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TRANSCRIPT
Beamforming andNull Formation*
Billy BarottSeptember 16, 2010
ATA/SETI/RAL DSP Meeting
*A thorough treatment of the subject and all related areas in 10 minutes or less
Talk Outline
• Introduction• Designing Beamformers• Mitigating Interferers• What the ATA has Done• Conclusion and Directions
!
2"
3"
Flexible phased array beams
Signals from wide FOV antennas
Multiple Beam-Forming Greatly Expands the Power of the Radio Telescope!
Beamforming is Simple
All
Pha
sors
Alig
ned
Antenna 1
Antenna 4
Antenna 3
Antenn
a 5
Antenna Phasors on Unit CircleVectors Must Be Processed
Geometric corrections are easy, but instrumental corrections must be found (and they change…)
(It’s Calibration that’s Hard)
Antenna 1
Antenna 4
Antenna 3
Antenn
a 5
Antenna Phasors on Unit CircleVectors Must Be Processed
The best way to calibrate is with a correlator – but that takes expensive space in the FPGA
TDBF vs. FDBF
• Time Domain– High FIR cost per beam to
minimize modulation errors– CFIR required for bandpass,
non-conjugate symmetric ops– Also Requires FFTs, but
smaller than FDBF– Cheaper for few beams
Per B
eam
Per B
eam• Frequency Domain
– Low Per-Beam Cost (one multiply/LUT*)
– FFT/PFB for each antenna must be long (free if part of a correlator)
– IFFT required for output beam– Cheaper for many beams
* Cost of LUT memory oughtn’t be neglected
A Perfect World
InterfererDesired Signal
-20 -10 0 10 20-30
-25
-20
-15
-10
-5
0
Azimith (arcmin)
Beam
Gai
n (d
B vs
. pea
k or
dina
ry)
Azimuth Slices on Galaxy 15
Phased BeamNull Beam
Interference Nulling
• Mitigating interference while retaining the ability to observe (vs. Blanking)
• Modify steering function to reduce synthetic beam response in vector of the interferer
• Many methods of varying complexity, performance
• Time-varying solutions influence depth of LUT in BF design
Types of Mitigation/Nulling
• Projection Nulls– Matrix operation on steering
vector– Deep, narrow null– One DOF per null– Good for known interferers,
orthogonal beamsets• Optimization Pattern
– Iterative/Evolutionary– Processing-intensive and no
guarantee of unique solution– Good for wide shallow
suppression, fewer DOFs
• Adaptive/ Correlation Nulls– Correlate on interferer to
determine steering direction– Feed-back steering vector in
real-time to projection null• Wiener Filtering
– Estimation and subtraction of a sampled interferer
– Requires a reference antenna or beam
– 30 dB on GPS/Glonass(Bower, ATA Memo 31)
– Experimented with on XM
-20 -15 -10 -5 0 5 10 15 20-30
-25
-20
-15
-10
-5
0
Offset Azimith (arcmin)
Bea
m G
ain
(dB
Rel
ativ
e to
Max
imum
Arra
y G
ain)
Measured Beam Patterns, ElOffset = 0 (Galaxy 15, 1575 MHz)
Ordinary BeamNull Beam
Projection Null
Projection Nulls from 11.4’ – 12.6’
Null-out interferers or form orthogonal beam-set
Orthogonal Beam Sets
• Used in multibeam surveys (SETI)• Each beam has nulls in the direction of every
other beam• Creates convenient set of continuous off-points
-20 -10 0 10 20-30
-25
-20
-15
-10
-5
0
Azimith (arcmin)
Beam
Gai
n (d
B vs
. pea
k or
dina
ry)
Azimuth Slices on Galaxy 15
Phased BeamNull Beam
Importance of Accuracy
Accuracy is calibration as well as instrumental– even 1 deg of error is important
(Harp, ATA Memo 51)
ATA: Time Domain Beamformer
• 3x Beamformers: Dual-pol, Two IFs– 84 Antpols– 104 MHz
• Some Users– Prelude / SonATA– setiQuest– BAPP/ GPU Pulsar– JPL-PRSR– MLM– REU Masers– LCROSS– Lunar X-Prize (Planned)
• Reconfigurable Hardware– 16x BEE2s, 54 iBobs– 45-node Foxtrot– CoBI?
BF3 BEE2s
BF2/3 iBobs
DAC iBobs
b16
BF2 BEE2s
BF2/3 iBobs
BF1 iBobs
BF1 iBobs
BF1 BEE2s
b01.bfaFPGA 1
X-pol / Ant1
X0
X2
X1 X3
b01.bfaFPGA 2
X-pol / Ant2
X0
X2
X1 X3`
b01.bfaFPGA 3
X-pol / Ant3
X0
X2
X1 X3
b02.bfaFPGA 1
X-pol / Ant4
X0
X2
X1 X3
b02.bfaFPGA 2
X-pol / Ant5
X0
X2
X1 X3`
b02.bfaFPGA 3
X-pol / Ant6
X0
X2
X1 X3
b01.bfaFPGA 4
X-pol / Sum1
X0
X2
X1 X3
b02.bfaFPGA 4
X-pol / Sum2
X0
X2
X1 X3`
b05.bfaFPGA 1
X-pol / Sum3
X0
X2
X1 X3
C33
B40
B39
C37
B46
B29
C39
C38
i1.bfa B1
i2.bfa
i3.bfa
i4.bfa
i5.bfa
i6.bfa
i7.bfa
i8.bfa
i9.bfa
i10.bfa
i11.bfa
i12.bfa
B2
B7
B4
B5
B6
B3
B45
B8
B12
B13
B14
id1.bfaB20
Signal Path
Branch Branch NodesNodes
Leaf Leaf NodesNodes
4 Ants4 AntsSubSub--beam beam
8 Ants8 Ants
SubSub--Beam Beam 24 Ants24 Ants
To DACTo DAC
48 Ants48 Ants
8x1 Corr.
8x1 Corr.
8x1 Corr.
8x1 Corr.
8x1 Corr.
8x1 Corr.
refant
refant
refant
refant
refant
refant
3x1 Corr.
3x1 Corr.
2x1 Corr.
refant
refant
Use “spare” CX4 to feed a cluster
Signal Path & Lessons Learned
• Bulk Delay: 1024-sample buffer memory
• Fine Delay: 6-tap Real FIR Filter (12-bit coefficients)
• Fringe Rotator: Programmable phase angle and rate
Beam
Sum
mer
Output
Spectra
Rb13/ June 2008A
TA Leaf N
odefirm
ware/ O
BM
Beam
Summ
er
Output
Spectra
Wv13/ June 2008
ATA Branch Node
firmw
are/ OBM
Output
Spectra
Nx1 Correlator –Missing sqrt(N)
Fringe Rotator – Only dx/dt, no satellites
FIR – 6 taps GLS, need better for best accuracy
The Future: Moore’s Law Helps• Dropping in a FFT (1970)
– 512 Channels x 4 streams– 19 KHz (a few Mbps)
• Today, slightly easier– Xilinx or CASPER blocks– Beamformer 128 channel, 8 stream
complex, 104 MHz in a little less space• Hardware is still improving: ROACH
– Smaller, less power, more gates, faster clock than the BEE2
– Less I/O, though – could this be a problem? Depends on architecture
• Designers are still improving:– Learn to use hardware efficiently– Re-learn old tricks, develop new ones
Karto: It’s Still
Faster than
Awk!
Conclusions
• Time vs. Frequency Domain depends on– Number of beams– Availability of free F-transform– Relative cost of LUT versus Multiplies
• Take pains to avoid instrumental errors– 1 deg (arc) on 300m is ±9 turns in 1 GHz BW (3 deg per ch in 1024ch)– Few deg, few % errors can wreck nulls (Harp, ATA Memo 51)– Errors on 1%-5% level can be “devastating” (Wright, SKA Memo 103)
• Time-varying terms require LUT or Taylor expansion– E.g., Fringe rate might require three derivative terms for some types of
sourcee• Need more work to bring real-time adaptive nulls into the instrument
– Real-time feed back from correlator• Foxtrot: Software Beamforming/Correlating at the ATA (?)
Done!