I’ve been thinking about modems for a VHF FreeDV mode. The right waveform and a good demodulator is the key to high performance. However it would be nice to make some re-use of existing FM VHF radios. So is it possible to come up with a waveform that can pass through legacy FM radios, but also be optimally demodulated with a SDR?

My first guess was that the problem with legacy radios is the 300Hz High Pass (HP) pass filtering. So I came up with a waveform with has no DC. Brady pointed out this was Manchester Encoding (ME), used in all sorts of applications for just this problem. Each data bit is Manchester encoded to two bits, so a 2400 bit/s bit-stream becomes a 4800 bit/s bit-stream that is then 2FSK modulated. Turns out the ME-2FSK signal doesn’t have much low frequency energy so passes happily through the audio pass band filtering of regular FM radios.

Here is a block diagram of the idea. We have the option to demodulate the signal using a legacy analog radio or, with higher performance, an optimal FSK demod:

This is what the spectrum of the ME-2FSK looks like at the output of the analog FM demodulator before high pass filtering. Notice how there is not much energy beneath 300Hz? So we are not going to lose much due to the 300Hz HP filter.

Here are the time domain modem signals before and after the 300Hz High Pass filter. Pretty similar.

The ME-2FSK scheme works OK in my simulation, so I think it’s possible to squirt 2400 bit/s through a $40 HT with acceptable modem performance using 2FSK. This means we can do VHF FreeDV using your laptop/SM1000 and a $40 radio, and it will work just as well as existing VHF DV modes, and even pass through analog repeaters.

Real gold would be a way to send 4FSK through a HT, that (if you have a SDR) can be optimally decoded at a much lower Eb/No. Unfortunately I couldn’t work out how to do that. For optimal 4FSK you need the tones spaced at the symbol rate Rs. This means -1.5Rs, -0.5Rs, 0.5Rs, 1.5Rs, which won’t fit into 5kHz deviation with Rs=4800. So how about Rs=2400? Well when I tried Rs=2400 through the FM demod the modem appears to be 3dB worse that Rs=4800. I’m not sure why. Possibly deviation, as I get the same results with the 300Hz HP filter removed. Or maybe I messed up the simulation. Oh Well. Working backwards, this suggests one reason the ME 2FSK waveform works so well at Rs=4800 is greater deviation.

Moving to the optimal 4FSK demod approach, here are the outputs of each filter from an optimal 4FSK demod. The pretty colours represent the different filter ouputs. The lower plot is the decimated filter outputs, after sampling at the ideal timing instant.

I’m inclined to use both 4FSK and ME-2FSK. We could run ME-2FSK on links with legacy radios and 4FSK on SDRs that support optimal demodulation. That 6dB Eb/No for optimal 4FSK, combined with Codec 2 running at a lower rate, is a huge gain over current analog and DV systems.

Summary of Candidate VHF Waveforms

I’ve now played with quite a few modem waveforms, and have compared them in the table below. Eb/No is for a BER of 2%, which is roughly where Digital Voice codecs fall over. There are two Eb/No figures, one for an ideal demodulator, the other when using a demod that works through a legacy FM analog radio.

Waveform Eb/No (ideal) Eb/No (FM) Comment Read More PSK 3.0 na requires linear PA, complex coherent demod GMSK 5.0 9.0 requires “data” port, complex coherent demod [1] [2] 4FSK 6.0 na simple demod, good fading ME-2FSK 8.5 12.0 simple demod, good fading, $40 HT! DMR 4FSK na 11.0 standardised [3] AFSK-FM na 16.0 As used in APRS [4]

The complexity of the demods required for coherent PSK and GMSK is not a show stopper, as we only have to write GPL modem code once. However coherent demodulation means other sources of “implementation loss” such as phase recovery that make the ideal performance hard to achieve. Non-coherent mFSK is rather simple in comparison, we just need a fine timing estimator. Less to go wrong. No phase estimation means fading will have less impact than coherent PSK/GMSK. Fine frequency offsets won’t bother us. mFSK is, however less bandwidth efficient.

GMSK coherently demodulated or through a legacy FM radio looks pretty good, but does require a “data port” with unfiltered access to the FM modem. So no $40 HTs.

Note the distinction between ideal non-coherent 4FSK, and the 4FSK modem used by DMR and similar Digital Voice modes like C4FSK. The latter are not optimal waveforms, and in our simulations under-perform by around 6dB. We can’t find any explanation of why these waveforms were chosen for DMR or C4FM. I am guessing that have been developed with the specific use of legacy FM radio architectures or reduced RF bandwidth in mind.

Running the simulation

I set up a bunch of simulations of various combinations so they all have about 2% BER:

octave:224> mancyfsk

Rs=4800 2FSK ideal demod

EbNodB: 8.5 BER 0.023

Rs=4800 2FSK analog FM demod, not too shabby and pushes 2400bit/s thru a $40 HT!

EbNodB: 12.0 BER 0.021

Rs=2400 2FSK analog FM demod, needs more power for same BER! Che?

EbNodB: 15.0 BER 0.027

Hmm, doesnt improve with no 300Hz HPF, maybe due to less deviation?

EbNodB: 15.0 BER 0.027

Rs=2400 4FSK ideal demod, nice low Eb/No!

EbNodB: 6.0 BER 0.025

Further Work

It would be great to test the work above in the real world, for example get the ME-2FSK modem software into a form that we can do calibrated noise (or MDS) tests on a real FM radio.