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Rick,<br>
<br>
Of course, the savings in a post-correlation beamformer is not so much
that the beamforming is after correlation per se, but that it is
post-integration. So, to understand the relative computational costs,
we would want to factor in typical integration times. If long enough,
the work required for post-correlation beamforming is essentially zero
relative to voltage beamforming. Post-correlation beamforming also
leaves open the flexibility to use different beamformer coefficients in
post-processing. So far, it seems clear hat a back-end will require
both modes - correlation for calibration and some observations, and
voltage beamforming for observations requiring time signals, and
perhaps both simultaneously.<br>
<br>
Both voltage beamforming and post-correlation beamforming will be done
in frequency sub-channels, but we don't yet know how wide the
beamforming sub-channels will be. That's a bit difficult to answer,
since beamshape distortion over frequency affects imaging performance
through both dynamic range and reduced sensitivity. Without doing a
careful analysis, I would say that the beamformer subchannels could
probably be larger than the typical correlation subchannels, so a
voltage beamforming back-end could use two F engines, one coarse before
beamforming, and another after for narrow spectral resolution. Wider
subchannels would require fewer beamformer coefficients but higher bit
rate per subchannel. Is there any savings in beamforming on wider
frequency bins, or is the computational burden independent of
beamformer subchannel bandwidth? <br>
<br>
Karl<br>
<br>
Rick Fisher wrote:
<blockquote
cite="mid:Pine.LNX.4.64.1002041313160.24888@clro.cv.nrao.edu"
type="cite">
<pre wrap="">Brian,
Thanks very much for the beamformer outline. How does Jason handle the
frequency dependence of the beamformer weights? Is there an FIR is each
signal path or maybe an FFT - iFFT operation?
What to do with the high bandwidth beam outputs at high time resolution is
a standard pulsar problem. Since the beam outputs are essentially the
same as you'd have with a conventional horn feed, all of the current
tricks of the trade will apply. As far as I know, all pulsar surveys are
done by generating spectra with a frequency resolution consistent with the
highest expected pulse dispersion, squaring the signals, integrating for
the selected resolution time, and streaming this to disk. Pulse searches
are then done off-line in computer clusters or supercomputers. (Our
pulsar experts can chime in here.) We'll need to match our output data
rates with available storage and post-processing capabilities - a
time-dependent target. Maybe someone could give us some currently
feasible numbers and time derivatives.
Before completely buying into the voltage sum real-time beamformer we
should keep in mind that a lot of single dish applications don't need
voltage outputs as long as the time and frequency resolution parameters
are satisfied. If there are big computational savings in a
post-correlation beamformer, and we satisfy ourselves that there's not a
hidden gotcha in this approach, we should keep it on the table. My guess
is that any computational advantages evaporate or even reverse when the
required time resolution approaches the inverse required frequency
resolution.
Rick
On Thu, 4 Feb 2010, Brian Jeffs wrote:
</pre>
<blockquote type="cite">
<pre wrap="">Rick,
See below:
</pre>
<blockquote type="cite">
<pre wrap="">Is your assumed beamformer architecture voltage sums or post-correlation?
In other words, are the beams formed by summing complex weighted voltages
from the array elements or by combining cross products of all of the
elements? John's reference at <a class="moz-txt-link-freetext" href="http://arxiv.org/abs/0912.0380v1">http://arxiv.org/abs/0912.0380v1</a> shows a
voltage-sum beamformer. The post-correlaion bamformer may use fewer
processing resources, but it precludes further coherent signal processing
of each beam.
</pre>
</blockquote>
<pre wrap="">Our plans are based on a correlator/beamformer developed by Jason Manley for
the ATA and some other users (the pocket packetized correlator). He recently
added simultaneous beamforming to the existing correlator gateware, so they
run concurrently. In our application the only time this is required is
during interference mitigation. Normally we correlate during calibration and
beamform otherwise.
His design is a voltage sum real-time beamformer. At this point he does not
compute as many simultaneous beams as we need to, so I think we will have to
exploit the computational trade-off to do either beamforming or correlation
but not both, or it will not fit in the FPGA. Post-correlation beamforming
is really quite trivial, and has a low computational burden, so that could be
added to the correlator and run simultaneously. I believe that when we need
simultaneous voltage sum beamforming and correlations (as when doing
interference mitigation) we will have to reduce the effective bandwidth. We
really cannot take Jasons' existing code and plug it right in for our
application, but it will serve as a very good template. That is why we have
Jonathan out at UC Berkeley for 6 months, so he can learn the ropes and then
work on our correlator/beamformer.
</pre>
<blockquote type="cite">
<pre wrap="">Very roughly, the science requirements for a beamformer fall into two
camps, which may be operational definitions of first science and
cadallac/dream machine: 1. spectral line surveys with bandwidths in the
3-100 MHz range and very modest time resolution and 2. pulsar and fast
transient source surveys with bandwidths on the order of 500+ MHz and <=50
microsecond time resolution. The 2001 science case says pulsar work
requires bandwidths of 200+ MHz, but the bar has gone higher in the
meantime. One can always think of something to do with a wide bandwidth,
low time resolution beamformer, but it would be a stretch. The GBT
sensitivity isn't high enough to see HI at redshifts below, say, 1350 MHz
in a very wide-area survey. Hence, building a beamformer with wide
bandwith but low time resolution may not be the optimum use of resources.
Also, the 2001 science cases assumes 7 formed beams, but the minimum now
would be, maybe, 19 and growing as the competition heats up.
</pre>
</blockquote>
<pre wrap="">We are operating under the assumption of at least 19, and probably more than
40 formed beams. If we only use the correlator for calibration, then we
should be able to achieve both relatively wide bandwidth (250 MHz) and high
time resolution (we will get a beamformer output per time sample, not just
per STI interval). Dan and Jason feed that based on their experience with
existing codes this is achievable on the 40 ROACH system we sketched out, but
we will have to wait and see. If we run into bottlenecks we will have to
reduce either bandwidth or the number of formed beams.
One issue I am not clear on yet is what we do with the data streams for 40+
voltage sum beams over 500+ frequency channels. How do we get it off the
CASPER array, and what will be done with it? For 8 bit complex samples at
the beamformer outputs you would need the equivalent of fourty 10 Gbit
ethernet links to some other big processor, such as a transient detector. If
this is unreasonable then either the number of bits per sample, bandwidth, or
number of beams will need to be reduced. Alternatively, it is not hard to
add a spectrometer to the beamformer outputs inside the
correlator/beamformer, and this provides a huge data rate reduction. But how
do we handle data for transient observations where fine time resolution is
critical?
Brian
</pre>
<blockquote type="cite">
<pre wrap="">Counter-thoughts?
Rick
On Wed, 3 Feb 2010, Brian Jeffs wrote:
</pre>
<blockquote type="cite">
<pre wrap="">Rick,
We have a rough architecture and cost estimate for a 40 channel
correlator/beamformer capable of 40 channels (19 dual pol antennas plus
reference or RFI auxiliary) over 250 MHz BW. We worked this out with
CASOER
head Dan Werthimer and his crack correlator/beamformer developer Jason
Manley. It will require 20 ROACH boards, 20 iADC boards, 1 20-port 10
Gbit
ethernet switch, and some lesser associated parts.
Our recent ROACH order was $2750 each, iADC: $1300 each, enclosures: $750
each, XiLinx chip: free or $3000, ethernet switch: $12000.
You can use your existing data acquisition array of PCs as the
stream-to-disk
farm, but will need to buy 10 Gbit cards and hardware RAID controllers.
The total (which will be a bit low) assuming no free XiLinx parts and not
including is: $168,000.
Of course this does not include development manpower costs.
Brian
On Feb 3, 2010, at 3:05 PM, Rick Fisher wrote:
</pre>
<blockquote type="cite">
<pre wrap="">This is an incomplete question, but maybe we can beat it into something
answerable: Do we know enough about existing applications on CASPER
hardware to make a conservative estimate of what it would cost to build
a
PAF beamformer with a given set of specs? I'm looking for at least two
estimates. What is a realistic set of specs for the first science PAF
beamformer, and what would the dream machine that would make a big
scientific impact cost? You're welcome to define the specs that go
with
either of these two questions or I'll start defining them by thinking
"out
loud". The first science beamformer will guide the initial system
design,
and the dream machine will help get a handle on longer range
expectations.
Cheers,
Rick
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</blockquote>
</blockquote>
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</blockquote>
<br>
<pre class="moz-signature" cols="72">--
Karl F. Warnick email: <a class="moz-txt-link-abbreviated" href="mailto:warnick@byu.edu">warnick@byu.edu</a>
Associate Professor Tel: (801) 422-1732
Department of Electrical & Computer Engineering FAX: (801) 422-0201
Brigham Young University
459 Clyde Building
Provo, UT 84602
</pre>
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