Microwave radiometers can be considerably affected by Radio Frequency Interference (RFI). These man-made interference conceal the underlying natural signal, preventing the retrieval of geophysical variables. Adopting on-board detection and mitigation techniques is a requirement to reduce the impact of RFI. Several families of RFI detection algorithms have been developed over the last years (e.g. [1]–[4]). In this work, a new detection technique is proposed and its performance analyzed. It is based in the distortion of the shape of the cross-correlation function at lags different from zero under the presence of RFI. Its performance is compared to other common RFI mitigation algorithms. Proposed methods' performance is found to surpass other common algorithms such as signal Kurtosis, while presenting some convenient properties for its practical application in correlation and synthetic aperture radiometers.Peer ReviewedPostprint (author's final draft

Camps Carmona, Adriano José

Díez García, Raúl

English

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   ON THE DETECTION OF RFI THROUGH THE CORRELATION ANOMALY AT DIFFERENT TIME LAGS  Raúl Dı́ez-Garcı́a and Adriano Camps  Department of Signal Theory and Communications, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain.   ABSTRACT Microwave radiometers can be considerably affected by Ra- dio Frequency Interference (RFI). These man-made interfer- ence conceal the underlying natural signal, preventing the re- trieval of geophysical variables. Adopting on-board detec- tion and mitigation techniques is a requirement to reduce the impact of RFI. Several families of RFI detection algorithms have been developed over the last years (e.g. [1–4]). In this work, a new detection technique is proposed and its perfor- mance analyzed. It is based in the distortion of the shape of the cross-correlation function at lags different from zero un- der the presence of RFI. Its performance is compared to other common RFI mitigation algorithms. Proposed methods’ per- formance is found to surpass other common algorithms such as signal Kurtosis, while presenting some convenient proper- ties for its practical application in correlation and synthetic aperture radiometers. Index Terms— Microwave, Radiometer, Interferometer, RFI, Mitigation, Correlation  1. INTRODUCTION  In this section, the effects of RFI on the autocorrelation shape of the received signal are discussed. As it will be shown, RFI can be detected by checking the correlation of the received signal. Thanks to the widespread access to fast correlators, this is a practical and very convenient approach for several radiometer topologies. For the sake of simplicity, the analysis presented here is for the autocorrelation, but the same con- cepts can be applied to the cross-correlation between pairs of antennas looking at the same radiometric source as well. Without loss of generality, assuming a sharp band-pass fil-where TA is the antenna temperature. This expression is no longer valid if the radiometric signal is contaminated by RFI. In this case, the received signal s = n + r, where n is the radiometric signal and r the RFI. Since RFI and radiometric noise are uncorrelated, Rs is then just the sum of the auto- correlation of the separate components:  Rs(t) = TA · sinc(Bw · t) + Rr(t), (2) where Rr is the autocorrelation of the RFI signal. The noise autocorrelation shape will be therefore additively distorted by the autocorrelation shape of the RFI. This fact is an indication of RFI presence. The shape of the autocorrelation function is dependent on the frequency contents of the RFI. Spectrally narrow RFI signals will exhibit distinctive autocorrelation signatures and, therefore, are more prone to detection. Moreover, the amount of distortion will depend on the central frequency of the RFI signal. This dependence on some RFI properties is not exclu- sive of this new family of detection methods, and indeed it is a common feature in most techniques (see for example [4–7]).  2. METHODOLOGY Two practical metrics on the autocorrelation distortion are de- fined hereafter: the Zero-Crossing correlation Ratio (ZCR) and the Pearson Correlation Detection (PCD). For a more de- tailed definition of the methods and their corresponding sta- tistical analysis, see [8].  2.1. Zero-Crossing correlation Ratio (ZCR) The ZCR is defined as: 𝑍𝑍𝑍𝑍𝑍𝑍 = 𝑅𝑅𝑠𝑠(𝜏𝜏1)𝑅𝑅𝑠𝑠(0),    (3)ters whose frequency response is described by a rectangular  function of bandwidth Bw, the auto-correlation of the Low- Pass Equivalent (LPE) noise signal collected by the radiome- ter antenna is given by:  Rn(t) = TA · sinc(Bw · t), (1)  This work has been sponsored by ”SPOT-Sensing with pioneer- ing opportunistic techniques” grant RTI2018-099008-B-C21/AEI/10.13039/501100011033.     where Rs is the autocorrelation of the signal. τ1 is the ap- propriate delay to make Rn(τ1) = 0, that is, the first zero- crossing of the autocorrelation of the noise component. By construction, ZCR = 0 in the absence of RFI, and therefore a value ZCR ≠ 0 may be indicative of RFI presence. In should be noted that ZCR can only be estimated from the data. In- deed, given the estimation noise of ZCR, a certain Probability of False Alarm (Pfa) has to be accepted. For a certain Pfa © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. DOI 10.1109/IGARSS47720.2021.9554188  ≈ and number of samples N , the confidence thresholds can be computed as [8, eq. 23]:  𝑡𝑡ℎ1,2 = ±√2 · 𝑒𝑒𝑒𝑒𝑒𝑒−1�1 − 𝑃𝑃𝑓𝑓𝑓𝑓� ·𝑁𝑁(𝑁𝑁−1)2,    (4) samples, a pulse width of PR/10 samples, and configurable central frequency. 3. A burst of pulses of 50% duty cycle: a train of rect- angular pulses with a pulse repetition period (PR) of N/128 samples, a pulse width of PR/2 samples, and configurable central frequency. Kurtosis   detection exhibits a  blind spot for this duty cycle, and it is therefore interesting, to study how correlation-based RFI detection behave in this scenario.With these thresholds, the measured ZCR can be tested for RFI: If ZCR < th1 or ZCR > th2, RFI is considered detected, and the sequence is flagged as such and discarded. Zero-Crossing Ratio provides reasonable good results with a simple implementation, as it will be shown. It relies, however, in sampling the autocorrelation only for a single non-zero lag, making it quite depending on how the RFI behaves around the zero-crossing.  2.2. Pearson Coefficient Detector (PCD) An alternative is the PCD, that assesses the amount of distor- tion for multiple lags. Let’s define X = [xN−m...xN+m] as the central m samples of the measured autocorrelation signal. Comparison with the theoretical shape Y given by eq. 1 can be achieved using the Pearson Coefficient Detector (PCD): 𝜌𝜌𝑋𝑋,𝑌𝑌����� =∑ (𝑥𝑥𝑖𝑖−𝜇𝜇𝑥𝑥����)�𝑦𝑦𝑖𝑖−𝜇𝜇𝑦𝑦�����𝑁𝑁+𝑚𝑚𝑁𝑁−𝑚𝑚𝜎𝜎𝑥𝑥����·𝜎𝜎𝑦𝑦����,   (5) 4. A narrowband chirp signal: A chirp signal sweeping with an arbitrary bandwidth of Bw/2 and a PR = N/16 samples. Chirp signatures are commonly found in RADAR signals and RF jammers. 5. A wideband chirp signal: A chirp signal sweeping lin- early with an arbitrary bandwidth of Bw and a PR = N/16 samples. 6. A generic wideband signal modulation: Simulated us- ing a pseudo-random noise code (PRN) of PR = N/2, with its bandwidth overlapping the entire noise band- width. The real and imaginary components of the LPE signal are equivalent to the I and Q components of the generic digital receivers. Complex auto-correlation is then computed as:  Rs = RsI ,sI + RsQ,sQ + (RsI ,sQ − RsQ,sI )· j,    (6)  have to be computed. Since the statistics of 𝜌𝜌𝑋𝑋,𝑌𝑌����� are non- Gaussian, it is possible to define them by using the Fisher transformation, as described in detail in [8, eq. 25-30].  3. MATERIALS AND METHODS Performance of the methods has been evaluated through sim- ulation, implementing a digital processing chain mimicking as much as possible the receiving chain of a radiometer. The radiometric signal is simulated as a digital complex random Gaussian process of 300 K of power with N independent sam- ples. A generic complex waveform of varying type and power is added into it, simulating contamination by RFI. The comwhere sI,Q are the IQ components of the signal, The resulting auto-correlation sequence is tested for RFI using the detection methods defined above, ZCR and PCD. Dif- ferent sample sizes m for PDC have been considered. To have some reference to compare with, signal has been also tested for RFI with two additional methods: the trivial Total Power Detection [8, 3.3], that assumes the noise power known be- forehand, and the widespread Signal Kurtosis [8, 3.4]. To assess the performance of the methods for an specific RFI type and power, Pdec can be estimated by conducting NMC = 5000 Monte-Carlo simulations:    bined signal is then filtered with a digital anti-aliasing filter of Bw=20 MHz, and sampled at the Nyquist frequency, Fs = 2Bw. This simulates the complex Low-Pass Equivalent (LPE) centered at fc = 0 of the acquired band-pass signal. Six different types of RFI have been studied: 1. A continuous wave (CW): A sinusoidal signal simulat- ing a narrow spectra modulation, of configurable fre- quency. 2. A burst of pulses of 10% duty cycle: a train of Gaussian pulses with a pulse repetition period (PR) of N/256 𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑 =𝑁𝑁𝑟𝑟𝑟𝑟𝑖𝑖𝑁𝑁𝑀𝑀𝑀𝑀,   (7) being Nrfi the number of sequences flagged as RFI-affected. By construction [8, eq. 19-22], Pdec  Pfa in the absence of RFI.  4. DETECTION PERFORMANCE OF CORRELATION-BASED RFI DETECTION The main figure of merit to evaluate the methods’ perfor- mance is the Probability of Detection Pdec for a given Pfa. In figure 1, Pdec has been plotted in function of the Interference   ·   (a) Continuous Wave (b) Train of Rectangular Pulses (Duty = 10%) (c) Train of Rectangular Pulses (Duty = 50%) (d) Narrowband Chirp   (e) Wideband Chirp (f) Wideband Signal Modulation  Fig. 1: Pdec in function of the INR for several RFI signal types.  to Noise Ratio (INR = Trfi /Tn, where Trfi and Tn are the Brightness Temperature for the RFI and Noise, respectively. As a first approximation, Pfa = 0.1, RFI central frequency fc = 0.3 Bw and N = 1024. The obtained results show that the proposed technique work in a practical scenario, being ca- pable of detecting all types of RFI. Performance is discussed in detail for each of the methods below:  1. ZCR: Performance is comparable to Total Power De- tection for narrowband RFI, but with the important advantage of not requiring an estimation of the noise level. In these cases, ZCR is able to detect RFI for INR<0.2, outperforming Signal Kurtosis. For spectrally wide RFI, however, ZCR performs worse. For Wide- band Chirp, for example, ZCR is not able to guarantee detection for INR<1. ZCR is dependent on the frequency contents of the RFI:For some selected cases, performance is remarkable, even outperforming more complex methods like PCD. For other cases, however, performance is much poorer. This is related to how the autocorrelation of the RFI impacts the zero-crossings of the noise autocorrelation. Nevertheless, and taking into account the simplicity of the implementation, ZCR is a strong candidate for RFI detection where system complexity is an issue.  2. PCD: Pearson Coefficient Detection outperforms Kur- tosis for all types of RFI, and even Total Power De- tection in selected cases. For RFI with narrow spectra, such as the Pulse Train and CW, Pearson is able to de- tect RFI of the order of INR = 0.05. For wider spectra RFI, Pearson performs worse, but always with better   ≈ results than Kurtosis. There is a marked dependence on the number of samples considered for PCD computation. This dependence is minor when detecting narrowband signals, but of high importance for spectrally- wide RFI: lower sample computation exhibits signif- icant lower performance or non-detection (see, as an example, Fig. 1.e). A good compromise is to choose m > 12, for which detection is achieved for all the cases studied. In order to quantitatively compare the different methods, it is interesting to define the Minimum Detectable RFI. For a given RFI type and Pfa, this can be defined arbitrarily as the minimum required INR to detect an RFI with a probability equal to 1 − Pfa: INRmin ≡ INR(1 − Pfa). (8) In table 1, INRmin is given for each type of RFI, under the same conditions than Fig. 1.  5. CONCLUSIONS In this work, a new family of RFI detection algorithms has been proposed. It is based on the comparison of the received signal autocorrelation shape with the autocorrelation of the radiometric noise which, in the absence of RFI, should be sinc-shaped. Two implementations of this idea have been pro- posed in this work: the Zero-Crossing Ratio (ZCR), based on measuring the correlation at its zero-crossings, and the Pear- son Coefficient Detection (PCD), based on the goodness of fit of the autocorrelation with the ‘sinc-shaped’ autocorrelation of the radiometric noise. Their performance has been tested and evaluated for several types of RFI types and power, illustrating that they outperform the reference metrics for most of the cases considered. Correlation-based methods are shown to be well suited for detecting frequency-narrow signals. For example, for a sinusoidal RFI of 0.3 frequency, and considering 1024 samples, PCD is able to detect RFI for INR 0.03, and ZCR for INR > 0.12, outperforming Total Power Detection (INR > 0.13) or Kurtosis methods (detection for INR > 0.77). This novel detector family is suitable for a broad range of radiometer topologies, such as Real Aperture, Synthetic Aperture, and Polarimetric Radiometers. 6. REFERENCES [1] S. Misra, P. N. Mohammed, B. Guner, C. S. Ruf, J. R. Piepmeier, and J. T. Johnson, “Microwave radiome- ter radio-frequency interference detection algorithms: A comparative study,” IEEE Transactions on Geoscience and Remote Sensing, vol. 47, no. 11, pp. 3742–3754, 2009. [2] T. W. Anderson and D. A. Darling, “A test of goodness of fit,” Journal of the American statistical association, vol. 49, no. 268, pp. 765–769, 1954. [3] A. Camps, J. Gourrion, J. M. Tarongi, M. Vall Llossera, A. Gutierrez, J. Barbosa, and R. Castro, “Radio- frequency interference detection and mitigation algo- rithms for synthetic aperture radiometers,” Algorithms, vol. 4, no. 3, pp. 155–182, 2011. [4] J. Querol, R. Onrubia, A. Alonso-Arroyo, D. Pas- cual, H. Park, and A. Camps, “Performance Assessment of Time-Frequency RFI Mitigation Techniques in Mi- crowave Radiometry,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens, vol. 10, pp. 1–11, 2017. [5] J. Querol, A. Perez, and A. Camps, “A Review of RFI Mitigation Techniques in Microwave Radiometry,” Re- mote Sensing, vol. 11, no. 24, p. 3042, 2019. [6] G. Forte, J. M. Tarong´ı Bauza, V. dePau, M. Vall, A. Camps et al., “Experimental study on the performance of RFI detection algorithms in microwave radiometry: Toward an optimum combined test,” IEEE transactions on geoscience and remote sensing, vol. 51, no. 10, pp. 4936–4944, 2013. [7] R. D. De Roo, S. Misra, and C. S. Ruf, “Sensitivity of the kurtosis statistic as a detector of pulsed sinusoidal RFI,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 7, pp. 1938–1946, 2007. [8] R. Díez-García and A. Camps, “A novel RFI detection method for microwave radiometers using multi-lag cor- relators,” IEEE Transactions on Geoscience and Remote Sensing, in press.  Table 1: INRmin to guarantee detection for all types of RFI considered  Total Power Kurtosis PCD (m = 6) PCD (m = 12) PCD (m = 24) ZCR Continuous Wave 0.13 0.77 0.05 0.04 0.03 0.12 10% DC Pulse Train 0.13 0.40 0.11 0.13 0.11 0.15 50% DC Pulse Train 0.14 N/D 0.06 0.05 0.06 0.13 Narrowband Chirp 0.13 0.85 0.19 0.20 0.19 0.11 Wideband Chirp 0.12 0.89 N/D 0.93 0.54 N/D Wideband Modulation 0.07 0.58 0.29 0.33 0.39 0.15  

On the detection of RFI through the correlation anomaly at different time lags

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On the detection of RFI through the correlation anomaly at different time lags

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