The newly released FreeDV 700C mode uses the Coherent PSK (COHPSK) modem which I developed in 2015. This post describes the challenges of building HF modems for DV, and how the COHPSK modem evolved from the FDMDV modem used for FreeDV 1600.

HF channels are tough. You need a lot of SNR to push bits through them. There are several problems to contend with:

When the transmit signal is reflected off the ionosphere, two or more copies arrive at the receiver antenna a few ms apart. These echoes confuse the demodulator, just like a room with bad echo can confuse a listener.

Here is a plot of a BPSK baseband signal (top). Lets say we receive two copies of this signal, from two paths. The first is identical to what we sent (top), but the second is delayed a few samples and half the amplitude (middle). When you add them together at the receiver input (bottom), it’s a mess:

The multiple paths combining effectively form a comb filter, notching out chunks of the modem signal. Loosing chunks of the modem spectrum is bad. Here is the magnitude and phase frequency response of a channel with the two paths used for the time domain example above:

Note that comb filtering also means the phase of the channel is all over the place. As we are using Phase Shift Keying (PSK) to carry our precious bits, strange phase shifts are more bad news.

All of these impairments are time varying, so the echoes/notches, and phase shifts drift as the ionosphere wiggles about. As well as the multipath, it must deal with noise and operate at SNRs of around 0dB, and frequency offsets between the transmitter and receiver of say +/- 100 Hz.

If commodity sound cards are used for the ADC and DAC, the modem must also handle large sample clock offsets of +/-1000 ppm. For example the transmitter DAC sample clock might be 7996 Hz and the receiver ADC 8004 Hz, instead of the nominal 8000 Hz.

As the application is Push to Talk (PTT) Digital Voice, the modem must sync up quickly, in the order of 100ms, even with all the challenges above thrown at it. Processing delay should be around 100ms too. We can’t wait seconds for it to train like a data modem, or put up with several seconds of delay in the receive speech due to processing.

Using standard SSB radio sets we are limited to around 2000 Hz of RF bandwidth. This bandwidth puts a limit on the bit rate we can get through the channel. The amplitude and phase distortion caused by typical SSB radio crystal filters is another challenge.

Designing a modem for HF Digital Voice is not easy!

**FDMDV Modem**

In 2012, the FDMDV modem was developed as our first attempt at a modem for HF digital voice. This is more or less a direct copy of the FDMDV waveform which was developed by Francesco Lanza, HB9TLK and Peter Martinez G3PLX. The modem software was written in GNU Octave and C, carefully tested and tuned, and most importantly – is open source software.

This modem uses many parallel carriers or tones. We are using Differential QPSK, so every symbol contains 2 bits encoded as one of 4 phases.

Lets say we want to send 1600 bits/s over the channel. We could do this with a single QPSK carrier at Rs = 800 symbols a second. Eight hundred symbols/s times two bit/symbol for QPSK is 1600 bit/s. The symbol period Ts = 1/Rs = 1/800 = 1.25ms. Alternatively, we could use 16 carriers running at 50 symbols/s (symbol period Ts = 20ms). If the multipath channel has echoes 1ms apart it will make a big mess of the single carrier system but the parallel tone system will do much better, as 1ms of delay spread won’t upset a 20ms symbol much:

We handle the time-varying phase of the channel using Differential PSK (DPSK). We actually send and receive phase differences. Now the phase of the channel changes over time, but can be considered roughly constant over the duration of a few symbols. So when we take a difference between two successive symbols the unknown phase of the channel is removed.

Here is an example of DPSK for the BPSK case. The first figure shows the BPSK signal top, and the corresponding DBPSK signal (bottom). When the BPSK signal changes, we get a +1 DBPSK value, when it is the same, we get a -1 DBPSK value.

The next figure shows the received DBPSK signal (top). The phase shift of the channel is a constant 180 degrees, so the signal has been inverted. In the bottom subplot the recovered BPSK signal after differential decoding is shown. Despite the 180 degree phase shift of the channel it’s the same as the original Tx BPSK signal in the first plot above.

This is a trivial example, in practice the phase shift of the channel will vary slowly over time, and won’t be a nice neat number like 180 degrees.

DPSK is a neat trick, but has an impact on the modem Bit Error Rate (BER) – if you get one symbol wrong, the next one tends to be corrupted as well. It’s a two for one deal on bit errors, which means crappier performance for a given SNR than regular (coherent) PSK.

To combat frequency selective fading we use a little Forward Error Correction (FEC) on the FreeDV 1600 waveform. So if one carrier gets notched out, we can use bits in the other carriers to recover the missing bits. Unfortunately we don’t have the bandwidth available to protect all bits, and the PTT delay requirement means we have to use a short FEC code. Short FEC codes don’t work as well as long ones.

**COHPSK Modem**

Over the next few years I spent some time thinking about different modem designs and trying a bunch of different ideas, most of which failed. Research and disappointment. You just have to learn from your mistakes, talk to smart people, and keep trying. Then, towards the end of 2014, a few ideas started to come together, and the COHPSK modem was running in real time in mid 2015.

The major innovations of the COHPSK modem are:

- The use of diversity to help combat frequency selective fading. The baseline modem has 7 carriers. A copy of these are made, and sent at a higher frequency to make 14 tones in total. Turns out the HF channel giveth and taketh away. When one tone is notched out another is enhanced (an anti-fade). So we send each carrier twice and add them back together at the demodulator, averaging out the effect of frequency selective fades:
- To use diversity we need enough bandwidth to fit a copy of the baseline modem carriers. This implies the need for a vocoder bit rate of much less than 1600 bit/s – hence several iterations at a 700 bits/s speech codec – a completely different skill set – and another 18 months of my life to develop Codec 2 700C.
- Coherent QPSK detection is used instead of differential detection, which halves the number of bit errors compared to differential detection. This requires us to estimate the phase of the channel on the fly. Two known symbols are sent followed by 4 data symbols. These known, or Pilot symbols, allow us to measure and correct for the current phase of each carrier. As the pilot symbols are sent regularly, we can quickly acquire – then track – the phase of the channel as it evolves.

Here is a figure that shows how the pilot and data symbols are distributed across one frame of the COHPSK modem. More information of the frame design is available in the cohpsk frame design spreadsheet, including performance calculations which I’ll explain in the next blog post in this series.

**Coming Next**

In the next post I’ll show how reading a few graphs and adding a few dBs together can help us estimate the performance of the FDMDV and COHPSK modems on HF channels.

**Links**

Modems for HF Digital Voice Part 2

cohpsk_plots.m Octave script used to generate plots for this post.

FDMDV Modem Page

“…the modem must sync up quickly…”

I think this is a design preference, rather than a necessity. As many voice modems use preambles. I don’t mind preambles that much, as all my experiences in the military used them, even at VHF. Actually, they are very short at VHF and above.

The modems of the early 70’s were a bit crude, in that you had to speak in a monotone and even volume. This was more of a pain then the preamble.