Quaternary Phase Shift Keying (QPSK)
Introduction
Quaternary Phase Shift Keying, QPSK, is one of the most popular digital carrier modulations
in use today.
The QPSK signal set consists of four waveforms that differ in phase:
they are each 90-degrees apart.
For this reason, the QPSK constellation consists of four points equally spaced on a circle.
In this exercise, you will design QPSK detector to process the data contained in the file
qpskdata.mat
Textbook References
M-ary QAM: Section 5.3 (pp. 238 - 260),
discrete-time realizations: Section 5.3.2 (pp. 256 - 260),
partial response pulse shapes: Section A.2 (pp. 682 - 687).
Specifications
 |
| normalized sample rate: |
8 samples/symbol |
| normalized carrier frequency: |
0.25 cycles/sample |
| carrier phase: |
0 degrees |
| average energy: |
9 |
| pulse shape: |
SRRC (50% excess bandwidth, span = 12 symbols) |
| symbol clock offset: |
0 |
| input file |
qpskdata.mat |
| input message length: |
56 symbols (112 bits or 16 ASCII characters) |
|
Preliminary Design
Design the Detector
Design the detector, shown below, using blocks from the Simulink, DSP System,
and Communications System Toolboxes.
Test the Detector Design
You should test the detector you designed by constructing a modulator to produce
a test signal.
The following procedure steps you through this design process:
- Design the modulator shown below to meet the above specifications except
make the input the four symbol sequence 0 2 1 3.
-
Connect the output of your modulator to the input of your detector.
-
Connect the output of your detector to a To Workspace block
(be sure to open the Properties Dialog Window and set the Save format to matrix)
and a Scope block.
-
Set the simulation parameters as follows:
| Simulation Time |
| Start Time: |
0.0 |
| Stop Time: |
(12+4)*8-1 |
| Solver Options |
| Type: |
Fixed-step |
| Solver: |
discrete (no continuous states) |
| Fixed step size: |
auto |
| Tasking and sample time options |
| Periodic sample time constraint: |
Unconstrained |
| Tasking mode for periodic sample times: |
SingleTasking |
Note: the stop time is computed as follows: 12 = 2*(span/2) [the delay of the
pulse shaping filter plus the delay of the matched filter];
4 = the number of data symbols;
8 = the number of samples/symbol.
We subtract because the start time is t = 0.0.
- Run the simulation and plot the demodulator input and the matched filter
output on the same set of axes.
The simulation produces 16 downsampled matched filter outputs --
the last 4 correspond to the sequence (0 2 1 3).
Check the values in the workspace to see if they agree with input
sequence (0 2 1 3).
-
Adjust the offset of the Downsample block to obtain the proper
values.
Exercise
-
Replace the modulator blocks with the From File block and set the
Filename to qpskdata.mat and the sample time to 1.
-
Set the simulation parameters as follows:
| Simulation Time |
| Start Time: |
0.0 |
| Stop Time: |
(12+56)*8-1 |
| Solver Options |
| Type: |
Fixed-step |
| Solver: |
discrete (no continuous states) |
| Fixed step size: |
auto |
| Tasking and sample time options |
| Periodic sample time constraint: |
Unconstrained |
| Tasking mode for periodic sample times: |
SingleTasking |
-
Run the simulation.
-
The detector produces 68 symbol estimates.
The last 56 of these correspond to 16 7-bit ASCII characters.
Determine the message using either your Matlab script or an
ASCII Table.
-
Plot the eye diagram and signal space projections.
