Main Content

Apply memoryless nonlinearity to complex baseband signal

The `comm.MemorylessNonlinearity`

System object™ applies memoryless nonlinear impairments to a baseband signal. Use this
System object to model memoryless nonlinear impairments caused by signal amplification in a
radio frequency (RF) transmitter or receiver. For more information, see Memoryless Nonlinear Impairments.

To apply memoryless nonlinear impairments to a complex baseband signal:

Create the

`comm.MemorylessNonlinearity`

object and set its properties.Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

creates a
memoryless nonlinearity System object that models RF nonlinear impairments.`mnl`

= comm.MemorylessNonlinearity

specifies properties using one or more name-value pair arguments. Enclose each property
name in quotes. For example, `mnl`

= comm.MemorylessNonlinearity(`Name`

,`Value`

)`'Method','Saleh model'`

sets the modeling
method to the Saleh method.

Unless otherwise indicated, properties are *nontunable*, which means you cannot change their
values after calling the object. Objects lock when you call them, and the
`release`

function unlocks them.

If a property is *tunable*, you can change its value at
any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`Method`

— Nonlinearity modeling method`'Cubic polynomial'`

(default) | `'Hyperbolic tangent'`

| `'Saleh model'`

| `'Ghorbani model'`

| `'Modified Rapp model'`

| `'Lookup table'`

Nonlinearity modeling method, specified as `'Cubic polynomial'`

,
`'Hyperbolic tangent'`

, `'Saleh model'`

,
`'Ghorbani model'`

, `'Modified Rapp model'`

, or
`'Lookup table'`

. For more information, see Memoryless Nonlinear Impairments.

**Data Types: **`char`

| `string`

`InputScaling`

— Input signal scaling factor`0`

(default) | scalarInput signal scaling factor in decibels, specified as a scalar. This property scales the power gain of the input signal.

**Tunable: **Yes

To enable this property, set the `Method`

property to `'Saleh model'`

or ```
'Ghorbani
model'
```

.

**Data Types: **`double`

`LinearGain`

— Linear gain`0`

(default) | scalarLinear gain in decibels, specified as a scalar. This property scales the power gain of the output signal.

**Tunable: **Yes

To enable this property, set the `Method`

property to `'Cubic polynomial'`

, ```
'Hyperbolic
tangent'
```

, or `'Modified Rapp model'`

.

**Data Types: **`double`

`TOISpecification`

— Third-order nonlinearity specification for cubic polynomial`'IIP3'`

(default) | `'OIP3'`

| `'IP1dB'`

| `'OP1dB'`

| `'IPsat'`

| `'OPsat'`

Third-order nonlinearity specification for cubic polynomial, specified as
`'IIP3'`

, `'OIP3'`

, `'IP1dB'`

,
`'OP1dB'`

, `'IPsat'`

, or `'OPsat'`

.
For more information, see Cubic Polynomial Third-Order Coefficient.

To enable this property, set the `Method`

property to `'Cubic polynomial'`

.

**Data Types: **`char`

| `string`

`IIP3`

— Third-order input intercept point`30`

(default) | scalarThird-order input intercept point in dBm, specified as a scalar.

**Tunable: **Yes

To enable this property, set the `Method`

property to `'Cubic polynomial'`

or ```
'Hyperbolic
tangent'
```

.

**Data Types: **`double`

`OIP3`

— Third-order output intercept point`30`

(default) | scalarThird-order output intercept point in dBm, specified as a scalar.

**Tunable: **Yes

To enable this property, set the `Method`

property to `'Cubic polynomial'`

and the `TOISpecification`

property to `'OIP3'`

.

**Data Types: **`double`

`IP1dB`

— One dB input compression point`30`

(default) | scalarOne dB input compression point in dBm, specified as a scalar.

**Tunable: **Yes

To enable this property, set the `Method`

property to `'Cubic polynomial'`

and the `TOISpecification`

property to `'IP1dB'`

.

**Data Types: **`double`

`OP1dB`

— One dB output compression point`30`

(default) | scalarOne dB output compression point in dBm, specified as a scalar.

**Tunable: **Yes

To enable this property, set the `Method`

property to `'Cubic polynomial'`

and the `TOISpecification`

property to `'OP1dB'`

.

**Data Types: **`double`

`IPsat`

— Input saturation point`30`

(default) | scalarInput saturation point in dBm, specified as a scalar.

**Tunable: **Yes

To enable this property, set the `Method`

property to `'Cubic polynomial'`

and the `TOISpecification`

property to `'IPsat'`

.

**Data Types: **`double`

`OPsat`

— Output saturation point`30`

(default) | scalarOutput saturation point in dBm, specified as a scalar.

**Tunable: **Yes

To enable this property, set the `Method`

property to `'Cubic polynomial'`

and the `TOISpecification`

property to `'OPsat'`

.

**Data Types: **`double`

`AMPMConversion`

— Linear AM/PM conversion factor`10`

(default) | scalarLinear 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

To enable this property, set the `Method`

property to `'Cubic polynomial'`

or ```
'Hyperbolic
tangent'
```

.

**Data Types: **`double`

`AMAMParameters`

— AM/AM parameters`[2.1587 1.1517]`

| `[8.1081 1.5413 6.5202 -0.0718]`

| row vectorAM/AM parameters used to compute the amplitude gain for an input signal, specified as a row vector.

When the

`Method`

property is set to`'Saleh model'`

, this property must be a two-element vector that specifies alpha and beta values. In this case, the default value is`[2.1587 1.1517]`

.When the

`Method`

property is set to`'Ghorbani model'`

, this property must be a four-element vector that specifies*x*_{1},*x*_{2},*x*_{3}, and*x*_{4}values. In this case, the default value is`[8.1081 1.5413 6.5202 -0.0718]`

.

For more information, see Saleh Model Method and Ghorbani Model Method.

**Tunable: **Yes

To enable this property, set the `Method`

property is set to `'Saleh model'`

or ```
'Ghorbani
model'
```

.

**Data Types: **`double`

`AMPMParameters`

— AM/PM parameters`[4.0033 9.1040]`

| `[4.6645 2.0965 10.88 -0.003]`

| row vectorAM/PM parameters used to compute the phase change for an input signal, specified as a row vector.

When the

`Method`

property is set to`'Saleh model'`

, this property must be a two-element vector that specifies alpha and beta values. In this case, the default value is`[4.0033 9.1040]`

.When the

`Method`

property is set to`'Ghorbani model'`

, this property must be a four-element vector that specifies*y*_{1},*y*_{2},*y*_{3}, and*y*_{4}values. In this case, the default value is`[4.6645 2.0965 10.88 -0.003]`

For more information, see Saleh Model Method and Ghorbani Model Method.

**Tunable: **Yes

To enable this property, set the `Method`

property is set to `'Saleh model'`

or ```
'Ghorbani
model'
```

.

**Data Types: **`double`

`PowerLowerLimit`

— Input power lower limit`10`

(default) | scalarInput power lower limit in dBm, specified as a scalar less than the
`PowerUpperLimit`

property value. The AM/PM conversion scales
linearly for input power values in the range [`PowerLowerLimit`

,
`PowerUpperLimit`

]. 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

To enable this property, set the `Method`

property is set to `'Cubic polynomial'`

or ```
'Hyperbolic
tangent'
```

.

**Data Types: **`double`

`PowerUpperLimit`

— Input power upper limit`inf`

(default) | scalarInput power upper limit in dBm, specified as a scalar greater than
`PowerLowerLimit`

. The AM/PM conversion scales linearly for input
power values in the range [`PowerLowerLimit`

,
`PowerUpperLimit`

]. If the input signal power is above the input
power upper limit, the phase shift resulting from AM/PM conversion is constant. For more
information, see Cubic Polynomial and Hyperbolic Tangent Model Methods.

**Tunable: **Yes

To enable this property, set the `Method`

property is set to `'Cubic polynomial'`

or ```
'Hyperbolic
tangent'
```

.

**Data Types: **`double`

`OutputScaling`

— Output signal scaling factor`0`

(default) | scalarOutput signal scaling factor in decibels, specified as a scalar. This property scales the power gain of the output signal.

**Tunable: **Yes

To enable this property, set the `Method`

property is set to `'Saleh model'`

or ```
'Ghorbani
model'
```

.

**Data Types: **`double`

`Smoothness`

— Amplitude smoothness factor`0.5`

(default) | scalarAmplitude smoothness factor, specified as a scalar. For more information, see Modified Rapp Model Method.

**Tunable: **Yes

To enable this property, set the `Method`

property is set to `'Modified Rapp model'`

.

**Data Types: **`double`

`PhaseGainRadian`

— Phase gain for modified Rapp model`0`

(default) | scalarPhase gain for modified Rapp model in radians, specified as a scalar. A value of
`-0.45`

is typical. For more information, see Modified Rapp Model Method.

**Tunable: **Yes

To enable this property, set the `Method`

property is set to `'Modified Rapp model'`

.

**Data Types: **`double`

`PhaseSaturation`

— Phase saturation for modified Rapp model`0.88`

(default) | positive scalarPhase saturation for modified Rapp model in radians, specified as a positive scalar. For more information, see Modified Rapp Model Method.

**Tunable: **Yes

To enable this property, set the `Method`

property is set to `'Modified Rapp model'`

.

**Data Types: **`double`

`PhaseSmoothness`

— Phase smoothness for modified Rapp model`3.43`

(default) | positive scalarPhase smoothness for modified Rapp model in radians, specified as a positive scalar. For more information, see Modified Rapp Model Method.

**Tunable: **Yes

To enable this property, set the `Method`

property is set to `'Modified Rapp model'`

.

**Data Types: **`double`

`OutputSaturationLevel`

— Output saturation level`1`

(default) | positive scalarOutput saturation level, specified as a scalar. For more information, see Modified Rapp Model Method.

**Tunable: **Yes

To enable this property, set the `Method`

property is set to `'Modified Rapp model'`

.

**Data Types: **`double`

`Table`

— Amplifier characteristics lookup tableAmplifier characteristics lookup table, specified as an *N*-by-3
matrix of measured power amplifier (PA) characteristics. Each row is of the form
[*P*_{in},
*P*_{out}, ΔΦ].
*P*_{in} specifies the input signal in dBm,
*P*_{out} specifies the output signal in dBm, and
ΔΦ specifies the output phase shift in degrees. The default value is ```
[-25,
5.16, -0.25; -20, 10.11, -0.47; -15, 15.11, -0.68; -10, 20.05, -0.89; -5, 24.79,
-1.22; 0, 27.64, 5.59; 5, 28.49, 12.03]
```

.

The measured PA characteristics defined by this property are used to compute the AM/AM (in dBm/dBm) and AM/PM (in deg/dBm) nonlinear impairment characteristics.

**Note**

To determine appropriate *P*_{out} and ΔΦ
values for any *P*_{in} values outside the
range of values specified in the `Table`

property, the
System object applies linear extrapolation from the first two or last two
[*P*_{in},
*P*_{out}, ΔΦ] rows of
`Table`

.

**Tunable: **Yes

To enable this property, set the `Method`

property to `'Lookup table'`

.

**Data Types: **`double`

`Reference impedance`

— Reference impedance`1`

(default) | positive scalarReference impedance in ohms, specified as a positive scalar. This value is used to convert voltage values to power values.

**Tunable: **Yes

**Data Types: **`double`

`insig`

— Input RF baseband signalscalar | column vector | matrix

Input RF baseband signal, specified as a scalar, column vector, or matrix.

**Data Types: **`double`

`outsig`

— Output RF baseband signalscalar | column vector | matrix

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

To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named `obj`

, use
this syntax:

release(obj)

`comm.MemorylessNonlinearity`

`release` | Release resources and allow changes to System object property values and input characteristics |

`clone` | Create duplicate System object |

`isLocked` | Determine if System object is in use |

```
plot
(memorylessnonlinearity)
``` | Plot nonlinearity AM/AM and AM/PM characteristics |

Apply cubic polynomial nonlinearity to two 16-QAM signals. The first input signal power level is in the linear region of the amplifier power characteristic curve. The second input signal power level is in the nonlinear region of the amplifier power characteristic curve. Show the amplifier power characteristic curve and the constellation diagram for the amplified 16-QAM signals.

**Initialize Simulation**

Initialize variables for simulation and create System objects for a memoryless nonlinearity amplifier impairment and a constellation diagram. So that the constellation shows power compression only (and no phase rotation), configure the memoryless nonlinearity amplifier impairment with AM-PM distortion set to zero.

M = 16; % Modulation order sps = 4; % Samples per symbol pindBm = [12 25]; % Input power gain = 10; % Amplifier gain amplifier = comm.MemorylessNonlinearity("Method","Cubic polynomial", ... "LinearGain",gain,"AMPMConversion",0,"ReferenceImpedance",50); refConst = qammod([0:M-1],M); axisLimits = [-gain gain]; constdiag = comm.ConstellationDiagram("NumInputPorts",2, ... "ChannelNames",["Linear" "Nonlinear"],"ShowLegend",true, ... "ReferenceConstellation",refConst, ... "XLimits",axisLimits,"YLimits",axisLimits);

**Amplify and Plot Signal**

Apply 16-QAM to an input signal of random data. Amplify the signal and use the `plot`

function of the `comm.MemorylessNonlinearity`

System object to show the output power and phase response curves. The first input signal power level is 12 dBm and is in the linear region of the amplifier power characteristic curve. The second input signal power level is 25 dBm and is in the nonlinear region of the amplifier power characteristic curve.

pin = 10.^((pindBm-30)/10); % Convert dBm to linear Watts data = randi([0 M-1],1000,1); modOut = qammod(data,M,"UnitAveragePower",true)*sqrt(pin*amplifier.ReferenceImpedance); ampOut = amplifier(modOut); plot(amplifier);

Add AWGN to the two amplified signals and show the constellation diagram for the signals.

snr = 25; noisyLinOut = awgn(ampOut(:,1),snr,"measured"); noisyNonLinOut = awgn(ampOut(:,2),snr,"measured"); constdiag(noisyLinOut,noisyNonLinOut);

Generate 16-QAM data with an average power of 10 mW and a reference impedance of 1 ohm. Pass the data through a nonlinear power amplifier (PA).

M = 16; data = randi([0 (M - 1)]',1000,1); avgPow = 1e-2; minD = avgPow2MinD(avgPow,M);

Create a memoryless nonlinearity System object, specifying the Saleh model method.

saleh = comm.MemorylessNonlinearity('Method','Saleh model');

Generate modulated symbols and pass them through the PA nonlinearity model.

modData = (minD/2).*qammod(data,M); y = saleh(modData);

Generate a scatter plot of the results.

scatterplot(y)

Average power normalization of input signal.

function minD = avgPow2MinD(avgPow,M) % Average power to minimum distance nBits = log2(M); if (mod(nBits,2)==0) % Square QAM sf = (M - 1)/6; else % Cross QAM if (nBits>4) sf = ((31*M/32) - 1)/6; else sf = ((5*M/4) - 1)/6; end end minD = sqrt(avgPow/sf); end

Plot the gain compression of a nonlinear amplifier for a 16-QAM signal.

Specify the modulation order and samples per symbol parameters.

M = 16; sps = 4;

Model a nonlinear amplifier, by creating a memoryless nonlinearity System object with a 30 dB third-order input intercept point. Create a raised cosine transmit filter System object.

amplifier = comm.MemorylessNonlinearity('IIP3',30); txfilter = comm.RaisedCosineTransmitFilter( ... 'RolloffFactor',0.3,'FilterSpanInSymbols',6, ... 'OutputSamplesPerSymbol',sps,'Gain',sqrt(sps));

Specify the input power in dBm and a reference impedance of 1 ohm. Convert the input power to W and initialize the gain vector.

pindBm = -5:25; pin = 10.^((pindBm-30)/10); gain = zeros(length(pindBm),1);

Execute the main processing loop, which includes these steps.

Generate random data symbols.

Modulate the data symbols and adjust the average power of the signal.

Filter the modulated signal.

Amplify the signal.

Measure the gain.

for k = 1:length(pin) data = randi([0 (M - 1)],1000,1); modSig = qammod(data,M,'UnitAveragePower',true)*sqrt(pin(k)); filtSig = txfilter(modSig); ampSig = amplifier(filtSig); gain(k) = 10*log10(mean(abs(ampSig).^2) / mean(abs(filtSig).^2)); end

Plot the amplifier gain as a function of the input signal power. The 1 dB gain compression point occurs for an input power of 18.5 dBm. To increase the point at which a 1 dB compression is observed, increase the third-order intercept point, `amplifier.IIP3`

.

arrayplot = dsp.ArrayPlot('PlotType','Line','XLabel','Power In (dBm)', ... 'XOffset',-5,'YLimits',[-5 5]); arrayplot(gain)

Apply nonlinear power amplifier (PA) characteristics with 50 $\Omega $ impedance to a 16-QAM signal. Load PA characteristics by setting the `Method`

property to `'Lookup table'`

. The `pa_performance_characteristics`

helper function outputs the amplifier performance characteristics lookup table.

Define parameters for the modulation order, samples per symbol, and input power. Create random data.

M = 16; % Modulation order sps = 4; % Samples per symbol pindBm = -8; % Input power pin = 10.^((pindBm-30)/10); % power in Watts data = randi([0 (M - 1)],1000,1); refdata = 0:M-1; refconst = qammod(refdata,M,'UnitAveragePower',true); paChar = pa_performance_characteristics();

Create a memoryless nonlinearity System object, a transmit filter System object, and a constellation diagram System object. The default lookup table values are used for the memoryless nonlinearity System object.

amplifier = comm.MemorylessNonlinearity('Method','Lookup table','Table',paChar,'ReferenceImpedance',50); txfilter = comm.RaisedCosineTransmitFilter('RolloffFactor',0.3, ... 'FilterSpanInSymbols',6,'OutputSamplesPerSymbol',sps,'Gain',sqrt(sps)); constellation = comm.ConstellationDiagram('SamplesPerSymbol',4, ... 'Title','Amplified/Distorted Signal','NumInputPorts',2, ... 'ReferenceConstellation', refconst,'ShowLegend',true, ... 'ChannelNames',{'Filtered signal','Amplified signal'});

Modulate the random data. Filter and apply the nonlinear amplifier characteristics to the modulation symbols.

```
modSig = qammod(data,M,'UnitAveragePower',true)*sqrt(pin * amplifier.ReferenceImpedance);
filtSig = txfilter(modSig);
ampSig = amplifier(filtSig);
```

Compute input and output signal levels and the phase shift.

pSig = abs(ampSig).^2 / amplifier.ReferenceImpedance; poutdBm = 10 * log10(pSig) + 30; pfiltSig = abs(filtSig).^2 / amplifier.ReferenceImpedance; simulated_pindBm = 10 * log10(pfiltSig) + 30; phase = rad2deg(angle(ampSig.*conj(filtSig)));

Plot AM/AM characteristics, AM/PM characteristics, and the constellation results.

figure set(gcf,'units','normalized','position',[.25 1/3 .5 1/3]) subplot(1,2,1) plot(simulated_pindBm,poutdBm,'.'); hold on plot(amplifier.Table(:,1),amplifier.Table(:,2),'.','Markersize',15); xlabel('Input Power (dBm)') ylabel('Output Power (dBm)'); grid on; title('AM/AM Characteristics'); leglabel = {'Simulated results','Measurement'}; legend (leglabel,'Location','south'); subplot(1,2,2) plot(simulated_pindBm,phase,'.'); hold on plot(amplifier.Table(:,1),amplifier.Table(:,3),'.','Markersize',15); legend (leglabel,'Location','south'); xlabel('Input Power (dBm)'); ylabel('Output Phase Shift (degrees)'); grid on; title('AM/PM Characteristics');

For the purpose of constellation comparison, normalize the amplified signal and the filtered signal. Generate a constellation diagram of the filtered signal and amplified signal. The nonlinear amplifier characteristics cause compression of the amplified signal constellation compared to the filtered constellation.

filtSig = filtSig/mean(abs(filtSig)); % Normalized filtered signal ampSig = ampSig/mean(abs(ampSig)); % Normalized amplified signal constellation(filtSig,ampSig)

**Helper Function**

`function paChar = pa_performance_characteristics()`

The operating specification for the LDMOS-based Doherty amplifier are:

A frequency of 2110 MHz

A peak power of 300 W

A small signal gain of 61 dB

Each row in `HAV08_Table`

specifies Pin (dBm), gain (dB), phase shift (degrees) as derived from figure 4 of Hammi, Oualid, et al. "Power amplifiers' model assessment and memory effects intensity quantification using memoryless post-compensation technique." IEEE Transactions on Microwave Theory and Techniques 56.12 (2008): 3170-3179.

```
HAV08_Table =...
[-35,60.53,0.01;
-34,60.53,0.01;
-33,60.53,0.08;
-32,60.54,0.08;
-31,60.55,0.1;
-30,60.56,0.08;
-29,60.57,0.14;
-28,60.59,0.19;
-27,60.6,0.23;
-26,60.64,0.21;
-25,60.69,0.28;
-24,60.76,0.21;
-23,60.85,0.12;
-22,60.97,0.08;
-21,61.12,-0.13;
-20,61.31,-0.44;
-19,61.52,-0.94;
-18,61.76,-1.59;
-17,62.01,-2.73;
-16,62.25,-4.31;
-15,62.47,-6.85;
-14,62.56,-9.82;
-13,62.47,-12.29;
-12,62.31,-13.82;
-11,62.2,-15.03;
-10,62.15,-16.27;
-9,62,-18.05;
-8,61.53,-20.21;
-7,60.93,-23.38;
-6,60.2,-26.64;
-5,59.38,-28.75];
```

Convert the second column of the HAV08_Table from gain to Pout for use by the memoryless nonlinearity System object.

```
paChar = HAV08_Table;
paChar(:,2) = paChar(:,1) + paChar(:,2);
end
```

Memoryless nonlinear impairments distort the amplitude and phase of the input signal. The amplitude distortion is amplitude-to-amplitude modulation (AM/AM) and the phase distortion is amplitude-to-phase modulation (AM/PM). These model methods are available for simulating the memoryless nonlinear impairment models.

Model Method | Memoryless Nonlinear Impairment |
---|---|

Cubic polynomial | Applies AM/AM and AM/PM |

Hyperbolic tangent | |

Saleh model | |

Ghorbani model | |

Modified Rapp model | |

Lookup table | Applies impairment according to
[P_{in},
P_{out}, ΔΦ] amplifier characteristics
specified by the `Table`
property |

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. For real-valued input signals, the imaginary component is set to zero.

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.

Combine the new magnitude and angle components into a complex signal. Then, multiply the result by an output gain factor.

The model methods apply AM/AM and AM/PM impairments as shown in this figure.

The lookup table method uses the power amplifier (PA) characteristics lookup table,
specified as an *N*-by-3 matrix of measured PA characteristics. Each row is
of the form [*P*_{in},
*P*_{out}, ΔΦ].
*P*_{in} specifies the PA input signal in dBm,
*P*_{out} specifies the PA output signal in dBm, and
ΔΦ specifies the output phase shift in degrees. The measured PA characteristics defined by
the `Table`

property
are used to compute the AM/AM (in dBm/dBm) and AM/PM (in deg/dBm) nonlinear impairment
characteristics. The System object distorts the input signal by the computed AM/AM (in dBm/dBm) and AM/PM (in
deg/dBm) values.

**Note**

To determine appropriate *P*_{out} and ΔΦ
values for any *P*_{in} values outside the range of
values specified in the `Table`

property, the System object applies linear extrapolation from the first two or last two
[*P*_{in},
*P*_{out}, ΔΦ] rows of `Table`

.

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.

The cubic polynomial model method uses linear power gain to determine the linear
coefficient of a third-order polynomial and either the input or output power in dBm for the
third-order intercept point (IP3), point one dB lower than output power (P1dB), or
saturation power (Psat) to determine the third-order coefficient of the polynomial. This
figure shows an example of the plot generated when you set the `Method`

property to `'Cubic polynomial'`

.

The general form of cubic nonlinearity models the AM/AM characteristics as

$${\text{F}}_{\text{AM/AM}}{\text{(|u|)=c}}_{\text{1}}\text{\xd7|u|+}\frac{\text{3}}{\text{4}}{\text{c}}_{\text{3}}{\text{\xd7|u|}}^{\text{3}}$$

where `F`

is the
magnitude of the output signal, _{AM/AM}*(|u|)**|u|* is the magnitude of the input signal,
*c*_{1} is the coefficient of the linear gain term,
and *c*_{3} is the coefficient of the cubic gain term.
The results for IIP3, OIP3, IP1dB, OP1dB, IPsat, and OPsat are taken from [6]. The coefficient
*c*_{3} values are given in this table.

Nonlinearity Type | Description | Equation |
---|---|---|

`IIP3` | Input power level at which the power from linear gain is equal to the power from a third-order nonlinearity | $${c}_{3}=-\frac{4{c}_{1}}{3\times {10}^{[(IIP3-30)/10]}}$$ where |

`OIP3` | Output power level at which the power from linear gain is equal to the power from a third-order nonlinearity | $${c}_{3}=-\frac{4{c}_{1}^{3}}{3\times {10}^{[(OIP3-30)/10]}}$$ where |

`IP1dB` | Input power level at which the output power is one dB less than the power from linear gain | $${c}_{3}=-\frac{2{c}_{1}({10}^{\raisebox{1ex}{$19$}\!\left/ \!\raisebox{-1ex}{$20$}\right.}-10)}{15\times {10}^{[(IP1dB-30)/10]}}$$ where |

`OP1dB` | Output power level one dB less than the power from linear gain | $${c}_{3}=-\frac{2{c}_{1}^{3}({10}^{\raisebox{1ex}{$19$}\!\left/ \!\raisebox{-1ex}{$20$}\right.}-10)}{15\times {10}^{[(OP1dB-30-LGdB+1)/10]}}$$ where |

`IPsat` | Input power at which the output power saturates | $${c}_{3}=-\frac{4{c}_{1}}{9\times {10}^{[(IPsat-30)/10]}}$$ where |

`OPsat` | Output saturation power | $${c}_{3}=-\frac{16{c}_{1}^{3}}{81\times {10}^{[(OPsat-30)/10]}}$$ where |

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.

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

The AM/AM parameters (*x*_{1},
*x*_{2},
*x*_{3}, and
*x*_{4}) 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 (*y*_{1},
*y*_{2},
*y*_{3}, and
*y*_{4}) 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.

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

The amplitude and phase distortion of the input signal are given by

$${F}_{\text{AMAM}}(u)=\frac{{g}_{\text{lin}}\times u}{{\left(1+{\left(\frac{{g}_{\text{lin}}\times u}{{O}_{\text{sat}}}\right)}^{\text{2}S}\right)}^{\text{1/2}S}}\text{,}$$

$${F}_{\text{AMPM}}(u)=\frac{A{u}^{q}}{\left(1+{\left(\frac{u}{B}\right)}^{q}\right)}\text{,}$$

where:

*g*_{lin}is 10^{(LinearGain/20))}and is the amplitude gain of the amplifier.*u*is the magnitude of the signal.*S*is the smoothness factor, specified by the`Smoothness`

property.*O*_{sat}is the output saturation level, specified by the`OutputSaturationLevel`

property.*A*is the phase gain in radians, specified by the`PhaseGainRadian`

property.*B*is the phase saturation, specified by the`PhaseSaturation`

property.*q*is the phase smoothness, specified by the`PhaseSmoothness`

property.

[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/.

[4] Choi, C., et.al. "RF impairment
models for 60 GHz-band SYS/PHY simulation." *IEEE
802.15-06-0477-01-003c*. November 2006.

[5] Perahia, E. "TGad Evaluation
Methodology." *IEEE 802.11-09/0296r16*. January 20, 2010.
https://mentor.ieee.org/802.11/dcn/09/11-09-0296-16-00ad-evaluation-methodology.doc.

[6] Kundert, Ken. "Accurate and Rapid
Measurement of IP2 and IP3." *The Designer Guide Community*. May 22,
2002.

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