Mebart wrote:

Decoding MSK as FSK will give you way less than optimum bit error rate
vs. noise. Unless the MSK is coming in on an FM channel you should
consider decoding it as PSK.



I did find a chip that does 2400 baud MSK. But, why should I use a PSK
method?

PSK transmits one frequency, but inverts the amplitude of the
modulation to represent a 1 (or 0).

PSK has an advantage in bandwidth, which has less noise due to the
narrower bandwidth. But, can a PSK modem actually decode MSK better?

The ap is amplitude modulated VHF and I want the best weak signal
perfirmance I can get. The AM carrier wastes some transmit power and
has a disadvantage over a single sideband supressed carrier. But, it
is still many db better than a very wasteful fm mode.

Anyway, I can't control the transmitters, so I'm stuck with AM.

Having the carrier received with the sidebands establishes the center
frequency, so the tuning in the receiver is not quite so critical. AM
is really quite practical in this case.

Can you tell me some more about decoding the signal as though it was
PSK?

Thanks,

Art

It acts as offset quadrature PSK with the bits weighted to be 1/2
cosines instead of rectangular pulses. You decode it just the way I said.

If you can find them the following two papers are quite useful. One of
them (the one from the IEEE Comm. Soc. IIRC) is easy enough that you can
just about design a demodulator straight from the paper.

[1] R. De Buda: "Coherent Demodulation of Frequency Shift Keying with
Low Deviation Ratio" -- IEEE Transactions, 1972, COM-20, pp. 429-435.

[2] S. Pasupathy: "Minimum Shift Keying: A Spectrally Efficient
Modulation" -- IEEE Communications Society Magazine, July 1979, Vol 17,
#4, pp 14-22.

And if you live in Worcester, MA, and you're wondering why I know:

[3] Tim Wescott: "A DGPS Radiobeacon Receiver for Minimum Shift Keying
with Soft Decision Capabilities" -- Master's Thesis, Worcester
Polytechnic Institute, 1990.

Stop by the library there -- I believe they'll have a copy.

Here's a summary of the reasoning (taken from Chapter 3 of [3] -- I like
the author). This is much better with pictures (the clearer paper of
[1] and [2] uses pictures, as does [3]):

The way that MSK works is to have FSK signal with a frequency shift that
is exactly 1/2 the baud rate. Thus the phase shift from one bit time to
the next is 90 degrees (1/4 of a circle).

Now consider a quadrature, offset PSK with 1/2 cosine weighting (really,
do). Thus even-numbered bits are transmitted as either positive-going
or negative-going cosine waves multiplied by the carrier, each one
lasting for exactly 1/2 cycle of the cosine, and the cosine having a
frequency of (bit rate/4). Odd-numbered bits are transmitted as either
positive-going or negative going _sine_ waves multiplied by the
quadrature of the carrier.

Take your bitstream, and make two signals a_i(t) and a_q(t). The signal
a_i(t) is +1 if it's corresponding bit is 1, -1 if the bit is 0, and it
only changes on boundaries of t = 2*k*T where T is the baud rate and k
is the bit number. The signal a_q(t) is similar, but it changes on
boundaries of t = (2*k+1)*T.

Then the transmitted signal is equal to

s(t) = a_i(t)*cos(pi*t/(2*T))*cos(2*pi*f*t) +
a_q(t)*sin(pi*t/(2*T))*sin(2*pi*f*t) (1)

where f is the carrier frequency (1200Hz in your case).

If you grind through those high school trig identities (1) becomes:

s(t) = cos(2*pi*f*t + b(t)*pi*t/(2*T) + phi(t)) (2)

where at any given moment b(t) = a_i(t) * a_q(t) and phi(t) = (a_i(t) +
a_q(t))*pi/2. Assuming I haven't messed up my expression for phi(t)
(the value I gave for it in my thesis is clearly a typo, I'm guessing
here) this is a phase continuous FSK signal who's frequency is the
carrier + 1/4 the baud rate for two consecutive 1's or two consecutive
0's, and carrier - 1/4 baud for a 1 followed by a 0 or visa-versa.

That's what MSK _is_, from a OQPSK sense, there's more about
demodulating it -- let me know if you can't find the articles, or
anything sensible on the web -- I'm thinking of scanning this stuff in...

-------------------------------------------
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com