[evlatests] Sensitivity Losses at edge of 1 GHz bandpass

[Barry Clark]

About as expected, qualitatively, but the numbers are a little
different than I would have expected.  It seems to display a clipping
noise floor at about -15 dB.  This is clipping noise from the
requantizer.  Clipping noise from the digitizer is a few dB further
down.  I would have expected the requantizer clipping noise to come
in at about -20 dB.  Somebody should look and see if the requantizer
power is low for subband zero.  I rather think it is.  If so, when
we implement requantizer level control, which we need to do anyway to
handle 3bit, we should get another few dB, which will pick up another
three channels or so.  In theory (I doubt if it's worth the work),
we could pick up another few dB, to the digitizer quantization noise,
by going to 7 bit correlation, which only picks up one or two more
channels.

I vaguely remember being told that the subband zero filter rolls off
harder to zero frequency than other subbands to avoid the poisonous
effect of digitizer DC offsets on the requantizer.  If so, it is
overdone - the DC offsets we see are only about 0.1 sigma, which
shouldn't be much problem; at worst they may force Hanning smoothing.
We may even be able to do something constructive by removing this
slope in the shape of subband zero in the digital filter, to boost
the low end above the requantizer noise (basically, the Dolby
principle).

Three bit digitizers are quite another game.  We are limited by the
digitizer clipping noise from the beginning, at about -17 dB.  Things
will be helped somewhat by the bandpass slope corrector, but it has
its limitations; it can't do anything about something that affects
mainly subband 0 as the 8bit path does.  And we may need the extra
rolloff, because the DC offsets run to at least 0.5 sigma, and WBC
spectra seem to indicate that the DC spike is slightly resolved.  We
could attack the latter problem by the rather heroic measure of using
the input lookup table to subtract a DC offset, in steps of half a bit
(if I remember how the thing works).

To summarize:  as things are now, we lose about 20 MHz at the bottom
of the band.  There are options to explore in software and firmware
that might reduce the loss to about 10 MHz.  The hardware slope
equalizer would straightforwardly reduce the loss to perhaps 4 MHz.
The three bit path probably will show the same problem to some degree,
but to what degree is pretty well unknown.

Rick Perley wrote:
>     The 1 GHz-wide path ('8-bit') has long been known to display a 
> mysterious roll-off in the bandpass on one side.  The roll-off is 
> gradual -- starting about 150 MHz from band edge, the atttenuation (in 
> power units) is about 10 to 15 dB down (relative to the average of the 
> middle portion of the bandpass) by the point where the anti-aliasing 
> bandlimiting filter sharply cuts off the spectrum. 
> 
>     The recent flurry of 3 and 8 bit sensitivity testing permits a test 
> of the relative noise as a function frequency through this rolloff 
> band.  Noise was measured in each channel, using the histogram plotting 
> program, after standard calibration (which include a bandpass 
> calibration to remove the bandpass attenuation).  The key question is 
> whether the noise is increased in the region of the anomalous attenuation. 
> 
>     The short answer is 'yes'.  A tougher question is whether the region 
> affected, and the noise increase, is unacceptably wide. 
> 
>     The observations have 8 subbands, spanning 1.024 GHz, from 4.5 to 
> 5.5 GHz -- a nice clean band.  I have determined the post-calibration 
> noise, using a blank field, for channels as a function of offset from 
> the band edge.  Shown are statistics from three subbands -- #1 (which 
> has the rolloff), #2 (which should be unaffected to any significant 
> degree), and #8, which provides a calibration of the noise we should see 
> due to the anti-aliasing filter, and without the anomalous rolloff.   
> Each entry has been normalized by the best sensitivity seen in each 
> subband (this is a slowly varying number across the various subbands) -- 
> it thus represents a noise multiplier.  To the right of each 'mult' 
> column is the approximate attenuation noted for that channel, using the 
> mid-band levels as normal. 
> 
>                  subband 1    subband 2   subband 8
> Channel
> Offset     Mult    Att      Mult  Att     Mult   Att
> -----------------------------------------------------------
> 0 (edge)   805     <-30    1.7   -6        3.8  -14
> 1              178     <-30    1.3   -4        3.1  -12
> 2                48      -30     1.2   -2        2.4   -11
> 3                15      -26     1.1   -1         1.9  -10
> 4                  6.7   -22     1.0               1.7   -8
> 5                  3.8   -19     1.0              1.4    -6
> 6                  2.6   -16     1.0              1.2    -4
> 7                  2.1             1.0              1.1    -2
> 8                  1.7              1.0             1.0    -1
> 9                  1.5   -12
> 10                1.4
> 11                1.3
> 12                1.2
> 13                1.1    -8
> 
>  From here on, the sensitivity in subband 1 slowly improves, reaching a 
> multiplies of 1.0 at channel #20. 
> 
> Some conclusions to note:
> 
>     1) For subbands 2 and 8 (defining 'normal behavior), the noise 
> increases by a factor of ~50% when the power is down by about 6 dB.  For 
> the central subbands (defined by the stationboard digital filters), only 
> the edge channel on each side reaches this level.  For subband 8, where 
> the right-hand edge is defined by the sharp analog anti-aliasing filter, 
> the 5 channels on the edge are affected to this level. 
>     2) For subband 1, the behavior is quite different -- the noise is 
> increased by ~50% for the nine channels on the edge, where the 
> attenuation seems to be down by more than 10 dB over mid-band levels.  
> It thus seems that most of the gradual rolloff is not accompanied by the 
> increase in noise seen at the edges of the other subbands. 
>     3) The bottom few channels of subband 1 are quite anomalous -- huge 
> attenuations and increases in noise -- which I believe are due to some 
> problem in the definition of the digital filter for the subband.  
> (Somebody please correct me if I'm wrong). 
> 
>     So, discounting the bottom half dozen channels of subband 1, the 
> gradual rolloff seen in the 1 GHz-wide path in the bottom ~100 MHz is 
> accompanied by a modest, but significant increase in noise -- factors of 
> up to 2. 
> 
>     Is this acceptable?  For some -- perhaps most--  experiments, if the 
> full sensitivity in a particular part of the band is required, one can 
> always adjust the LO to shift that part of the spectrum to the 2nd 
> subband.  HI observations, for example, could do this to optimize 
> sensitivity below 1.1 GHz -- the cost would be loss of the upper 128 
> MHz, (1.9 to 2.1 GHz), which may be of rather little interest to HI 
> observers ... 
>     Within L-band, the bottom 128 MHz of continuum is likely to be of 
> little interest from a sensitivity point of view (full of interference, 
> and system performance is not very good there). 
>     Within S-band, the situation is not as simple, as the 2.0 -- 2.1, 
> and 3.0 -- 3.1 GHz regions (which are affected by this roll-off) are 
> important for sensitivity, and potentially for other spectral 
> applications. 
> 
>     I think it worth it to spend some more effort to find the origin of 
> this rolloff in the 1 GHz path.
> 
> 
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