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Digital Communications: A Discrete-Time Approach
by Michael Rice

M-ary Quadrature Amplitude Modulation (MQAM)

Introduction

M-ary Quadrature Amplitude Modulation -- or QAM -- is a modulation where data bits select one of M combinations of amplitude and phase shifts that are applied to the carrier. The M possible waveforms may be described by M constellation points. In this exercise, the M = 16 constellation points are confined to a square grid. In this exercise, you will design an 16-QAM detector to process the data contained in the file qam16data.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: 40
pulse shape: SRRC (30% excess bandwidth, span = 16 symbols)
symbol clock offset: 0
input file qam16data.mat
input message length: 322 symbols (1288 bits or 184 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 8 15 1 6.




  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: (16+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: 16 = 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 19 downsampled matched filter outputs -- the last 5 correspond to the sequence (8 15 1 6). Check the values in the workspace to see if they agree with input sequence (8 15 1 6).

  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: (16+322)*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 338 symbol estimates. The last 322 of these correspond to 184 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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