[Ground-station] Baseband => decimation - questions

[Phil Karn]

I see one important  design decision related to decimation, sample
rates, IF selections and so forth.

If you need, say, 10 MHz of bandwidth you can get it by complex sampling
a direct conversion receiver at 10 MHz. That gives you a complex base
band stream extending from -5 MHz to +5 MHz.

This does have some drawbacks; the question here is whether they are
sufficiently serious for this application to switch to another
technique. The main drawback is the spike at 0 Hz (DC) in the base band
due to mixer imbalance, usually from the LO cross feeding into the mixer
input.

This DC component is pretty stable unless you retune, so I've found it
fairly easy to remove with simple exponential high-pass filters (one
each in I and Q). If the signal has a residual carrier component, it'd
be wise to not tune it down exactly to DC, though this is actually hard
to do except in simulation with perfect oscillators. The carrier
tracking that puts the carrier at exactly 0 Hz will be done later in DSP
where these imperfections don't exist.

Although the DC spike is easy to remove, there is still a small mound of
1/f noise surrounding the now-suppressed DC spike. This may or may not
pose a problem to the specific modulation; it depends on how much signal
energy is in this region vs the whole thing. For a broadband 10 MHz PSK-
or QAM-like signal, it probably won't cause much problem.  Again the
signal can be shifted slightly in frequency if necessary, with this
shift compensated for in the subsequent carrier tracking.

There are two other imperfections that have to be corrected. The I and Q
channels won't have exactly the same gain, and they won't be in exact
quadrature. This shows up as imperfect image suppression between the
negative and positive frequencies. You fix the first problem with AGCs
to make the two channels have the same average power. You fix the second
by rotating the Q axis slightly to drive the average dot product between
the I and Q channels to zero.

This doesn't handle frequency-dependent imperfections, but it may be
good enough for our modulation. In a recent local IEEE talk, Fred Harris
talked about how images can be a serious problem but his examples were
of extremely complex OFDM signals with thousands of 2048-QAM carriers
(or similarly absurd numbers). It's probably not significant with a
single signal carrier with low order modulation designed for a satellite
channel with a relatively low SNR. (Has one of the DVB-S2 formats been
chosen yet?)

But if these imperfections *do* turn out to be a problem, there's
another approach involving faster sampling and more DSP: you shift the
center of your signal to +/-Fs/4. That is, you center it halfway between
zero and either the negative or positive Nyquist frequency and filter
out (throw away) the signal on the other side of zero. This is sometimes
called a "low IF" system since the last IF is less than the sample rate
(it's 1/4 of it) and DSP is still used to get rid of the mixer image.

The DC spike and 1/f noise are now gone (they're actually moved to the
Nyquist frequency on one side, which you're not using anyway). Any
images are now just thermal noise instead of signal (unless we have some
nearby interferers which seems unlikely). This obviously requires A/D
converters that are twice as fast, followed by DSP that can handle twice
the samples. The Fs/4 frequency shift is easy, you just rotate each
complex sample by 90 degrees: 1, j, -1, -j, 1...

It provides a cleaner signal but again it may not be necessary for our
specific modulation. And anything we do to keep the sample rate down
will help keep costs down.

73, Phil