>On Thu, 07 Aug 2008 11:31:48 -0700, ane wrote:
>
>> I am trying to implement a GMSK receiver I have a block diagram of the
>> receiver which is like this
>>
>> Received IQ Samples - > constellation derotation -> CIR estimation
from
>> training sequence -> MLSE (viterbi) equalizer
>>
>> The constellation derotation is supposed to collapse the four end
points
>> of GMSK constellations (+1, +j,-1,-j) to a two point (+1,-1)
>> constellation.
>>
>>
>> My question is how exactly are the constellation derotation and CIR
>> estimation are supposed to performed? From what I have figured it out
>> so far, the constellation derotation is supposed to by a
multiplicaiton
>> by exp{-j*n*pi/2} for n=1,2,3,4 i.e. every four received IQ samples
>> are multiplied by {-j,-1,+j,1}. The goal is to limit the binary
symbols
>> to 2 (+1,-1) so that the MLSE equlaizer has 2^L states. However, this
>> multiplication by exp{-j*n*pi/2} seem to totally change the pulse
>> sequence. For example, if we skip the filtering for a moment (MSK
>> modulation) and consider a pulse train +1,+1,-1,-1,+1,+1,+1,-1,-1,...
>> and starting phase 0, then the modulated IQ samples are
>> +j,-1,+j,+1,+j,-1,+j,+1,...multiplication by - j,-1,+j,+1,... results
in
>> the derotated sequence of +1,+1,-1,+1,+1,-1,+1,+1... Which, while
>> limited to symbols(+1,-1), is a different pulse train sequence than
the
>> input. Would it not mess up the CIR calculation based on a known
>> training sequence? Would it not result in incorrect sequence
estimation
>> by the viterbi equalizer?
>
>Could they be using differential GMSK, where a transmitted '1' means a
>forward rotation of the phase, and a transmitted '0' means a reverse
>rotation of the phase?
>
>Seems like after derotation you'd still have a differential BPSK-ish
>signal to decode...
>
>--
>Tim Wescott
>Control systems and communications consulting
>http://www.wescottdesign.com
>
>Need to learn how to apply control theory in your embedded system?
>"Applied Control Theory for Embedded Systems" by Tim Wescott
>Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
>
Hi Tim,
Yes, you are right. GMSK can be interpreted a differential BPSK after a
-PI/2 derotation being employed.
But here I want also to point out a mistake in ane's example. The right
one is below.
A(n): 0, 0, 1, 1, 0, 0, 0, 1, 1
Original: +1,+1,-1,-1,+1,+1,+1,-1,-1 original= 1-2A(n)
phase=0: +j,-1,+j,+1,+j,-1,-J,-1,+j;
derotate: -j,-1,+j,+1,-j,-1,+j,+1,-j
result: +1,+1,-1,+1,+1,+1,+1,-1,+1
B(n): 0, 0, 1, 0, 0, 0, 0, 1, 0
D(n): 0, 0, 1, 1, 0, 0, 0, 1, 1
A(n)=D(n). This means that after derotation we have to decode the
differential code.
Hope I say it clear.
Fan