Radio-frequency interference excision

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Figure 2.2: A schematic representation of a standard pulsar searching pipeline. Solid lines show the control flow for processing of a single observation, while dashed lines show optional steps that can be performed after many observations have been processed.

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1250 1300 1350 1400 1450 1500

Observing frequency MHz

A rb it ra ry po w er

Figure 2.3: The bandpass of the 21-cm Effelsberg multi-beam receiver’s central beam.

Red areas show ‘bad’ observing frequencies which have been flagged by automatic spike finding algorithms. It should be noted that such automatic algorithms are not infallible, ocasionally flagging a channel that is unaffected by RFI. This can clearly be seen at

∼1465 MHz, where the local bandpass shape has produced a spurious RFI detection.

Therefore, it is imperative that the first stage of any pulsar search should attempt to suppress or remove these unwanted signals from the data.

Here we review several techniques used to mitigate the effects of RFI. Generalised ver-sions of these techniques are described in (Fridman and Baan, 2001). We will only consider cases applicable to pulsar search observations.

2.2.2.1 Frequency domain techniques

By integrating all frequency channels across the length of the observation, a bandpass is obtained showing the distribution of power throughout the spectral channels. The data in channels identified as containing excess power can be replaced with zeros to suppress the effects of persistent narrowband RFI. The selection of channels to be replaced with zeros can be done either dynamically, using algorithms which process the bandpass to identify significant power levels, or statically, using a list of observing frequencies known to be contaminated by RFI. Figure 2.3 shows an example bandpass of the 21-cm multi-beam receiver at Effelsberg and its RFI affected channels.

2.2.2.2 Time domain techniques

By integrating all time samples across the observing bandwidth, a time series is obtained at a DM of zero, the so-calledzero-DM time series. Performing a statistical analysis on

Pulsar searching 36 this time series allows for the identification of signals generated by strong impulsive RFI. The data in each channel of a sample identified as being contaminated by RFI can then be replaced by Gaussian noise indistinguishable from the data in the adjacent samples, or clipped such that its power is greatly reduced.

A variant of the above method, known aszero-DM filtering, has been used to good effect in re-processing the PMPS (Eatough et al., 2009). In this technique, each time sample in the original filterbank is normalised by subtraction of its average across all frequency channels. While this method has been shown to be an excellent method of RFI removal in single-bit data, trials using multi-bit data have been met with limited success.

2.2.2.3 Fourier domain techniques

A powerful method of mitigating against period RFI in an observation, is to examine it in the Fourier domain. Using prior knowledge of the local RFI environment, it is possible to remove power from Fourier bins likely to be contaminated by RFI. To do this, the discrete Fourier transform (DFT, see Section 2.2.4.2) of the zero-DM time series is taken. Fourier frequencies which have been identified as containing periodic RFI can then be zeroed or replaced with noise such that they do not influence candidate selection or acceleration searching procedures at later stages of data processing.

2.2.2.4 Multi-beam techniques

Through the use of multi-beam (or multi-pixel) receivers, the above techniques may be applied dynamically, significantly enhancing their ability to nullify the effects of man-made interference.

Unlike the signal from a pulsar, RFI is not usually detected in only a single beam of a pointing. Instead RFI tends to show in some or all beams simultaneously. By examining the spatial distribution and temporal coherence of an incident signal, it is possible to determine if a signal is RFI, down to much lower thresholds than possible via other methods.

By first understanding the noise statistics of each frequency channel in the data, the detection significance of temporally coherent data points may be compared and thresh-olded. For example, in a seven-beam receiver the probability of a single data point having a significance of 3-σ is 0.26%, assuming the data are purely Gaussian noise. However, considering that all beams are observing simultaneously, the same 3-σ data point cannot be considered independent of data points taken by other beams at the same time. The

Pulsar searching 37 probability of having a 3-σ or greater detection in all beams is therefore 10⁻¹⁸%. Miti-gating against impulsive RFI therefore becomes a case of selecting a threshold number of beams in which a signal must be detected above a given significance in a single time bin⁶. Signals which satisfy these criteria may be replaced by Gaussian noise based on the statistics of the surrounding data.

A similar methodology may be applied to mitigate against multi-beam RFI in the Fourier domain. In this case, the data from each beam may be examined in the Fourier domain, with Fourier bins which have power above some threshold in multiple beams, being removed. For a discussion on thresholds for signals in the Fourier and time domain see Sections 2.2.4.6 and 2.2.5.2.

As part of this work, we have developed a system to perform multi-beam RFI excision using all of the methods outlined above. In particular, this is the first system to im-plement multi-beam RFI filtering using the full time and frequency resolution of the incoming data. This system has been used to good effect in the processing of data from the High Time Resolution Universe North pulsar survey (see Chapter 4).

Other, arguably more elegant, forms of multi-beam RFI excision exist, such as the method proposed by Kocz et al. (2012), which considers the covariance matrix for each time sample of the observation. Unfortunately, this method, however powerful, is cur-rently limited by the amount of computation it requires.