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CPM Phase Tree Demo
The CPM Phase Tree demo, cpmphasetree, illustrates a way to use the Discrete-Time Eye Diagram Scope block to view the phase trajectory, phase tree, and instantaneous frequency of a CPM modulated signal. This document highlights these aspects of the demo:
Structure of the demo
This demo uses various Communications Blockset, DSP Blockset and Simulink blocks to model a baseband CPM signal. The demo includes the following blocks:
- Random Integer block, which provides a source of uniformly distributed random integers in the range [0, M-1], where M is the constellation size of the CPM signal
- Integer to Bit Converter block
- CPM Modulator Baseband block
- Complex to Magnitude-Angle Converter block
- Phase Unwrap block
- Zero-Order Hold block
- Discrete Transfer Function block
- Gain block
- Four copies of the Discrete-Time Eye Diagram Scope block
Variables
When the model is loaded, cpmphasetree_init.m is called to create several variables in the MATLAB workspace, using the PreLoadFcn model callback parameter.
Visible Results of the Demo
When you run the demo, the four Discrete-Time Eye Diagram Scope blocks in the model show how the CPM signal changes over time:
- The block labeled "Modulated Signal" displays the in-phase and quadrature signals. Double-click the block to open the scope.
- The modulated signal is easy to see in the eye diagram only when the Modulation index parameter in the CPM Modulator Baseband block is set to
0.5. If you set the Modulation index to another value, for example 2/3, the features of the modulated signal are difficult to decipher for this more complex modulation. Unwrapping the phase and plotting it is another way to illustrate these more complex CPM modulated signals.
- The block labeled "Phase Trajectory" displays the CPM phase. Double-click the block to open the scope.
- The Phase Trajectory Eye Diagram Scope block reveals that the signal phase is also difficult to view because it drifts with the data input to the modulator.
- The block labeled "Phase Tree" displays the phase tree of the signal.
- The CPM phase is processed by a few simple blocks to make the CPM pulse shaping easier to view. This processing holds the phase at the beginning of the symbol interval and subtracts it from the signal. This resets the phase to zero every three symbols. The resulting plot shows the many phase trajectories that can be taken by the signal from any given symbol epoch.
- The block labeled "Instantaneous Frequency" displays the instantaneous fequency of the signal.
- The CPM phase is differentiated to produce the frequency deviation of the signal. Viewing the CPM frequency signal enables you to observe the frequency deviation qualitatively, as well as make quantitative observations, such as measuring peak frequency deviation.
Experimenting with the Demo
To learn more about the demo, try changing the following parameters in the CPM Modulator Baseband block:
- Change Pulse length to one of the values
1, 2, ... 6.
- Change Frequency pulse shape to one of the other settings, such as Raised Cosine or Gaussian.
You can observe the effect of changing these parameters on the phase tree and instantaneous frequency of the modulated signal.
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