Amplitude Modulation Examples

These examples demonstrate amplitude modulation (AM) techniques.

Compute Symbol Error Rate

In this example, you generate a random digital signal, modulate it, add noise, demodulate the noisy signal, and compute the symbol error rate. Then you plot the noisy, modulated data in a constellation diagram. The numerical results and plot may vary due to the random input data.

Create a random digital message and a constellation diagram System object™.

M = 16; % Alphabet size, 16-QAM
x = randi([0 M-1],5000,1);

cdpts = qammod(0:M-1,M);
constDiag = comm.ConstellationDiagram( ...
    ReferenceConstellation=cdpts, ...
    XLimits=[-4 4], ...
    YLimits=[-4 4]);

Apply 16-QAM modulation and transmit the signal through an AWGN channel.

y = qammod(x,M);
ynoisy = awgn(y,15,'measured');

Demodulate the noisy data, ynoisy, to recover the message and check the symbol error rate.

z = qamdemod(ynoisy,M);
[num,errrate] = symerr(x,z)

num = 79

errrate = 0.0158

Plot the noisy data in a constellation diagram. The signal reference constellation has 16 precisely located points, but the noise added to the transmitted signal causes the scatter plot to have a small cluster of points scattered around each reference constellation point.

constDiag(ynoisy)

Estimate Symbol Rate for General QAM Modulation in AWGN Channel

Transmit and receive data using a nonrectangular 16-ary constellation in the presence of Gaussian noise. Show the scatter plot of the noisy constellation and estimate the symbol error rate (SER) for two different SNRs.

Create a 16-QAM constellation based on the V.29 standard for telephone-line modems.

c = [-5 -5i 5 5i -3 -3-3i -3i 3-3i 3 3+3i 3i -3+3i -1 -1i 1 1i];
sigpower = pow2db(mean(abs(c).^2));
M = length(c);

Generate random symbols.

data = randi([0 M-1],2000,1);

Modulate the data by using the genqammod function. General QAM modulation is necessary because the custom constellation is not rectangular.

modData = genqammod(data,c);

Pass the signal through an AWGN channel with a 20 dB SNR.

rxSig = awgn(modData,20,sigpower);

Display a scatter plot of the received signal and the reference constellation c.

h = scatterplot(rxSig);
hold on
scatterplot(c,[],[],'r*',h)
grid
hold off

Demodulate the received signal by using the genqamdemod function. Determine the number of symbol errors and the SER.

demodData = genqamdemod(rxSig,c);
[numErrors,ser] = symerr(data,demodData)

numErrors = 1

ser = 5.0000e-04

Repeat the transmission and demodulation process with an AWGN channel with a 10 dB SNR. Determine the SER for the reduced SNR. As expected, the performance degrades when the SNR is decreased.

rxSig = awgn(modData,10,sigpower);
demodData = genqamdemod(rxSig,c);
[numErrors,ser] = symerr(data,demodData)

numErrors = 461

ser = 0.2305

Plot Noisy 16-QAM Constellation in Simulink

The doc_qam_mod model uses the Rectangular QAM Modulator Baseband block to modulate random data and applies noise to the signal by using the AWGN Channel block. After passing the symbols through a noisy channel, the model produces a constellation diagram of the noisy data. When the noise level is increased, the constellation points show increased signal distortion.

A Random Integer Generator block generates integers in the range [0,15] for a modulator configured to apply 16-QAM. The modulated signal passes through an AWGN channel, and a constellation diagram displays the resulting symbols.

Run the model with Eb/N0 set to 20 dB in the AWGN channel.

Change the Eb/No from 20 dB to 10 dB. Observe the increase in the noise.