Coherent MFSK

There are communication systems with orthogonal multitone physical layer. 
That is, one of N frequencies in the set is sent at a time. An example of 
such system is "Olivia": http://en.wikipedia.org/wiki/Olivia_MFSK .
In the systems like that, they usually demodulate signal by incoherent 
detector. The loss due to incoherent demodulation is 1dB ballpark. There 
are, of course, technical reasons to do it in that way in each particular 
case (unknown/variable channel, simplification, etc. etc.), however  I 
wonder if it would be possible to demodulate such signal optimally, assuming 
AWGN and known channel.
Problem is inconvenient autocorrelation function of  MFSK symbol. That is, 
small variation of the symbol sync could result in the large variation of 
phase, and also different proportionally to the bin number. Whereas the 
envelope of the autocorrelation function has relatively low slope, so it 
would be difficult to pinpoint exact position of sync.
Could you suggest an algorithm applicable to this case, or a book or an 
article ?

Vladimir Vassilevsky
DSP and Mixed Signal Consultant
www.abvolt.com

>There are communication systems with orthogonal multitone physical layer.

>That is, one of N frequencies in the set is sent at a time. An example of

>such system is "Olivia": http://en.wikipedia.org/wiki/Olivia_MFSK .
>In the systems like that, they usually demodulate signal by incoherent 
>detector. The loss due to incoherent demodulation is 1dB ballpark. There 
>are, of course, technical reasons to do it in that way in each particular

>case (unknown/variable channel, simplification, etc. etc.), however  I 
>wonder if it would be possible to demodulate such signal optimally,
assuming 
>AWGN and known channel.
>Problem is inconvenient autocorrelation function of  MFSK symbol. That is,

>small variation of the symbol sync could result in the large variation of

>phase, and also different proportionally to the bin number. Whereas the 
>envelope of the autocorrelation function has relatively low slope, so it 
>would be difficult to pinpoint exact position of sync.
>Could you suggest an algorithm applicable to this case, or a book or an 
>article ?
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Consultant
>www.abvolt.com
>
>
>

If the signal is continuous phase AND the symbol rate is some ratio of
integers relationship to the frequency spacing of the tones, then you can
coherently demodulate it.

I did this once with a V.23 modem signal where the symbol rate was 1200
baud and the frequency spaceing is 400 Hz.  You will note that during the
period of one symbol the carrier phase will rotate 60 degrees CCW or CW
depending on whether the symbol was a one or zero.  Therefor depending on
what the previous ending phase of the signal was you can rotate only +/-60
degrees.  There are 6 rotations, but only two are possible at any given
time.  The demodulator can then test (correlate) against these six
rotations and assign a probability.  The a maximum likelihood sequence
estimator -like algorithm can then choose the most likely sequence of
rotations over the long term.  Then you decode the bits from this
sequence.

Of course you need to integrate in some symbol timing and carrier phase
recovery in order to make it all work, but these can be obtained from
preliminary estimates (prior to MLSE) of the above correlations and
integrated with a suitable PLL.

Depending on the integer relationship of symbol timing to carrier phase,
the complexity can be large or small.  Also, the technique can be extended
to the general case where no such relationship exists - you just have to
have suitably large number of correlations such that the resulting error is
small.

I got excellent results when I tried it and was able to decode signals that
a non-coherent demod could not operate on.

-Doug

On Wed, 28 Nov 2012 10:34:36 -0600, Vladimir Vassilevsky wrote:

> There are communication systems with orthogonal multitone physical
> layer. That is, one of N frequencies in the set is sent at a time. An
> example of such system is "Olivia":
> http://en.wikipedia.org/wiki/Olivia_MFSK . In the systems like that,
> they usually demodulate signal by incoherent detector. The loss due to
> incoherent demodulation is 1dB ballpark. There are, of course, technical
> reasons to do it in that way in each particular case (unknown/variable
> channel, simplification, etc. etc.), however  I wonder if it would be
> possible to demodulate such signal optimally, assuming AWGN and known
> channel.
> Problem is inconvenient autocorrelation function of  MFSK symbol. That
> is, small variation of the symbol sync could result in the large
> variation of phase, and also different proportionally to the bin number.
> Whereas the envelope of the autocorrelation function has relatively low
> slope, so it would be difficult to pinpoint exact position of sync.
> Could you suggest an algorithm applicable to this case, or a book or an
> article ?

Keeping in mind that I'm just going from theory, with little practice to 
back it up in this case:

At least in the case of Olivia_MFSK, the deal-killer that I see is "The 
phase is not preserved from one tone to the next".  They do go on to say 
that the phase is randomly shifted by +/- 90 degrees, though.  If this 
were the case then you could use that for synchronization.

Just going by the description of Olivia_MFSK in Wikipedia, I don't think 
that the bit errors due to synchronization errors are going to be all 
that great, since the pulses are shaped to be pretty soft at the edges.  
I suspect that a traditional-ish Costas loop should get you synched up on 
both carrier and bit timing, then use a 32-point FFT to pick out the 
actual bits.

In fact, could you not use OFDM methods for synchronization and coherent 
demodulation?

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

>>There are communication systems with orthogonal multitone physical
layer.
>
>>That is, one of N frequencies in the set is sent at a time. An example
of
>
>>such system is "Olivia": http://en.wikipedia.org/wiki/Olivia_MFSK .
>>In the systems like that, they usually demodulate signal by incoherent 
>>detector. The loss due to incoherent demodulation is 1dB ballpark. There

>>are, of course, technical reasons to do it in that way in each
particular
>
>>case (unknown/variable channel, simplification, etc. etc.), however  I 
>>wonder if it would be possible to demodulate such signal optimally,
>assuming 
>>AWGN and known channel.
>>Problem is inconvenient autocorrelation function of  MFSK symbol. That
is,
>
>>small variation of the symbol sync could result in the large variation
of
>
>>phase, and also different proportionally to the bin number. Whereas the 
>>envelope of the autocorrelation function has relatively low slope, so it

>>would be difficult to pinpoint exact position of sync.
>>Could you suggest an algorithm applicable to this case, or a book or an 
>>article ?
>>
>>Vladimir Vassilevsky
>>DSP and Mixed Signal Consultant
>>www.abvolt.com
>>
>>
>>
>
>If the signal is continuous phase AND the symbol rate is some ratio of
>integers relationship to the frequency spacing of the tones, then you can
>coherently demodulate it.
>
>I did this once with a V.23 modem signal where the symbol rate was 1200
>baud and the frequency spaceing is 400 Hz.  You will note that during the
>period of one symbol the carrier phase will rotate 60 degrees CCW or CW
>depending on whether the symbol was a one or zero.  Therefor depending on
>what the previous ending phase of the signal was you can rotate only
+/-60
>degrees.  There are 6 rotations, but only two are possible at any given
>time.  The demodulator can then test (correlate) against these six
>rotations and assign a probability.  The a maximum likelihood sequence
>estimator -like algorithm can then choose the most likely sequence of
>rotations over the long term.  Then you decode the bits from this
>sequence.
>
>Of course you need to integrate in some symbol timing and carrier phase
>recovery in order to make it all work, but these can be obtained from
>preliminary estimates (prior to MLSE) of the above correlations and
>integrated with a suitable PLL.
>
>Depending on the integer relationship of symbol timing to carrier phase,
>the complexity can be large or small.  Also, the technique can be
extended
>to the general case where no such relationship exists - you just have to
>have suitably large number of correlations such that the resulting error
is
>small.
>
>I got excellent results when I tried it and was able to decode signals
that
>a non-coherent demod could not operate on.
>
>-Doug
>

One thing I forgot as I did this a LONG time ago is that the above
technique would also work when the integer relationship was not there - as
long as it was close, say within 5% I still got excellent results.  The
signal just has to be continuous phase.

-Doug

>>>There are communication systems with orthogonal multitone physical
>layer.
>>
>>>That is, one of N frequencies in the set is sent at a time. An example
>of
>>
>>>such system is "Olivia": http://en.wikipedia.org/wiki/Olivia_MFSK .
>>>In the systems like that, they usually demodulate signal by incoherent 
>>>detector. The loss due to incoherent demodulation is 1dB ballpark.
There
>
>>>are, of course, technical reasons to do it in that way in each
>particular
>>
>>>case (unknown/variable channel, simplification, etc. etc.), however  I 
>>>wonder if it would be possible to demodulate such signal optimally,
>>assuming 
>>>AWGN and known channel.
>>>Problem is inconvenient autocorrelation function of  MFSK symbol. That
>is,
>>
>>>small variation of the symbol sync could result in the large variation
>of
>>
>>>phase, and also different proportionally to the bin number. Whereas the

>>>envelope of the autocorrelation function has relatively low slope, so
it
>
>>>would be difficult to pinpoint exact position of sync.
>>>Could you suggest an algorithm applicable to this case, or a book or an

>>>article ?
>>>
>>>Vladimir Vassilevsky
>>>DSP and Mixed Signal Consultant
>>>www.abvolt.com
>>>
>>>
>>>
>>
>>If the signal is continuous phase AND the symbol rate is some ratio of
>>integers relationship to the frequency spacing of the tones, then you
can
>>coherently demodulate it.
>>
>>I did this once with a V.23 modem signal where the symbol rate was 1200
>>baud and the frequency spaceing is 400 Hz.  You will note that during
the
>>period of one symbol the carrier phase will rotate 60 degrees CCW or CW
>>depending on whether the symbol was a one or zero.  Therefor depending
on
>>what the previous ending phase of the signal was you can rotate only
>+/-60
>>degrees.  There are 6 rotations, but only two are possible at any given
>>time.  The demodulator can then test (correlate) against these six
>>rotations and assign a probability.  The a maximum likelihood sequence
>>estimator -like algorithm can then choose the most likely sequence of
>>rotations over the long term.  Then you decode the bits from this
>>sequence.
>>
>>Of course you need to integrate in some symbol timing and carrier phase
>>recovery in order to make it all work, but these can be obtained from
>>preliminary estimates (prior to MLSE) of the above correlations and
>>integrated with a suitable PLL.
>>
>>Depending on the integer relationship of symbol timing to carrier phase,
>>the complexity can be large or small.  Also, the technique can be
>extended
>>to the general case where no such relationship exists - you just have to
>>have suitably large number of correlations such that the resulting error
>is
>>small.
>>
>>I got excellent results when I tried it and was able to decode signals
>that
>>a non-coherent demod could not operate on.
>>
>>-Doug
>>
>
>One thing I forgot as I did this a LONG time ago is that the above
>technique would also work when the integer relationship was not there -
as
>long as it was close, say within 5% I still got excellent results.  The
>signal just has to be continuous phase.
>
>-Doug

The V.23 symbol rate is usually within a percent or so, but the mark space
ratio can be massively distorted. The frequencies are only specified
+-100Hz. The phase is not specified as being continuous between symbols,
and frequently isn't. Other than that your technique sounds great. :-)

Steve

"DougB" <60916@dsprelated> wrote in message 
news:1PWdnUVFLLaq1CvNnZ2dnUVZ_uidnZ2d@giganews.com...
> >There are communication systems with orthogonal multitone physical layer.
>>That is, one of N frequencies in the set is sent at a time.
>>In the systems like that, they usually demodulate signal by incoherent
>>detector.
>> I wonder if it would be possible to demodulate such signal optimally,
>>Problem is inconvenient autocorrelation function of  MFSK symbol. That is,
>>small variation of the symbol sync could result in the large variation of
>>phase,

> I did this once with a V.23 modem signal where the symbol rate was 1200
> baud and the frequency spaceing is 400 Hz.  You will note that during the
> period of one symbol the carrier phase will rotate 60 degrees CCW or CW
> depending on whether the symbol was a one or zero.

There is no problem to recover the carrier phase if the phase windup over 
the symbol duration is less then 2xPi. If the phase could do several turns, 
I don't see algorithm other then trying all possibilities. This looks heavy 
and non-elegant.

Vladimir Vassilevsky
DSP and Mixed Signal Consultant
www.abvolt.com

"Tim Wescott" <tim@seemywebsite.com> wrote:
> On Wed, 28 Nov 2012 10:34:36 -0600, Vladimir Vassilevsky wrote:
>
>> There are communication systems with orthogonal multitone physical
>> layer. That is, one of N frequencies in the set is sent at a time.
>> they usually demodulate signal by incoherent detector. The loss due to
>> incoherent demodulation is 1dB ballpark.
>> I wonder if it would be
>> possible to demodulate such signal optimally
>> Problem is inconvenient autocorrelation function of  MFSK symbol. That
>> is, small variation of the symbol sync could result in the large
>> variation of phase
>> Could you suggest an algorithm applicable to this case, or a book or an
>> article ?
>
> I suspect that a traditional-ish Costas loop should get you synched up on
> both carrier and bit timing,

There is no problem to lock on frequency. The problem is to lock on phase 
without ambiguity.

> In fact, could you not use OFDM methods for synchronization and coherent
> demodulation?

OFDM is totally different case. In OFDM, they usually start with preamble 
with sharp autocorrelation peak to establish the sampling instant, and then 
they maintain timing by unmodulated pilot tones.

Vladimir Vassilevsky
DSP and Mixed Signal Consultant
www.abvolt.com

>
>"DougB" <60916@dsprelated> wrote in message 
>news:1PWdnUVFLLaq1CvNnZ2dnUVZ_uidnZ2d@giganews.com...
>> >There are communication systems with orthogonal multitone physical
layer.
>>>That is, one of N frequencies in the set is sent at a time.
>>>In the systems like that, they usually demodulate signal by incoherent
>>>detector.
>>> I wonder if it would be possible to demodulate such signal optimally,
>>>Problem is inconvenient autocorrelation function of  MFSK symbol. That
is,
>>>small variation of the symbol sync could result in the large variation
of
>>>phase,
>
>> I did this once with a V.23 modem signal where the symbol rate was 1200
>> baud and the frequency spaceing is 400 Hz.  You will note that during
the
>> period of one symbol the carrier phase will rotate 60 degrees CCW or CW
>> depending on whether the symbol was a one or zero.
>
>There is no problem to recover the carrier phase if the phase windup over

>the symbol duration is less then 2xPi. If the phase could do several
turns, 
>I don't see algorithm other then trying all possibilities. This looks
heavy 
>and non-elegant.
>
>Vladimir Vassilevsky
>DSP and Mixed Signal Consultant
>www.abvolt.com
>
>
>

That's true.  In my example there are a total of 12 states and since 6 are
the inverse of the other 6 you really only have to deal with 6 states.  It
probably doesn't matter if the phase rotates more than 2pi over the
duration of a baud.  You just need to figure out how many states this will
result in and if the baud rate is slow, even a light-weight processor can
handle an enormous number.

If you do have the situation where there are an enormous number of states,
then you might try using a reduced state technique as the benefit of
increasing the states diminishes as the number goes up.

There is a book on this subject "Digital Phase Modulation" by Anderson,
Aulin, and Sundberg, but it is only marginally beneficial - probably not
worth the money.

-Doug

On Wednesday, November 28, 2012 12:26:15 PM UTC-5, DougB wrote:
> >There are communication systems with orthogonal multitone physical layer.
> 
> 
> 
> >That is, one of N frequencies in the set is sent at a time. An example of
> 
> 
> 
> >such system is "Olivia": http://en.wikipedia.org/wiki/Olivia_MFSK .
> 
> >In the systems like that, they usually demodulate signal by incoherent 
> 
> >detector. The loss due to incoherent demodulation is 1dB ballpark. There 
> 
> >are, of course, technical reasons to do it in that way in each particular
> 
> 
> 
> >case (unknown/variable channel, simplification, etc. etc.), however  I 
> 
> >wonder if it would be possible to demodulate such signal optimally,
> 
> assuming 
> 
> >AWGN and known channel.
> 
> >Problem is inconvenient autocorrelation function of  MFSK symbol. That is,
> 
> 
> 
> >small variation of the symbol sync could result in the large variation of
> 
> 
> 
> >phase, and also different proportionally to the bin number. Whereas the 
> 
> >envelope of the autocorrelation function has relatively low slope, so it 
> 
> >would be difficult to pinpoint exact position of sync.
> 
> >Could you suggest an algorithm applicable to this case, or a book or an 
> 
> >article ?
> 
> >
> 
> >Vladimir Vassilevsky
> 
> >DSP and Mixed Signal Consultant
> 
> >www.abvolt.com
> 
> >
> 
> >
> 
> >
> 
> 
> 
> If the signal is continuous phase AND the symbol rate is some ratio of
> 
> integers relationship to the frequency spacing of the tones, then you can
> 
> coherently demodulate it.
> 
> 
> 
> I did this once with a V.23 modem signal where the symbol rate was 1200
> 
> baud and the frequency spaceing is 400 Hz.  You will note that during the
> 
> period of one symbol the carrier phase will rotate 60 degrees CCW or CW
> 
> depending on whether the symbol was a one or zero.  Therefor depending on
> 
> what the previous ending phase of the signal was you can rotate only +/-60
> 
> degrees.  There are 6 rotations, but only two are possible at any given
> 
> time.  The demodulator can then test (correlate) against these six
> 
> rotations and assign a probability.  The a maximum likelihood sequence
> 
> estimator -like algorithm can then choose the most likely sequence of
> 
> rotations over the long term.  Then you decode the bits from this
> 
> sequence.
> 
> 
> 
> Of course you need to integrate in some symbol timing and carrier phase
> 
> recovery in order to make it all work, but these can be obtained from
> 
> preliminary estimates (prior to MLSE) of the above correlations and
> 
> integrated with a suitable PLL.
> 
> 
> 
> Depending on the integer relationship of symbol timing to carrier phase,
> 
> the complexity can be large or small.  Also, the technique can be extended
> 
> to the general case where no such relationship exists - you just have to
> 
> have suitably large number of correlations such that the resulting error is
> 
> small.
> 
> 
> 
> I got excellent results when I tried it and was able to decode signals that
> 
> a non-coherent demod could not operate on.
> 
> 
> 
> -Doug

From the wikipedia article: 

"The phase is not preserved from one tone to the next: instead a random shift of �90 degrees is introduced in order not to transmit a pure tone when the same symbol is repeatedly sent. Because the symbols are smoothly shaped there is no need to keep the phase constant, which normally is the case when no (e.g. square) shaping is used."

"John" <sampson164@gmail.com> wrote in message 
news:d2bc2b03-9d9c-4b97-8345-66c3c0678a2d@googlegroups.com...
On Wednesday, November 28, 2012 12:26:15 PM UTC-5, DougB wrote:
> >There are communication systems with orthogonal multitone physical layer.
>
>
>
> >That is, one of N frequencies in the set is sent at a time. An example of
>
>
>
> >such system is "Olivia": http://en.wikipedia.org/wiki/Olivia_MFSK .
>
> >In the systems like that, they usually demodulate signal by incoherent
>
> >detector. The loss due to incoherent demodulation is 1dB ballpark. There
>
> >are, of course, technical reasons to do it in that way in each particular
>
>
>
> >case (unknown/variable channel, simplification, etc. etc.), however  I
>
> >wonder if it would be possible to demodulate such signal optimally,
>
> assuming
>
> >AWGN and known channel.
>
> >Problem is inconvenient autocorrelation function of  MFSK symbol. That 
> >is,
>
>
>
> >small variation of the symbol sync could result in the large variation of
>
>
>
> >phase, and also different proportionally to the bin number. Whereas the
>
> >envelope of the autocorrelation function has relatively low slope, so it
>
> >would be difficult to pinpoint exact position of sync.
>
> >Could you suggest an algorithm applicable to this case, or a book or an
>
> >article ?
>
> >
>
> >Vladimir Vassilevsky
>
> >DSP and Mixed Signal Consultant
>
> >www.abvolt.com
>
> >
>
> >
>
> >
>
>
>
> If the signal is continuous phase AND the symbol rate is some ratio of
>
> integers relationship to the frequency spacing of the tones, then you can
>
> coherently demodulate it.
>
>
>
> I did this once with a V.23 modem signal where the symbol rate was 1200
>
> baud and the frequency spaceing is 400 Hz.  You will note that during the
>
> period of one symbol the carrier phase will rotate 60 degrees CCW or CW
>
> depending on whether the symbol was a one or zero.  Therefor depending on
>
> what the previous ending phase of the signal was you can rotate only +/-60
>
> degrees.  There are 6 rotations, but only two are possible at any given
>
> time.  The demodulator can then test (correlate) against these six
>
> rotations and assign a probability.  The a maximum likelihood sequence
>
> estimator -like algorithm can then choose the most likely sequence of
>
> rotations over the long term.  Then you decode the bits from this
>
> sequence.
>
>
>
> Of course you need to integrate in some symbol timing and carrier phase
>
> recovery in order to make it all work, but these can be obtained from
>
> preliminary estimates (prior to MLSE) of the above correlations and
>
> integrated with a suitable PLL.
>
>
>
> Depending on the integer relationship of symbol timing to carrier phase,
>
> the complexity can be large or small.  Also, the technique can be extended
>
> to the general case where no such relationship exists - you just have to
>
> have suitably large number of correlations such that the resulting error 
> is
>
> small.
>
>
>
> I got excellent results when I tried it and was able to decode signals 
> that
>
> a non-coherent demod could not operate on.
>
>
>
> -Doug

From the wikipedia article:

"The phase is not preserved from one tone to the next: instead a random 
shift of &#4294967295;90 degrees is introduced in order not to transmit a pure tone when 
the same symbol is repeatedly sent. Because the symbols are smoothly shaped 
there is no need to keep the phase constant, which normally is the case when 
no (e.g. square) shaping is used."