Table Of ContentXXV European Cosmic Ray Symposium, Turin, Sept. 4-9 2016 1
Improving reconstruction methods for radio measurements with Tunka-Rex
P.A. Bezyazeekova, N.M. Budneva, O. Fedorova, O.A. Gressa, A. Haungsb, R. Hillerb, T. Huegeb,
Y. Kazarinaa, M. Kleifgesc, E.E. Korostelevad, D. Kostuninb, O. Kr¨omerc, V. Kungelb,
L.A. Kuzmichevd, V. Lenoka, N. Lubsandorzhievd, T. N. Marshalkinaa, R.R. Mirgazova, R. Monkhoeva,
E.A. Osipovad, A. Pakhorukova, L. Pankova, V.V. Prosind, F.G. Schr¨oderb, A. Zagorodnikova
aInstitute of Applied Physics ISU, Irkutsk, Russia;
bInstitut fu¨r Kernphysik, Karlsruhe Institute of Technology (KIT), Germany;
cInstitut fu¨r Prozessdatenverarbeitung und Elektronik, KIT, Germany; and
dSkobeltsyn Institute of Nuclear Physics MSU, Moscow, Russia;
Tunka-Rex is a detector for radio emission produced by cosmic-ray air showers. It is located in
Siberia, and triggered by Tunka-133, a co-located air-Cherenkov detector during night, and by the
7 scintillator array Tunka-Grande during day. Tunka-Rex demonstrates that the radio technique can
1 provide a cost-effective extension of existing air-shower arrays. Operating in the frequency range
0
of 30-80 MHz, Tunka-Rex is limited by the galactic background and suffers from the local radio
2
interferences. Weinvestigatethepossibilitiesofimprovingmeasureddatausingdifferentapproaches,
b particularly,amultivariatetreatmentofbackgroundisconsidered,aswellasanimprovedlikelihood
e fit of the lateral distribution of amplitudes.
F
9
I. INTRODUCTION radio amplitudes.
]
M
Tunka-Rex [1, 2] is an antenna array for the de-
II. STANDARD PROCEDURE OF DATA
I tection of radio emission of extensive atmospheric
. RECONSTRUCTION
h showers (EAS) created by cosmic rays [3]. It works
p jointly with the non-imaging air-Cherenkov light de-
- tector Tunka-133 [4] and the scintillators of Tunka- For signal reconstruction Tunka-Rex uses a modi-
o fied radio extension of the Offline software framework
Grande [5] and receives triggers from both of them.
r
t ComparingtoclassicalopticalmethodsofEASdetec- developed by the Pierre Auger Collaboration [10].
s
Raw Tunka-Rex data consist of ADC traces from the
a tion,detectionofradioemissionisinterestingbecause
[ itisindependentofthetimeoftheday(measurements detector containing measured amplitudes in two or-
are possible during sunlight) and of weather condi- thogonal polarizations. The signal reconstruction in-
3
cludes following steps:
v tions (except thunderstorms). Consequently, radio
8 has higher duty-cycle than optical methods. Tunka-
1. Upsampling of recorded traces by a factor of 4,
5 Rexantennasarestableandcost-effectiveandableto
and applying the following filters: first, a band-
1 operate in a sparse large-scale configuration [6, 7].
stop filter suppresses narrowband interferences
5
At the present moment Tunka-Rex consists of 63
0 occurringeach5MHz;second,abandpassfilter,
antennas covering an area of about 3 km2. Each
. restricts the band to 35–76 MHz;
1 Tunka-Rex antenna station consists of two perpen-
0
dicularly aligned SALLAs (Short Aperiodic Loaded 2. The amplitude of the measured signal S is de-
7
Loop Antenna) [8, 9] with 120 cm diameter mounted finedasmaximumofHilbertenvelopeinthesig-
1
: on a wooden pole on a height of about 2.5 m. At nal window of the recorded trace;
v
the top they are connected to a low noise amplifier
i 3. The noise level N is defined as RMS of ampli-
X (LNA). This LNA is connected to a filter-amplifier
tudes in the noise window.
via30mcoaxialRG213cables. THefilter-amplifieris
r
a connectedtotheTunka-133orTunka-GrandeFADCs
The SNR is calculated as square of ratio between
with a short 1 m RG52 cable. The sampling rate of
measured signal and noise:
the FADCs is 200 MHz, and the length of the trace is
1024 samples with a bit depth of 12 bit. SNR=S2/N2. (1)
Tunka-Rex operates in an environment with low
signal-to-noiseratio(SNR)conditions,thatrequiresa AntennastationswithSNR<10inatleastoneofthe
sophisticated post-processing of recorded traces. The channels are rejected.
standard approach is to use different filters (broad- The rest of the stations is used for the reconstruc-
band or narrowband) to increase the SNR. Then, the tionofthearrivaldirectionbyfittingpeaktimeswith
signalpeakisdefinedasmaximumofthefilteredtrace. a plane wavefront model. Knowing the arrival direc-
The aim of the present work is developing and test- tion (shower axis), the electrical field is reconstructed
ingnewmethodsfortheimprovementofsignalrecon- by applying the antenna pattern and assuming that
struction and for fitting the lateral distribution of the theelectricalfieldalongtheshoweraxisiszero. Then
eConf C16-09-04.3
2 XXV European Cosmic Ray Symposium, Turin, Sept. 4-9 2016
the cut SNR≥10 is applied again for the vectorial 0.2 σ from Tunka-Rex simulations
n
traces of the electrical field on the antenna station. 0.18 LOPES parametrization (w/o systematics)
Let us consider the influence of the noise on the
0.16
measured signal. The signal measured at the fre-
quency ν is defined as sum of the true signal and the )m 0.14
A
noise contribution: A|/t 0.12
Aνmeiφm =Aνteiφt +Aνneiφn, (2) (|A-nm 0.1
σ 0.08
where Aν , Aν, Aν are the amplitudes of the mea-
m t n 0.06
sured,trueandnoisesignals,inthefrequencydomain,
and φ , φ , φ are their phases. The unknown phase 0.04
m t n
of the noise component can shift resulting amplitude 0.02
by ±30% for SNR=10. 0 20 40 60 80 100
The contribution of the noise to the total power of SNR
measured signal is corrected using the parameteriza- FIG.1: Dependenceoftheuncertaintyofthesignalrecon-
tion: structionontheSNR.Thepointsareobtainedasstandard
deviation of normalized difference between simulated and
At =f(SNR)Am, (3) reconstructed amplitudes using the Tunka-Rex noise li-
brary and hardware response (thespread betweenneight-
where boring bins is due to low statistics); the curve is obtained
(cid:112) from a LOPES parameterization (see Eq. 5), and is in
f(SNR)= 1−k/SNR, (4)
agreement with Tunka-Rex simulations.
where parameter k is extracted from a fit to simu-
lations (details in [6]), and then this parameteriza-
containing separated samples containing pure noise
tion is applied to the measured signals. Besides this
and samples with background pulses The network re-
effect, the measured amplitude is characterized by
turns two values: first the probability of pure noise
the uncertainty defined as standard deviation σ of
n and,second,theprobabilityofbackgroundpulse(with
(A −A )/A . This uncertainty is parameterized by
m t m high SNR). Resulting efficiency of that classification
LOPES [11] as a function of SNR (see Fig. 1):
is98%. Fortheamplitudereconstructionwedesigned
a (cid:16) √ (cid:17) another type of neural network, with the following
σ = √ b+cexp(− SNR/a) , (5)
n structure:
SNR−a2
• 200 input neurons
where a=0.602, b=0.616 and c=0.213 are dimen-
sionless parameters. This uncertainty is included in
• 3 hidden layers, with each 500 neurons
the chi-square fit of the lateral distribution function
(LDF) [12]: • 1 output neuron
E(r)=E exp(cid:0)a (r−r )+a (r−r )2(cid:1) , (6) The activation function of the neurons is sigmoid, for
0 1 0 2 0
trainingweuseresilientpropagationmethod. Thein-
where E(r) is the amplitude at the antenna station put layer takes the Hilbert envelope of trace with 200
with distance r from the shower axis, E is a normal- ADCcountsofthetracecenteredaroundtheassumed
0
ization factor proportional to the energy of the pri- signalasinput. Theoutputneuronreturnstherecon-
mary cosmic ray, r is an arbitrary parameter chosen structed amplitude. As training dataset we simulated
0
to obtain maximum correlation with the primary en- radio pulses with CoREAS [14] (for two Tunka-Rex
ergyandthedistancetotheshowermaximum,a and channels) and then distort them using a background
1
a areparametersproportionaltotheslopeandwidth library collected by the Tunka-Rex experiment. The
2
of the LDF, respectively. example of traces is given in Fig. 2. Training dataset
contains about 7000 distorted traces with different
SNR levels and known amplitude of true (simulated)
III. SIGNAL RECONSTRUCTION WITH A signal. In each training epoch, the network takes 200
NEURAL NETWORK valuesofdistortedtracesasinputandthevalueofthe
true amplitude as output.
For the design of the neural network we use the For training and test of the neural network we se-
PyBrain library [13] written in Python. At the first lectedonlytracescontainingatruesignalhigherthan
stage we have trained a test network which performs the noise level (i.e. SNR>1). Thus, network is not
the classification of the transient background in a sig- able to distinguish between pure noise and low-SNR
nal window. It is simple “perceptron” (neural net- signals,butisabletoreconstructamplitudeforsignals
work with single hidden layer) trained on a dataset with SNR>1.
eConf C16-09-04.3
XXV European Cosmic Ray Symposium, Turin, Sept. 4-9 2016 3
e) m]
cal True (simulated) signal V/500
arbitrary s 1200000 plitude [µ400 slope estimator
de ( -100 Am300
plitu -200 old
m 0 100 200 300 400 500 600 700 200
A Upsampled ADC counts (each 1.25 ns) new
ale) True signal + noise trace 100 threshold
c
s
y 200
bitrar 100 100 200 300 400 500 600 700 800
ar 0 Distance to radio shower axis [m]
e ( -100
d
mplitu -2000 100 200 300 400 500 600 700 F(oIlGd). 4a:ndDimffoerdeinficeedb(entewwe)enlikbeelishtoLoDdFfufintcstiuonsisn.gAstlathnoduagrhd
A Upsampled ADC counts (each 1.25 ns) the visual change of the slope is not very significant, the
reconstructed depth of shower maximum has changed by
about100g/cm2inthiscase. Letusnote,thatsuchevents
are not passing standard X quality cuts of Tunka-Rex
FIG. 2: Example of ADC trace with clear (top) and dis- max
reconstruction.
torted (bottom) signal.
IV. OPTIMIZATION OF LIKELIHOOD LDF
FIT
500 Forthefittingoflateraldistributionfunction(LDF)
fit
the standard chi-square fit is used, where uncertain-
σ=20.27
ties are defined as a function of SNR (see Sec. 2).
400 µ=3.16
Thisway,theamplitudesfromantennasstationswith
nts SNR>10 are included in the fit and weighted with
ve 300 theiruncertainties. Theinformationfromtheantenna
e
of stations without signal was not used. However, they
er still contain information about the confidence levels
b 200
m of the signal amplitudes, i.e. these stations provide
u
N an upper limit for the amplitude. They are weighted
100 according to the general threshold of signal detection
if the fitted LDF is higher than this threshold, and
the get zero weigth if the LDF is already below the
0 threshold.
-100 -50 0 50 100
Thus, we modified the LDF fit and defined a likeli-
Deviation between true and reconstructed amp. in %
hood function as follows:
FtuIdGe.g3i:veDnebvyiatthioennebuertawleneentwtrourekafonrdsirgencaolnsswtriutchtSedNRam<pl5i-. L=(cid:89)N exp(cid:26)−(cid:20)(fi2−σ2yi)2Θ(yi−yth)
i=0 i
(f −y )2 (cid:21)(cid:27)
+ i th Θ(f −y )Θ(y −y ) , (7)
2y2 i th th i
th
and the chi-square becomes
ingRduantnaisnegththaessdheoswignnetdhantetuhrealunnceetwrtoarikntyonofththeetaemst-- χ2 =(cid:88)N (cid:20)(fi−yi)2Θ(y −y )
σ2 i th
plitude reconstruction is about 20%, which is worse, i=0 i
than given by our standard methods. However, the (f −y )2 (cid:21)
same uncertainty is obtained for very low SNRs, and + i y2 th Θ(fi−yth)Θ(yth−yi) , (8)
the correction for the bias due to noise is obtained th
automatically. The distribution of (A −A )/A for where f and y are the fitted and measured values of
m t m i i
signals with SNR<5 processed with the neural net- theamplitudes, σ istheuncertaintyofi-thstationof
i
work is given in Fig. 3. N, Θ(x) is the Heaviside step function.
eConf C16-09-04.3
4 XXV European Cosmic Ray Symposium, Turin, Sept. 4-9 2016
One can note, that antenna stations with am- resulting precision of the reconstructed ampli-
plitudes y <y are weighted with y , where tude is worse comparing to our standard meth-
i th th
y ≈90 µV/m is the threshold of signal detec- ods, however the neural network shows better
th
tion [15]. Since y ≥10σ for SNR > 10 the weights performance at low SNRs (<5). We plan to
th i
of the antenna stations without signals are relatively continue this study by testing different configu-
small. The first tests of this modified LDF fitting rations of neural networks and another machine
have shown, that the reconstruction of air-shower pa- learning methods, e.g decision trees.
rameters is slightly improved, however this simple
• Modification of LDF fit. We added weights of
parameter-free weighting can be further developed.
antenna stations without signal into the stan-
An example of a modified fit is given in Fig. 4. It is
dard chi-square fit. The simple parameteriza-
worthnoticing,thatonlyreconstructionoflow-quality
tion of the weights shows a slight improvement
events (e.g. not passing X quality cut, see Ref [6]
max
of the air-shower reconstruction. We plan to
for details) is significantly affected, the result of the
tune parameters in order to optimize weighting
reconstruction of the standard event set is almost the
of the antenna stations without signal. After
same. Which means, that such improvement of LDF
thisweincludethisstationsalsoforshowercore
fitting can increase the statistics near threshold.
reconstruction with radio.
V. SUMMARY
Acknowledgments
We present our current progress on the improve-
The construction of Tunka-Rex was funded by the
ments of reconstructing radio events from cosmic-ray
GermanHelmholtzAssociationandtheRussianFoun-
air-showers. We have worked in two directions: re-
dationforBasicResearch(grantHRJRG-303). More-
constructionofthelow-SNRradiopulsesusingneural
over, this work was supported by the Helmholtz Al-
networks,andimprovingthefitoftheLDFbyinclud-
liance for Astroparticle Physics (HAP), by Deutsche
ing stations with amplitudes below the SNR cut.
Forschungsgemeinschaft (DFG) grant SCHR 1480/1-
• Low-SNR signal reconstruction. This study 1, and by the Russian Federation Ministry of Educa-
shows that machine learning has a potential tion and Science (agreement 14.B25.31.0010). More-
forsolvingtasksrelatedtomulti-variablecondi- over,thisworkwassupportedbytheRussianFundof
tions,likeradiobackground. ForhighSNRsthe Basic research grants 16-32-00329 and 16-02-00738.
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eConf C16-09-04.3
