# Simulating the DMR Modem

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.

## 5 thoughts on “Simulating the DMR Modem”

1. Steve says:

Not a mathematical derived number, but I understand the practical result of 4FSK is about 10 miles reduction in range for the same power as FSK.

Probably everything below .02 on the chart is unreachable in practice anyway.

I’m wondering if your COHPSK modem (even at 700 bps) wouldn’t make a nice VHF modem. Would the diversity channel work well against multipath?

Communication grade, rather than telephone quality being the goal. Course that brings back the need for a cheap AM transceiver to build on.

2. david says:

Hi Steve,

Actually the Eb/No results indicate 4FSK is 2.5dB better than 2FSK, so its will go further at the same bit rate. Or you can double your bit rate for free (well, it uses extra bandwidth).

The COHPSK modem has multiple carriers to deal with frequency selective fading. At VHF it’s flat fading over the bandwidth of one channel, so we could use just one carrier. To get diversity we would need two carriers spaced several hundred kHz apart, which is something I’d like to try. This would improve the PAPR as well. A linear(ish) PA would be required but it would have very good performance, as listed in the table above.

– David

3. Steve says:

I was thinking that the loss of sideband power with the 4FSK versus 2FSK would reduce the range.

For example packet radio with a modulation index of (3 kHz/2.2 kHz) 1.36
and DMR with (1.9/4.8) .405 and (.648/4.8) .135 radians.

These figures show the effect of narrowband, in that DMR has maybe 2 sidebands
max, versus packet radio at 8 sidebands.

1.36 = 17.6 kHz 8 sidebands
.405 = 9.6 kHz 2 sidebands
.135 = 9.6 kHz 2 sidebands

4. Steve says:

Not to beat a horse to death, but I remembered the spreadsheet had a besselj function, so thought I would plot the carrier and first four sideband amplitudes.

What I notice when I switch my 2 metre rig to narrow, is that the audio is weak, but the power of the carrier remains high. So, you can see that in the chart. In packet radio, the carrier surrenders its power to the sidebands, while DMR is a big honking carrier with these little sidebands tickling the ether

https://goo.gl/hE3z73

1. david says:

Thanks Steve. DMR is designed to fit in 12.5kHz channels so they may have traded off modem performance for bandwidth. Bandwidth being a scarce resource and SNR usually being high for VHF radio. Need to run some bandwidth numbers on the modems I have been playing with.