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

In1 — Input RF baseband signal

scalar | column vector

Input RF baseband signal, specified as a scalar or column vector. Values in this input must be complex.

Data Types: double
Complex Number Support: Yes

Output

Out1 — Output RF baseband signal

scalar | column vector

Output RF baseband signal, returned as a scalar or column vector. The output is of the same data type as the input.

Parameters

Method — Nonlinearity modeling method

Cubic polynomial (default) | Hyperbolic tangent | Saleh model | Ghorbani model | Rapp model

Nonlinearity modeling method, specified as Cubic polynomial, Hyperbolic tangent, Saleh model, Ghorbani model, Rapp model, or Lookup table. For more information, see Memoryless Nonlinear Impairments.

Linear gain (dB) — Linear gain

0 (default) | scalar

Linear gain in decibels, specified as a scalar. This parameter scales the power gain of the output signal.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Cubic polynomial, Hyperbolic tangent, or Rapp model.

Data Types: double

IIP3 (dBm) — Third-order input intercept point

30 (default) | scalar

Third-order input intercept point in dBm, specified as a scalar.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Cubic polynomial or Hyperbolic tangent.

Data Types: double

AM/PM conversion (degrees per dB) — AM/PM conversion factor

10 (default) | scalar

AM/PM conversion factor in degrees per decibel, specified as a scalar. For more information, see Cubic Polynomial and Hyperbolic Tangent Model Methods.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Cubic polynomial or Hyperbolic tangent.

Data Types: double

Lower input power limit for AM/PM conversion (dBm) — Input power lower limit

10 (default) | scalar

Input power lower limit in dBm, specified as a scalar less than the Upper input power limit for AM/PM conversion (dBm) parameter value. The AM/PM conversion scales linearly for input power values in the range [Lower input power limit for AM/PM conversion (dBm), Upper input power limit for AM/PM conversion (dBm)]. If the input signal power is below the input power lower limit, the phase shift resulting from AM/PM conversion is zero. For more information, see Cubic Polynomial and Hyperbolic Tangent Model Methods.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Cubic polynomial or Hyperbolic tangent.

Data Types: double

Upper input power limit for AM/PM conversion (dBm) — Input power upper limit

inf (default) | scalar

Input power upper limit in dBm, specified as a scalar greater than the Lower input power limit for AM/PM conversion (dBm) parameter value. The AM/PM conversion scales linearly for input power values in the range [Lower input power limit for AM/PM conversion (dBm), Upper input power limit for AM/PM conversion (dBm)]. If the input signal power is below the input power lower limit, the phase shift resulting from AM/PM conversion is zero. For more information, see Cubic Polynomial and Hyperbolic Tangent Model Methods.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Cubic polynomial or Hyperbolic tangent.

Data Types: double

Input scaling (dB) — Input signal scaling factor

0 (default) | scalar

Input signal scaling factor in decibels, specified as a scalar. This parameter scales the power gain of the input signal.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Saleh model or Ghorbani model.

Data Types: double

AM/AM parameters [alpha beta] — AM/AM parameters for Saleh model

[2.1587 1.1517] (default) | two-element vector

AM/AM parameters for Saleh model, used to compute the amplitude gain for an input signal, specified as a two-element vector. For more information, see Saleh Model Method.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Saleh model.

Data Types: double

AM/PM parameters [alpha beta] — AM/PM parameters for Saleh model

[4.0033 9.1040] (default) | two-element vector

AM/PM parameters for Saleh model, used to compute the phase change for an input signal, specified as a two-element vector. For more information, see Saleh Model Method.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Saleh model.

AM/AM parameters [x1 x2 x3 x4] — AM/AM parameters for Ghorbani model

[8.1081 1.5413 6.5202 -0.0718] (default) | four-element vector

AM/AM parameters for Ghorbani model, used to compute the amplitude gain for an input signal, specified as a four-element vector. For more information, see Ghorbani Model Method.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Ghorbani model.

Data Types: double

AM/PM parameters [y1 y2 y3 y4] — AM/PM parameters for Ghorbani model

[4.6645 2.0965 10.88 -0.003] (default) | four-element vector

AM/PM parameters for Ghorbani model, used to compute the phase change for an input signal, specified as a four-element vector. For more information, see Ghorbani Model Method.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Ghorbani model.

Data Types: double

Output scaling (dB) — Output signal scaling factor

0 (default) | scalar

Output signal scaling factor in decibels, specified as a scalar. This parameter scales the power gain of the output signal.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Saleh model or Ghorbani model.

Data Types: double

Smoothness factor — Smoothness factor

0.5 (default) | scalar

Smoothness factor, specified as a scalar. For more information, see Rapp Model Method.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Rapp model.

Data Types: double

Output saturation level — Output saturation level

1 (default) | scalar

Output saturation level, specified as a scalar. For more information, see Rapp Model Method.

Tunable: Yes

Dependencies

To enable this parameter, set the Method to Rapp model.

Data Types: double

Model Examples

Add Saleh Model of Memoryless Nonlinearity to 16-QAM Signal

This model applies the Saleh Model of the memoryless nonlinearity to a 16-QAM modulated signal. To demonstrate and visualize the memoryless impairment levels applied in this model are exaggerated and not representative of typical levels for modern radios.

Add RF Impairments to DQPSK Signal

This model applies RF impairments to a signal modulated by differential quadrature phase shift keying (DQPSK). To demonstrate and visualize the RF impairments, levels applied in this model are exaggerated and not representative of typical levels for modern radios.

Block Characteristics

Data Types	double | single
Multidimensional Signals	no
Variable-Size Signals	no

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.

1. 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.

2. Split the complex signal into its magnitude and angle components.

3. 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.

4. 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.

5. 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, α_AMAM and β_AMAM, are used to compute the amplitude distortion of the input signal by using

$$F_{\text{AMAM}}(u)=\frac{{\alpha }_{\text{AMAM}}\times u}{1+{\beta }_{\text{AMAM}}\times u^2}\text{,}$$

where u is the magnitude of the scaled signal.

The AM/PM parameters, α_AMPM and β_AMPM, are used to compute the phase distortion of the input signal by using

$$F_{\text{AMPM}}(u)=\frac{{\alpha }_{\text{AMPM}}\times u^2}{1+{\beta }_{\text{AMPM}}\times u^2}\text{,}$$

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.

Ghorbani Model Method

The Ghorbani model method applies AM/AM and AM/PM distortion as described in this section.

The AM/AM parameters (x₁, x₂, x₃, and x₄) are used to compute the amplitude distortion of the input signal by using

$$F_{\text{AMAM}}(u)=\frac{x_1{u}^{x_2}}{1+x_3{u}^{x_2}}+x_{4}u\text{,}$$

where u is the magnitude of the scaled signal.

The AM/PM parameters (y₁, y₂, y₃, and y₄) are used to compute the phase distortion of the input signal by using

$$F_{\text{AMPM}}(u)=\frac{y_1{u}^{y_2}}{1+y_3{u}^{y_2}}+y_{4}u\text{,}$$

where u is the magnitude of the scaled signal.

Rapp Model Method

The Rapp model method applies AM/AM distortion as described in this section. The Rapp model does not apply AM/PM distortion to the input signal.

The smoothness factor and output saturation level are used to compute the amplitude distortion of the input signal given by

$$F_{\text{AMAM}}(u)=\frac{g_{\text{lin}}\times u}{{\left(1+{\left(\frac{g_{\text{lin}}\times u}{O_{\text{sat}}}\right)}^{\text{2}S}\right)}^{\text{1/2}S}}\text{,}$$

where

• u is the magnitude of the scaled signal.

• S is the smoothness factor.

• O_sat is the output saturation level.

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/.

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