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Apply various RF impairments to a QAM signal. Observe the effects by using constellation diagrams, time-varying error vector magnitude (EVM) plots, and spectrum plots. Estimate the equivalent signal-to-noise ratio (SNR).

Set the sample rate, modulation order, and SNR. Calculate the reference constellation points.

```
fs = 1000;
M = 16;
snrdB = 30;
refConst = qammod(0:M-1,M,'UnitAveragePower',true);
```

Create constellation diagram and time scope objects to visualize the impairment effects.

constDiagram = comm.ConstellationDiagram('ReferenceConstellation',refConst); timeScope = dsp.TimeScope('YLimits',[0 40],'SampleRate',fs,'TimeSpan',1, ... 'ShowGrid',true,'YLabel','EVM (%)');

Generate a 16-QAM signal, and pass it through an AWGN channel. Plot its constellation.

```
data = randi([0 M-1],1000,1);
modSig = qammod(data,M,'UnitAveragePower',true);
noisySig = awgn(modSig,snrdB);
constDiagram(noisySig)
```

Estimate the EVM of the noisy signal from the reference constellation points.

evm = comm.EVM('ReferenceSignalSource','Estimated from reference constellation', ... 'ReferenceConstellation',refConst, ... 'Normalization','Average constellation power'); rmsEVM = evm(noisySig)

rmsEVM = 3.1768

The modulation error rate (MER) closely corresponds to the SNR. Create an MER object, and estimate the SNR.

mer = comm.MER('ReferenceSignalSource','Estimated from reference constellation', ... 'ReferenceConstellation',refConst); snrEst = mer(noisySig)

snrEst = 30.1071

The estimate is quite close to the specified SNR of 30 dB.

Create an amplifier using the memoryless nonlinearity object.

amp = comm.MemorylessNonlinearity('IIP3',38,'AMPMConversion',0);

Pass the modulated signal through the nonlinear amplifier, and plot its constellation diagram.

txSig = amp(modSig); constDiagram(txSig)

The corner points of the constellation have moved toward the origin due to amplifier gain compression.

Introduce a small AM/PM conversion, and display the received signal constellation.

amp.AMPMConversion = 1; txSig = amp(modSig); constDiagram(txSig)

The constellation has rotated due to the AM/PM conversion. To compute the time-varying EVM, release the EVM object and set the `AveragingDimensions`

property to 2. To estimate the EVM against an input signal, omit the `ReferenceSignalSource`

property definition. This method produces more accurate results.

```
evm = comm.EVM('AveragingDimensions',2);
evmTime = evm(modSig,txSig);
```

Plot the time-varying EVM of the distorted signal.

timeScope(evmTime)

Compute the RMS EVM.

evmRMS = sqrt(mean(evmTime.^2))

evmRMS = 35.5919

Compute the MER.

mer = comm.MER; snrEst = mer(modSig,txSig)

snrEst = 8.1392

The SNR (≈8 dB) is reduced from its initial value (∞) due to amplifier distortion.

Specify input power levels ranging from 0 to 40 dBm. Convert those levels to their linear equivalent in W. Initialize the output power vector.

powerIn = 0:40; pin = 10.^((powerIn-30)/10); powerOut = zeros(length(powerIn),1);

Measure the amplifier output power for the range of input power levels.

for k = 1:length(powerIn) data = randi([0 15],1000,1); txSig = qammod(data,16,'UnitAveragePower',true)*sqrt(pin(k)); ampSig = amp(txSig); powerOut(k) = 10*log10(var(ampSig))+30; end

Plot the power output versus power input curve.

figure plot(powerIn,powerOut,powerIn,powerIn,'--') legend('Amplifier Output','Ideal Output','location','se') xlabel('Power In (dBm)') ylabel('Power Out (dBm)') grid

The output power levels off at 30 dBm. The amplifier exhibits nonlinear behavior for input power levels greater than 25 dBm.

Apply an amplitude and phase imbalance to the modulated signal.

ampImb = 3; phImb = 10; gainI = 10.^(0.5*ampImb/20); gainQ = 10.^(-0.5*ampImb/20); imbI = real(modSig)*gainI*exp(-0.5i*phImb*pi/180); imbQ = imag(modSig)*gainQ*exp(1i*(pi/2 + 0.5*phImb*pi/180)); rxSig = imbI + imbQ;

Plot the received constellation.

constDiagram(rxSig)

The magnitude and phase of the constellation has changed as a result of the I/Q imbalance.

Calculate and plot the time-varying EVM.

evmTime = evm(modSig,rxSig); timeScope(evmTime)

The EVM exhibits a behavior that is similar to that experienced with a nonlinear amplifier though the variance is smaller.

Create a 100 Hz sine wave having a 1000 Hz sample rate.

sinewave = dsp.SineWave('Frequency',100,'SampleRate',1000, ... 'SamplesPerFrame',1e4,'ComplexOutput',true); x = sinewave();

Apply the same 3 dB and 10 degree I/Q imbalance.

ampImb = 3; phImb = 10; gainI = 10.^(0.5*ampImb/20); gainQ = 10.^(-0.5*ampImb/20); imbI = real(x)*gainI*exp(-0.5i*phImb*pi/180); imbQ = imag(x)*gainQ*exp(1i*(pi/2 + 0.5*phImb*pi/180)); y = imbI + imbQ;

Plot the spectrum of the imbalanced signal.

spectrum = dsp.SpectrumAnalyzer('SampleRate',1000,'PowerUnits','dBW'); spectrum(y)

The I/Q imbalance introduces a second tone at -100 Hz, which is the inverse of the input tone.

Apply phase noise to the transmitted signal. Plot the resulting constellation diagram.

pnoise = comm.PhaseNoise('Level',-50,'FrequencyOffset',20,'SampleRate',fs); pnoiseSig = pnoise(modSig); constDiagram(pnoiseSig)

The phase noise introduces a rotational jitter.

Compute and plot the EVM of the received signal.

evmTime = evm(modSig,pnoiseSig); timeScope(evmTime)

Determine the RMS EVM.

evmRMS = sqrt(mean(evmTime.^2))

evmRMS = 6.1989

Specify the samples per symbol parameter. Create a pair of raised cosine matched filters.

sps = 4; txfilter = comm.RaisedCosineTransmitFilter('RolloffFactor',0.2,'FilterSpanInSymbols',8, ... 'OutputSamplesPerSymbol',sps,'Gain',sqrt(sps)); rxfilter = comm.RaisedCosineReceiveFilter('RolloffFactor',0.2,'FilterSpanInSymbols',8, ... 'InputSamplesPerSymbol',sps,'Gain',1/sqrt(sps), ... 'DecimationFactor',sps);

Determine the delay through the matched filters.

fltDelay = 0.5*(txfilter.FilterSpanInSymbols + rxfilter.FilterSpanInSymbols);

Pass the modulated signal through the matched filters.

filtSig = txfilter(modSig); rxSig = rxfilter(filtSig);

To account for the delay through the filters, discard the first `fltDelay`

samples.

rxSig = rxSig(fltDelay+1:end);

To accommodate the change in the number of received signal samples, create new constellation diagram and time scope objects.

constDiagram = comm.ConstellationDiagram('ReferenceConstellation',refConst); timeScope = dsp.TimeScope('YLimits',[0 40],'SampleRate',fs,'TimeSpan',1, ... 'ShowGrid',true,'YLabel','EVM (%)');

Estimate EVM. Plot the received signal constellation diagram and the time-varying EVM.

evm = comm.EVM('ReferenceSignalSource','Estimated from reference constellation', ... 'ReferenceConstellation',refConst, ... 'Normalization','Average constellation power','AveragingDimensions',2); evmTime = evm(rxSig); constDiagram(rxSig) timeScope(evmTime)

Determine the RMS EVM.

evmRMS = sqrt(mean(evmTime.^2))

evmRMS = 2.7199

Determine the equivalent SNR.

mer = comm.MER; snrEst = mer(modSig(1:end-fltDelay),rxSig)

snrEst = 31.4603

Combine the effects of the filters, nonlinear amplifier, AWGN, and phase noise. Display the constellation and EVM diagrams.

Create EVM, time scope and constellation diagram objects.

evm = comm.EVM('ReferenceSignalSource','Estimated from reference constellation', ... 'ReferenceConstellation',refConst, ... 'Normalization','Average constellation power','AveragingDimensions',2); timeScope = dsp.TimeScope('YLimits',[0 40],'SampleRate',fs,'TimeSpan',1, ... 'ShowGrid',true,'YLabel','EVM (%)'); constDiagram = comm.ConstellationDiagram('ReferenceConstellation',refConst);

Specify the nonlinear amplifier and phase noise objects.

amp = comm.MemorylessNonlinearity('IIP3',45,'AMPMConversion',0); pnoise = comm.PhaseNoise('Level',-55,'FrequencyOffset',20,'SampleRate',fs);

Filter and then amplify the modulated signal.

txfiltOut = txfilter(modSig); txSig = amp(txfiltOut);

Add phase noise. Pass the impaired signal through the AWGN channel. Plot the constellation diagram.

rxSig = awgn(txSig,snrdB); pnoiseSig = pnoise(rxSig); rxfiltOut = rxfilter(pnoiseSig); constDiagram(rxfiltOut)

Calculate the time-varying EVM. Plot the result.

evmTime = evm(rxfiltOut); timeScope(evmTime)

Determine the RMS EVM.

evmRMS = sqrt(mean(evmTime.^2))

evmRMS = 6.6444

Estimate the SNR.

mer = comm.MER('ReferenceSignalSource','Estimated from reference constellation', ... 'ReferenceConstellation',refConst); snrEst = mer(rxfiltOut)

snrEst = 23.6978

This value is approximately 6 dB worse than the specified value of 30 dB, which means that the effects of the other impairments are significant and will degrade the bit error rate performance.