Rfi Subtraction with a Reference Horn: Application to Pulsars and Vlbi

Cross correlation of an RFI reference signal with the corrupted radio astronomy data channels permits construction of the adaptive correction that is suitable for radio spectroscopy where time-averages are recorded. The reference signal is constructed from the cross power spectrum of the signals from the two polarizations of a reference horn pointed at the source of the RFI signal. The method is immune to the effects of multi-path scattering in both the astronomy and reference signal channels. Here, we demonstrate the generality of our result by applying it to the correction of time sequence data, such as pulsar timing observations. INTRODUCTION We have been experimenting with an intuitive but powerful RFI cancellation technique that is especially well suited for radio astronomical spectroscopy, where time-averages are recorded. The method requires computation of cross power spectra between the RFI contaminated astronomical signals and high signal-to-noise ratio RFI “reference signals” obtained from a separate receiving system that senses the RFI but not the astronomical signal. The correction terms that remove the unwanted RFI are computed from closure relations obeyed by the RFI signal. The test applications reported here derived the reference signal from a separate horn antenna aimed at the RFI. For the present new experiments, we used the publicly available data sets [1] from the Parkes Telescope, recorded by digitally sampling baseband signals from two polarizations for both the reference horn and astronomy feeds. We performed the cross correlations in software off-line. However, the method could use correlation spectrometers of the sort already in use at radio observatories to perform much of the computational task in real time. The purpose of this paper is to demonstrate that the method can be used to build an adaptive filter for correcting time series data. We further comment on how the method could be implemented in VLBI applications. OVERVIEW OF THE METHOD During these experiments, both orthogonal linear polarizations A and B from the Parkes Telescope were recorded, along with two orthogonal linear polarizations, labeled 1 and 2, obtained from the reference horn aimed at the source of the rfi. The full mathematical development [2] shows how the rfi contamination |gAI| <|I|> in the power spectrum PA(f) measured for the ‘A’ polarization, PA(f) = |gA| <|A|> + |gAI| <|I|> + <| NA | >, (1) can be estimated and subtracted. Here, gA(f) and gAI(f) are the complex, frequency-dependent voltage gains describing the coupling of the astronomical signal A and the interfering signal I to the measured power spectrum, and NA gives the strength of the noise in the A polarization data channel. The symbols <...> are used to signify averages over an integration time that could be as long as 1 s in the tests described here. When similar expressions are adopted for the power spectra and cross power spectra between all pairs of the data channels, an estimate of the contamination term can be written as |gAI| <|I|> = <|I|> (gAI g1*)(gAI* g2)/(g1*g2) ≈ CA1 CA2*/C12* (2) where * is used to indicate complex conjugation and Cij (f) represents the complex cross power spectrum between the i and j data channels. The term C12 represents the cross power spectrum of the two polarizations sensed by the reference horn, for example. The approximate relation at the right side of (2) applies provided the rfi signals are the only strongly correlated signals in the cross power spectrum; this is expected to be the case, since none of the noise N1, N2, NA or the astronomical signal should be present in all three channels. In fact, a simple way to implement (2) that copes with low INR (interference to noise ratio) ranges in the spectrum is to compute the correction as |gAI| <|I|> ≈ CA1 CA2* C12 /(ψ(f)+ C12 C12*) (3) where ψ(f) represents the noise level in this data channel. Here we approximate that ψ0 ≈ ψ(f) ≈ constant across the band. Fig. 1. The scan-average power spectra for scan SRT00502 (approximately 25 seconds of data). A passband calibration has been applied to compensate for the gain dependence of the 5 MHz band limiting filters. The upper spectra are the two polarizations from the Parkes Telescope receivers -both before and after cancellation. The lower spectra are orthogonal polarizations recorded through the reference horn. Fig.1 shows the result of applying this technique to Parkes observations centered at 1499 MHz [1]. For display purposes, a 5 MHz band is split into 512 spectral channels. The spectra in the figure were corrected on time scales of 0.1 s and then averaged to obtain the result shown in Fig.1. For integrations longer than 1 s, the complex gain factors apparently begin to vary, as the telescope sidelobes falling on the rfi source change, and the subtraction loses precision. APPLICATION TO PULSARS Once the complex gains that couple the rfi signal to the astronomical data channel have been measured by the cross correlation technique, then those gains can be applied for the length of time that they are stable to correct the time series data. In [2], a procedure is outlined for constructing the appropriate filter to apply to the reference horn signals that will produce an estimate of the rfi contribution to the Parkes data streams. In fact, these filters could be Fourier transformed to obtain a set of coefficients that could be used in FIR time-domain filters. In the implementation used here, the frequency domain filters were computed on a 100 msec time-scale, and these filters were applied to the Fourier transforms of short 8192 sample segments of the time-series. For simplicity, the filtered data was inverse transformed to form a clean time-series that was then folded on the pulsar period in order to coherently integrate the pulse profile. (A more practical implementation could be made that avoided much of the computational overhead.)