# RFI Detection and Mitigation for Advanced Correlators in Interferometric Radiometers

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- X
_{In}, X_{Qn}, Y_{In}, Y_{Qn}: four 1-bit data streams per receiver element n (from n = 1...N_{receivers}) at 57.69375 MHz, X/Y being the polarization, and I/Q the in-phase/quadrature components; - X
_{Pn}, Y_{Pn}: two multi-bit Power Measurement System (PMS) streams per receiver element n (from n = 1...N_{receivers}) and per polarization at ~28 kS/s.

- N is the number of samples per integration period. In this study, N = 11,538,432, corresponding to an integration time of ~200 ms at the clock sampling frequency.
- K is the number of points of the Fourier transform or the number of points in the spectrum. K is an optimization parameter that can be reduced to a smaller power-of-two number during the implementation phase, if needed for Field-Programmable Gate Array (FPGA) resource utilization optimization.
- M is the number of time segments of the Short-Time Fourier Transform (STFT) in which the signal is divided. It is defined as M = γ·N/K, where γ is the windowing factor. As will be shown in the next section, γ = 2, which is the minimum windowing factor necessary to apply a non-rectangular window function.
- R
_{tot}is the total number of receivers of the system. - R
_{avg}is the number of receivers that are averaged in the RFI detection process. It will be assumed that R_{avg}= R_{tot}. In the case of a real aperture radiometer, R_{avg}= R_{tot}= 1. - ${\alpha}_{th}^{}$ is the detection threshold for statistical and polarimetry metrics to determine whether an RFI signal is present or not, and it controls the probability of detection and the probability of false alarm. The parameter ${\alpha}_{th}^{}$ may take three different specific values: ${\alpha}_{th}^{time}$ for temporal moments, ${\alpha}_{th}^{freq}$ for spectral moments, and ${\alpha}_{th}^{all}$ for all-signal moments.
- ${\beta}_{th}^{}$ is the maximum blanking threshold. The RFI mitigation is based on the excision of the contaminated samples out of the set of all transformed samples. The RFI mitigation operates efficiently if a reduced number of samples contain the largest fraction of the RFI power.

#### 2.1. RFI Detection and Mitigation Algorithm Description

#### 2.1.1. Windowing

#### 2.1.2. Spectral Computation

#### 2.1.3. Calibration and Equalization

#### 2.1.4. Statistic and Polarimetry Tests

- Stokes Parameters

_{avg}is the number of receivers whose outputs are averaged.

- Kurtosis and Polarimetric Kurtosis

- Time-Frequency Moments

#### 2.1.5. Computation of the OR/AND Masks

- the OR approach is computed by a tensor-logical OR operation between the vector results of the time and frequency RFI detector, denoted as ∨, whereas
- the AND approach is computed analogously using a tensor-logical AND operation, and it is denoted as ∧.

#### 2.1.6. RFI Mitigation

- Signal Blanking

- PMS RFI Mitigation

- RFI Detection Flag

## 3. Results

- K is the number of points of FFT. The initial value of K was 4096, but it was proposed to run simulations with K = 16,384, 4096, 2048, 1024, and 256 and then to select the best K for the default CFAR and β
_{th}. - α
_{th}is the RFI detection threshold for the statistical and polarimetry metrics: temporal, spectral, and all-bin moments. α_{th}(P_{FA}) is obtained mathematically for each value of the CFAR. - The following CFAR values were simulated for the selected value of K: 10
^{−8}, 10^{−6}, 10^{−4}, 10^{−2}, 0.1, and 0.5. - β
_{th}is the maximum blanking threshold from 100% to 50%.

#### 3.1. Sensitivity Performance as a Function of the Number of Averages

_{avg}. As can be appreciated in Figure 4, for very low SNR values the variance reduction with respect to R

_{avg}becomes 1/R

_{avg}, but as the SNR increases, the improvement (i.e., the slope) decreases because of the signal correlation. For typical SMOS values, the typical SNR is $SN{R}_{typ}=10\xb7lo{g}_{10}\left({\left|V\right|}_{max}/{T}_{R}\right)\approx 10\xb7lo{g}_{10}\left(10\mathrm{K}/210\mathrm{K}\right)\approx -13\mathrm{dB}$, ${\left|V\right|}_{max}$ being the maximum value of the visibility samples or cross-correlation in units of Kelvin, and therefore, the 1/R

_{avg}approximation holds. Note that the use of 1 bit (Figure 5b) instead of multi-bits (Figure 5a) leads to a smaller variance reduction factor, i.e., it is even less sensitive to the SNR.

_{D}) of RFI vs. the Interference-to-Noise Ratio (INR). It shows a sudden increase above an INR value, which increases with increasing values of $\epsilon $. As compared to the multi-bit case (Figure 6a), in the case of 1-bit quantization (Figure 6b), the plots are shifted ~2 dB towards the right due to larger noise ($10\xb7lo{g}_{10}\left(\sqrt{2.46}\right)\approx 1.95\mathrm{dB}$). Note that the 2.46 factor is the ratio of the integration time and the effective integration time for the case of 1-bit/2 level correlators [19]. As shown in Figure 7, these ~2 dB are nearly constant as a function of the number of receivers averaged.

#### 3.2. Algorithm Parameter Optimization

_{th}. The percentages of the mitigated RFI and degraded RFI (the result is worse than no mitigation) are also provided, together with their mean values. In Table 1, Table 2 and Table 3, the range of values with a similar performance, i.e., where the optimum is, is indicated in the light blue color. In Table 4, the effect of the number of points of the FFT is clearly seen: the longer the FFT, the larger the PD; it is between 73–76% for PFA < 1% and K = 4096; between 70–72% for PFA < 1% and K = 2048; and ~59% for PFA < 1% and K = 1024.

_{FA}and reasonable probability of detection. The values of the CFAR and β

_{th}parameters are now refined for K = 1024. The results are presented in Table 5, confirming the optimum values of CFAR = 10

^{−8}and β

_{th}= 100%.

_{D}and P

_{FA}. Note that the P

_{D}value is slightly higher than in Table 4 due to the finite number of realizations conducted (1200).

- K = 1024, no significant improvement was found for larger Ks except a better P
_{D}(from 63 to 73%), at the expense of more hardware resources to compute the FFTs. - CFAR = 10
^{−8}, with no significant variation up to 10^{−6}, with a moderate P_{D}, and a negligible PFA (not detectable with the number of realizations performed). This offers less radiometric degradation and no big impact on mitigation. - β
_{th}= 100%, no significant impact down to 95%, but 100% offers the best mitigation vs. degradation trade-off.

## 4. Discussion

- Quantize the signals in the frequency domain and perform the products with a reduced number of bits (1 to 5) so that multipliers can be more easily implemented using look-up tables (LUT).
- Transform the signals back to the time domain, quantize the signals in the time domain, and perform the products with a reduced number of bits (1 to 5).

^{−16}) + 40 = −8.16 dBcu (1 cu = 10

^{−4}= 1 correlator unit) as in SMOS. The horizontal lines represent the quantization noise floor for the different quantization levels. As can be appreciated, for a virtually infinite number of levels (top left scatter plot) there is no saturation effect. As the number of quantization bits (levels) decreases (5 to 1 bits: 31 to 2 levels) a saturation effect appears at the increasing levels: for 31 levels, the saturation occurs very close to the SMOS quantization noise floor and increases at ~+3 dB for every bit that is decreased. Note that the performance is significantly worse when the correlation is performed in the time domain due to the fact that the truncation to compute the FFTs already spreads the spectra, and the subsequent truncation degrades it even further.

## 5. Conclusions

^{−8}, it was found that the optimum parameters were: length of the FFTs equal to 1024 (without significant improvement found for larger values, except for a slightly better probability of detection: from 63 to 73%), β

_{th}equal to 100% (i.e., only if the AND approach does not mitigate at all is the OR approach used), and application of Parseval’s theorem to compute the cross-correlations in the frequency domain using 31, 15, or even 7 quantization levels, with very similar performances among the three of them.

_{avg}= 1, and (2) the algorithm’ performance can be significantly improved if softer quantization schemes are used (i.e., more than 1 bit).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Quantization Effects and Their Compensation

^{−4}), computed as the root mean squared error between the cross-correlation and the reference cross-correlation in the time domain, for the different number of bits/levels used in the quantization:

**Figure A1.**Evolution of the RMSE in [CU] as a function of $\mathit{\delta}={\mathit{V}}_{\mathit{T}\mathit{r}\mathit{u}\mathit{n}\mathit{c}}/{\mathit{\sigma}}_{\mathit{x},\mathit{y}}$, for different quantization levels.

**Figure A2.**Evolution of the RMSE in [CU] as a function of the $\mathit{\delta}={\mathit{V}}_{\mathit{T}\mathit{r}\mathit{u}\mathit{n}\mathit{c}}/{\mathit{\sigma}}_{\mathit{x},\mathit{y}}$, for different quantization levels. showing the entire range in (

**a**), and the local behavior for < 1000 CU in (

**b**).

**Table A1.**Slope correction factor due to quantization scheme applied when cross-correlations are computed in the frequency domain. Note: the larger the slope correction, the larger the noise amplification.

FQ31 | FQ15 | FQ7 | FQ3 | FQ2 | |
---|---|---|---|---|---|

Correct. Fact. (m^{−1}) | 1.0092 | 1.0321 | 1.1128 | 1.1558 | 3.3670 |

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**Figure 1.**Characterization of the different RFI opportunities identified for present and future technologies. Modified from: “The Dimensions of RFI, and how ngVLA is Being Designed to Accommodate Them”, RFI 2019 [3].

**Figure 3.**Modulus square of the STFT of the X-pol. at a sample receiver (

**a**) before and (

**b**) after equalization. The vertical lines appearing in both figures are due to the clipping of the input receiver signal due to the strong RFI signal.

**Figure 4.**PDF (

**left**) and CDF (

**right**) of 2012 (yellow) and 2020 (orange) SMOS RFI observations. The simulated PDF and CDF is in blue.

**Figure 5.**Multi-receiver kurtosis variance reduction as a function of the number of receivers averaged (R

_{avg}) and SNR for a (

**a**) multi-bit and (

**b**) 1-bit quantization. SNR is the power relation between the correlated divided by the uncorrelated noise power.

**Figure 6.**Probability of detection (PD) as a function of the INR, parameterized as a function of the variance reduction factor (ε), for (

**a**) multi-bit, and (

**b**) 1-bit quantization.

**Figure 7.**Sensitivity improvement of the RFI detection [dB] as a function of the number of receivers averaged (R

_{avg}) for the multi-bit and 1-bit quantization approaches.

**Figure 8.**(

**a**) Detection regimes after applying the algorithm; (

**b**) average mitigation [dB] wrt. input INR [dB]; (

**c**) input–output PMS error for CFAR = 10

^{−8}and β

_{th}= 100%.

**Figure 9.**Mitigation performance in the (

**a**) frequency and (

**b**) time domains as a function of the quantization levels: 2, 3, 7, 15, and 31 and multi-bit reference case (top left).

K-FFT 4096 | β_{th} 100% | β_{th} 90% | β_{th} 75% | β_{th} 50% | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | |

CFAR10^{−8} | M: −2.31dB σ: 3.73 dB | %. It. 59.3% M: −4.04 dB | %. It. 7.35% M: 1.14 dB | M: −2.58 dB σ: 5.05 dB | %. It. 56.2% M: −5.48 dB | %. It. 10.4% M: 4.80 dB | M: −2.58 dB σ: 5.05 dB | %. It. 56.2% M: −5.48 dB | %. It. 10.4% M: 4.80 dB | M: −2.58 dB σ: 5.05 dB | %. It. 56.2% M: −5.48 dB | %. It. 10.4% M: 4.80 dB |

CFAR10^{−6} | M: −2.33 dB σ: 3.75 dB | %. It. 60.8% M: −3.97 dB | %. It. 7.65% M: 1.10 dB | M: −2.56 dB σ: 5.11 dB | %. It. 57.5% M: −5.41 dB | %. It. 11.0% M: 4.98 dB | M: −2.56 dB σ: 5.12 dB | %. It. 57.5% M: −5.41 dB | %. It. 11.0% M: 4.98 dB | M: −2.56 dB σ: 5.12 dB | %. It. 57.5% M: −5.41 dB | %. It. 11.0% M: 4.98 dB |

CFAR10^{−4} | M: −2.35 dB σ: 3.82 dB | %. It. 62.2% M: −3.92 dB | %. It. 7.94% M: 1.10 dB | M: −2.52 dB σ: 5.24 dB | %. It. 58.2% M: −5.39 dB | %. It. 11.9% M: 5.24 dB | M: −2.52 dB σ: 5.24 dB | %. It. 58.2% M: −5.39 dB | %. It. 11.9% M: 5.24 dB | M: −2.52 dB σ: 5.24 dB | %. It. 58.2% M: −5.39 dB | %. It. 11.9% M: 5.24 dB |

CFAR10^{−2} | M: 5.88 dB σ: 27.8 dB | %. It. 69.0% M: −3.28 dB | %. It. 28.9% M: 28.16 dB | M: 6.24 dB σ: 29.3 dB | %. It. 63.5% M: −4.98 dB | %. It. 34.4% M: 27.3 dB | M: 6.24 dB σ: 29.3 dB | %. It. 63.5% M: −4.98 dB | %. It. 34.4% M: 27.3 dB | M: 6.24 dB σ: 29.3 dB | %. It. 63.5% M: −4.98 dB | %. It. 34.4% M: 27.3 dB |

CFAR10^{−1} | M: 6.35 dB σ: 28.3 dB | %. It. 73.6% M: −2.86 dB | %. It. 26.4% M: 32.0 dB | M: 12.0 dB σ: 33.0 dB | %. It. 41.3% M: −5.04 dB | %. It. 58.7% M: 23.9 dB | M: 12.0 dB σ: 33.0 dB | %. It. 41.3% M: −5.04 dB | %. It. 58.7% M: 23.9 dB | M: 12.0 dB σ: 33.0 dB | %. It. 41.3% M: −5.04 dB | %. It. 58.7% M: 23.9 dB |

K-FFT 2048 | β_{th} 100% | β_{th} 90% | β_{th} 75% | β_{th} 50% | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | |

CFAR10^{−8} | M: −2.21 dB σ: 3.72 dB | %. It. 57.3% M: −4.02 dB | %. It. 7.31% M: 1.26 dB | M: −2.20 dB σ: 5.20 dB | %. It. 56.2% M: −5.46 dB | %. It. 12.0% M: 5.57 dB | M: −2.20 dB σ: 5.20 dB | %. It. 56.2% M: −5.46 dB | %. It. 12.0% M: 5.57 dB | M: −2.20 dB σ: 5.20 dB | %. It. 56.2% M: −5.46 dB | %. It. 12.0% M: 5.57 dB |

CFAR10^{−6} | M: −2.24 dB σ: 3.77 dB | %. It. 58.4% M: −4.01 dB | %. It. 7.72% M: 1.26 dB | M: −2.19 dB σ: 5.30 dB | %. It. 57.5% M: −5.45 dB | %. It. 12.6% M: 5.72 dB | M: −2.19 dB σ: 5.30 dB | %. It. 57.5% M: −5.45 dB | %. It. 12.6% M: 5.72 dB | M: −2.19 dB σ: 5.30 dB | %. It. 57.5% M: −5.45 dB | %. It. 12.6% M: 5.72 dB |

CFAR10^{−4} | M: −2.20 dB σ: 4.72 dB | %. It. 60.3% M: −3.95 dB | %. It. 8.29% M: 2.09 dB | M: −2.06 dB σ: 6.08 dB | %. It. 58.2% M: −5.39 dB | %. It. 14.1% M: 6.24 dB | M: −2.06 dB σ: 6.08 dB | %. It. 58.2% M: −5.39 dB | %. It. 14.1% M: 6.24 dB | M: −2.06 dB σ: 6.08 dB | %. It. 58.2% M: −5.39 dB | %. It. 14.1% M: 6.24 dB |

CFAR10^{−2} | M: 5.79 dB σ: 26.6 dB | %. It. 66.9% M: −2.83 dB | %. It. 30.5% M: 25.2 dB | M: 6.52 dB σ: 28.8 dB | %. It. 63.5% M: −4.88 dB | %. It. 36.5% M: 26.1 dB | M: 6.52 dB σ: 28.8 dB | %. It. 63.5% M: −4.88 dB | %. It. 36.5% M: 26.1 dB | M: 6.52 dB σ: 28.8 dB | %. It. 63.5% M: −4.88 dB | %. It. 36.5% M: 26.1 dB |

CFAR10^{−1} | M: 6.50 dB σ: 28.2 dB | %. It. 72.9% M: −2.66 dB | %. It. 27.1% M: 31.2 dB | M: 12.2 dB σ: 32.9 dB | %. It. 41.3% M: −5.02 dB | %. It. 59.8% M: 23.8 dB | M: 12.2 dB σ: 32.9 dB | %. It. 41.3% M: −5.02 dB | %. It. 59.8% M: 23.8 dB | M: 12.2 dB σ: 32.9 dB | %. It. 41.3% M: −5.02 dB | %. It. 59.8% M: 23.8 dB |

K-FFT 1024 | β_{th} 100% | β_{th} 90% | β_{th} 75% | β_{th} 50% | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | |

CFAR10^{−8} | M: −1.76 dB σ: 3.30 dB | %. It. 48.8% M: −3.79 dB | %. It. 6.73% M: 1.35 dB | M: −2.08 dB σ: 4.67 dB | %. It. 46.8% M: −5.36 dB | %. It. 8.73% M: 4.92 dB | M: −2.08 dB σ: 4.67 dB | %. It. 46.8% M: −5.36 dB | %. It. 8.73% M: 4.92 dB | M: −2.08 dB σ: 4.67 dB | %. It. 46.8% M: −5.36 dB | %. It. 8.73% M: 4.92 dB |

CFAR10^{−6} | M: −1.73 dB σ: 3.30 dB | %. It. 50.1% M: −3.64 dB | %. It. 7.26% M: 1.34 dB | M: −2.06 dB σ: 4.73 dB | %. It. 47.9% M: −5.30 dB | %. It. 9.54% M: 4.96 dB | M: −2.06 dB σ: 4.73 dB | %. It. 47.9% M: −5.30 dB | %. It. 9.54% M: 4.96 dB | M: −2.06 dB σ: 4.73 dB | %. It. 47.9% M: −5.30 dB | %. It. 9.54% M: 4.96 dB |

CFAR10^{−4} | M: −1.08 dB σ: 8.32 dB | %. It. 51.2% M: −3.46 dB | %. It. 9.16% M: 7.52 dB | M: −1.43 dB σ: 9.05 dB | %. It. 49.1% M: −5.21 dB | %. It. 11.2% M: 10.1 dB | M: −1.43 dB σ: 9.05 dB | %. It. 49.1% M: −5.21 dB | %. It. 11.2% M: 10.1 dB | M: −1.43 dB σ: 9.05 dB | %. It. 49.1% M: −5.21 dB | %. It. 11.2% M: 10.1 dB |

CFAR10^{−2} | M: 8.19 dB σ: 28.5 dB | %. It. 63.9% M: −1.86 dB | %. It. 35.7% M: 26.2 dB | M: 8.57 dB σ: 31.5 dB | %. It. 60.9% M: −4.37 dB | %. It. 38.7% M: 29.1 dB | M: 8.58 dB σ: 31.5 dB | %. It. 60.9% M: −4.37 dB | %. It. 38.7% M: 29.1 dB | M: 8.58 dB σ: 31.5 dB | %. It. 60.9% M: −4.37 dB | %. It. 38.7% M: 29.1 dB |

CFAR10^{−1} | M: 8.87 dB σ: 30.7 dB | %. It. 69.7% M: −2.04 dB | %. It. 30.3% M: 33.3 dB | M: 14.7 dB σ: 35.8 dB | %. It. 37.5% M: −4.84 dB | %. It. 62.5% M: 26.4 dB | M: 14.7 dB σ: 35.8 dB | %. It. 37.5% M: −4.84 dB | %. It. 62.5% M: 26.4 dB | M: 14.7 dB σ: 35.8 dB | %. It. 37.5% M: −4.84 dB | %. It. 62.5% M: 26.4 dB |

**Table 4.**Summary of algorithm performance in terms of PD and PFA for K = 4096, 2048, and 1024 and variable CFAR for β

_{th}=100%.

CFAR | K-FFT 4096 | K-FFT 2048 | K-FFT 1024 | |||
---|---|---|---|---|---|---|

P_{FA} | P_{D} | P_{FA} | P_{D} | P_{FA} | P_{D} | |

10^{−8} | <1% | 73.1% | <1% | 69.8% | <1% | 59.4% |

10^{−6} | <1% | 74.7% | <1% | 71.7% | 6% | 64.2% |

10^{−4} | <1% | 76.2% | 1% | 74.5% | 68% | 81.8% |

10^{−2} | 87% | 97.1% | 91% | 97.1% | 100% | 100% |

10^{−1} | 100% | 100% | 100% | 100% | 100% | 100% |

K-FFT 1024 | β_{th} 100% | β_{th} 99% | β_{th} 95% | β_{th} 90% | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | All #1200 | Mitigating (<0) | Degrading (>0) | |

CFAR10^{−8} | M: −2.00 dB σ: 3.69 dB | %. It. 52.0% M: −4.03 dB | %. It. 7.65% M: 1.16 dB | M: −2.04 dB σ: 5.16 dB | %. It. 48.6% M: −5.48 dB | %. It. 11.1% M: 5.62 dB | M: −1.85 dB σ: 5.19 dB | %. It. 47.7% M: −5.36 dB | %. It. 11.9% M: 5.95 dB | M: −1.85 dB σ: 5.18 dB | %. It. 47.7% M: −5.36 dB | %. It. 11.9% M: 5.95 dB |

CFAR10^{−6} | M: −2.00 dB σ: 3.68 dB | %. It. 52.4% M: −4.00 dB | %. It. 7.81% M: 1.15 dB | M: −2.05 dB σ: 5.21 dB | %. It. 48.8% M: −5.50 dB | %. It. 11.4% M: 5.57 dB | M: −1.85 dB σ: 5.21 dB | %. It. 48.0% M: −5.35 dB | %. It. 12.2% M: 5.90 dB | M: −1.85 dB σ: 5.21 dB | %. It. 48.0% M: −5.35 dB | %. It. 12.2% M: 5.90 dB |

CFAR10^{−4} | M: −1.99 dB σ: 3.68 dB | %. It. 52.4% M: −3.97 dB | %. It. 8.01% M: 1.13 dB | M: −2.04 dB σ: 5.23 dB | %. It. 48.8% M: −5.50 dB | %. It. 11.6% M: 5.61 dB | M: −1.83 dB σ: 5.23 dB | %. It. 48.0% M: −5.35 dB | %. It. 12.4% M: 5.93 dB | M: −1.83 dB σ: 5.22 dB | %. It. 48.0% M: −5.35 dB | %. It. 12.4% M: 5.93 dB |

CFAR10^{−2} | M: −1.98 dB σ: 3.67 dB | %. It. 52.7% M: −3.94 dB | %. It. 8.15% M: 1.12 dB | M: −2.03 dB σ: 5.26 dB | %. It. 49.1% M: −5.50 dB | %. It. 11.8% M: 5.65 dB | M: −1.83 dB σ: 5.25 dB | %. It. 48.2% M: −5.35 dB | %. It. 12.6% M: 5.97 dB | M: −1.82 dB σ: 5.25 dB | %. It. 48.2% M: −5.35 dB | %. It. 12.6% M: 5.97 dB |

CFAR10^{−1} | M: −1.99 dB σ: 3.69 dB | %. It. 53.3% M: −3.92 dB | %. It. 8.22% M: 1.16 dB | M: −2.03 dB σ: 5.29 dB | %. It. 49.3% M: −5.50 dB | %. It. 12.2% M: 5.60 dB | M: −1.81 dB σ: 5.29 dB | %. It. 48.5% M: −5.34 dB | %. It. 13.0% M: 5.95 dB | M: −1.81 dB σ: 5.28 dB | %. It. 48.5% M: −5.34 dB | %. It. 13.0% M: 5.95 dB |

**Table 6.**Summary of algorithm performance in terms of PD and PFA for K = 1024 and variable CFAR for β

_{th}= 100%.

CFAR | K-FFT 1024 | |
---|---|---|

P_{FA} | P_{D} | |

10^{−8} | <1% | 63.5% |

3 · 10^{−8} | ~2% | 64.1% |

10^{−7} | ~2% | 64.6% |

3 · 10^{−7} | ~2% | 66,2% |

10^{−6} | 6% | 67.7% |

**Table 7.**Comparison results for the different correlator architectures under consideration. In green: optimum values.

Correlation Approach | All [1200 it.] | Mitigating (<0) | Degrading (>0) | |||
---|---|---|---|---|---|---|

FRef | Mean −3.00 dB | Std 4.22 dB | %. It. 57.5% | Mean −4.36 dB | %. It. 4.6% | Mean 1.82 dB |

FQ31 | Mean −3.28 dB | Std 4.25 dB | %. It. 65.9% | Mean −4.04 dB | %. It. 10.8% | Mean 1.00 dB |

FQ15 | Mean −3.37 dB | Std 4.28 dB | %. It. 65.6% | Mean −4.21 dB | %. It. 11.7% | Mean 1.14 dB |

FQ7 | Mean −3.35 dB | Std 4.35 dB | %. It. 64.1% | Mean −4.39 dB | %. It. 13.5% | Mean 1.49 dB |

FQ3 | Mean −2.73 dB | Std 4.45 dB | %. It. 59.9% | Mean −4.24 dB | %. It. 17.7% | Mean 2.33 dB |

FQ2 | Mean 0.06 dB | Std 5.27 dB | %. It. 40.1% | Mean −3.92 dB | %. It. 37.6% | Mean 4.32 dB |

TRefIFFT | Mean −3.10 dB | Std 4.31 dB | %. It. 64.6% | Mean −3.85 dB | %. It. 12.3% | Mean 0.67 dB |

TQ31 | Mean −3.33 dB | Std 4.89 dB | %. It. 58.9% | Mean −4.88 dB | %. It. 18.9% | Mean 1.50 dB |

TQ15 | Mean −1.88 dB | Std 5.00 dB | %. It. 49.9% | Mean −4.34 dB | %. It. 27.9% | Mean 2.53 dB |

TQ7 | Mean 0.99 dB | Std 5.74 dB | %. It. 30.1% | Mean −4.34 dB | %. It. 47.8% | Mean 4.35 dB |

TQ3 | Mean 2.03 dB | Std 5.82 dB | %. It. 24.8% | Mean −4.13 dB | %. It. 53.0% | Mean 4.91 dB |

TQ2 | Mean 12.04 dB | Std 7.14 dB | %. It. 2.9% | Mean −3.28 dB | %. It. 74.9% | Mean 12.64 dB |

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**MDPI and ACS Style**

Perez-Portero, A.; Querol, J.; Camps, A.; Martin-Neira, M.; Suess, M.; Ramirez, J.I.; Zurita, A.; Closa, J.; Oliva, R.; Onrubia, R. RFI Detection and Mitigation for Advanced Correlators in Interferometric Radiometers. *Remote Sens.* **2022**, *14*, 4672.
https://doi.org/10.3390/rs14184672

**AMA Style**

Perez-Portero A, Querol J, Camps A, Martin-Neira M, Suess M, Ramirez JI, Zurita A, Closa J, Oliva R, Onrubia R. RFI Detection and Mitigation for Advanced Correlators in Interferometric Radiometers. *Remote Sensing*. 2022; 14(18):4672.
https://doi.org/10.3390/rs14184672

**Chicago/Turabian Style**

Perez-Portero, Adrian, Jorge Querol, Adriano Camps, Manuel Martin-Neira, Martin Suess, Juan Ignacio Ramirez, Alberto Zurita, Josep Closa, Roger Oliva, and Raul Onrubia. 2022. "RFI Detection and Mitigation for Advanced Correlators in Interferometric Radiometers" *Remote Sensing* 14, no. 18: 4672.
https://doi.org/10.3390/rs14184672