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!