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comm.MemorylessNonlinearity

Apply memoryless nonlinearity to complex baseband signal

Description

The comm.MemorylessNonlinearity System object™ applies memoryless nonlinear impairments to a complex 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.

Note

All values of power assume a nominal impedance of 1 ohm.

To apply memoryless nonlinear impairments to a complex baseband signal:

  1. Create the comm.MemorylessNonlinearity object and set its properties.

  2. Call the object with arguments, as if it were a function.

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

Creation

Description

mnl = comm.MemorylessNonlinearity creates a memoryless nonlinearity System object that models RF nonlinear impairments.

example

mnl = comm.MemorylessNonlinearity(Name,Value) specifies properties using one or more name-value pair arguments. Enclose each property name in quotes. For example, 'Method','Saleh model' sets the modeling method to the Saleh method.

Properties

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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.

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.

Data Types: char | string

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

Tunable: Yes

Dependencies

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

Data Types: double

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

Tunable: Yes

Dependencies

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

Data Types: double

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

Tunable: Yes

Dependencies

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

Data Types: double

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 property, set the Method property to 'Cubic polynomial' or 'Hyperbolic tangent'.

Data Types: double

AM/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 x1, x2, x3, and x4 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

Dependencies

To enable this property, set the Method property is set to 'Saleh model' or 'Ghorbani model'.

Data Types: double

AM/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 y1, y2, y3, and y4 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

Dependencies

To enable this property, set the Method property is set to 'Saleh model' or 'Ghorbani model'.

Data Types: double

Input 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

Dependencies

To enable this property, set the Method property is set to 'Cubic polynomial' or 'Hyperbolic tangent'.

Data Types: double

Input 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

Dependencies

To enable this property, set the Method property is set to 'Cubic polynomial' or 'Hyperbolic tangent'.

Data Types: double

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

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Saleh model' or 'Ghorbani model'.

Data Types: double

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

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Rapp model'.

Data Types: double

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

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Rapp model'.

Data Types: double

Amplifier characteristics lookup table, specified as an N-by-3 matrix of measured power amplifier (PA) characteristics. Each row is of the form [Pin, Pout, ΔΦ]. Pin specifies the PA input signal in dBm, Pout specifies the PA 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. 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 Pout and ΔΦ for Pin values outside the range of values specified in the Table property, the System object applies linear extrapolation from the first two or last two [Pin, Pout, ΔΦ] rows of Table.

Tunable: Yes

Dependencies

To enable this property, set the Method property is set to 'Lookup table'.

Data Types: double

Usage

Description

example

outsig = mnl(insig) applies memoryless nonlinear impairments to the input RF baseband signal.

Input Arguments

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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 Arguments

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

Object Functions

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)

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stepRun System object algorithm
releaseRelease resources and allow changes to System object property values and input characteristics
resetReset internal states of System object

Examples

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Generate 16-QAM data with an average power of 10 mW and 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. 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(var(ampSig)/var(filtSig));
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 to a 16-QAM signal by setting the Method property to '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 = -2; % 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);

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');
txfilter = comm.RaisedCosineTransmitFilter('RolloffFactor',0.3, ...
    'FilterSpanInSymbols',6,'OutputSamplesPerSymbol',sps,'Gain',sqrt(sps));
constellation = comm.ConstellationDiagram('SamplesPerSymbol',4,'ReferenceConstellation',refconst, ...
    'Title','Amplified/Distorted Signal');

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

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

Compute input and output signal levels and the phase shift.

poutdBm = (20*log10(abs(ampSig))) + 30;
simulated_pindBm = (20*log10(abs(filtSig))) + 30;
phase = angle(ampSig.*conj(filtSig))*180/pi;

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');
leglabels = {'Simulated results','Measurement'};
legend (leglabels,'Location','north');

subplot(1,2,2)
plot(simulated_pindBm,phase,'.');
hold on
plot(amplifier.Table(:,1),amplifier.Table(:,3),'.','Markersize',15);
legend (leglabels,'Location','north');
xlabel('Input Power (dBm)'); 
ylabel('Output Phase Shift (degrees)');
grid on; title('AM/PM Characteristics');

Generate a constellation diagram of the amplified signal and reference constellation. The nonlinear amplifier characteristics cause compression of the amplified signal constellation compared to the reference constellation.

constellation(ampSig)

Apply nonlinear power amplifier (PA) characteristics to a 16-QAM signal by setting the Method property to '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);
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);
filtSig = txfilter(modSig);
ampSig = amplifier(filtSig);

Compute input and output signal levels and the phase shift.

poutdBm = (20*log10(abs(ampSig))) + 30;
simulated_pindBm = (20*log10(abs(filtSig))) + 30;
phase = angle(ampSig.*conj(filtSig))*180/pi;

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)

The pa_performance_characteristics helper function calculates the amplifier performance characteristics. The data is extracted 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.

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).

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

More About

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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/.

Extended Capabilities

Introduced in R2012a