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Digital Communications: A Discrete-Time Approach
by Michael Rice

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: 49 symbols (98 bits or 14 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:
  1. Design the modulator shown below to meet the above specifications except make the input the four symbol sequence 0 2 1 3.




  2. Connect the output of your modulator to the input of your detector.

  3. 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.

  4. 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.

  5. Run the simulation and plot the demodulator input and the matched filter output on the same set of axes. The simulation produces 18 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).

  6. Adjust the offset of the Downsample block to obtain the proper values.

Exercise

  1. Replace the modulator blocks with the From File block and set the Filename to qpskdata.mat and the sample time to 1.

  2. Set the simulation parameters as follows:
    Simulation Time
    Start Time: 0.0
    Stop Time: (12+49)*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

  3. Run the simulation.

  4. The detector produces 61 symbol estimates. The last 49 of these correspond to 14 7-bit ASCII characters. Determine the message using either your Matlab script or an ASCII Table.

  5. Plot the eye diagram and signal space projections.
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