Development Toward a Ground-Based Interferometric Phased Array for Radio Detection of High Energy Neutrinos
J. Avva, K. Bechtol, T. Chesebro, L. Cremonisi, C. Deaconu, A. Gupta, A. Ludwig, W. Messino, C. Miki, R. Nichol, E. Oberla, M. Ransom, A. Romero-Wolf, D. Saltzberg, C. Schlupf, N. Shipp, G. Varner, A. G. Vieregg, S. A. Wissel
DDevelopment Toward a Ground-Based Interferometric Phased Array for Radio Detectionof High Energy Neutrinos
J. Avva a,b , K. Bechtol c,b , T. Chesebro d , L. Cremonesi e , C. Deaconu b , A. Gupta e , A. Ludwig f,b , W. Messino g , C. Miki h , R. Nichol e ,E. Oberla b , M. Ransom b , A. Romero-Wolf i , D. Saltzberg d , C. Schlupf d , N. Shipp j,b , G. Varner h , A. G. Vieregg f,k,b , S. A. Wissel l,d a Dept. of Physics, University of California Berkeley, Berkeley, CA 94720, USA b Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA c Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin-Madison, Madison, WI 53703, USA d Dept. of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA e Dept. of Physics and Astronomy, University College London, London, United Kingdom f Dept. of Physics, University of Chicago, Chicago, IL 60637, USA g Electrical Engineering Dept., California Polytechnic State University, San Luis Obispo, CA 93407, USA h Dept. of Physics and Astronomy, University of Hawaii, Manoa, HI 96822, USA i Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA j Dept. of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637, USA k Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA l Physics Dept., California Polytechnic State University, San Luis Obispo, CA 93407, USA
Abstract
The in-ice radio interferometric phased array technique for detection of high energy neutrinos looks for Askaryan emission fromneutrinos interacting in large volumes of glacial ice, and is being developed as a way to achieve a low energy threshold and a largee ff ective volume at high energies. The technique is based on coherently summing the impulsive Askaryan signal from multipleantennas, which increases the signal-to-noise ratio for weak signals. We report here on measurements and a simulation of thermalnoise correlations between nearby antennas, beamforming of impulsive signals, and a measurement of the expected improvementin trigger e ffi ciency through the phased array technique. We also discuss the noise environment observed with an analog phasedarray at Summit Station, Greenland, a possible site for an interferometric phased array for radio detection of high energy neutrinos. Keywords:
Ultra-high energy neutrinos, radio detection, phased array
1. Introduction
In recent years, the IceCube experiment has detected apopulation of astrophysical neutrinos with energies up to ∼
10 PeV [1, 2]. The sources of these astrophysical neutrinosremain a mystery, their spectral index remains uncertain, andalthough there is no evidence for a spectral cuto ff , the behav-ior at higher energies remains unknown [3]. In addition to theastrophysical population discovered by IceCube, there is a sep-arate population of cosmogenic ultra-high energy (UHE) neu-trinos ( E > eV), created as a byproduct of the GZK pro-cess (the interaction of UHE cosmic rays with the cosmic mi-crowave background), that awaits discovery [4, 5, 6]. The twinscience goals of following up on the IceCube measurement ofastrophysical neutrinos at and above PeV energies, and discov-ering the highest energy cosmogenic neutrinos drive the designof developing and proposed experiments that aim to detect highenergy neutrinos.One promising method for detection of high energy neutri-nos is via the Askaryan e ff ect: the coherent, impulsive radioemission from electromagnetic showers induced by neutrinosin a dielectric [7]. At long wavelengths (frequency less than afew GHz), the emission is coherent, so for high energy show-ers, the long-wavelength radio emission dominates. A large volume of a dielectric material with a long radio attenuationlength ( L α ∼ . eV, and the proposed balloon-borne EVA experiment is anovel way to improve sensitivity at these highest energies [8, 9].The ARA and ARIANNA experiments, ground-based radio ar-rays in early stages of development each with a small num-ber of stations deployed in Antarctica, have energy thresh-olds (cid:39)
100 PeV, probing the heart of the cosmogenic neutrinoregime [10, 11].The concept for an in-ice radio interferometric phased arrayfor detection of high energy neutrinos was introduced in Ref-erence [12] and is being explored as a way to push the energythreshold of radio detection down to the PeV scale while in-creasing the achievable e ff ective volume at the highest energies.Interferometric techniques have been extensively used in radioastronomy (for a review, see [13]) to image radio sources, andhere we apply an interferometric technique to improve sensitiv-ity to broadband, impulsive radio signals. Rather than imaging, Preprint submitted to Nuclear Instruments and Methods A July 26, 2017 a r X i v : . [ a s t r o - ph . I M ] J u l e are interested in achieving high instantaneous sensitivity toa large solid angle.An in-ice interferometric phased array coherently combinessignals from multiple low-gain antennas deployed down sub-surface boreholes with proper time delays to account for dis-tances between antennas to e ff ectively increase the gain of thesystem of antennas for incoming plane waves from a given di-rection. Many di ff erent sets of delays of signals from the sameantennas can create multiple e ff ective antenna beam patternsthat would together cover the same solid angle as each individ-ual antenna but with much higher gain. The closer the antennasare physically, the fewer beams are needed to cover a givensolid angle.This paper addresses the assumption that a phased arraymade of closely packed antennas receives uncorrelated noise ineach antenna. We show using realistic detector designs in bothan anechoic chamber and in the ice in Greenland that thermalnoise is uncorrelated between antennas. In developing phasedarrays for use in the lab, we also demonstrate how the beam-forming technique can be used for impulsive signals in practice.In Section 2, we discuss measurements of thermal noise cor-relation between closely-spaced antennas, relevant for an inter-ferometric phased array trigger. Section 3 details a validation ofthe beamforming technique for impulsive signals in an anechoicchamber. In Section 4, we discuss the implications of beam-forming for a realistic triggering scheme. Section 5 reviews anddetails new measurements of the relevant ice and noise charac-teristics of Summit Station, Greenland, the site where we per-formed an in situ noise correlation studies of a prototype detec-tor. We conclude in Section 6.
2. Thermal Noise Correlation Studies
One of the underlying assumptions in the interferometricphased array calculations is that the thermal noise measuredby each antenna in the array is uncorrelated with the ther-mal noise measured in its nearest neighboring antenna. Thelevel at which thermal noise signals are correlated between an-tenna channels is one factor that determines the e ff ective gainachieved by phasing together many antennas. In the limit offully overlapping antennas, the thermal noise observed fromthe ice ( ∼
250 K) would be completely correlated, and the noisefrom the system would be completely uncorrelated ( ∼
75 K forthe systems described in this paper). To determine how closelypacked the antennas in a phased array can be without introduc-ing a significant correlated noise contribution, we performedtests in an anechoic chamber and designed a simulation of ther-mal noise to compare to the measurements.
We performed noise correlation measurements using a sim-ple system in an anechoic chamber. Figure 1 shows a schematicdiagram of the system setup, which consists of two antennaslaid out end-to-end, with each antenna in its neighbor’s null. Signals from each antenna were amplified by a dual-stage front-end amplifier chain that included a 46 dB low-noise ampli-fier (MITEQ AFS4-00100200-10-15P-4) and a 40 dB ampli-fier (Mini-Circuits ZKL-1R5) separated by a 3 dB attenuator.DC power for the amplifiers was carried through the radio fre-quency (RF) cable, coupled by bias tees inside and outside theanechoic chamber. Signals were then filtered using a Mini-Circuits NHP-200 and NLP-450 or NLP-600, depending on thetype of antenna used for the test. For all antenna types, whichwe discuss in Section 2.1.2, we used the NLP-600, except forthe broadband dipole antennas that we developed, where weused an NLP-450. We used Times Microwave LMR-240 andLMR-400 cable, and cable lengths were identical in each sig-nal chain. The noise temperature of each channel was ∼
75 K,dominated by noise from the front-end amplifier. Signals werethen read out using a Tektronix MSO5204B oscilloscope, sam-pling at 5 GSa / sec. The walls of the anechoic chamber werebetween 1 m and 3 m from the antennas.We changed the spacing between the antennas, ranging fromas close as physically possible to a distance of over 1.5 m be-tween antenna feeds, to measure the level of correlated noisebetween channels as a function of the distance between the an-tennas. We used five di ff erent pairs of antennas for measurements inthe anechoic chamber. We used two types of commercial an-tennas: folded dipole antennas from Telewave, Inc. (ANT275Dand ANT400D) with bandpasses at 230-330 MHz and 360-450 MHz respectively . We also took data with two typesof antennas that have been developed for the ARA experiment.The first is a broadband bicone antenna, used by ARA to detectvertically-polarized signals, and the second is a slot antenna thatis sensitive to horizontal polarization when the antennas are de-ployed in boreholes [14]. The bicone antennas have a bandpassof 150-850 MHz and the slot antennas span 200-850 MHz.Additionally, we took data with broadband dipole antennasthat we developed, which we describe in detail here. Each an-tenna consists of two 20 cm copper cylinders, each with a di-ameter of 8 cm. The two sides of the antenna are connected atthe feed with 0.64 cm copper rods. The antennas are read outvia a 1.3 cm diameter Heliax cable. A 5.1 cm polyvinyl chlo-ride collar separates the two halves of the antenna and providesstrain relief at the feed. An antenna and the simulated designare shown in Figure 2a.The antenna frequency range is chosen to match the expectedAskaryan emission and the physical constraints of in-ice de-ployment in boreholes. The Askaryan signal is coherent up toa few GHz, but undergoes less propagation loss at low frequen-cies in glacial ice, so we preferred antennas in the 100-600 MHzrange. The diameter of the dipoles was chosen to increase thebandwidth while ensuring that they would fit within reasonablesub-surface in-ice boreholes. http: // / products / antennas / pdfs / TWDS-7048.pdf http: // / products / antennas / pdfs / TWDS-7079.pdf ntenna +46 dB Miteq LNA +40 dBMinicircuits Amplifier3dB attenuator Bias T Bias T10 dB attenuator, NHP 200 Filter NLP 450 Filter Ch1Ch2Anechoic Chamber Enclosure TektronixMSO5204BOscilloscopeAntenna Bias T Bias T 3dB splitter Ch3 (Beam)3dB combiner Figure 1: A schematic of the setup in the anechoic chamber for thermal noise correlation testing and validation of beamforming. For thermal noise correlationtesting, there were no splitters or combiners before the oscilloscope. For validation of beamforming, described in Section 3, we added 3 dB splitters to each antennachannel and combined the signals to form a beam in hardware (shown with the dashed lines). We also set up a transmitter 4 m away inside the chamber for themeasurements described in Section 3, which is shown schematically in Figure 6. ( a ) ( b ) ( c ) − − − − − S ( d B ) ± (cid:1) (cid:1) (cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:1)(cid:1)(cid:1)(cid:1)(cid:18)(cid:17) (cid:1) Gain (cid:1) (dBi)
200 MHz266 MHz300 MHz350 MHz400 MHz450 MHz500 MHz
Figure 2: (a) A simulated (using HFSS, left) and constructed (right) broadband dipole. (b) The reflective S-parameter (S ) for all the constructed antennas (colored,solid lines) in air compared with the HFSS simulation (dashed). These antennas have good transmission response from 230 MHz to 800 MHz, demonstrated by thesmall ( < − value over that frequency range. (c) Radiation patterns (solid lines) compared with HFSS simulations (dashed lines). ) in Figure 2b, reaches its first resonance at 262MHz in air, which is reduced to 196 MHz when surrounded byglacial ice ( n = . , is shown with a dashed line in Fig-ure 2b. The higher-frequency dip corresponds to a second modeof the antenna. Simulations of the beam pattern in the antenna’sE-plane indicate that the beam pattern becomes slightly moredirective with increasing frequency, rather than forming an ad-ditional null. However, the measured E-plane radiation patternis no longer azimuthally symmetric above 450 MHz. The bore-sight gain is within 3 dB of its maximum of 2.9 dBi between220 MHz and 755 MHz. We model thermal noise in a multiple antenna system as thesum of multiple noisy transmitters following Reference [15].Consider antennas A and B located distances r An and r Bn from atransmitter n with random uncorrelated phases but equal ampli-tudes ψ . The statistical average of the cross-correlation coef-ficient, (cid:104) C AB (cid:105) , of many sources is non-zero only when consid-ering terms from a single transmitter, giving an average cross-correlation coe ffi cient of (cid:104) C AB (cid:105) = ψ (cid:42) N (cid:88) n = e − ik ( r An − r Bn ) r An r Bn (cid:43) . (1)Two cases may result in correlation between the antennas. Ifthe transmitters are arranged in an arbitrary configuration, butthere are boundaries, such as the ice-sky horizon that is relevantfor balloon-borne neutrino experiments, partial correlation ex-ists near the bounds. When the antenna separation and distancebetween the transmitters are much smaller than a wavelength,the source is unresolved and the average correlation is non-zero,as may be found with a closely packed phased array deployeddown a borehole. Generally speaking, the correlation of thenoise between a pair of antennas depends on a combination ofthe antenna separation and spatial distribution of the transmit-ters.For comparison to the anechoic chamber measurements, wetreat sources of thermal noise as oscillators each with an am-plitude drawn from a Rayleigh distribution corresponding to atemperature of 300 K and a random phase drawn from a uni-form distribution. We create 10 of these oscillators, each witha frequency drawn from a uniform distribution over a 2 GHzbandwidth. The oscillators are thrown uniformly on a spheri-cal shell that has a radius of 5 m and is centered on the pointbetween two simulated antennas. We weight the amplitude ofeach oscillator by the sine of the incident angle on the antennafeed, where a zenith angle of zero corresponds to the location ofthe null of the antenna, to approximate a dipole antenna beampattern. We add the electric fields, weighted by the sine of thephase at each antenna, for all generated oscillators in Fourier http: // / Products / Electronics / ANSYS-HFSS space for each antenna and filter the result using the magni-tude of the frequency response of the filters we used in ther-mal noise correlation measurements (see Section 2.1). Becausethe phase of each oscillator is chosen randomly from a uniformdistribution, we do not need to take into account the phase re-sponse of the filters, since the resulting phase would still be ran-domly drawn from a uniform distribution. Uncorrelated noise isadded to the simulated thermal noise over the same bandwidthfor each channel that corresponds to the 75 K system temper-ature for each channel by generating noise with a spectral am-plitude drawn from a Rayleigh distribution and a random phasedrawn from a uniform distribution over the same bandwidth asthe thermal noise. We generate simulated noise traces at eachantenna by taking the inverse Fourier transform of the filteredspectra. By generating many sets of noise traces for antennaswith di ff erent feed-to-feed spacings, we can make direct com-parisons with measurements.We developed two independent simulations, which we usedas a validation technique, and the results of the simulations areconsistent with each other. We run identical analyses on simulated noise data sets andon noise correlation data taken in the anechoic chamber. Fig-ure 3 shows the results of the noise correlation measurementsfor the ARA bicone antennas spaced as closely as physicallypossible (a feed-to-feed distance of 0.73 m), compared to mea-surements with the inputs to the front-end amplifiers terminatedwith a 50 Ω load and results from the thermal noise simulation.The configuration with terminated amplifier inputs is used as ameasure of the baseline level of correlated noise in the systembetween the two antenna channels.The left-hand panel of Figure 3 is a histogram showing thecross-correlation coe ffi cient between the two antenna channelsover a causal time window ( ± ∼
500 recordedevents. This causal time window corresponds to possible timedi ff erences between antennas for incident plane wave signalsfrom an arbitrary direction, determined by the spacing betweenthe antenna feeds. The causal time window ( ∆ t ) is determinedby ∆ t = ∆ d / c , where ∆ d is the feed-to-feed spacing betweenthe antennas (0.73 m), and c is the speed of light. We definethe cross-correlation coe ffi cient, C , between two time-domainwaveforms, x ( t ) and y ( t ), at a relative time delay τ between thewaveforms, as C ( x ( t ) , y ( t ) , τ ) = N σ x σ y N (cid:88) i = ( x ( t i ) − ¯ x )( y ( t i + τ ) − ¯ y ) , (2)where N is the number of points in each waveform, σ x and σ y are the standard deviation of each waveform, and ¯ x and ¯ y are the mean of each waveform. Since the causal time win-dow ( ± ∼ . ffi cient val-ues shown in the left-hand plot for each recorded event. The4 aximum Cross-Correlation Coefficient in Causal Window Simulated Uncorrelated NoiseARA BiconeTerminated Amplifier Input
Cross-Correlation Coefficient in Causal Window − − Figure 3: Left: a histogram of cross-correlation coe ffi cient values between the two antenna channels over a time window ± . ∼
500 recorded events compared to results from the simulation. This time window corresponds to possible time di ff erences between antennas for incidentplane wave signals from an arbitrary direction, determined by the spacing between the antenna feeds. Right: a histogram of the maximum of the absolute value ofcross-correlation coe ffi cient values between the two antenna channels in the causal time window for each of ∼
500 recorded events. The correlation values for adata set with the inputs to the front-end amplifiers terminated with a 50 Ω load are shown in blue, and the values for the configuration with the ARA bicone antennaswith their feeds separated by 0.73 m (the closest possible physical spacing) are shown in red. The black line shows results from the thermal noise simulation foruncorrelated noise inputs. √ N error bars are shown per bin. three overlaid histograms are consistent within statistical errors,shown on the histograms. There is no significant correlationseen between the two channels when compared to the data takenwith terminated amplifier inputs, even when the antennas werespaced as closely as physically possible. The correlation ob-served is consistent with simulated uncorrelated noise, shownby the black line in Figure 3.We repeated this measurement with the antennas spaced far-ther apart and with a variety of types of antennas (TelewaveANT275D, Telewave ANT400D, and the ARA bicone anten-nas), and all results are consistent with no observed correlationbetween adjacent antennas. Figure 4 shows the results of a com-parison between the thermal noise simulation and data takenwith each of the types of antennas at a variety of feed-to-feeddistances. For these antennas, the feeds are at the centers of theantennas, and a spacing of zero in the simulation corresponds tofully overlapping antennas. Shown is the peak cross-correlationcoe ffi cient averaged over 500 simulated or measured events ina ± . ∼ ffi cient valuesacross the 500 events.At very small hypothetical feed-to-feed distances, the simu-lation approaches a maximum correlation coe ffi cient that corre-sponds to the fraction of total noise in each channel due to the300 K thermal noise compared to the total noise (the sum ofthe thermal noise and the 75 K system temperature). The ther-mal noise is filtered by both the antenna and the in-line filters,whereas the 75 K system temperature filtered by the in-line fil- ters only, which are broader band than the Telewave antennas.The 75 K system temperature is independent between channels.At large spacings, the simulated data has a peak correlationcoe ffi cient of 0.05 for all three antenna types, which wouldchange with di ff erent allowed time windows. True physicalnoise correlation, beyond the correlation level expected fromthe noise statistics alone (in our case ∼ e.g. , > .
73 m for the ARA bicone antennas), the mea-sured and simulated noise correlation for all antenna typesagrees to within <
50% of the measured and simulated standarddeviation. The di ff erence between the measurements and thesimulation for the ARA Bicone antennas is shown in Figure 5.We attribute these small di ff erences to imperfect assumptionsin the simulation, such as ignoring di ff erences in antenna phaseresponse as a function of angle, which would serve to furtherdecorrelate channels.
3. Validation of Beamforming Technique
We also performed a simple validation measurement of thebeamforming technique in the anechoic chamber. We used asystem configuration shown in the schematic in Figure 1. Theconfiguration was identical to the system described in Section 2,except for the following di ff erence: after the second bias tee, wesplit the signal from each antenna channel and combined onebranch of the signal from each channel to form a single beamthat corresponds to zero time delay between the channels. Thisis shown with the dashed line in Figure 1. This beam is broad-side to the antennas, at the highest-gain angle of each antenna.5 igure 4: The peak cross-correlation coe ffi cient averaged over 500 simulatedor measured events in a ± . ∼ ffi cient values across the 500 events. The data for each antenna goes to thesmallest physically-allowed spacing. Predictions from the simulation are shownin blue and results from the measurements are shown in green. Top: ARAbicone antennas. Middle: Telewave ANT275D antennas. Bottom: TelewaveANT400D antennas. For this measurement, we used the broadband dipole antennasthat we developed (see Section 2.1.2).We sent broadband, impulsive signals to the two receivingantennas from an identical transmitting antenna that was 4 maway inside the anechoic chamber, and was positioned broad-side to the receivers for maximum transmission strength in thedirection of the formed beam. A layout of the antennas insidethe chamber for this transmission measurement is shown in Fig-
Figure 5: Top: The peak cross-correlation coe ffi cient for the ARA bicone an-tennas. Predictions from the simulation are shown in blue and results from themeasurements are shown in green. (The same as the top panel in Figure 4.) Bot-tom: The di ff erence between the measured and simulated values for the ARAbicone antennas. The error bars represent the quadrature sum of the error barsshown in the top panel. ure 6. The signals are generated using an Avtech AVP-AV-1S-C-P pulse generator, and are filtered before transmission with aMini-Circuits NHP-200 and an NLP-450 filter.Figure 7 shows the results of the measurement. The left-hand panel shows the impulsive signal received in the two inde-pendent antenna channels, averaged over 500 events recordedon the oscilloscope. Each channel had a slightly di ff erent im-pulse response, dominated by di ff erences between individualantennas. Each channel also had a slightly di ff erent gain andnoise temperature, dominated by di ff erences in the individualfront-end low-noise amplifiers. The right-hand panel showsthe beam that we formed in hardware, compared to the idealbeam that should be formed, calculated by summing the wave-forms shown in the left-hand panel. Some di ff erence is evidentbetween the beam formed in hardware and the ideal versionformed in analysis; the peak-to-peak voltages agree to within15%, and the di ff erence is consistent with the additional lossexpected from the splitters and combiners added to the systemto create the hardware-formed beam.Before averaging together many waveforms to produce thehigh signal-to-noise ratio (SNR) waveform shown in Figure 7,we calculate the SNR of the signal that was received in eachchannel, including the hardware-formed beam, compared to thenoise level in the system. We define SNR as half of the sig-nal’s peak-to-peak voltage divided by the RMS of the noise( V pk2pk σ ). The results are shown in Table 1. We then calculatethe ideal beam that should be formed and the noise level cor-responding to superimposed noise from the individual antennachannels. Note that because of the di ff erences between the twosignal chains, we do not expect to see the √ eceiving Antenna 1Anechoic Chamber EnclosureReceivingAntenna 2TransmittingAntenna 4 m Figure 6: A schematic of the layout of the antennas for the transmission mea-surement described in Section 3.
Noise Signal SNR V RMS V pk2pk ( σ )(mV) (mV)Antenna Ch. 1 (measured) 37.6 194.7 2.6Antenna Ch. 2 (measured) 28.5 154.3 2.7HW Beam (measured) 35.5 217.2 3.1Ideal Beam (calculated) 37.2 246.1 3.3 Table 1: A summary of the validation of the beamforming technique using datataken in an anechoic chamber. Shown are the noise levels, signal amplitude, andSNR of the signals measured for each antenna channel and the beam formed inhardware, as well as the properties of the expected ideal beam calculated usingdata from each antenna channel.
SNR that should be obtained for identical antennas and signalchains. Instead, we expect to see the improvement shown inthe last line of Table 1. The hardware beam matches the idealbeam well in terms of SNR, although both the signal level andnoise level su ff er slightly from additional losses introduced bythe additional components in the signal chain at the 10% level.
4. Trigger Studies for Impulsive Events
We investigate the trigger rate and e ffi ciency of a broad-band phased array using the anechoic chamber measurementsin combination with a simulation study of both noise and tran-sient signals. A linear array of three Telewave ANT400D foldeddipole antennas was placed in the anechoic chamber approx-imately 4 m from an ARA bicone antenna that was used asa transmitter (see Section 2.1.2). The Telewave antennas aremounted on a steel ground mast with a separation of 36 cm be-tween the antenna phase centers and the ground mast. The an-tennas are spaced at a pitch of 55 cm. Each receiving antennahas the same signal chain as shown in Figure 1, and the signalsare recorded at 5 GSa / sec.We model the digital phasing and event triggering of a lin-ear antenna array. The antenna channels are formed into beams Time (ns)
140 150 160 170 180 190 200 V o l t age ( m V ) -200-150-100-50050100150200 Channel 1Channel 2
Time (ns)
140 150 160 170 180 190 200 V o l t age ( m V ) -200-150-100-50050100150200 Ideal BeamHardware Beam
Figure 7: Left: an overlay of waveforms, averaged over 500 events, for Chan-nels 1 and 2 in the system shown in Figure 1, when transmitting a fast impulseto the antennas. Right: an overlay of waveforms, averaged over 500 events, forthe hardware-summed beam recorded in Channel 3 in the configuration shownin Figure 1 and the coherent waveform calculated directly from the averagedwaveforms shown in the left-hand panel. This test uses the broadband dipoleantennas described in 2.1.2. by digitally delaying and coherently summing the individualantenna channels. A relative delay is applied between the dig-itized waveforms received at a pair of antennas, which corre-sponds to a beam angle, θ n , of n ∆ t = dc sin θ n , (3)where n is an integer, ∆ t is the the sampling time interval, c isthe speed of light in the medium, and d is the baseline betweenthe pair of antennas. Many beams can be formed simultane-ously in hardware to cover a wide angular range, either digi-tally using FPGA or analog ( e.g. , as described in Section 5.2).For this trigger study, we form beams in analysis by coher-ently adding waveforms from individual antenna channels. Fora fixed antenna spacing, the sampling rate sets the number ofindependent beams and the granularity of the angular coverage.With an antenna spacing of 1 m and a sampling rate of2 GSa / sec, we use Equation 3 to find that 17 independentbeams, formed using the smallest 1 m baseline, are neededto cover the elevation angle range between -45 ◦ to + ◦ . Thebeamwidth is determined by the number of antennas in the ar-ray. As the beamwidth narrows, more beams can be added to fillthe coverage gaps by utilizing correlations between antennas atall baselines in the array.The optimal sampling interval for the power calculation isrelated to the dispersion of the signal going into the trigger. Forthe case in which the impulse response of the system is decon-volved before triggering, it may be optimal to sample the powerat every data sample because the signal power is contained ina short time interval. However, the system response is not un-folded from the signal in the baseline algorithm described here.A more e ffi cient algorithm for the dispersive pulses recordedin the anechoic chamber calculates the power every eight sam-ples, thereby including the majority of the power from a singletransient pulse.7 s / L P Z T r i gge r R a t e [ H z ] Anechoic data, 1-sampleSimulated, 1-sampleAnechoic data, 8-sampleSimulated, 8-sample
Figure 8: Trigger rate vs. normalized power threshold, PZ L /σ , for noise tracestaken in the anechoic chamber using the three Telewave antennas (data points)compared to simulations of thermal noise (solid lines). Two trigger configura-tions are shown: the blue data points indicate the trigger rate when the aver-age power is taken over a 9.6 ns window and incremented every eight samples(4.8 ns). The red data points show the singles rate when the power is calculatedat every sample point. We use the simulation to predict the threshold for rateslower than several kHz due to the limited amount of data taken in the anechoicchamber. To detect transient events, a time-windowed power calcula-tion is performed on each coherently summed beam, given by P window = N s Z L N s (cid:88) j = N ant (cid:88) i = V i j , (4)where N s is the number of digitized samples in the time win-dow, Z L is the load impedance, N ant is the number of antennasused in the beam, and V i j is the digitized voltage at sample j within the time window for antenna i .The relationship between the per-beam singles rate and trig-ger threshold is determined by N s , as shown in Figure 8, wherethe power threshold, P , is normalized by the square of thenoise RMS ( σ ) divided by Z L . For these measurements, thedata are down-sampled from 5 GSa / sec to 1.67 GSa / sec to re-flect a Nyquist sampling rate for a system with a bandwidth of ∼
800 MHz.Two power calculations are shown in Figure 8: one in whichthe average power is calculated in a window of N s =
16 sam-ples (9.6 ns) and sampled every N s / = √ PZ L , of 2.34 σ , 2.21 σ ,and 2.07 σ , for noise singles rates of 10, 100, and 1000 Hz, re-spectively, which corresponds to the range of achieved rates inradio-detection experiments.To measure the trigger e ffi ciency, event rates were measuredfrom the 3-antenna array in the anechoic chamber while send-ing impulsive signals from the transmitting antenna at severalattenuation levels. For each attenuation setting, we recorded500 events. The SNR is defined as V pk2pk σ for a single antenna.We choose 100 Hz as a baseline per-beam trigger rate, compara-ble to achieved trigger rates by currently-deployed radio exper- T r i gg e r E ff i c i e n c y Simulated efficiencyshown as solid lines
Measured Efficiency
100 Hz Trigger Rate3-antenna beam2-antenna beamsingle antenna T r i gg e r E ff i c i e n c y
10 Hz100 Hz1000 Hz
Simulated Efficiency
Linear phased array
Figure 9: Trigger e ffi ciency vs. SNR. The top plot shows anechoic chamberresults from a 3-antenna array (data points) compared to a simulation of uncor-related noise added to the system impulse response (lines). The data points aretaken from anechoic chamber measurements with a fast impulsive signal, andthe average power was calculated at 8-sample intervals using a power thresholdcorresponding to a 100 Hz singles rate (dashed line from Figure 8). The bottomplot shows the simulated trigger e ffi ciencies for 3, 8, and 16-antenna broad-band phased arrays in a single formed beam. For each configuration, e ffi ciencycurves are drawn for per-beam trigger rates of 1 kHz, 100 Hz, and 10 Hz by thedark-solid, dashed, and light-solid line, respectively. iments, such as ANITA. We measure the e ffi ciency for a singleantenna, the 0 ◦ beam formed by using 2 antennas, and the full3-antenna 0 ◦ beam by comparing the power, calculated withinthe time window corresponding to the time when the pulse wastransmitted using Equation 4, to the appropriate threshold levelfor the chosen trigger rate. The measured trigger e ffi ciency at atrigger rate of 100 Hz, specified by Figure 8 using the 8-sampleinterval, is shown in the left plot in Figure 9.These measurements compare well with simulation resultsshown by the solid lines in the left-hand plot of Figure 9. Thesimulated curves include 5000 events in which the average im-pulse response of each antenna is added to the appropriate levelof uncorrelated system noise (75 K for our system plus 300 Kof room temperature thermal noise). We chose to simulate 5000events to achieve standard errors that are < ffi ciency curves for the 8- and 16-antenna arrays assume equal impulse response for each antennachannel. A 16-antenna linear phased array that is set to triggeron impulsive events in a single beam at 100 Hz achieves a 50%e ffi ciency at a SNR of about one. This is an improvement ofa factor of four in SNR over single-antenna trigger thresholds,which reach 50% e ffi ciency at an SNR of about four at the sametrigger rate.
5. An In-Ice Phased Array at Summit Station
We have also studied thermal noise using an analog interfer-ometric phased array in the ice at Summit Station in Greenland.In this Section, we describe the site, the analog phased arraydeployed there, and the noise environment observed with thephased array.
Summit Station is a year-round NSF-operated site, located atN 72 ◦
37’ W 38 ◦ ff ective volumeof ice in which neutrino interactions are observable for a givenradio detector configuration, directly related to the sensitivityof the experiment. The depth-averaged field attenuation lengthat Summit Station has been measured to be (cid:104) L α (cid:105) = + − m at75 MHz [18]. To directly compare this measurement with radioattenuation length measurements that have been made previ-ously at other sites of developing and proposed neutrino detec-tors, such as the South Pole (the site of ARA) and Moore’s Bayon the Ross Ice Shelf (the site of ARIANNA), this measurementis extrapolated to 300 MHz and averaged over only the upper1500 m of ice, which is where the interaction vertex would befor most neutrino events that are detectable by a surface or sub-surface detector. Assuming the measured temperature profile ofice at Summit Station and measured dependence of attenuationlength on frequency, this indicates an average field attenuationlength of 1022 + − m over the upper 1500 m [18], comparedto 1660 + − m over the top 1500 m at 300 MHz at the SouthPole [14] and 411 m with an experimental uncertainty of about40 m averaged over all depths for the 578 m thick Moore’s Baylocation [19, 20].We can compare the electric field loss as a function of dis-tance traveled through ice for the three candidate sites, whichis the metric that is directly related to neutrino e ff ective volumefor a given detector. Figure 10 shows the electric field loss asa function of radio propagation distance through ice at candi-date sites for neutrino detectors (Moore’s Bay, the South Pole,
500 1000 1500 2000
Distance (m) -6 -5 -4 -3 -2 -1 R e l a t i v e E - f i e l d L o ss Summit/GNOSouth Pole/ARARoss Ice Shelf/ARIANNA
Figure 10: The electric field loss at 300 MHz as a function of radio propagationdistance through ice at potential sites for neutrino detectors (Moore’s Bay, theSouth Pole, and Summit Station). and Summit Station), including both the 1 / r geometric factorand the measured attenuation length at each site. For neutrinoevents, which typically occur hundreds of meters from the de-tector, the loss seen through the ice at Summit Station is com-parable to the loss seen through the ice at South Pole, and ismuch less than at Moore’s Bay. An instrument was deployed at Summit Station in June 2015to characterize the site and validate the phased array tech-nique with an array deployed in the ice, as discussed in Ref-erence [21]. The system used analog beamforming to combinesignals from multiple antennas, as shown in the schematic of theRF signal chain in Figure 11. The system used the same front-end amplifier system described in Section 2.1.1. Each front-endamplifier was preceded by a 200 MHz high pass filter to protectthe first stage amplifier from the 8 MHz transmitter at SummitStation. Coaxial Times Microwave LMR-240 transmitted theantenna signal to the surface over 115 m of cable. Variations inthe cable lengths led to sub-ns variation in arrival times betweenantenna channels.The signal from each antenna was split into two signal chainbranches using 3 dB splitters. The first branch of the chain car-ried signals from individual antennas, while the second branchformed beams in the beamformer by splitting signals from eachantenna eight ways, propagating signals from each antennathrough fixed delay lines of Times Microwave LMR-200, andcombining signals into eight beams at fixed angles from the hor-izontal. The LMR-200 delay lines ranged from 1.0 ns to 14 ns,corresponding to 0.25 m to 5.0 m and the signals were split andcombined into beams using 8-way Mini-Circuits ZCSC-8-13-S + power splitters. The system architecture allowed simultane-ous digitization of both the antenna channels and the beams.The instrument included up to eight broadband dipole an-tennas, described in Section 2.1.2. The number of antennas9 nalog Beamformer antennas x beams antennas + 200 MHz HP Filters + LNAs m LMR
240 450
MHz LP Filters X DRS Boards
MHz
BWBeam
Digitizers X DRS Boards
MHz
BWAntenna
Digitizers Beams Antennas
GHz
Tektronix
Mixed
Signal
Oscilloscope
Provides trigger from either beams or antennas Trig Figure 11: A schematic of the system deployed in Greenland. Only four signal chains and beam channels are shown for simplicity.Figure 12: Pictures of the system deployment in Greenland. Upper left: laying out the antennas on the surface, before lowering the front-end system down theborehole. Upper right: lowering the antennas, amplifiers, and cabling down the borehole. Lower left: the system installed down the borehole. Lower right: thedeployment camp, including deployment gantry and data-taking tent. / swith record lengths of 1024 points with four DRS4 evalua-tion boards . A Tektronix MSO5204B oscilloscope generateda global trigger for the digitizers using either automatic (unbi-ased) triggers or a threshold crossing on either an antenna orbeam channel.The eight antennas and front-end amplifiers were lowereddown the DISC borehole using the gantry and winch systemshown in Figure 12. The DISC borehole is located approxi-mately 0 . ff as theballoon drifts away. Intermittent, transient signals at 150 MHzand 433 MHz also appear in the downhole antennas, due to sta-tion communications at those frequencies. Figure 13 shows the power spectrum measured by a sin-gle downhole antenna. The power spectrum shown is themean of 200 individual power spectra of 500-sample wave-forms recorded on the oscilloscope and is corrected for the over-all gain in the signal chain. Uncertainties in the temperatures ofthe in-ice amplifiers and cables lead to a ± V RMS , beam , is the quadrature sum of the RMS voltages, V RMS , i , in the individual antennas after accounting for the rel-ative loss in the beamformer, L , which is -19.9 dB in powerfor the system deployed in Greenland. The loss in the beam-former is dominated by the 8-way splitter and 8-way combinerin each channel. Although digitizer noise is small ( <
2% forbeam channels and < .
5% for antenna channels) compared tothe system noise (thermal noise plus amplifier noise) level, weaccount for the RMS voltage from digitizer noise in both theantenna channels, V RMS D , i , and the beam channel, V RMS D , beam .The expected V RMS, beam is given by https: // / drs / evaluation-board http: // / equipment / disc.shtml Frequency (MHz)150 200 250 300 350 400 450 500 Sp e c t r a l P o w e r ( d B / G H z ) − − − − − − Downhole AntennaExpected Thermal Level (241 K)
Figure 13: The average power spectral density for unbiased, thermal-noise trig-gers of a downhole antenna (blue solid line) compared with 241 K thermal noise(dashed line). A ± V = L / (cid:16) (cid:88) N antennas (cid:0) V , i − V D , i (cid:1)(cid:17) + V D , beam . (5)Figure 14 compares the expected to the measured V RMS,beam for five antennas combined using the analog beamformer. Thisdata set consists of events recorded at a constant rate (unbiased)over the course of one night. A small fraction ( < . <
10% di ff erence between the expected and measured V RMS,beam shows that the noise observed by the downhole an-tennas adds incoherently when forming a beam, indicating thatnoise from adjacent in-ice antennas is uncorrelated. This is con-sistent with our results from anechoic chamber measurements(see Section 2.1).
6. Conclusions
The in-ice phased array for detection of high-energy neu-trinos is a promising technique. We have performed studiesthat demonstrate that thermal noise is uncorrelated betweentightly-packed neighboring antennas in each other’s nulls bothin an anechoic chamber and with an in-ice phased array atSummit Station. In the anechoic chamber, we have also vali-dated the beamforming technique through simulations and mea-surements, achieving the expected improvement in SNR whenbeamforming using an experimental system. Measurements atSummit Station of the noise environment and ice characteris-tics indicate that the site is suitable for an in-ice radio neutrinotelescope.11 (mV)
RMS
Expected Beam V ( m V ) R M S B ea m V Incoherent ExpectationCoherent Expectation
Mean 0.0093 − Std Dev 0.061
RMS ) / Expected Beam V
RMS - Beam V
RMS (Expected Beam V − − − Mean 0.0093 − RMS 0.061
Figure 14: Expected V RMS from a beam formed with five antennas compared to the measured V RMS (left) and the fractional di ff erence between the two (right). Thewidth of the distribution is dominated by the non-Gaussian behavior of the digitizer noise. A simulation including realistic parameters for an FPGA-based correlation trigger indicates that phasing signals frommultiple low-gain antennas yields significant improvement inachieved trigger threshold, consistent with idealized expecta-tions and anechoic chamber measurements. We are design-ing and constructing such a trigger to be implemented first atthe South Pole on the ARA experiment. Pending successfuldemonstration of the technique, a larger array with hundredsof antennas per station could be proposed either at the SouthPole or in Greenland to achieve a low energy threshold capableof providing significant overlap in energy with IceCube in thePeV energy range, and extending the measurement of high en-ergy neutrinos through the higher-energy cosmogenic neutrinorange.We would like to thank CH2M Hill and the US National Sci-ence Foundation (NSF) for the dedicated, knowledgeable, andextremely helpful logistical support team enabling us to per-form our work at Summit Station, particularly to J. Jenkins. Weare deeply indebted to those who dedicate their careers to helpmake our science possible in such remote environments. Wewould like to thank the University of Wisconsin-Madison Ice-Cube and ARA groups for allowing us to use their anechoicchamber and the ARA collaboration for lending the ARA bi-cone and slot antennas for testing. We also thank D. Arakakifor the use of anechoic chambers at the California Polytech-nic State University for antenna characterization measurements.This work was supported by the Kavli Institute for Cosmologi-cal Physics at the University of Chicago, Department of EnergyGrant de-sc0009937, and the Leverhulme Trust. Computing re-sources were provided by the University of Chicago ResearchComputing Center.
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