Re: [Discuss-gnuradio] Demodulating CPFSK with Viterbi algorithm using gr-trellis

[Jeff Long]

Hi Sean,

Don't really know much about this but I played around with the FSM code 
a little. Outputs would read the same as the state transitions:

if in state 0 and a 0 is received, output A, else output B

Using the fsms generation routines, I got a different shape FSM than 
yours (higher output cardinality). For instance (and I might be using 
this routine totally wrong),

t=trellis.fsm(3, 2, 1)
Parameters:
    P   ???? h=K/P (relatively prime)
    M   alphabet size
    L   pulse duration

generates:

2 3 6

0 1
1 2
2 0

0 3
1 4
2 5

Since the FSM is used internally by the decoder, it doesn't have output 
states that map to output data bits. If L=2, then it's:

2 6 12

0 3
1 4
2 5
1 4
2 5
0 3

0 6
1 7
2 8
3 9
4 10
5 11

Judging by the FSM examples, definition of useful FSMs is black magic.

- Jeff

On 09/09/2015 09:17 PM, Nowlan, Sean wrote:
> I’m trying to demodulate a CPFSK signal using the Viterbi algorithm. The
> gr-trellis module seems to have most of the components I’ll need, but
> I’m having trouble figuring out how to wrangle my problem into the FSM
> format. Basically, I have a binary CPFSK signal with a modulation index,
> h=25/3. Following the guidance of [1] section 3.3-2, I know that for CPM
> with rational h=m/p, (here, m=25 and p=3), with m odd, I have 2p=6 phase
> states. I worked out the phase trajectories and took them modulo 2*pi to
> get this set of terminal phase states: {0, pi/3, 2*pi/3, pi, 4*pi/3,
> 5*pi/3}.
>
> I’m trying to understand the FSM format in gr-trellis, and how to build
> my FSM. If you consider the set of terminal phase states above as being
> zero-indexed, the phase transitions should go according to the “Next
> state” mapping of the FSM file format below. I’ve added my comments as
> to my understanding of the format. Please correct me if I’m wrong.
>
> FSM file:
>
> 2 6 2       # 2 possible input symbols // 6 possible FSM states // 2
> possible output symbols
>
> # Next state mapping
>
> 5 1          # if in state 0 and a 0 is received, go to state 5, else (1
> is received, and) go to state 1
>
> 0 2          # if in state 1 and a 0 is received, go to state 0, else go
> to state 2
>
> 1 3          # ...
>
> 2 4
>
> 3 5
>
> 4 0
>
> # Output symbol mapping
>
> […]
>
> I’m having trouble understanding how to define the output symbol
> mapping. Is there a plain-language interpretation like the one I spelled
> out for Next state mapping in my comments above?
>
> Thanks!
>
> Sean
>
> [1] Proakis & Salehi, Digital Communications, 5ed.
>
>
>
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