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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
hold off

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains 2 objects of type line. One or more of the lines displays its values using only markers This object represents Channel 1.

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

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