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Robust Mean Estimation for Real-Time Blanking in Radioastronomy

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Robust Mean Estimation for Real-Time Blanking in Radioastronomy ROBUST MEAN ESTIMATION FOR REAL-TIME BLANKING IN RADIOASTRONOMY Philippe Ravier1, Cedric Dumez-Viou1−2 1Laboratory of Electronics, Signals, Images, Polytech'Orleans´ - University of Orleans 12, rue de Blois, BP 6744 Cedex 2, F-45067 Orleans,´ France 2Observatoire de Paris/(CNRS No.704), Station de radioastronomie, F-18330 Nanc¸ay, France phone: + (33).2.38.49.48.63, fax: + (33).2.38.41.72.45, email: [email protected] web: www.obs-nancay.fr/rfi ABSTRACT assumption does not hold anymore and the exact PDF must be taken into account for precise threshold derivation. Radio astronomy observations suffer from strong interfer- ences that need to be blanked both in the time and frequency domains. In order to achieve real-time computations, in- 2. PROCEDURE USED FOR REAL-TIME terference detection is made by simple thresholding. The In order to achieve real-time computation, a simple thresh- threshold value is linked to the mean estimation of the power olding drives the time and/or frequency blanking decision. 2 of clean observed data that follows a χ distribution. Spu- The problem is formulated as the following binary hy- rious values insensitivity is obtained by replacing mean by pothesis test: robust mean. A theoretical study of the variance of three es- timators of the mean is presented. The study leads to a prac- tical trimmed percentage that is chosen for the robust mean. H0 : the SOI only is present, H1 : the SOI is polluted with additive interference. 1. INTRODUCTION The SOI is supposed to be Gaussian. On the other hand, Radioastronomy benefits from protected bands for the study no a priori information about the interference PDF is avail- of radio-sources. However, useful information is some- able. Nevertheless, the interference is usually powerful com- times only available in bands occupied by telecommunica- pared to the SOI. So the decision of blanking is made accord- tion users. In those cases, signals of interest (SOI) are gener- ing to the false alarm probability (Pf a) that may be acceptable ally polluted by strong radio frequency interferences (RFI). by the radio astronomers. The compromise for a good rejec- Observation is still possible if a receiver is designed to han- tion of the interferences is to give up the smallest number of dle high dynamic signals composed of weak SOI with su- the highest values of the observations without compromis- perimposed strong RFI. Then, signal processing make RFI ing clean data with residual RFI. In practice, the Pf a is taken mitigation possible to retrieve the SOI. between 0.1% and 0.0001%. One solution to make the deci- Such a receiver is one of the current projects at the sion concerning the hypothesis testing problem is to compare 3 Nanc¸ay Observatory [1]. Robust Radio Receiver (R ) can the observation to a threshold: the H0 hypothesis is realized connect to 3 instruments (Nanc¸ay Radio Telescope, Nanc¸ay when the observation is smaller than the threshold. The H1 Decameter Array, Surveillance Antenna) and process up to 8 hypothesis is realized in the other case. When H0 is realized, independent bands ranging from 875 kHz to 14 MHz band- the threshold value is updated with the new observation in- width that can be combined to provide a larger band of anal- put. When H1 is realized, the blanking decision is made and ysis. This band can be channelized into 64 to 8192 sub- the threshold value remains unchanged. bands. Either Blackman windowing or 49152-coefficients The threshold is calculated for a desired Pf a. Theoretical polyphase filter can be used for FFT apodisation. RFI mit- values may be derived when the PDF is known. Since the igation procedures can be applied in time and/or frequency SOI is Gaussian, the power of the observation follows a χ 2 domain, i.e. before and/or after FFT calculation. Current im- distribution in both time and frequency domains. Assuming plementations are based on a robust threshold power detector. the SOI follows a N (0;σ 2) distribution, the observation re- They allow real-time RFI mitigation : interference rejection sults in the sum of ν squared SOI independent realizations. is processed while observation is running. The χ2(ν) cumulative distribution function may be written For long time exposure, noise power probability density as an incomplete normalized Gamma function P : function (PDF) is assumed to be Gaussian. However RFI mitigation may require high time resolution. The Gaussian ν x Fc2(n)(x) = P ; ; The Nanc¸ay Radio Observatory is the Unite´ scientifique de Nanc¸ay of 2 2 the Observatoire de Paris, associated as Unite´ de Service et de Recherche No. 704 to the French Centre National de la Recherche Scientifique where the function P is defined as (CNRS). The Nanc¸ay Observatory also gratefully acknowledges the financial support of the Conseil Regional´ de la Region´ Centre in France. G(ν;x) 1 x The work of C. Dumez-Viou was financially supported by Observatoire P(ν;x) = = tn−1e−t dt de Paris and by the European Social Fund. G(ν) G(ν) Z0 and G(ν) = G(ν;+¥) is the Gamma function [2]. Given an admissible false alarm rate Pf a = α leads to the following 2 −1 n −1 value threshold = 2σ P 2 ;1 − α where P is the in- verse tabulated P function. Ho wever,the variance σ 2 of each SOI realization is not precisely known and that value fluctu- ates over time due to changes in signal transmission (antenna position, ionosphere properties, . ). Since the mean value 2 2 µc2(n) of a χ (ν) pdf equals νσ , the threshold is finally estimated as: µc2(n) ν threshold = 2 P−1 ;1 − α (1) b ν 2 Power (log arbitrary unit) The key point therefore relies on a good estimation of the mean value of the power of the data that has to be RFI- mitigated. Different estimators have been computed in time and/or frequency domains for the best detection possible fit- ting the nature of the interferences. 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 Frequency (MHz) 2.1 Time Blanking Time blanking needs to detect aberrant points, with real-time Figure 1: Illustration of sky noise background observation constraints. The input data are the real part and imaginary without (top) and with (bottom) radar blanking using the part of the complex-demodulated band-shifted received data. Nanc¸ay Radio Telescope. Time-exposure of 40s. The curves Time blanking is processed on the waveform that holds the are shifted for display purpose. instantaneous power of the received data. In this case, the thresholding procedure involves estimating the mean µx of independent realizations following χ 2(2) distributions. On- based on 50% overlapped temporal slices. Beyond weight- line computation naturally leads to an adaptive way forb the ing functions, the spectrum analyser offers two degrees of estimation of µx with respect to time: freedom for the computation of the power spectral density (PSD): the FFT length ranging from N=64 to N=4096 and b the number of accumulations A (from 20 to 217) generating µx[t] = µx[t − 1] + ε · (x[t] − µx[t − 1]) 2 the average PSD. Each periodogram is computed as jXi( f )j 2 2 th The wbaveformb is computed as x[tb] = xQ[t] + xI [t]. The with Xi( f ) being the FFT of the i temporal slice. components xQ[t] and xI [t] follow a centered Gaussian dis- The resulting estimator writes: tribution with unknown variance σ 2. The time t − 1 stands for the acquisition time of the samples preceding the current A one. The choice of ε is a compromise between a short time 2 P( f ) = ∑ jXi( f )j response, a low variance of the mean estimator and RFI in- i=1 sensitivity. First, a short settling time of the estimator is required to so that P( f ) follows a χ2(ν) with ν = 2A varying from 21 perform RFI mitigation as soon as possible after the begin- to 218 degrees of freedom. Note that the average periodogram 1 ning of the acquisition sequence. Then, the mean estima- theoretically rescales P( f ) by A . This stage is performed a tor is unbiased and the small value of ε corresponds to a re- posteriori for implementation constraints. 4 duced variance of the estimator since Var(µx) = 2εσ (with A frequency blanking procedure is applied each time a σ 2 generally weak). Finally, RFI insensitivity is achieved by PSD is estimated. The threshold procedure is applied on the using a time constant longer than RFI events.b For example, whole PSD. The threshold calculus (1) therefore holds, how- specifications of ground-based aviation radars give a pulse ever the mean µ is estimated on the PSD samples. 3 rate frequency of To = 1 ms for the emitted signal. On the R Nevertheless, the mean of the PSD may be strongly cor- receiver, ε is set to 0:00012 resulting in a settling time of 2-3 rupted, due to bsome channels that may be occupied by RFI To. polluters. The median estimator may be preferred instead. Note that when interference is detected, the mean esti- The problem is the computation cost of such an estimator as mator value is not updated with the new sample in order to well as its deviation to the desired mean when the distribu- prevent the estimation to be polluted by incoherent values. tion is asymmetric (i.e. for low ν values). Another solution The last computed estimator is kept unchanged. This time relies on robust mean estimators such as the trimmed mean blanking procedure is real-time operational in the R3 instru- or the Winsorized mean.
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