Overview of Technical Approaches Robust receivers Edit / excise / blank - frequency / time domain - might lose/corrupt astronomy signal Cancel / subtract / null - identify / characterize / subtract - frequency / time domain - treat RFI as carefully as astronomy signals - goal = keep astronomy (known distortions)
Overview of Technical Approaches Edit / excise / blank highly non-linear Cancel / subtract / null doing THIS may exclude this
Outline: multi-path scattering ( time-freq equivalence) application of correlation coefficient closure relations (and adaptive filter equivalent) eigen decomposition of correlation matrix ( equiv to array calibration / nulling )
R F I
Antenna I I(t) = Σ h α (t) * i o (t τ α ) Impulse Response h(t) for each path α Signal radiated by transmitter with DELAY τ α Convolution operator
Antenna I I(t) = Σ h α (t) * i o (t τ α ) α I(f) = (Σ G α (f) e- i2π τ αf ) I o (f) Time Domain Frequency Domain = G(f) I o (f)
Instrumental constraints Time Domain: must encompass maximum delay T delay Frequency Domain: need frequency resolution f f < 1 / T delay If T delay = D/c = 1 km/c, f < 300 khz <<?
multipath summary not fatal for cancellation in frequency domain nor in time domain, with suitable adaptive filters (?? strong airport radars -- Arecibo??)
Canceller using Closure Information S R x g A S + g 1 I Σ g A S I - g 1 I Cross Correlation Signal Processing X g 1 g 3 g 3 I I
Cross correlation: single polarization feed with 2 reference signals 1. Pol A G 1 G 4 * I o 2 3. Ref 1 G 3 G 4 * I o 2 4. Ref 2?? G 1 G 3 = G 1 G 4 * I o 2 G 3 G 4 * I 2 o
Cross correlation: single polarization feed with 2 reference signals 1. Pol A G 1 G 4 * I o 2 = C 14 3. Ref 1 4. Ref 2 G 3 G 4 * I o 2 = C 34 G G 1 G 4 * I 2 1 o = G 3 G 3 G 4 * I 2 o = C 14 (f) C 34 (f)
Practical Application: Auto-Correlation Spectrometer S A/C spectrometer Power Spectrum P(f) g 2 A S 2 + g 2 1 I 2 I g 1 2 I 2 = g 1 g 3 * I 2 g 4 g 1 * I 2 g 4 g 3 * I 2 = C 13 (f) C 14 *(f) C 34 *(f) Gain closure relation for an unresolved source
Practical Application: Auto-Correlation Spectrometer S A/C spectrometer Power Spectrum P(f) g 2 A S 2 + g 2 1 I 2 I g 1 2 I 2 = Advantage: g 1 g 3 * I 2 g 4 g 1 * I 2 g 4 g 3 * I 2 = C 13 (f) C 14 *(f) C 34 *(f) Cross Correlation Spectra NO BIAS due to NOISE power
Cross correlation: single polarization feed with 2 reference signals 1. Pol A G 1 G 3 * I o 2 = C 13 G 1 G 4 * I o 2 = C 14 3. Ref 1 4. Ref 2 G 3 G 4 * I o 2 = C 34 A/C Spectrum Contamination g 1 2 I 2 = C 13 (f) C 14 *(f) C 34 *(f)
Cross correlation: dual polarization feed with 2 reference signals 1. Pol A 2. Pol B G 1 G 3 * I o 2 = C 13 G 1 G 4 * I o 2 = C 14 3. Ref 1 G 2 G 3 * I o 2 G 2 G 4 * I o 2 = C 23 = C 24 G 3 G 4 * I o 2 = C 34 4. Ref 2
650 720 MHz Hydrogen @ Z~1 Real observation w. RFI Cancellation Little Ord Staveley-Smith Reynolds Catlin Dawson
courtesy of M. Smith 37 40 43 46 600 700 800 MHz
Line of sight to feed over edge of dish
known broadcast towers Mt Canobolas Mt Ulandra
Yagi
21 db gain
CPSR2 Swinburne University 64 MHz BW 8K channels for Four Feeds real time spectroscopy + cancellation
Frequency [channels] Ref 1 Relative Signal Strength [db] Ref 2 Pks A Pks B
Frequency [channels] Ref 1 Relative Signal Strength [db] Ref 2 Pks A Pks B
Time outside the dig-tv band Freq 10 minutes, 8 MHz
Time dig-tv band Freq 10 minutes, 8 MHz
Time Cancelled Freq 10 minutes, 8 MHz birdies not in Refs => not cancelled => astro not damaged noise level is reduced to system noise no added rfi power
Spectral Domain Contamination: the VOLTAGE spectrum Estimate { g 1 (f) I(f) } = X 13 (f) g 3 (f) I(f) stable on 0.1 second time scale C 14 (f) C 34 (f) Update every 1 second f ch Time Domain Contamination: Ref Horn Estimate { g 1 I(t) } = x 13 (t) * g 3 I(t) Effectively FIR filter coefficients
FIR Coefficients + Delay 0.1µs steps Time 0.1 sec steps
Pol A Pol B using Ref. 3 using Ref. 4
Dynamic Pulsar Spectra Pol. A Pol. B Phase Average Spectra Frequency
Dynamic Pulsar Spectra Cancellation Applied Pol. A Pol. B Phase Average Spectra Frequency
Summary: Gain closure relation and its time-domain equivalent subtract voltages I(t) => removes rfi noise phase coherency of Corr. Fncts => same effect in freq. domain
Arrays and Eigen Decomposition: Australia Telescope Compact Array *Bell, Kesteven, Ekers, Sault, et al 2001 *Jonathon Kocz (ANU)
Bell s Bucket Rx (with and without reference antennas)
Steve Ellingson: 17 Dec 1999 A Variation on the Ekers-Sault Correlation Idea Also, Leshem, van der Veen, Boonstra Crosscorrelation matrix Eigen decomposition Partition
Refs
Refs P [db] channels
Refs Coupling of Refs to Astro 512 spectral channels => 512 12x12 correlation matrices
need to solve 512 correlation matrices for each channel: R = U Λ U H r 1,1 r 1,2 r 1,12 r 2,1 r 2,2 g 1,1 g 1,2 g 1,12 g 2,1 g 2,2 P 1 0 0 0 P 2 g* 11 g* 21 g* 12,1 g* 12 g 22 *. =... r 12,1 r 12,12 g 12,1 g 12,12 0 P 12 g* 1,12 g* 12,12 Complex Voltage Gains 12 Powers g 1,1 g 1,2 g 1,12 = vector with 12 coefficients coupling the 12 P i to Antenna 1A
consider Special Case: Calibration of an Array point at bright calibration source S ν one source dominates powers r 1,1 r 1,2 r 1,12 r 2,1 r 2,2. r 12,1 r 12,12 = g 1,1 g 2,1. g 12,1 S ν 0 0 0 0 0. 0 0 0 g* 11 g* 21 g* 12,1 The vector g 1,1 g 2,1. has the complex voltage gains g 12,1
Do 512 decompositions get spectra for 12 eigenvalues Kocz 2004 Power [ db ] Frequency channel
throwing away P 1 the Autocorrelation Spectra Power [ db ] before after
Nulling setting P1 = 0 equivalent to placing a null on the interferer! but no directional information has been included The math solution provides: * strength of interferer * gain coefficients
Where is directional information? Phase spectra for g 1i Phase [radians]
Summary: multi-path scattering ( time-freq equivalence) application of correlation coefficient closure relations (and FIR filter equivalent) eigen decomposition of correlation matrix ( compared to array calibration / nulling )