Create a sawtooth wave.

t = (0:0.1:60)'; x = sawtooth(t);

Add 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 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 thegenqammodfunction. 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 constellationc.

h = scatterplot(rxSig); holdonscatterplot(c,[],[],'r*',h) grid holdoff

Demodulate the received signal by using thegenqamdemodfunction. 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

Generate random data symbols and the 4-PSK modulated signal.

M = 4; k = log2(M); snr = 3; data = randi([0 M-1],2000,1); x = pskmod(data,M);

Set the random number generator seed.

seed = 12345;

Generate repeatable random noise using therngfunction before calling theawgnfunction.

rng(seed); y = awgn(x,snr);

Compute the bit errors.

dataHat = pskdemod(y,M); numErr1 = biterr(data,dataHat,k)

numErr1 = 321

Reset the random number generator seed.

rng(seed);

Demodulate the PSK signal and compute the bit errors.

y = awgn(x,snr); dataHat = pskdemod(y,M); numErr2 = biterr(data,dataHat,k)

numErr2 = 321

ComparenumErr1tonumErr2. The errors are equal even after you reset the random number generator seed.

isequal(numErr1, numErr2)

ans =logical1

Generate white Gaussian noise addition results using aRandStreamobject and theresetobject function.

Specify the power of X as0dBW, add noise to produce an SNR of10dB, and use 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 white Gaussian noise tosigin. Useisequalto comparesigout1tosigout2. The outputs are not equal when you do not reset the random stream.

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

ans =logical0

Reset the random stream object, returning the object to its state prior to adding AWGN tosigout1. Add AWGN tosiginand comparesigout1tosigout3. The outputs are equal when you reset the random stream.

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

ans =logical1