MULTICHANNEL INTERFERENCE MITIGATION FOR RADIO ASTRONOMY Spatial filtering at the WSRT Albert-Jan Boonstra 1;2 Alle-Jan van der Veen 2, Amir Leshem 2;
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1 MULTICHANNEL INTERFERENCE MITIGATION FOR RADIO ASTRONOMY Spatial filtering at the WSRT Albert-Jan Boonstra 1;2 Alle-Jan van der Veen 2, Amir Leshem 2;3 Jamil Raza 2, Roger Calders 2 1 ASTRON, Dwingeloo, The Netherlands 2 Delft University of Technology, Dept. EE/DIMES, The Netherlands 3 Metalink Broadband Access, Israel IUCAF RFI mitigation workshop, Bonn, May 28-3, 21 1 Introduction Radio frequency interference (RFI) mitigation techniques for radio astronomy receives increasing interest [1, 2] because the radio spectrum occupancy is increasing in time and also because new generations of radio telescopes become much more sensitive than the current generations, thus making them (in principle) more vulnerable to effects of RFI. In the Netherlands, one of the projects to tackle this problem is the project Nulling Obstructing Electromagnetic Interferers (NOEMI). The purpose of the NOEMI project is to investigate the effectiveness of digital array signal processing techniques for RFI mitigation. The main goals of the project are to study the RFI mitigation algorithms theoretically, to measure and characterize the interfering signals, and to demonstrate the effectiveness of the algorithms in a small scale demonstrator at the WSRT. Finally, the implications of the acquired knowledge for the RFI mitigation aspects of the Square Kilometer Array (SKA) radio telescope design will be reported. The project is a four-year joint project of ASTRON and the Technical University Delft, supported by the Dutch technology foundation, STW. 1
2 The small scale demonstrator consists of an industrial PC equipped with eight analog to digital converters which can be connected to the Westerbork Sythesis Radio Telescope (WSRT), see the figure 1. geometric delay T 1 T 2 T 3 T 14 x 1 (t) x 2 (t) x 3 (t) x 14 (t) Figure 1: The Westerbork Synthesis Radio Telescope The WSRT consists of 14 radio telescopes. The sky signals are downconverted to baseband where they can be tapped by the NOEMI data recorder. The data recorder either stores the raw sampled data on disk or stores processed data on disk. The processing consists of a fourier transform and a correlation process in which a covariance matrix is formed by cross correlation of all recorded telescope channels. The telescope signals x i are stored in a vector x(t) =[x 1 (t) :::x 14 (t)] t and the correlation process can be estimated by averaging the product of x and x H, where H is the conjugate transpose operator: R(fi) = Efx(t)x(t fi) H g ο Figure 2 schematically shows the data flow. 1 N X1s k= x(kt)x(kt fi) H The time data sequences (x(t)) are fourier transformed and correlated with each other and integrated to :5 1 ms. For RFI localized in time-frequency, 2
3 1 MHz 1 khz 1 ms 1 s 1 μs T 1 14x2 x(t) x! (k) x! x Λ! P R 1ms! filter bank.5 1 ms P.5 1 s R 1s! Tp detector ss filter subspace estim. Figure 2: WSRT-NOEMI data flow a detection on the presence of RFI is done, and the time-frequency bin is deleted if RFI is detected. Spatial filtering can be done on datasets with time-continuous RFI, in which case the blanking algorithm is switched off. The output covariance matrices are integrated to :5 ms to 1 seconds, depending on the type of RFI mitigation method. Excision will work well if the interference is concentrated in frequency and time, as for example in the GSM system or Iridium. Otherwise we need to do spatial filtering. 3
4 2 The measurement system In a previous project phase, interfering signals at the WSRT were recorded using a personal computer based, data recorder. The signals of eight telescope channels were recorded with a maximum recording length of a few seconds. In order to investigate some subtle effects of the RFI mitigation algorithms on the astronomical signals, longer integration times were needed. This was the reason for installing an online digital processing system (DSP) in the NOEMI data recorder. The system can do online sub-band processing (FFTs), short term correlation, sub-band-detection and temporal blanking, and further integration to second, minute or hour level. Due to this data compression, online RFI mitigation was made possible instead of off-line processing on limited size CDROM data. The system was used for mitigation of time slotted RFI such as mobile telephone signals (GSM) and aeroplane radar (DME). frontend 28 equalizer 1 MHz IF system bits A A 12 bits A D D D 12 bits geometric delay comp. T 2 MS/s 2 MS/s correlator host PC 384 MB RAM DSP system R 1ms! (t) R(fi) x(t) (t =; ; 8s) host PC R 1ms! (t) (t =; ; 8min) Figure 3: Connecting the NOEMI data recorder to the WSRT 4
5 Figure 4: NOEMI data recorder Figure 3 schematically shows the connection of the NOEMI data recorder to the WSRT. The section left in the figure represents the WSRT. The signals are tapped before the WSRT ADC's and digital delays. The middle section shows the raw data recording mode of the NOEMI recorder and the most right section in the figure shows the online DSP section of the recorder. The duty cycle of the DSP system is about 3%; the limiting factor here is the PCI bus speed. The 3% duty cycle is enough for make long integration times possible, needed to investigate subtle effects of the RFI mitigation processes. The photograph shown in figure 4, shows the interior of the NOEMI data recorder, which is commercially off the shelf equipment. The pcb board in front is a Daytona C67 DSP board equipped with two TI C67 DSPs. The four boards behind it are Spectrum ADC boards. Each board contains two ADCs which have 32 Mbyte RAM per ADC and which have a sampling speed up to 4 M Samples per second. 5
6 3 RFI Excision in the time-frequency domain Results of a test of the DSP system on previously recorded GSM data obtained at the WSRT is shown in figure 5. The figure upper left shows the passband with the GSM.5 ms - 2 khz communication bursts. The spectra obtained at different times are plotted in the same figure. The figure upper right shows the spectrogram of the same measurement. The strength of the signals are indicated by different colours / intensities, four GSM users can be distinguished. Using a threshold detector, the GSM bursts are detected, shown as bright rectangles in the lower right figure. Finally, the fraction of detected (and blanked) signals is shown in the figure lower left. The challenge here is to suppress interference with a power approximately.4 spectra, threshold curve (+) 95 spectrogram frobenius norm blanked fraction 95 spectrogram: detected RFI blanked fraction Figure 5: WSRT - Noemi data: detection and blanking of GSM signals equal to the system noise. Strong interference is easy to detect, weak interference is not. Several approaches to detect RFI are considered in literature [3]. 6
7 4 Spatial filtering Time continuous RFI is best tackled with spatial filtering methods [2]. One of the possible spatial filtering techniques is described in the following sections. 4.1 Narrowband interference models The signal processing model of the received signal (q interferers s j (t)) is given by: x i (t) = qx j=1 a ij s j (t fi ij ) + n i (t) + where a ij is the RFI direction vector component and n i is the system noise of telescope i. The array signal processing is simpler if a narrowband assumption holds: Z sky Bfi fi 1 ) delay fi translates into phase shift e j!cfi In NOEMI observations carried out at the WSRT, narrowband means a bandwidth smaller than ß 5 khz. Under the narrow-band assumption the following is valid: x(t) = qx j=1 a j s j (t) + n(t) + x(t) :=[x 1 (t) :::x 14 (t)] t d; Z sky a j := [a 1j :::a 14;j ] t If q < p(number of interferers in a band smaller than number of sensors), the interferer signatures are short-term stationary, and the noise is i.i.d., then ^R 1ms! := 1 M MX k=1 x! (k)x H! (k) ' qx ff 2 j a ja H j j=1 z } rank q + ff 2 I + R v z} skyfiff 2 has `numerical' rank q. ) narrowband interference detection via rank detection w.r.t. threshold ff 2. no interference: all eigenvalues i of R are equal to ff 2 interference: q eigenvalues larger than ff 2 The q largest eigenvectors of R span the `interferer subspace', span ([a 1 ; ; a q ]). This can be used for spatial filtering (projection). 7
8 4.2 Estimating the spatial signature vector Suppose we detect a single interferer: R ' ffs 2 aah spatial signature a can be estimated by + ff 2 I + R v Then the ffl Largest eigenvector of R (assumes noise covariance is ff 2 I, and sky signal R v small), or ffl Using a reference antenna (with improved gain towards interferer) a1s(t) P a1ff s(t) am s(t) P am ff a ff ffs(t) Figure 6: Experimental setup for estimating the spatial signature vector 4.3 Spatial filtering in space - time by projection Suppose we detect an interferer: br 1ms ' ff 2 s aah + ff 2 I + R v and have an estimate ^a. The interferer can be removed by a projection P? a := I a(a H a) 1 a H ; since ; P? a a = This gives ~R := P? a RP? a = ff 2 P? a + P? a R vp? a 8
9 Note: ffl With estimated ^a, there will be a residual component since P?^a a 6= ffl Sky covariance (visibility matrix) R v is affected (one dimension missing :::) ) need to correct for the filtering after averaging over longer time periods. 4.4 Correction We project on short time scales, then average to longer time scales. The projection matrices are averaged and stored too: where ~br1s = 1 N NX k=1 P?^a k (b R 1ms k )P?^a k ' Cfff 2 I + R v g C := 1 N NX k=1 P?T ^a k Ω P?^a k Knowing the effective projection" C, we can simply correct for it: ) ff 2 I + R v ' C 1 f ~ R 1s g Invertibility requires that the ^a k are not all the same. 9
10 5 Spatial filtering: some preliminary measurement results Time continuous interference, observed at the WSRT and recorded by the NOEMI data recorder, was suppressed by the spatial filtering technique. Both narrow band television sound carrier signals of TV Lingen at MHz, and a wideband signal of the GPS satellite at MHz were suppressed using the spatial filter. Prior to the suppression operation, the recorded channels were calibrated using a gain calibration technique [4]. After this pre-whitening step, the projection and astronomical source signal reconstruction were conducted according to the description described earlier in the text. 5 TV Lingen, eigenvalue stationarity, f = MHz 5 GPS, eigenvalue stationarity, f = MHz 4 4 eigen value (db) eigen value (db) Figure 7: Mitigation of TVL and GPS transmissions, recorded at the WSRT: stationarity of eigenvalues In order to be able to reconstruct the astronomical signal after projection by applying the inverted C matrix operation, it is required that the projection matrix P k is stationary over short time intervals but varying over the entire interval which is to be processed. Figure 7 shows the eigenvalues of one of the two sound carrier waves and of the GPS signal as a function of time. Figures 8 and 9 respectively show the stationarity of the largest eigenvector inner product and of the projection matrix as a function of time. In both cases the stationarity is determined with respect to the values of the eigenvector and projection matrix of the first time slot / sample. Apparently the projection matrix fulfills the stationarity requirements. Which fraction of the nonstationarity is caused by the fringe stopping and which fraction 1
11 is caused by other effects is subject of further study. In the data analysis, the number of frequency channels N f was set to 64; the number of covariance matrices to be averaged to one data point N dt was set to 512, and the number of time slices N tsl was set to eigenvector inner product w.r.t. initial vector, f = MHz eigenvector inner product w.r.t. initial vector, f = MHz 1 1 largest eigenvector inner product largest eigenvector inner product Figure 8: Mitigation of TVL / GPS transmissions, recorded at the WSRT: stationarity of eigenvectors 1.4 projection matrix frobenius norm w.r.t. initial value, f = MHz 1.4 projection matrix frobenius norm w.r.t. initial value, f = MHz projection matrix frobenius norm stationarity projection matrix frobenius norm stationarity Figure 9: TV Lingen sound carrier waves recorded at the WSRT: stationarity of projection matrices 11
12 Figure 1 shows spectra of the TV Lingen sound carrier transmissions before applying the projections (upper left). The upper left figures shows seven cross correlation spectra and one auto correlation spectrum. The lower left figure shows the same correlation channels as in the upper figure after applying spatial projections. The figure to the right shows the average of the ratio of covariance spectra before and after applying the spatial projection. The dataset was pre-whitened (i.e. the gains were calibrated) and the largest eigenvalue was removed. The obtained suppression is 25 db,which is close to the detection limit of 1 1 log(2=ndt)=1 1 log(2=512) = 24dB. Figure 11 shows spectra of a broadband GPS satellite before applying the projections (upper left). The upper left figures shows seven cross correlation spectra and one auto correlation spectrum. The lower left figure shows the same correlation channels as in the upper figure after applying spatial projections. The figure to the right shows the average of the ratio of covariance spectra before and after applying the spatial projection. The dataset was pre-whitened (i.e. the gains were calibrated) and the largest eigenvalue was removed. The obtained maximum suppression numbers of the GPS signal is 2 db, which is less than the detection limit of 1 1 log(2=ndt)=1 1 log(2=512) = 24dB. The reason for this is subject for further study. 12
13 4 original Rcov 3 RFI mitigation 2 25 power proj. Rcov RFI attenuation (db) Figure 1: Mitigation of TV lingen sound carrier waves recorded at the WSRT: attenuation (conditions: pre-whithened, removal largest eigenvalue) 2 original Rcov 3 RFI mitigation power proj. Rcov RFI attenuation (db) Figure 11: Mitigation of GPS waves recorded at the WSRT: attenuation (conditions: pre-whithened, removal largest eigenvalue) 13
14 6 Conclusions Preliminary spatial projection results: ffl Short-time and long-time stationarity fits the requirements for spatial projections for the datasets considered ffl RFI suppression up to 25 db Possible causes of limits on RFI suppression: ffl narrow band (tradeoff short term - long term stationarity) ffl finite sample effects ffl system nonlinearities ffl SNR Plans: ffl observe time-continuous RFI for longer time periods with the new NOEMI DSP system ffl improve observed stationarity statistics ffl investigate effectiveness of spatial projections ffl find limiting factors in obtainable suppression ffl investigate effect on astronomical signals (verification) References [1] C.Barnbaum and R.F. Bradley. A new approach to interference excision in radio astronomy: Real-time adaptive cancellation. The Astronomical Journal, (115): , November [2] A. Leshem, A.J. van der Veen, and A.J. Boonstra. Multichannel interference mitigation techniques in radio astronomy. Astrophysical Journal Supplements, 131(1): , November 2. [3] A. Leshem and A.J. van der Veen. Multichannel detection of gaussian signals with uncalibrated receivers. IEEE Signal Processing Letters, 8:12 122, April 21. [4] A.J.Boonstra and A.J. van der Veen. Gain decomposition methods for radio telescope arrays. In IEEE Workshop on Statistical Signal Processing (SSP). to be published, August
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