[Pafgbt] save PAF cross-correlations rather than formed beam outputs

[Karl Warnick]

I agree that correlations are important. Correlated outputs will 
probably be the default mode for most PAF observations, and real time 
beams would only be used when phase information is important, such as 
for pulsar surveys (can pulsar searches be done with fine grained, 
narrowband correlations?)

I'm not sure whether the bandwidth issue is the real driver. Real time 
beams also have to be formed in subbands and then either processed for 
pulsar surveys or integrated for power spectra. I don't think bandwidth 
is really what drives the difference between a B engine and an X engine. 
It's true that if one only forms a few PAF beams, then with a given disk 
storage data rate one could store the beam outputs over finer frequency 
subbands than correlations, but if fully sampled beams are formed, the 
data rate wouldn't be very different between beam outputs and 
correlations with the same integration time and frequency resolution. Am 
I missing something?

There is another motivation for beamformers in the broader PAF 
community, and that is for synthesis arrays. The correlator for the dish 
array is expensive, so one would only want to correlate as small a 
number of beams from each PAF as possible. This raises a question - 
could correlations from each PAF be used to get correlations of the dish 
array somehow? Is there an efficient two-level correlator architecture, 
with a PAF correlator for each dish, followed by the synthesis array 
correlator? I suspect not, but I can't quite convince myself. In any 
case, it seems that for single dish telescopes, there's less motivation 
to use a beamformer back end instead of a correlator.

Finally, there is probably a bit of analysis one could to to show how 
closely beams must be spaced in order for the information in the beams 
to be equivalent to the correlations. It's essentially the problem of 
recovering the matrix R from a set of inner products w'*R*w for many 
vectors w. I suspect that if one forms HPBW/2 spaced beams over the PAF 
FoV, the information in the beams is less than but on the order of the 
information in R in some quantiable sense. Information in the deep 
sidelobes is lost, but most of the large eigenvalues of R represent 
sources in the field of view. With finer beams, even just over the PAF 
field of view, all information even out in deep sidelobes could well be 
contained in the beam outputs, but that's a moot point, as one would not 
form that many beams in practice. There's also the idea of eigenbeams 
proposed by Cornwell et al., so that one can form very few PAF beams yet 
still have information over the full field of view.

Karl


On 5/20/2013 9:25 AM, Brian Jeffs wrote:
> Rick,
>
> I agree that you have much more flexibility to try different 
> beamformer designs, detection algorithms, interference mitigation 
> techniques, superresolution, calibration correction, etc. if you store 
> and operate on the accumulated cross products (correlation matrices). 
>  However, you give up the ability to do fine resolution spectral 
> processing.  You are stuck with the coarseness of the correlator's 
> frequency channelization.  I don't know how problematic this is for 
> some applications, such as pulsar searches, where fine spectral 
> resolution may be needed.
>
> Brian
>
> On May 20, 2013, at 6:38 AM, Anish Roshi wrote:
>
>>
>> Yes indeed. We can form images with beams with different optimization 
>> if the correlations are recorded.
>> Anish
>>
>>
>> On Sun, May 19, 2013 at 9:57 AM, Rick Fisher <rfisher at nrao.edu 
>> <mailto:rfisher at nrao.edu>> wrote:
>>
>>     Brian, Karl,
>>
>>     In trying to understand the ASKAP data processing architecture, I'm
>>     beginning to understand the fundamental importance of saving the
>>     cross-products between array element outputs in our own PAF data
>>     processing.  In forming beams you throw away a lot of information
>>     in the
>>     array's field of view that can be recovered only by forming many
>>     beams
>>     with very close spacing (much closer than HPBW/2).  This has
>>     important
>>     consequences for the sensitivity to point sources, as in the
>>     search for
>>     pulsars.  Hence, I would suggest that the most important archived
>>     outputs
>>     from your signal processor are the cross-products rather than formed
>>     beams.  For a given data storage volume, there's more information
>>     in the
>>     cross-products than in the formed beam outputs.  In some
>>     respects, the
>>     "beam" concept is a holdover from a waveguide feed where there's
>>     only one
>>     output, and most of the information in the focal plane is
>>     reflected back
>>     into the sky.
>>
>>     Rick
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-- 
Karl F. Warnick
Department of Electrical and Computer Engineering
Brigham Young University
459 Clyde Building
Provo, UT 84602
(801) 422-1732





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