BER vs SNR simulation for GFSK modulation (Closed-form BER for GFSK)

Question

I'm in the process of simulating the performance of a GFSK modem in GNU Radio. I have managed to get a curve similar to the curves I see in a number of literature sources. However, I need an accurate baseline that can show how accurate (or far of) the performance is. This might be trivial but I have spent quite a number of hours trying to find out a closed-form BER vs SNR for GFSK. All I have seen so far is BER vs SNR for GMSK only. So my questions are:

1. Does the closed form of BER for GFSK exist at all?
2. Is there any explanation as to why it doesn't exist?

All answers and references will be highly appreciated.

Regards,

M.

Answer 1

Well, GFSK is a whole class of modulations, essentially with your freedom being the choice of symbol duration/pulse shaping filter breadth ($\sigma$ in the Gaussian); of this whole class, M makes most sense, so GMSK is really what you'd most probably would want to deal with.

Now, a BER curve really only makes sense if you can describe the "theoretical" receiver of your signal.

In that sense, you could understand GFSK as "extended" GMSK, where you don't use the shortest possible symbol duration, but a multiple thereof, and hence, would need to adjust the $E_b$ in your $E_b/N_0$ curve. But: there should really just be a factor between the $E_b$ in GMSK and generally GFSK, so if you just shift your curve, you'd get a measure of how well your system compares.