Subspace Projection Methods for RFI Mitigation in Radio Astronomy Brian Jeffs July 25, 2002

Subspace Projection Methods for RFI Mitigation in Radio Astronomy

Brian Jeffs

July 25, 2002

References

1. J. Raza, A-J Boonstra and A-J van der Veen, “Spatial Filtering of RF Interference in Radio Astronomy,” IEEE SP Letters, vol. 9, no. 2, Feb. 2002.

2. A. Leshem, A-J van der Veen, “Radio-Astronomical Imaging in the Presence of Strong Radio Interference,” IEEE Trans. On Information Theory, vol. 46, no. 5, Aug. 2000.

Correlation Across Array Elements

AuxiliaryAntenna

GLONASSsatellite

Primary Array

][][1ˆ

1

0nn

NH

N

nxxR

The Array Covariance Matrix is the Basis for Synthesis Imaging

Elements of R are image frequency domain samples.

Earth rotation moves baselines for new R, more frequency samples.

Interference effects must be removed from R directly, beamforming to place nulls is not possible since correlations from all array pairs are needed.

(b) VLA frequency samples with Earth Rotation(d) VLA frequency sample snapshot

Subspace Projection Approach

Interference component of R spans a subspace of rank P = number of interferers.

ap is array response to pth interferer with power .

Find a projection operator orthogonal to Ri

].,,diag[ ],,[,

,ˆ

2211 PP

Hi

is

aaAAAR

RRRR

sss

i

RRRPRPR

0RP

)(ˆˆ

,

Use this in imaging. No interferer left!!

2p

Methods of computing P

If array is calibrated and interference direction known:

If ISNR >> 0 dB at feeds and direction unknown:

If interference moves, use short-term integration for

HH AAAAIP 1)(

Hss

sisi

UU

UUUU

P

R ,]|[]|[ˆ

, and ˆkk PR

HN

kkks kNPRPR

1

1ˆ

Problems

Interference moves durning integration. Solution: use short-term integartions, short term projections

Projection biases signal subspace, Can not invert because P is singular.

Solution: use smoothing over short-term integrations to build rank

Now

.}ˆ{ RPRPR ssE

.1ˆ

1

1

1

1

1,

PPRPPR

PP

N

kKkks

N

kk

N

N

.}ˆ{ RRR ssE

N

nkkks

1

ˆˆ PRPR

Problems (cont.)

For high gain antennas, usually ISNR << 0 dB at feed. Poor interference subspace estimate leads to poor

interference rejection from projection matrix P.

Sometimes the signal is identified as the interferer, and is projected out.

Solution to Bad Subspace Estimates:Use Auxiliary Antennas

Array consists of high gain “primaries” and low gain “auxiliaries,” perhaps steered to interference,

Auxiliary antennas see high ISNR to guide subspace estimation for the primary array.

Four different approaches for computing P have been evaluated.

.,][

][][

aaap

papp

a

p

n

nn

RR

RRR

x

xx

1. Conventional Full Array Subspace Projection

Use the full array, including auxiliaries, with no distinction as to antenna type.

Compute a truncated projection matrix:

Significant performance improvement over using primaries only. Handles weaker interferers.

HSSFSSFs

appN

HssNSSF

sisi

NNN

UU

UUUU

p

p

PRPR

0II

IP

R

ˆˆ

)(:,

,

,]|[]|[ˆ

2. Array Multiple Sidelobe Canceller (MSC)

Form an MSC adaptive array processor separately on each primary antenna.

This is an “oldie but a goodie.”

Low probability of signal capturing the interference subspace.

HMSCMSCs

aapaNMSC p

PRPR

RRIP

ˆˆ

ˆˆ, 1

3. Auxiliary Assisted Subspace Projection

Use only the primaries in final estimate:

Projection uses only cross correlations between primaries and auxiliaries to strongly emphasize the interferer.

Best overall performance.

SSPAppSSPAs PRPR ˆˆ

HssSSPA

sisiappa

UU

UUUU

P

RR ,]|[]|[ˆˆ

Examples

VLA, 1612 MHz with one 3m aux. dish, 200 Jy source with one GLONASS interferer.

Examples (cont.)

VLA, 1612 MHz with two 3m aux. dishes, 20 Jy source with two GLONASS interferers.

Examples (cont.)

VLA, 1612 MHz with one 0 dB omni aux., 200 Jy source with one GLONASS interferer.