Hi David,
 From a practical standpoint I wonder how much of an advantage a 
theoretical limit synchronous GMSK demodulator would be in the VHF/UHF 
mobile environment where signals rarely hover around the Shannon limit.  
They are either well above or well below due to multipath/Doppler etc. 
My gut feeling is an interleaver and FEC would do much more in that 
environment.  I know folks are paranoid about turn around delays but in 
reality hundreds of mSecs is not that big a deal and not having to 
listen to squawks from a bit starved vocoder might be worth it.

For whatever reason, the commercial world seems to have moved to C4FM 
instead of GMSK so might be worth a look as to why.  Here is a(of course 
biased) report but I think the arguments at the low level modulation 
level are valid, the system level arguments not so much.

http://www.yaesu.com/downloadFile.cfm?FileID=7146&FileCatID=151&FileName=DigitalCommunicationsGuide%5FE%5B1%5D.pdf&FileContentType=application%2Fpdf

One could also leverage some of the existing signalling technology 
instead or re-inventing the wheel.
Google for ts_102658v010201p.pdf will find an ETSI TS 102 658 spec for 
dPMR which has a section on the physical layer that might be of use.

As a side note it looks like the STM32F7 series will be pin for pin 
compatible with the stm32f4 and give us a little more of everything 
especially ram which is what I seem to run out of first when doing DSP.

73,
Moe ae4jy


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