RFI Subtraction with a reference horn…

F. Briggs & M. Kesteven

• illustrations from Parkes Telescope… (Jon Bell et al.)

• origins in Int-Mit group at CSIRO – ATNF

Rx

gASS

I

+ g1I

I

g3I

- g1I

SignalProcessing

gAS

g1g3

XCross

Correlation

R F I

Reference Antenna

I

I(t) = h(t) * io(t

Impulse Response h(t) for each path

Convolution operator

Signal radiated by transmitter

… with DELAY

= G(f) Io(f)

I(f) = (G(f) e-i2f ) Io(f)

Reference Antenna

I

TimeDomain

FrequencyDomain

I(t) = h(t) * io(t

Cross correlation: single polarization feed with 2 reference signals

1. Pol A

3. Ref 1

4. Ref 2

…G1 G4* | Io2|

G3 G4* | Io2|

?? G1G3

= G1 G4* | Io2|

G3 G4* | Io2|

G1G3

Cross correlation: single polarization feed with 2 reference signals

1. Pol A

3. Ref 1

4. Ref 2

…G1 G4* | Io2|

G3 G4* | Io2|

G1G3

= G1 G4* | Io2|

G3 G4* | Io2|

= C14 (f)

C34 (f)

= C14

= C34

Practical Application: Auto-Correlation Spectrometer

|gA2||S2|S

I

A/Cspectrometer

+ |g12| |I2|

|g12| |I2| =

Power Spectrum P(f)

g1g3* |I2| g4g1* |I2|

g4g3* |I2|=

C13(f) C14*(f)

C34*(f)

Advantage:

Cross Correlation Spectra NO BIAS due to NOISE power

Cross correlation: single polarization feed with 2 reference signals

1. Pol A

3. Ref 1

4. Ref 2

G1 G3* | Io2|

G1 G4* | Io2|

G3 G4* | Io2|

= C14

= C34

|g12| |I2| =

C13(f) C14*(f)

C34*(f)

= C13

A/C SpectrumContamination

Cross correlation: dual polarization feed with 2 reference signals

1. Pol A

2. Pol B

3. Ref 1

4. Ref 2

G1 G3* | Io2|

G1 G4* | Io2|

G2 G3* | Io2|

G2 G4* | Io2|

G3 G4* | Io2|

= C13

= C34

= C14

= C23

= C24

Duration 56 s with 0.1 s

steps

Bandwidth 5 MHz

RawDynamic Spectra:

Time

Pol A Pol Bfrequency

Pol A Pol BfrequencyCanceledDynamic Spectra:

Time

RFI not in reference horn

is NOTNOT subtracted !

Non-Toxic Non-Toxic to celestial signals

Spectral Domain Contamination: the VOLTAGEVOLTAGE spectrum

Estimate { g1(f) I(f) } = X13(f) g3(f) I(f)

C14(f)

C34(f)

stable on 0.1 second time scale

Update every second 1 f

Time Domain Contamination:

Estimate { gI(t) } = x(t) * gI(t

Ref Horn

Effectively… FIR filterFIR filter coefficients

Tim

e 0

.1 s

ec

step

s

FIR Coefficients + Delay 0.1s steps

Pol A Pol B

using Ref. “3”

using Ref. “4”

Phase

Dynamic Pulsar SpectraPol. A Pol. B

AverageSpectra

Frequency

Phase

Dynamic Pulsar Spectra

Pol. A Pol. B

Frequency

AverageSpectra

Cancellation Applied

Pulse Phase

SNR

RAW

Self-Norm

1 Cancelled

2 Cancelled

INTEGRATEDPULSE

PROFILES

uncorrected

cancelled

self- normalized

Phase

Dynamic Pulsar Spectra

Pol. A Pol. B

AverageSpectra

Frequency

Self-Normalized by Total Power Spectra

VLBI

VLBI

Westerbork

Jodrell Bank

Power Spectrum at840 MHz at Jodrell Bank

nearby TV station

Cross Correlation SpectrumJodrell Bank x Westerbork

HI absorption z = 0.68

1504+377

VLBI recorder

VLBI recorder

Celestial SignalRFI

off-linecorrelation

+ post- correlation processing ….

Conclusions

• complications of multi-path are contained in complex gains G(f)

• adaptive filtering with correlation functions preserves phase information….

… equivalent to subtraction of the voltage waveform