Create a sawtooth wave.

t = (0:0.1:10)';
x = sawtooth(t);

Apply white Gaussian noise and plot the results.

y = awgn(x,10,'measured');
plot(t,[x y])
legend('Original Signal','Signal with AWGN')

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 signal-to-noise ratios.

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];
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 having a 20 dB signal-to-noise ratio (SNR).

rxSig = awgn(modData,20,'measured');

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 symbol error ratio.

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 having a 10 dB SNR. Determine the symbol error rate for the reduced SNR. As expected, the performance degrades when the SNR is decreased.

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

numErrors = 462

ser = 0.2310

Generate white Gaussian noise addition results using a RandStream object and the reset object function.

Specify the power of X to be 0 dBW, add noise to produce an SNR of 10 dB, and utilize a local random stream.

S = RandStream('mt19937ar','Seed',5489);
sigin = sqrt(2)*sin(0:pi/8:6*pi);
sigout1 = awgn(sigin,10,0,S);

Add AWGN to sigin. Use isequal to compare sigout1 to sigout2. The outputs are not equal when the random stream was not reset.

sigout2 = awgn(sigin,10,0,S);
isequal(sigout1,sigout2)

ans = logical
   0

Reset the random stream object, returning the object to its state prior to adding AWGN to sigout1. Add AWGN to sigin and compare sigout1 to sigout3. The outputs are equal after the random stream was reset.

reset(S);
sigout3 = awgn(sigin,10,0,S);
isequal(sigout1,sigout3)

ans = logical
   1