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Re: ao40 today



>This means that we can, inside the modem,
>completely determine the parameters for this
>spin modulation and then PREDICT the frequency
>and phase of the carrier based on our signal
>determined parameters and greatly improve the
>performance of the demodulator.  If we are going

True, we can do this. But it's not necessary. Here's why.

The P3 telemetry format does not use FEC. That means the energy per
modem symbol (Es) and the energy per data bit (Eb) are the same.
Furthermore, uncoded BPSK requires an Eb/No ratio of at least 10 dB or
so for good copy.

When we coherently demodulate BPSK, we need a carrier phase reference.
A tracking loop can produce a carrier phase estimate that, for the
purpose of demodulating BPSK, is nearly perfect when the SNR in the
loop is 15 dB or more. That's only 5 dB more than the energy we
already know we need in a single symbol, so the loop need only process
the energy in 3-4 symbols. At a symbol rate of 400 Hz, that's a loop
bandwidth of 100-133 Hz. That should easily follow the spin-induced
"wobbulation" we see. Going narrower, or implementing a model that
takes the sinusoidal modulation of carrier frequency into account,
would maintain carrier lock at lower SNRs, but they'd be too low to
permit error free demodulation anyway. So what's the point?

Things would be very different if FEC were added to the P3 format.
Then it would make sense to make the modem operate at much lower Es/No
ratios. This is for two reasons: the FEC would permit much lower Eb/No
ratios to be used, and the Es/No would be even lower than the Eb/No
by the code rate.

If the IHU were loaded with software to do the RS/convolutional
combination already used for years by nearly every (non-amateur)
spacecraft with a digital link, the required Eb/No would drop to about
2.5 dB. For a code rate of (223/255) * (1/2) = 0.437 or -3.59 dB, the
required Es/No would drop to only 2.5 - 3.59 = -1.09 dB. That's 10 -
(-1.09) = **11 dB** of additional link margin on a non-fading channel
-- and quite a bit more on a fading channel like the one we have now.

But that means we'd have to keep our modem tracking carrier at a much
lower Es/No than before. Achieving a carrier loop SNR of 15 dB would
require the energy from 15 - (-1.09) = 16.1 dB-symbols, or about 41
symbols.  Making things worse is the "squaring loss" that appears in
Costas and squaring loops at low Es/No ratios, which in this case
would be about 8 dB. So we're talking about a loop operating off the
energy in about 250 symbols. That's over half a second's worth, or a
loop bandwidth of less than 2 Hz. So we'd obviously have trouble
tracking the present spin Doppler, and any help from a model of the
spin would certainly be welcome here.

As an alternative, we could abandon coherent demodulation and do
differential detection. This wouldn't be as good, but it might work
well enough considering the spin fading and the ability of coding to
fill in the deep nulls.

Phil


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