Question

Problem 3: This is a Matlab study. Download the matlab file (QPSKModulationInFlatFadingExample) from Moodle, which implements a QPSK transmission over a Rayleigh fading channel. First understand what this codes implement. Also, find a solution to have a frequency selective fading when symbolRate in the code is 500 and find a solution to have flat fading when symbolRate is 500e3. Plot your results with Matlab.

Answer 1

QPSK Modulation in Flat Fading
Set the symbol rate parameter to 500 bps.

symbolRate = 500;
Generate random data symbols and apply QPSK modulation.

data = randi([0 3],10000,1);
modSig = pskmod(data,4,pi/4,'gray');
Set the path delays and average path gains for the fading channel.

pathDelays = [0 3 10]*1e-6; % Discrete delays of three-path channel (s)
avgPathGains = [0 -3 -6]; % Average path gains (dB)
By convention, the delay of the first path is typically set to zero. For subsequent paths, a 1 microsecond delay corresponds to a 300 meter difference in path length. The path delays and path gains specify the average delay profile of the channel.

Create a Rayleigh channel using the defined parameters. Set the Visualization property to display the impulse and frequency responses.

fsamp = symbolRate;
channel = comm.RayleighChannel(...
'SampleRate',fsamp, ...
'PathDelays',pathDelays, ...
'AveragePathGains',avgPathGains, ...
'MaximumDopplerShift',0.01, ...
'Visualization','Impulse and frequency responses');
Pass the signal through the Rayleigh channel and apply AWGN.

rxSig = awgn(channel(modSig),25);

The impulse and frequency responses show that the channel behaves as though it were flat. This is because the signal bandwidth, 500 Hz, is much smaller than the coherence bandwidth, 50 kHz. Alternatively, the delay span of the channel (10 microseconds) is much smaller than the QPSK symbol period (2 milliseconds) so the resultant bandlimited impulse response is approximately flat.

Plot the constellation.

constDiagram = comm.ConstellationDiagram;
constDiagram(rxSig)