Brady O’Brien has been doing some fine work simulating the 4FSK DMR modem, based on the waveform description in the ETSI spec. It’s not a classic non-coherent 4FSK modem design. Rather it appears designed to easily integrate with legacy analog FM modulators and demodulators.
Here is the block diagram of a regular non-coherent 2FSK demod. For 4FSK there would be 4 arms, but you get the idea:
The DMR modem uses Root Raised Cosine (RRC) filters and a FM modulator and demodulator:
Here are the performance curves produced by fsk4.m:
The best we could do with our simulation is 5-6dB poorer than the theoretical performance of non-coherent 4FSK. This made me suspect we had a bug. However this performance loss compared to theory is consistent with other FSK modems I have simulated that run through legacy analog modulators, rather than using ideal demodulators.
Have we done something wrong? Does anyone have figures for DMR modem Eb/No versus BER? Perhaps with have an error in our simulation. Perhaps the high BER is tolerable for the higher layers of DMR, given the amount of FEC they’ve got it wrapped in. Once you’re over a certain threshold, FEC will take care of it.
Our simulation is consistent with the Minimum Detectable Signal (MDS) figures given for commercial DMR radios, for example 2% BER at a MDS of -120dBm. Our curve above suggests Eb/No=11dB for BER=0.02. Plugging that into a MDS calculation, and assuming a receiver Noise Figure (NF) of 2dB, and the DMR bit rate of 9600 bit/s:
MDS = -174 + 10log10(Rb) + Eb/No + NF
= -174 + 10*log10(9600) + 11 + 2
= -121 dBm
If we had an ideal modem, and Codec 2 at 1200 bit/s, we could get a MDS of -135dBm, or -132dBm with 2400 bit/s over the channel to support two-slot TDMA just like DMR. That’s a huge margin. The modem matters. A lot.
It’s been really nice to have some one else working with me on modem code – thanks Brady! He has done a great job on getting his head around modem implementation. Brady also worked out how to run Octave code on simulation on parallel cores which is a fine innovation. Until now I had been stuck on one core.