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Re: [Discuss-gnuradio] Why not use matched filter in GMSK demodulator

From: Bob McGwier
Subject: Re: [Discuss-gnuradio] Why not use matched filter in GMSK demodulator
Date: Sat, 01 Aug 2009 14:46:55 -0400
User-agent: Thunderbird (Windows/20090605)

This is NOT optimal. CPM and FM detector is a noncoherent detection of MSK/GMSK. The near optimal receiver for MSK and GMSK does two things:

1) it does a coherent detection of the received symbols and
2) it does something like a trellis/viterbi decode for the correct phase path through the symbols using the fact that at each symbol time the phase transition is +/- pi/2.

Should you follow this type of construction, the performance of coherent detection/with "viterbi error correction" for the paths, the performance is approximately the same as QPSK with the same bit rate.


Shizheng Li wrote:
Thank you for your reply!

I think the generic receiver for CPM you mentioned is the optimal receiver for CPM and the projection onto basis functions (correlation with basis functions) is equivalent to the matched filters, am I right?

Go back to the GMSK transceiver I mentioned in the file


The modulator structure is NRZ mapping --> Gaussian filter --> FM modulator And the demodulator structure is FM demodulator --> Timing recovery --> detector

I think after the FM demodulator the signal can be viewed as a PAM modulated signal and what if I add a matched filter before the timing recovery? Can I improve the BER performance? I think the matched filter can maximize the output SNR. Will it make the detector work better?

Best regards,
Shizheng Li

On Thu, Jul 30, 2009 at 2:07 PM, Achilleas Anastasopoulos <address@hidden <mailto:address@hidden>> wrote:

    There is no reason why you should not use a matched filter.
    However make sure you understand that a symbol-spaced MF
    generates sufficient statistics only for detection,
    ie, not for (epoch) synchronization.
    Also note that in the case of GMSK (CPM in general) a bank of MFs
    will generate colored noise.
    Another appropriate implementation of a front end projects the
    entire oversampled signal to a set of orthonormal basis functions
    which has the advantage of generating white noise samples for
    (simpler) further processing.

    Take a look at how a generic receiver for an arbitrary CPM
    is developed in


    There, the signal is first projected to its basis functions (which
    is calculated by a helper python application in "fsm_utils.py")
    to generate a sufficient statistic which is then used in
    conjunction with trellis decoding to do soft-decision sequence
    What is missing though is epoch and phase syncronization (to do at
    some point...)


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Best Regards,
Shizheng Li
Ph.D. Student and Research Assistant
Department of Electrical and Computer Engineering
Iowa State University


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