Continuous Phase Modulation (CPM) - Maximum Likelihood Sequence Detection - Viterbi Receiver.

A Matlab code for the "Maximum Likelihood Sequence Detection" for any CPM modulation (GMSK-RECT-RC....) using the Viterbi Algorithm. This work is based on the book: ' Digital Communication (Proakis)', and thesis: Comparison of Noncoherent detectors for SOQPSK and GMSK in Phase Noise Channels.

How to cite this Work ?

If you use this package for your own work, please consider citing it with this piece of BibTeX:

@ARTICLE{9406053,
  author={Kassan, Karim and Farès, Haïfa and Christian Glattli, D. and Louët, Yves},
  journal={IEEE Transactions on Communications}, 
  title={Performance vs. Spectral Properties For Single-Sideband Continuous Phase Modulation}, 
  year={2021},
  volume={},
  number={},
  pages={1-1},
  doi={10.1109/TCOMM.2021.3073792}
  }

How to run the code ?

1. Make sure that you have a compatible version of Matlab (this code was tested on Matlab 2018b)
2. Download (clone) the files from the repository.
3. Open the file called MLSD_Viterbi_CPM.m
4. Select the section called Pulse shape & Variable ini
5. Select the type of pulses by changing the variable pulse number
   • 1 is for Lorentzian
   • 2 is for GMSK
   • 3 is for Raised Cosine
   • 4 is for Rectangular
   • We can define a new pulse if the wanted pulse is not presented. Go to the file called MainFunctions.m, in the first function CREATECPMPULSE and add the pulse, using the same method used to define the other pulses.
6. Change the pulse length by changing the variable pulse_length.
7. Select the oversampling by changing the variable os.
8. Select M-ary by changing the M_ary (e.g., M=2 for Binary).
9. Select the minimum Euclidean distance of the modulation by changing the variable dmin.
10. Select after how many observation symbols the Viterbi receiver can make a decision on the detected bit by changing the variable decision_delay (usually 50 is high enough).

Note:

For points number 9 and 10. We can obtain dmin and the number of observation symbols from the code we provided in this link: https://github.com/kassankar/ContinuousPhaseModulation-CPM---EuclideanDistance.

Example

In this example we present the BER of GMSK CPM modulation with BT=0.3.

pulse            = 2;
pulse_length     = 3;     
os               = 2^2;    
Ts               = 1/os;   
M_ary            = 2^1;    
modulation_index = 0.5;    
dmin             = 1.78;   % GMSK BT=0.3
decision_delay   = 50;

Results Plot:

Known bug

For pulse_length = 1 (Full response), with M_ary >2, we may obtain an error for some modulation indices.

License

© 2020-2021 Karim Kassan