### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Description of the Calculations
- 3. Results
- 4. Discussion
- 5. Conclusions
- Appendix A
- Acknowledgments
- References

[1] The Allen Telescope Array (ATA) is a multiuser instrument and will perform simultaneous radio astronomy and radio search for extraterrestrial intelligence (SETI) observations. It is a multibeam instrument, with 16 independently steerable dual-polarization beams at four different tunings. Here we describe a new method for identifying radio frequency interference (RFI) that leverages the unique attributes of the ATA. Given four beams at one tuning, it is possible to distinguish RFI from true ETI signals by pointing the beams in different directions. Any signal that appears in more than one beam can be identified as RFI and ignored. We discuss the effectiveness of this approach using realistic simulations of the fully populated 350 element configuration of the ATA as well as the interim 32 element configuration. Over a 5 min integration period, we find RFI rejection ratios exceeding 50 dB over most of the sky.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Description of the Calculations
- 3. Results
- 4. Discussion
- 5. Conclusions
- Appendix A
- Acknowledgments
- References

[2] Radio frequency interference (RFI) is a growing problem for all radio astronomy applications, but is especially problematic in the search for extraterrestrial intelligence (SETI) [*Ekers et al.*, 2002; *Davis et al.*, 2004]. A key element of any RFI mitigation strategy is to discriminate RFI from naturally occurring signals, or in the case SETI, from artificial signals originating outside our solar system. Once the RFI is identified, corrective action can be taken. One approach keeps an ongoing database of RFI signals as they are identified, and abandons frequency ranges where RFI is recently or persistently observed. This approach is currently implemented in the signal processing system employed for the SETI Institute's Project Phoenix [*Ekers et al.*, 2002; P. R. Backus et al., manuscript in preparation, 2005].

[3] In this paper we examine a new method of RFI discrimination that is especially appropriate for SETI observations and based on correlating the signals arriving from multiple single-pixel beams of an interferometer telescope. Two or more beams are pointed in different directions on the sky. If a signal appears strongly in more than one beam it must be RFI since identical signals could never appear from two different stars. This is just a generalization of an approach customarily used in SETI observations with single dish telescopes. When a candidate signal is found at one sky direction, one points the dish away from the target to see if the signal disappears (on/off test). To complete the analogy with the present approach, search efficiency could be improved by choosing a second target star for the “off” position. Because here we work with an interferometer, the on and off measurements are made simultaneously.

[4] To quantify the effectiveness of multibeam RFI identification, we must examine the beam sidelobe pattern through which the RFI enters the telescope. As a concrete example we consider the sidelobe pattern of synthetic beams at the Allen Telescope Array (ATA). The Allen Telescope Array (ATA) is a radio interferometer under construction at the Hat Creek Radio Observatory in Northern California. Each ATA element is a 20' diameter offset Gregorian telescope, and is operable over 0.5–11.2 GHz. The ATA will be constructed in three stages comprising 32, 206, and 350 elements at each stage. We simulate the synthetic beam patterns of the 350 element ATA (ATA-350) and the 32 element ATA (ATA-32) and examine the sidelobes through which RFI may enter the synthetic beam. From the statistical distribution of sidelobe levels, we estimate the probability that an RFI signal will enter strongly into one beam while being weaker or absent in all others. This is the probability of a “false positive,” or that a bit of RFI masquerades as an ETI signal. We find that multibeam discrimination is an effective way to identify RFI. Once identified, RFI can be eliminated from subsequent follow-up protocols thereby increasing search speed.

### 2. Description of the Calculations

- Top of page
- Abstract
- 1. Introduction
- 2. Description of the Calculations
- 3. Results
- 4. Discussion
- 5. Conclusions
- Appendix A
- Acknowledgments
- References

[5] We simulate observations where multiple synthetic beams are formed within the primary beam of a single antenna. The RFI is assumed to enter in a sidelobe of the primary beam because we avoid pointing at known RFI and because the primary beam (FWHM of 3.5–0.35° between 1–10 GHz) represents only a small fraction of the sky. Although the primary sidelobe pattern varies from high to low on a scale of half the primary beam width, we shall assume that this multiplicative factor does not change the statistical behavior of the synthetic beam sidelobe level (i.e., the sidelobe statistics are the same as for an isotropic antenna). This seems reasonable since all synthetic beams are within one primary beam width of one another.

[7] In the calculations that follow, beam patterns are calculated on a square grid with ∼4 million points over an angular range that does not include the beam maximum. A histogram of sidelobe power is accumulated, which when normalized to the number of grid points, gives an estimate of the probability density *P*(*s*) of finding a sidelobe with level *s*. Such a histogram is displayed in Figure 2 which shows the levels in a “snapshot” observation.

[8] Using these data we calculate the probability that RFI will appear as a “false positive” ETI signal by using the following trick. We place the synthetic beam maximum on the RFI and the observation beams in the far out sidelobe region. This is justified by the inversion symmetry of the beam pattern: for a beam placed on a source, the sidelobe power for the RFI is the same as the sidelobe power on the source when the beam is placed on the RFI. We then compare the sidelobe levels at the positions of the different beams and set a rejection threshold of *N* dB for a false positive event. If one beam has a sidelobe level *N* dB higher than all the others, this is a false positive. For *M* observation beams, the probability of false positive *P*_{M} (a.k.a. rejection ratio) is calculated from:

where *n* = 10^{−N/10}. The term in curly brackets is the probability that a given beam will have a level less than or equal to (*s*/*n*). The prefactor *M* appears because we don't care in which beam displays the strong RFI. This equation is derived in Appendix A.

[9] Figure 3 shows a plot of *P*_{4}(*N*) calculated from the data in Figure 2. In most of our calculations we use *M* = 4 because this is the natural number of independent beams produced at the ATA for a given frequency tuning.

[10] There is one more subtlety to consider. In the version of the SETI search system belonging to the SETI Institute, a single point on the sky is observed for ∼5 min before moving on to the next point or next frequency. During this time, the observed signal is Fourier transformed to obtain the frequency power spectrum, which is then examined for characteristic ETI signals. It is not possible to perform a direct Fourier transform (FT) of all 5 min of data. Instead, 1-s windows are FT'd and the resulting windows are integrated incoherently over the observation period (P. R. Backus et al., manuscript in preparation, 2005). This feature of the analysis greatly improves the rejection ratio since, as the source moves across the sky, the RFI (assumed fixed) moves through the beam sidelobes. Averaging over many sidelobes both narrows and heightens the distribution of *P*(*s*). The degree of averaging depends on the source position and RFI position.

[11] For simplicity, we put the RFI on the ground due east of the array. The antenna primary beam is placed at various declinations and the array is assumed to be at latitude 41° (where the ATA is located). The probability distribution is calculated by generating 300 beam patterns simulating 1 s integrations over a 5 min observation period. For each source position, the sidelobe level power is averaged over all patterns. After averaging, the probability density is calculated as before.

[12] Figure 4 shows *P*(*s*) for a 5 min track at declination 20° near transit. The sidelobe distribution is substantially narrowed as compared with Figure 2. The peak of the distribution is also about 10 times higher, but this rise is offset by the choice of a smaller bin size in Figure 4, as compared with Figure 2.

[13] Such averaging leads to a greatly improved rejection ratio as shown by the diamonds in Figure 5 (compare Figure 3). We find that the chances are less than 1 in 10^{5} that the RFI will appear only 3 dB higher in one beam than in all the others.

### 3. Results

- Top of page
- Abstract
- 1. Introduction
- 2. Description of the Calculations
- 3. Results
- 4. Discussion
- 5. Conclusions
- Appendix A
- Acknowledgments
- References

[14] We begin by examining the sensitivity of the rejection ratio to the number of beams used. Figure 5 plots the rejection ratio for two, three, and four beams as determined from the data in Figure 4. Using more beams substantially improves the rejection ratio. As a rule of thumb, we find that the rejection ratio for 4 beams is approximately the square of the rejection ratio for 2 beams, for any rejection threshold. In all subsequent calculations we shall assume 4 beams are used.

[15] Next we examine the declination dependence of the rejection ratio (Figure 6). We assume an observation frequency of 1420 MHz and consider two threshold levels, *N* = 1 dB and 3 dB. We also consider two hour angles, 0° (transit) and 45°. These results are easy to understand once you realize that the sidelobe velocity is proportional to the cosine of the declination and becomes stationary at the celestial pole (90° declination). Thus at high declinations the rejection ratio worsens while it is best near declination 0°. We find that at 1420 MHz and over a wide range of declination angles, a 3 dB RFI threshold will be very effective at discriminating RFI (rejection ratio ∼ 10^{−5}).

[16] Figure 7 examines the frequency dependence of the rejection ratio. The sidelobe angular width varies inversely with the frequency. Thus at higher frequencies we average over a larger number of sidelobe levels, which improves the rejection ratio. We find that at the highest frequencies, even a 1 dB threshold level is sufficient to discriminate a large proportion of RFI.

[17] We conclude this section by considering the ATA-32 configuration. Figure 8 shows the declination dependence of the rejection ratio at 1420 MHz. Because the spatial extent of ATA-32 is smaller than ATA-350 and because there are fewer antennas, the sidelobe pattern for ATA-32 is broader and less complex. Both of these factors reduce the effectiveness of pattern averaging. Even so, with a 3 dB rejection threshold and over most of the sky, the chances of false positive are typically 1 in 1000.