM/PM conversion) × (upper input power limit – lower input power limit), respectively.
Saleh Model Method
This figure shows the AM/AM behavior (output voltage versus input voltage for the AM/AM distortion) and the AM/PM behavior (output phase versus input voltage for the AM/PM distortion) for the Saleh model method.
The AM/AM parameters, αAMAM and βAMAM, are used to compute the amplitude distortion of the input signal by using
where u is the magnitude of the scaled signal.
The AM/PM parameters, αAMPM and βAMPM, are used to compute the phase distortion of the input signal by using
where u is the magnitude of the scaled signal. The α and β parameters for AM/AM and AM/PM are similarly named but distinct.
References
[1] Saleh, A.A.M. “Frequency-Independent and Frequency-Dependent Nonlinear Models of TWT Amplifiers.” IEEE Transactions on Communications 29, no. 11 (November 1981): 1715–20. https://doi.org/10.1109/TCOM.1981.1094911.
[2] Ghorbani, A., and M. Sheikhan. "The Effect of Solid State Power Amplifiers (SSPAs) Nonlinearities on MPSK and M-QAM Signal Transmission." In 1991 Sixth International Conference on Digital Processing of Signals in Communications, 193–97, 1991.
[3] Rapp, Ch. "Effects of HPA-Nonlinearity on a 4-DPSK/OFDM-Signal for a Digital Sound Broadcasting System." In Proceedings Second European Conf. on Sat. Comm. (ESA SP-332), 179–84. Liege, Belgium, 1991. https://elib.dlr.de/33776/.