[Pafgbt] PAF beamformer size and cost
Brian Jeffs
bjeffs at byu.edu
Thu Feb 4 15:05:11 EST 2010
Rick and all,
On Feb 4, 2010, at 11:47 AM, Rick Fisher wrote:
> 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?
>
The beamformer weights are applied per frequency channel, each of
which is less than 1 MHz wide. Thus broadband beamforming is
effectively implemented by using potentially different weights for
each narrow band. This is actually overkill since the fractional
bandwidth per freq. channel is very small. We could probably get away
with using the same weights over 20 MHz of adjacent channels.
> 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.
The real driver here seems to me to be the required time resolution.
This will control the integration time, and thus the data rate. The
numbers I quoted for data rate assumed no integration, i.e. output
every sample to the next downstream system. This is clearly beyond
our near term capabilities, so we must have some integration going on
in the CASPER beamformer.
There are no computational advantages to post correlation beamforming
unless either a) you need to do the correlation anyway; then
beamforming is almost free, or b) the number of computed beams is
significantly larger than the number of array elements. In either
case, the time resolution imposed by the correlator STI time must
match the observation goals.
> My guess
> is that any computational advantages evaporate or even reverse when
> the
> required time resolution approaches the inverse required frequency
> resolution.
I agree with this statement.
Brian
>
> Rick
>
> On Thu, 4 Feb 2010, Brian Jeffs wrote:
>
>> Rick,
>>
>> See below:
>>
>>>
>>> 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 http://arxiv.org/abs/0912.0380v1
>>> shows a
>>> voltage-sum beamformer. The post-correlaion bamformer may use fewer
>>> processing resources, but it precludes further coherent signal
>>> processing
>>> of each beam.
>>
>> 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.
>>
>>
>>> 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.
>>>
>>
>> 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
>>
>>
>>
>>
>>> Counter-thoughts?
>>>
>>> Rick
>>>
>>> On Wed, 3 Feb 2010, Brian Jeffs wrote:
>>>
>>>> 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:
>>>>
>>>>> 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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>>>>
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