I reseach gmsk modulation with linear approximation + laurent decomposition.

In the answere to the my previous post, MR Boschen:

L is the overlap of successive symbols as L is given in symbol duration. "Full response signaling" is with L=1 and one symbol completes before the next symbol starts. Any L>1 is partial response signaling where subsequent symbols start before prior symbols complete their response (resulting in inter-symbol interference but also better spectral efficiency since we send more data in less time).

In case gmsk, we talk about inter symbol interference as well. I want to reseach this in my simlation, bit still have no idea how to do it

Does anyone study ISI in gmsk modulation? How did you do it?


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  • $\begingroup$ Questions requesting working code written to a specification are off-topic as they are unlikely to benefit anyone else. Instead, describe the problem you're solving and where you're stuck. $\endgroup$ Commented Apr 12, 2022 at 11:45
  • $\begingroup$ @MarcusMüller, oh no. I am not asking a code. I dont understand what I have to do and how I can reseach ISI of my signal $\endgroup$
    – FrimHart64
    Commented Apr 12, 2022 at 12:01

1 Answer 1


Please see this post for which I have copied the primary figure here below:

GMSK Modulator

This is a very simple way to implement a GMSK transmitter with partial response signaling. The Data is represented as rectangular pulses to the input of an FIR filter. The coefficients of the FIR filter are the properly weighted frequency pulse shape (a Gaussian) for the $BT$ specified by the waveform and the filter duration is exactly one symbol long. The output of the filter (the impulse response of the filter) IS directly proportional to the frequency versus time of the waveform. Since the NCO converts the waveform magnitude to the frequency at its output (the offset to center at any particular frequency is not shown), the output of the NCO is the GMSK modulated waveform.

If the data at the input is spaced in time by the symbol duration, then we would get Full Response Signaling and no ISI since each impulse response would complete before the next symbol starts. If the data at the input is spaced closer, then we get ISI and Partial Response Signaling.

ISI is typically studied or represented in GMSK using phase trellis diagrams as further detailed in this post. The phase trellis diagrams show all the possible phase trajectories based on the current symbol and all previous symbols within the memory of the Gaussian filter as given by $1/(BT)$ symbols.

  • $\begingroup$ I did as you suggested before ( see results in EDIT 1). It si a plot of y = conv(h, x), where h- filter coeff of Gaussian filter, x- NRZ sequence. My results doesnt look similar, i cant define ISI... $\endgroup$
    – FrimHart64
    Commented Apr 12, 2022 at 14:35
  • 1
    $\begingroup$ x should not be an NRZ sequence; read my answer carefully and let me know what wasn’t clear - x is a series of impulses in time spaced by the symbol rate for full response signaling or spaced closer for partial response signaling $\endgroup$ Commented Apr 12, 2022 at 14:57
  • $\begingroup$ @FrHart64 Did I answer your question here or is there still some confusion? $\endgroup$ Commented Apr 19, 2022 at 12:56

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