BURSTT: Bustling Universe Radio Survey Telescope in Taiwan

To achieve a complete census of FRBs, monitoring observations of the nearby universe with a very wide FoV are required (Bochenek et al. 2020a; Connor et al. 2021).

For any array of antennas, the FoV is inversely proportional to the effective collecting area of the array, so the wide field of BURSTT means that it will have a smaller collecting area than many previous telescopes. In estimating the detection rate (see below), the area and FOV factors partially compensate, and the resulting detection rate is not strongly dependent on the choice of FoV. However, for the wide-field (low collecting area) telescope, the detected sources are on average closer.

The redshift of the CHIME/FRB sample is in the range of 0.3–0.5 (Rafiei-Ravandi et al. 2021). The CHIME/FRB team is currently adding outriggers to CHIME, which will localize many FRB events in this redshift range (Cassanelli et al. 2022; Mena-Parra et al. 2022). For many of these, optical follow-up observations will be needed to get the redshift of the host galaxy. In contrast, we anticipate that the median redshift of the BURSTT FRB sample will be in the range of 0.03–0.05. This means that many of the BURSTT host galaxies will be present in existing optical redshift survey catalogs (Cutri et al. 2003; Karachentsev et al. 2013; Bilicki et al. 2014, 2016; Dey et al. 2019), which will allow an immediate redshift determination to be made without the need for follow-up observations. This will allow for a rapid improvement in the measured FRB luminosity function (Shin et al. 2022).

To estimate the system equivalent flux density (SEFD) sensitivity of the BURSTT, we assume a conservative system temperature (Tsys) of ∼150 K, which is achievable with commercially available LNAs, and an effective area for 256 antennas of ∼100 m² at 600 MHz. The corresponding SEFD is ∼5000 Jy. For an FRB with a duration of 1 ms across 400 MHz bandwidth with a fluence of 100 Jy ms, the corresponding signal-to-noise ratio (S/N) is ∼12. In the future, we hope to achieve Tsys of 50 K, which will improve the sensitivity.

To estimate the event rate, we assume a Euclidean distribution to scale from a previously measured reference rate,

$$\begin{eqnarray}&&N(S)={N}_{0}{\left(\displaystyle \frac{S}{{S}_{0}}\right)}^{-1.5},\end{eqnarray} \tag{ 1 }$$

where N(S) is the event rate above fluence S and N₀ is the reference rate above reference fluence S₀. We use the reference event rate reported by CHIME (CHIME/FRB Collaboration et al. 2021), 300 FRBs per day per sky, with S₀ = 5 Jy ms at 600 MHz, and two additional constraints: scattering time at 600 MHz below 10 ms and DM above 100 pc cm⁻³. The FoV of BURSTT is ∼10⁴ deg² or 0.24 sky. Thus, we estimate that BURSTT-256 can detect ∼100 bright FRBs per year with the threshold of fluence higher than 100 Jy ms at 600 MHz. Note that the CHIME FRB rate is at the low end of published rate estimates, which makes our estimate conservative.

The properties of repeating FRBs are poorly constrained (e.g., Fonseca et al. 2020) because only a small number have been detected. Uncertain parameters include the event rate and its dependence on flux density, the possibility of non-Poisson distribution of events (Oppermann et al. 2018), and the host environment of these FRBs. With its all-sky coverage, BURSTT will likely uncover a larger fraction of repeaters, sharply localize the sources, and provide detailed data for each received pulse. This should substantially improve our understanding of repeating FRBs.

Figure 1 shows the FoV versus the SEFD and the effective area for the existing, planned, and future-concept FRB surveys, including CHIME (CHIME/FRB Collaboration et al. 2018), Australian Square Kilometre Array Pathfinder (ASKAP) (Macquart et al. 2010), the Canadian Hydrogen Observatory and Radio-transient Detector (CHORD) (Vanderlinde et al. 2019), STARE2 (Bochenek et al. 2020a), Galactic Radio Explorer (GReX) (Connor et al. 2021), Deep Synoptic Array 2000 (DSA-2000), ¹⁹ Five-hundred-meter Aperture Spherical Telescope (FAST) (Jiang et al. 2019), Green Bank Telescope (GBT) (Connor et al. 2016), the Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) (Newburgh et al. 2016), MeerKAT (Rajwade et al. 2021), Parkes (Petroff et al. 2014), Packed Ultra-wideband Mapping Array (PUMA) (Slosar et al. 2019), Square Kilometre Array Phase 1 (SKA-1) (Braun et al. 2019), SKA-2 (Torchinsky et al. 2016), and the Very Large Array (VLA) (Law et al. 2018).

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The critical step to reveal the origin of FRBs is to measure the accurate positions of FRBs (i.e., localization) to identify their progenitors. Out of more than 600 FRBs published to date (Petroff et al. 2016; CHIME/FRB Collaboration et al. 2021), there has been only one successful case of localization to a stellar progenitor, which identified the FRB as a Galactic magnetar, SGR 1935+2154 (Bochenek et al. 2020b; CHIME/FRB Collaboration et al. 2020; Kirsten et al. 2021), and clearly indicates the magnetar as the progenitor of this particular FRB.

Recently, three repeating FRB sources have been localized in nearby star-forming regions of galaxies (Bassa et al. 2017; Marcote et al. 2020; Piro et al. 2021). This may indicate young stellar populations as a possible origin of repeating FRBs. In contrast, another repeating FRB source was localized in the globular cluster in M81, a nearby galaxy, which suggests that FRB origins are to be found in old stellar populations (Kirsten et al. 2022). This apparent contradiction could be due to the small sample size. A statistical relation between localized FRBs and their host galaxies has been studied (Li & Zhang 2020), while more localized samples are necessary to understand the host environments. BURSTT will detect and localize ∼100 bright FRB per year to further distinguish their local environment, and such statistics are important to understand the population (Leung et al. 2021; Cassanelli et al. 2022; Mena-Parra et al. 2022).

Very-Long Baseline Interferometry (VLBI) along with outrigger stations have been proposed to localize both non-repeating and repeating FRBs (Cassanelli et al. 2022). For the latter, the European VLBI Network (EVN) has localized several repeating FRBs to their hosts (Marcote et al. 2020; Kirsten et al. 2022). Along with the VLBI outrigger stations, BURSTT can localize FRBs to their hosts. For instance, an outrigger located a few hundred km away from the main array will provide ∼1'' localization for the host galaxy. This localization will lead to the identification of FRB hosts and potentially the progenitors of the nearby sources, which will allow us to understand the nature of FRBs.

The observational classification of FRBs as repeating and non-repeating has caused a major problem over the past decade: non-repeating FRBs can be contaminated by repeating FRBs because this classification is a purely observational definition (Ai et al. 2021; Chen et al. 2022). Due to limited observational time, a significant fraction of repeating bursts may be missed and thus such FRBs could be misclassified as non-repeating FRBs. However, long-term monitoring observations are extremely expensive and difficult using current and planned radio telescopes.

BURSTT will monitor a fixed large patch of the sky all the time (See Table 1). This is essential for non-stop monitoring of repeating and non-repeating FRBs. Repeating FRBs could originate from the repeating activities of progenitors, such as pulsars and magnetars, while non-repeating FRBs may be generated by catastrophic one-off events, such as compact merger systems (Platts et al. 2019). BURSTT will thus provide great statistics of source repetitions, as well as precise constraints on apparent non-repetition of one-off events.

BURSTT can monitor the northern hemisphere at least 7 hr per day (24 hr for North pole and ∼7 hr for the equator). BURSTT's longer monitoring minimizes the chance it will miss any repeating FRBs, which will resolve the missing repeating FRB problem. Ravi (2019a) compared the event rate of nearby FRB samples and those of cataclysmic progenitor events. The event rate of nearby FRBs exceeds the cataclysmic progenitor events,which indicates that the FRB sample cannot be explained by cataclysmic events alone. Hence, Ravi (2019a) concluded that most observed cases of FRBs must originate from sources that emit several bursts over their lifetimes.

The CHIME/FRB Collaboration et al. (2021) reported 474 non-repeating FRBs and 62 repeating bursts from 18 repeaters, which implies the probability that a burst originates at a repeater is equal to 62/(62+474) = 11.5%. As exposure time increases (Ai et al. 2021), we expect that more repeating and bright bursts will be detected. For instance, Herrmann (2021) reported a high-fluence FRB (334 Jy ms) from the FRB 20201124A repeating source with observation times of 90 hr. As a result of the small number of detections, the properties of repeating FRBs are poorly constrained (e.g., Fonseca et al. 2020). This uncertainty includes the event rate and its dependence on flux density, the possibility of non-Poisson distribution of events (Oppermann et al. 2018), and the host environment of the FRB. With its all-sky, continuous sensitivity to high-fluence events, BURSTT will explore a unique parameter space for repeaters. Since BURSTT will detect ∼100 high-fluence FRBs from the nearby universe, the non-detections of repeats will shed some light on the underlying population using statistical methods.

Finding repeaters requires either high sensitivity or long exposure time. To detect more repeaters, we take the advantage of BURSTT's long exposure time (given by the large FoV) as a compensation to the sensitivity issue. We expect that BURSTT will detect high-fluence bursts from repeaters, and other telescopes with high sensitivity can do follow-up observations to detect more fainter bursts from the sources. For instance, the bright repeaters can then be readily followed-up by larger apertures, including the Five-hundred-meter Aperture Spherical Telescope (FAST), Giant Meterwave Radio Telescope (GMRT), and the Very Large Array (VLA). Historically, repetition rates increase rapidly with sensitivity, and thus we expect repeaters detected by the BUTSTT to have the highest rates in follow-up campaigns.

With the high cadence, BURSTT may detect bright pulses from pulsars and rotating radio transients (Good et al. 2021), and further study their connections to FRBs (Bij et al. 2021; Majid et al. 2021; Thulasiram & Lin 2021).

Our plan to reveal the origin of FRBs is to explore the nearby universe because this maximizes the chance of detecting possible multi-wavelength and multi-messenger counterparts of FRBs, including FRB progenitors. For example, follow-up was key to the association of a repeating FRB with the Galactic magnetar SGR 1935+2154 (Bochenek et al. 2020b; CHIME/FRB Collaboration et al. 2020; Kirsten et al. 2021). This progenitor was identified because it is located nearby. Simultaneous X-ray emissions from SGR 1935+2154 were also detected with X-ray telescopes (e.g., Tavani et al. 2021). This observed association gives hope that FRBs in nearby galaxies may also have detectable X-ray counterparts. (Li et al. 2021). BURSTT will monitor a large fraction of nearby galaxies.

An important wavelength range to examine for counterparts is the optical. No optical-FRB coincidence has been found (MAGIC Collaboration et al. 2018; Tominaga et al. 2018) to date. In addition, improved constraints would be very valuable because the expected flux density of the optical counterpart strongly depends on the physical mechanism of the FRB; for example, the magnetosphere model predicts optical counterparts, whereas the maser model predicts a negligible flux density in optical (e.g., Yang et al. 2019; Yalinewich & Pen 2022).

BURSTT is the ideal compliment to the current generation of multi-messenger detectors, such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) (Abbott et al. 2009), IceCube (Aartsen et al. 2017), and the Rubin Observatory's Legacy Survey of Space and Time (LSST) (LSST Science Collaboration et al. 2009), which (like BURSTT) monitor the nearby universe with near full-sky coverage. It will be instructive to search for FRBs associated with gravitational waves detected with the LIGO-Virgo-KAGRA Gravitational Wave Detector Network in near future (The LIGO Scientific Collaboration et al. 2022). Some FRB models predict an association with Gravitational-Wave (Wei et al. 2018) or neutrino counterparts (Metzger et al. 2020). If FRBs originate from neutron star mergers, which are known to generate gravitational waves (Abbott et al. 2017) and potentially neutrinos (Fang & Metzger 2017; Kimura et al. 2018), then the expected time window of radio emission is on the millisecond timescale comparable to that of FRBs (e.g., Yamasaki et al. 2018). So far, no FRB has been found in association with gravitational-wave sources (e.g., Abbott et al. 2016; The LIGO Scientific Collaboration et al. 2022). If no significant GW-FRB associations can be detected in future despite the greatly improved detection rate of BURSTT, then the neutron star merger scenario for the origin of FRBs can be strongly constrained. Scenarios involving cosmic-ray acceleration (e.g., Li et al. 2014; Metzger et al. 2020) can produce neutrinos that can be detected by Large Volume Neutrino detectors, such as IceCube, KM3NeT (Adrián-Martínez et al. 2016), and Baikal-GVD (Avrorin et al. 2022). Although no neutrinos from FRBs have been detected so far, the probability of finding neutrino associations significantly improves with the total number of FRB detections (Aartsen et al. 2018, 2020). These observations would bring clarity to the role of FRBs within the non-thermal universe and constrain the still unknown acceleration mechanisms of the highest energy cosmic rays.

The diffuse Galactic foreground is known to be pervasive, bright, and dynamic, thus making it challenging to be observed properly. Only a few surveys have a large enough coverage to observe the low-frequency radio sky below 1 GHz (e.g., Haslam et al. 1981, 1982; Guzmán et al. 2011), including MSSS (Heald et al. 2015), GLEAM (Wayth et al. 2015), and TGSS (Intema et al. 2017). It is therefore complementary to generate low-frequency high resolution sky maps using (for example) the Long Wavelength Array (LWA) (e.g., Eastwood et al. 2018) and the Engineering Development Array 2 (EDA2) (e.g., Kriele et al. 2022). With the large FoV of BURSTT below 1 GHz, it has the potential to improve the removal of the Galactic foreground contamination in many Cosmic Microwave Background radiation and Epoch of Reionization works (see e.g., Ichiki 2014; Spinelli et al. 2021).

BURSTT-256 will consist of a combination one 256 antenna main station, and smaller outriggers at other sites in Taiwan and Hawaii.

We have surveyed several sites, and have permission to deploy the main station at the Fushan Botanical gardens ²⁰ in Northern Taiwan. Our survey indicates acceptable radio frequency interference (RFI) conditions at that site. We are continuing to survey other sites, sheltered from RFI, for the outrigger stations in Taiwan and surrounding islands, as well as in Hawaii. The outriggers will each employ 64 antennas, allowing VLBI source localization (Leung et al. 2021; Cassanelli et al. 2022; Mena-Parra et al. 2022).

We will process an effective bandwidth of 400 MHz selected within the 300–800 MHz analog range through direct digital polyphase filterbanks (PFB). The CHIME/FRB team has demonstrated that processing a 400 MHz bandwidth is practical (CHIME/FRB Collaboration et al. 2018). we would like to explore the FRB rate at frequencies below 400 MHz, which is at the bottom of the CHIME band. Our design offers frequency agility. Should a shift in band improve the rate, then BURSTT will be able to adapt through a simple software change.

Due to its modular nature, BURSTT is flexible enough to be expanded by deploying more antennas or outrigger stations. We plan to expand the main station from 256 antennas (BURSTT-256) to 2048 antennas (BURSTT-2048), and more outrigger stations could be deployed with longer baselines, which will increase the localization precision. The main properties of the BURSTT are summarized in Table 1.

For the BURSTT-256 project, the main station will search for bursts with fluence higher than 100 Jy ms, which is mentioned in Section 2.1. Assuming the duration of 1 ms and the bandwidth of 400 MHz, the corresponding S/N at the main station is 12. Once the main station detects a candidate burst, the data in the ring buffer in the outrigger will be copied out for the offline analysis. We expect a burst with a fluence of 100 Jy ms would yield an S/N at least of six in the cross-correlation analysis for the localization purpose.

We plan to use single-polarization antennas in BURSTT. These are simpler to design and build than dual-polarization antennas, and optimization of the antenna-LNA match is more effective when only one polarization is involved. We plan to start with all antennas in one polarization direction within the main-station array because this enhances sensitivity for linearly polarized sources, such as FRBs. Later, we have the option to rotate some antennas to the orthogonal polarization if we determine that dual-polarization data is essential to test FRB source models.

Even in the initial configuration, we plan to provide some polarized properties of all detected FRBs, such as rotation measure and polarization position angle swings (Masui et al. 2015), using two sub-stations with orthogonal polarization at one of the outrigger sites.

The back-end includes correlator hardware that will process the radio signals and accompanying software including fast Fourier transform (FFT) techniques, and establish the capability to locate FRB events. Much of the development effort of the BURSST program lies in the development and testing of real-time software. BURSTT will develop an upgraded version of the real-time processing digitizer and FRB search engines employed for CHIME (The CHIME Collaboration et al. 2022).

An overview of the front- and back-ends of the main station is given in Figure 2. The front-end receives the signal from the sky through the bandpass (BP) filter and the noise amplifiers. The back-end digitizes the signals, performs the frequency-domain channelization, forms beams on the sky, and searches for FRBs. The hardware at outrigger stations will be similar to the main station, except that no beamforming or FRB search will be performed. Rather the outriggers just record the arriving signal streams. This is discussed further in Sections 3.2 and 3.3.

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BURSTT will use Log-Periodic Dipole Array (LPDA) antennas. The LPDA antennas, which provide the required gain (7–9 dBi) with a simple structure, have been characterized and measured for use in numerous scientific and industrial applications. Millions of LPDAs have been deployed over the decades for use as home television antennas. Because LPDA antennas have a structure that can withstand strong winds, they are suitable for the environment in Taiwan, which experiences typhoons. Figure 3 shows some photographs of various prototype antennas that are currently in development. The first, which is shown in the left-hand panel, is a standard design that has been characterized well but it is expensive to manufacture. In addition, the long elements for low frequencies would be weak against strong winds. The second, which is shown in the middle panel, is the planar LPDA, which is a cost-effective design that simplifies the manufacturing process. However, because the elements have a long band-like structure, they can easily vibrate in the wind. The third design, which is shown in the right-hand panel, is the planar LPDA attached to a quadrangular pyramid structure that is composed of insulator plates, which is cost-effective and raises the structure resonance frequency of the elements so that they can withstand strong winds. However, the structure can be heated by the Sun, which can degrade the amplifier's noise temperature. We will continue development and will test several prototypes in the field.

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Received signals pass through the front-end electronics (FEE) before arriving at the digitizer. We will use a sampling rate of 1600 MHz, so our passband lies in the first Nyquist zone. This means that no mixers or local oscillators are needed in the RF system. To minimize noise temperature due to transmission line losses, the first-stage low-noise amplifier (LNA) is closely integrated into the feed point of the LDPA (as shown in Figure 4). The external second-stage FEE module consists of two equalizers cascaded with second-stage amplifiers (LNAs) and filter modules to eliminate RFI at low frequencies, and to prevent aliased detection of signals and noise above 800 MHz. Figure 5 shows the measured forward gain and the noise temperature (20–30 K) of a first-stage LNA that we are developing. Comparing this to typical sky brightness temperature values, which fall with frequency from ∼50 K at 300 MHz to ∼6 K at 800 MHz, we see that the further effort to reduce LNA noise temperature can improve sensitivity, particularly at the high end of our frequency range. The required system gain is 65 dB, which is obtained by combining the first-stage LNA gain (25–30 dB), the second-stage amplifier assembly (35–40 dB), and slope-equalizer losses (−5 dB). We will continue to optimize the LNA design and plan to install an in-house developed low-noise amplifier in the 2048 antenna array.

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The antenna array of BURSTT-256 station has a footprint of 32 × 32 m, and the distance to the data acquisition (DAQ) hut where the digitizer is located is up to 50 m, which requires cable lengths of ∼60 m (Figure 6). When using the most popular and reliable coaxial cable, LMR-400, the transfer losses are −4 dB and −48 dB for 200 MHz and 900 MHz, respectively, which can be corrected in the RF slope equalizer or in the correlator after channelization.

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3.2.1. The Beam Pattern

Figure 7 shows simulated far field radiation patterns of the LPDA antenna calculated using the Ansys high-frequency structure simulator (HFSS) software. With the HFSS software, we utilize the finite element method to compute the EM field distribution of components. The 3 dB beam widths (FWHM) of the prototype LPDA antenna are around 80° on the H plane and 60° on the E plane from 300 to 800 MHz (Table 2).

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Table 2. The FWHM of the Beam Pattern

	300 MHz	400 MHz	600 MHz	800 MHz
E plane	580	560	580	540
H plane	800	780	770	800

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When the BURSTT main station detects a candidate FRB, it sends a SAVE message to the outriggers, which then transfer recently buffered data from RAM to disk. The outriggers and main station transmit the data to a VLBI processing facility for localization processing. This process synthesizes an instrument with a nominal VLBI resolution λ/(2D) of a 7800 km × 270 km baselines with 13 mas and 370 mas resolution in E-W and N-S, respectively. This allows not only unique identification of each FRB's host galaxy but also ∼100 parsec-scale localization of the FRB within that galaxy.

3.3.1. Digitizer and Engines

We employ the Xilinx ZCU216 field programmable gate array (FPGA) boards as the platform of our digitizer and channelizer. The ZCU216 is equipped with a radio frequency system on chip (RFSoC) FPGA that can process 16 RF inputs. RFSoC systems include an embedded analog to digital converter (ADC) inside the FPGA chip, which simplifies wiring and saves physical space. This is the highest bandwidth RFSoC that is currently available. Figure 8 summarizes the functional block diagram of the RFSoC F-engine. We will be clocking the ADC at sampling rate 1600MHz for a Nyquist bandwidth of 800 MHz. A polyphase filter bank will channelize the data, forming 2048 bands of width ∼390 kHz, and we will select 1024 of these for further analysis, choosing RFI-clear bands. We then re-quantized to resolution 4+4i bits to reduce the data rate. Gathering all of the 16 input frequency-domain data streams, a 100G Ethernet system will transmit the 100G UDP packets to the server for further data processing. The ADCs have 14 bit resolution, which is substantially higher than the 8 bits sampling that has been commonly used to date.

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3.3.2. Preprocessing and RFI Mitigation

We discuss the steps of preprocessing in this section, including the RFI-removal techniques, beamforming, and frequency channelization.

For BURSTT-256, the antennas will be organized into 16 columns, each with 16 antennas. The 16 antennas in a N-S column will be connected to one FPGA F-engine. It is thus efficient to perform 1D beamforming within the FPGA from Ng et al. (2017). Each beam from the 16 F-engines is then similarly combined in the CPU array to form the E-W direction beams, This process occurs independently for each frequency channel. This approach is similar in spirit to the 2D-FFT telescope (Tegmark & Zaldarriaga 2009) although with an implementation that is tailored to our F-engine design. For BURSTT-2048, a second layer of 2D spatial FFT will be carried out in the CPU array to synthesize all full-resolution beams.

The bandpass calibration and the system SEFD will be derived from observations of the Sun during the day. A pulsed broadband noise source will be used to monitor the gain variation during the night. Phase calibration will be achieved by using the many radio sources that are continuously available within the large FoV.

RFI Surveys in the Fushan candidate site shows that about 60% of the 300–800 MHz frequency range is free of noticeable RFI, while an additional 15% is affected by weak RFI. The FPGA F-engine offers a possibility of mitigating the weak RFI contamination using the using a spatial filtering technique applied to time streams from the antennas. (Kocz et al. 2010). The basic idea is that for a spatially fixed RFI source, the cross-correlation between any two antennas will record a distinct phase relation. The covariance matrix of all the antennas contains all of the phase information that one can measure with the array. Any source, not just the RFI sources, will contribute to the covariance matrix. However, for signals that are above the thermal noise, one can identify them by solving the eigenvalues and eigenvectors of the covariance matrix. This procedure is performed independently on each spectral channel. The antennas' voltage data can be projected onto the eigenvectors to form the eigenmodes. The eigenmodes with the strongest variances (i.e., the largest eigenvalues) are assumed to be from the RFI source. It is therefore possible to remove the RFI contribution by nulling or zeroing out the RFI eigenmodes and deprojecting them back to the antenna data space. The antenna data after the RFI removal are passed onto the beamforming stage.

Figure 9 gives an example of this technique applied to the TV station signal that was recorded in Fushan Botanical Garden (the main-station site) with a four antenna test system. Three TV stations, each with a 6 MHz bandwidth, are within the recorded 40 MHz bandwidth. We note here that the eigenmode decomposition works better when the variance of the antennas are comparable. For this example, the four antennas have been normalized to the mean of the four antennas at each spectral channel. It is shown that for the TV signal centered on 581 MHz, the signal is reduced by about 20 dB after nulling out the strongest eigenmode. The TV signal centered on 569 MHz is only reduced by a similar amount after nulling two of the strongest eigenmodes. At Fushan, we may be receiving the TV signals from multiple towers or multi-path propagation may be an important factor. As the project expands the testing to more sites and with more antennas, the RFI-removal technique will be refined.

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The performance of the RFI mitigation improves as the number of antennas is increased. Using the entire array in principle gives the best RFI nulling, but at substantial increase in the cost of the computation. To keep this system simple, we plan to update the RFI nulling solutions just once several hours or once a day. For the 16 antennas connected to one F-engine, applying the nulling solution is accomplished simply by multiplying the 16 antenna time streams for each frequency channel by a 16 × 16 complex matrix, similar to the beamforming operation. In fact, the two operations can be combined. Therefore, the RFI mitigation can be applied for each column of antennas at no additional real-time computational cost. An additional test will determine if 16 antenna RFI mitigation is sufficient or if more antennas should be combined to achieve the desired improvement.

3.3.3. Dedispersion, Search, and Follow-up