DATA PREPROCESSING FOR DECAMETRE WAVELENGTH EXOPLANET DETECTION: AN EXAMPLE OF CYCLOSTATIONARY RFI DETECTOR

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1 5th Euroean Signal Processing onference (EUSIPO 7 Poznan Poland Setember coyright by EURASIP DATA PREPROESSIG FOR DEAMETRE WAVELEGTH EXOPLAET DETETIO: A EXAMPLE OF YLOSTATIOARY RFI DETETOR R.Weber P.Zarka V. B. Ryabov 3 R.Feliachi J.M. Grieβmeier L. Denis 4 R. V. Kozhyn 5 V. V. Vinogradov 5 P. Ravier LESI Polytech Orléans Université d Orléans Orléans France rodolhe.weber rym.feliachi hilie.ravier@univ-orleans.fr LESIA Observatoire de Paris RS UPM Université Paris Diderot France hilie.zarka jean-mathias.griessmeier@obsm.fr 3 omlex Systems De. Future University Hakodate Hokkaido Jaan riabov@fun.ac.j 4 Station de radioastronomie de ançay Observatoire de Paris RS/ISU ançay France laurent.denis@obs-nancay.fr 5 Institute of Radio Astronomy ational Academy of Sciences of Ukraine Microwave Electronic De. Kharkiv Ukraine vin@radar.kharkov.com krv@ira.kharkov.ua ABSTRAT The relatively high contrast between lanetary and solar low-frequency radio emissions suggest that the lowfrequency radio range may be well adated to the direct detection of exolanets. Detection is based on temoral and sectral ower integration to remove statistical fluctuations of the sky background noise. However strong limitations in articular due to radio frequency interference (RFI may imair such detection. Indeed if not detected a RFI may be interreted as an exolanet signal or may conceal it. After a short summary of the detection rincile in radio astronomy we describe the algorithms roosed to remove RFI. First method designed for rather strong RFI is based on ower threshold detection. The second one is based on the cyclostationary roerties of amlitude modulation RFI. The main advantages of the latter are the detection of weak RFI without confusion with otential signal. The statistics of this RFI detector are derived as a function of the integration time and the interference to noise ratio.. ITRODUTIO The main limitation to the direct detection of exolanets in the infra-red or visible range is the very high contrast between star and lanet luminosity together with their small angular searation as measured from stellar distance. However in the low-frequency radio range ( MHz to 4 MHz the relatively high contrast between lanetary and solar radio emissions suggests that direct exolanet detection could be erformed. In articular it has been shown [] that a secific class of Juiter-like lanets called hot Juiters may roduce very intense radio emissions due to electromagnetic interactions with their nearby star. The exected flux in the vicinity of these exolanets can be 3 to 6 times higher than that of our Juiter. Thus in site of the stellar distance detection of such low frequency emissions from ground-based radio telescoes seems ossible. In order to rove it we have thus started an observational roject which associates a very large decametre array in Ukraine and a modern digital sectrometer and waveform receiver (see Figure and Table. The technical art of this roject is described in the resent aer. However this detection is not straightforward. Indeed decametre radio observations suffer strong limitations due to severe sky background noise ionosheric erturbations and natural or man-made radio frequency interferences (RFI. The scoe of this article is to describe the strategies chosen to overcome these limitations. In articular we will focus on the digital signal re-rocessing techniques used to clean the data before any exolanet detection attemt. In section the rincile and limitation of detection in low frequency radio astronomy are briefly described. The main characteristics of the radio telescoe and the receiver used are also given. In section 3 the RFI mitigation strategy is resented. The case of low level RFIs is discussed in section 4 where a secific detector based on cyclostationarity is roosed. Its statistical roerties are defined and its erformances are analysed.. PRIIPLE AD LIMITATIOS OF THE DETETIO PROESS From a radio astronomer oint of view an ideal world would be a centred Gaussian one. Thus the ideal measured signal would be written as: s( n = ( + ( + ( sys sky source system noise skybackground noise source of interest if any where ( are centred Gaussian noise with variance. With this model only second order statistics are needed and raw data rovided by radio telescoes can be limited to time-frequency (t-f reresentations of the measured ower: ( ( = Sτ B ( t f s( n dn B τ where B is the frequency bandwidth with central frequency f and τ is the time interval centred at the instant t. From Equ.( and Equ.( the S ( t f statistics are easily derived. Its standard deviation σ is called the measurement sensitivity. In radio astronomy and in articular for deca- 7 EURASIP 459

2 5th Euroean Signal Processing onference (EUSIPO 7 Poznan Poland Setember coyright by EURASIP sys + sky + source + sys sky Sτ B( t f OFF metre wavelength we can consider that source << sys << sky. Thus the sensitivity verifies the following relation: σ sky (3 Bτ As shown in Figure assuming that sys+ sky is obtained by a calibration rocedure a source can be detected when the sensitivity σ is less than source σ O Figure Detection and sensitivity. During the OFF (resectively O rocedure the source is suosed to be out of (res. in the radio telescoe beam. A source can be detected when the sensitivity σ is less than its mean ower source. The sensitivity can be adjusted through the integrated bandwidth B the integration time τ and the sky background noise ower sys. In our case the exected exolanet flux is between 5. - Jy (Jy= -3 W/m /Hz and 5 Jy to be comared with the sky background flux which is around 7 Jy [].. To imrove this sensitivity several otions are ossible: Using a large effective area telescoe Ae. Indeed sky is inversely roortional to Ae. Figure gives some characteristics of the radio telescoe used for our observations. Its Ae will reduce sky by 5 db. Frequency smoothing by enlarging the bandwidth B. A secific broadband receiver has been designed for the roject. Its characteristics are given in Table. If the full bandwidth can be used the sensitivity will gain 36 db more. Temoral smoothing by adjusting the integration time τ. In ractice other limiting factors may degrade the ultimate sensitivity: ionosheric roagation effects (strong scintillations for frequencies below f<3 MHz. Mitigation of these effects requires a secific O-OFF rocedure using the radio telescoe multi-beam caability (descrition is beyond the scoe of this article. natural RFI. They are generally broadband and imulsive (e.g. lightning. Bτ Table Overview of the digital receiver designed for the roject Digital Receiver for exolanet detection Samling 6 bits baseband Embedded direct recording of waveform rocessing dynamic ower sectrum (496 channels dynamic cross-sectrum (496 channels recording Waveform snashots u to Gb U to 4 MHz sectrum anywhere within the band of -33 MHz sectral resolution 4kHz current minimum temoral resolution ms sky tf Figure Overview of the UTR- radio telescoe located near Kharkov (Ukraine. It is a T-shae hased array with 4 dioles. Its effective area is around 4 m. Its frequency range of oeration is 7 MHz to 3 MHz. manmade RFI. They are most often narrowband amlitude modulation (AM signals. Sensitivity otimisation in the resence of RFIs is based on their detection and blanking (i.e. t-f blocks S ( t f must be discarded when olluted before any further t-f ower integration. If not detected a RFI may be interreted as an exolanetory signal or may conceal it. So the t-f resolution becomes one of the key arameters of RFI mitigation. In [] a study on this question is roosed. Practically there is a comromise in terms of t-f resolution between the hardware comlexity and the RFI t-f characteristics. For the roject a 4 khz sectral resolution and a ms temoral resolution have been selected. Table summarizes the other characteristics of the receiver. The second key arameter for efficient RFI mitigation is the erformance of RFI detection algorithms. This toic is a growing subject of research in radio astronomy [34] but not only [5]. In the following our RFI detection strategy will be described. 3. RFI DETETIO STRATEGY By including the RFI the received signal becomes: s( n = b( n + ( n (4 Where b(n is the clean Gaussian signal defined by Eq. and (n is the RFI only defined for the moment by its mean ower. Let us define the interference to noise ratio: inr= where = + ( + which are defined by Eq.. sky sys source Given that the RFI are imulsive or narrow band they will ollute horizontal or vertical lines of S ( t f blocks on the t-f ower lane (an examle is given on Figure 3 for strong RFI. A first algorithm has been develoed to remove the olluted (t-f blocks. The rincile is based on a robust threshold 7 EURASIP 46

3 5th Euroean Signal Processing onference (EUSIPO 7 Poznan Poland Setember coyright by EURASIP Dedisersion of the ulse of interest Figure 4 (a raw dynamic sectrum after the first ste RFI detection algorithm described in Figure 6. The ulses (observed from a ulsar are drifting from high to low frequencies; (b dedisersed dynamic sectrum. The ulse is now vertical and can be easily detected by integrating all the frequencies at a given time. Figure 3 (a Dynamic sectrum of the galactic background covers a time interval of s (time resolution ms and the frequency band 4 8 MHz (sectral resolution 7 khz. The normalized distribution lotted on the right has a high intensity tail corresonding to RFI. (b is the ma resulting from an automated offline recognition of surious t-f blocks (in black. (c = (a (b is the original dynamic sectrum with surious blocks masked out. Statistical background fluctuations are clearly visible due to the stretched dynamic range of the image. The corresonding distribution of intensities is lotted above it and is nearly erfectly Gaussian indicating that all RFI have been effectively suressed down to the 3σ level. detector. This kind of method is generally limited by the recision of the reference estimation [56]. The comlete rocedure is described in [78] and Figure 3 illustrates some of the stes. In this way RFI above 3σ can be removed but it is not sufficient to reach the sensitivity which is necessary for exolanet detection. For lower inr RFI detection the two kind of RFI will be rocessed differently. The weak imulsive case will be rocessed during the exolanet detection hase. Indeed to enhance the exolanet detection we must correct the effects of roagation of radio signals through the interstellar medium and esecially the disersion of broadband short ulses. omensation of the ulse distortion (dedisersing can be erformed by introducing recalculated time delays to the outut of each receiver frequency channel. An examle of alication of this rocedure to ulsar signals detected at UTR- is shown in Figure 4. Inversely dedisersing will sread imulsive RFI ower over time. Unfortunately it will useless for narrowband AM RFIs. The next section will describe a narrowband AM detector based on the cyclostationary roerties of such RFI. 4. YLOSTATIOARY DETETOR A signal is cyclostationary at order if its correlation function is a eriodic function of time [9]. From a sectral oint of view the following criterion can be derived: α τ τ ( τ = lim s( n+ s( n / iπα n e (5 + n= / where α is the frequency related to the eriodicity (α is also called the cyclic frequency. If s(n is stationary α ( τ will be null. Otherwise if s(n is cyclostationary with cyclic frequency α then α ( τ will be non zero. In τ τ other words the quadratic signal s( n+ s( n will resent a sectral line at frequency α. Most of the signals generated by telecommunication systems resent such cyclostationarity due to their modulation. In articular the following AM modulation RFI is cyclostationary: ( n = a( ncos( π f n+ ϕ (6 where a(n is stationary signal with unit mean ower. This AM signal has a cyclic frequency equal to f o and Eq. 5 can be rewritten as [9]: ( τ = R ( τ e ϕ f i a where R a (τ denotes the autocorrelation function of a(n. If we limit the revious equation to τ= we obtain the following criterion: = / lim s( n + n= / o i fn e π if no AM modulation at f = if AM modulation at f These two cases are called resectively H and H hyothesis and they are erfectly searated. Unfortunately this erformance is asymtotic. In ractice the number of samle is limited. Thus is no more deterministic and its statistics must be studied to derive the new contrast between these two hyotheses. The next sections will state the statistics for the following functions: α iπα n = s( n with α= and f. n= e 7 EURASIP 46

4 5th Euroean Signal Processing onference (EUSIPO 7 Poznan Poland Setember coyright by EURASIP Figure 5 D distribution comarison. For the theoretical distributions Equ. 9 (resectively Equ. is used for H (res. H hyothesis. The measured histograms are based on trials of each configuration. Two extreme scenarios has be chosen: a ure sine wave (a(n fully correlated or a modulated white noise (no correlation between the a(n. For low inr the theory fits the simulations. The case α= will be used to define a normalized criterion in section 4.3. Besides the following assumtions will be used in the rest of the aer: (A is large enough to aly the central limit theorem. (A The inr is low (i.e inr <. 4. H hyothesis statistics Under this hyothesis s(n is a i.i.d Gaussian noise with variance. By using the assumtion (A the statistics of α are easily derived: f : ( f π : R( and E( H = f π var( H = ( where R(.. is a Raleigh-Rice distribution defined in the aendix. The first remark is that the mean of more equal to zero. 4. H hyothesis fo is no Under this hyothesis s(n is given by Equ. 4 and Equ. 6. The first following result is derived: Figure 6 Power detector vs. cyclostationary detector. One of the advantages of the cyclostationary detector is its insensitivity to ower fluctuations. (a In the examle above the inr is maintained at -db but the total ower may fluctuate with time. It aears that the classical ower detector may misinterret at least of the 3 last cases: the (RFI+sky/. can not be detected if it rejects the (RFI+sky case it will also reject the (sky+source case 3 if it kees the (sky+source case it will also kees the (RFI+sky case. (b On the contrary the cyclostationary detector D detects the RFI roerly. = + E( s s + var( 4. For the latter equation we use the assumtion (A to remove any contribution due the correlation between the a(n samles. Then with the assumtion (A and the aroximation given in Equ. 7 the statistics of α becomes: : (. f + R : ( From these statistics a normalized detector criterion is defined in the next section. 4.3 ormalized detection criterion We define a normalized version of our criterion as: D f (7 = (8 By using the following aroximation E( the theoretical D statistics becomes : H or H H: R( under the H hyothesis (9 inr + inr H: R( ( + inr ( + inr ( 7 EURASIP 46

5 5th Euroean Signal Processing onference (EUSIPO 7 Poznan Poland Setember coyright by EURASIP this case it can outerform classical ower detectors. A blind detector is also roosed. Its oerational imlementation (on the receiver used for the exolanet detection is still under study. 6. APPEDIX The Raleigh-Rice distribution R ( µ λ is defined by: r + µ r µ r λ e R( r / µ λ = I ( r λ λ Figure 7 Probability of detection vs. robability of false alarm for the detector resented in section 4.4. This simulation is based on runs of each scenario. In cases (a to (d f o is chosen so that f o is multile of / (i.e. the f sectral line is in the middle of the bin FFT channel no attenuation. In case (e the f sectral line is between two bin FFT channels which is the worst case. The channel attenuation at nyquist frequency for a rectangular window is db. Thus (e should be similar to (a. In Figure 5 Monte-arlo simulations are resented. For low inr theoretical statistics from Equ. 9 and Equ. are verified. One of interest of such detector is its insensitivity to ower fluctuations (see Figure 6. From Equ. 9 the threshold can be easily derived and is equal to ln( fa where fa is the false alarm robability. 4.4 Final detection algorithm From the revious analysis we roose an oerational detector which can be alied on comlex (i.e. not real channel with unknown carrier AM modulation RFIs: hannelization of the signal coming from the radio telescoe. The signal in each channel is suosed to be comlex. This rocess is done in real time by the digital receiver (see Table. M is the number of channels. s r (n and s i (n are resectively the real and imaginary art of the signal from one of the M channels. We comute the Fourier transform FFT r i ( f over samles on both s r (n² and s i (n². 3 According to a given threshold ξ we will consider that a RFI is resent on this channel if: r i FFT ( k FFT ( k k > / + ξ r i FFT ( FFT ( Figure 7 shows erformance measurements of such detector. To be otimally detected the RFI carrier frequency should be multile of /. If not the erformance in term of inr will decrease. For examle with a rectangular windowing the maximum degradation will be around db. 5. OLUSIOS In the context of exolanet detection we have described the algorithms roosed to remove RFI from a time-frequency ower lane. In articular we have defined an original method based on the cyclostationary roerties of the RFI. This cyclostationary detector is useful for low level RFI. In where I (. is the modified Bessel function of order. Its mean is given by : 4 e µ λ π µ µ µ µ E( r = λ + I ( + I ( λ 4λ λ 4λ where I (. is the modified Bessel function of order. And its variance is given by: AKOWLEDGMETS var( r = µ + σ E( r This roject is suorted by the french national research agency (AR under contract number T5-_453 RADIO- EXOPLA. REFEREES [] P. Zarka Plasma interactions of exolanets with their arent star and associated radio emissions Planetary and Sace Science doi:.6/j.ss [] V. lerc R. Weber L. Denis. Rosolen high erformance receiver for mitigation in radio astronomy: alication at decameter wavelengths in Proc. EUSIPO Toulouse France [3] P.A. Fridman and W.A. Baan RFI Mitigation Methods in Radio Astronomy Astronomy & Astrohysics vol [4] P.A. Fridman RFI Excision using a higher order statistics analysis of the ower sectrum Astronomy & Astrohysicsvol [5] M. Ghozzi M.Dohler F.Marx J. Palicot ognitive radio: methods for the detection of free bands.r. Physique [6] R.Weber.Viou A.offre L.Denis P. Zarka and A.Lecacheux DSP Enabled Radio Astronomy: Towards IIIzw35 Reconquest JASP Vol [7] P. Zarka and al. Ground-based high sensitivity radio astronomy at decameter wavelengths. In: Rucker H.O. Bauer S.J. Lecacheux A. (Eds. Planetary Radio 997 [8] Ryabov V. B. P.Zarka and B. P. Ryabov Search of exolanetary radio signals in the resence of strong interference : Enhancing sensitivity by data accumulation Planet. Sace Science [9] W. A. Gardner Statistical Sectral Analysis - A onrobabilistic Theory. ew Jersey: Prentice Hall EURASIP 463