Cross-Validation of Radio-Frequency-Interference Signature in Satellite Microwave Radiometer Observations over the Ocean

: Radio-frequency-interference (RFI) signals have gradually become a more serious problem in active and passive microwave remote sensing. However, currently, there is no reliable RFI source distribution data to evaluate the accuracy of existing RFI identiﬁcation methods. In this study, a simpliﬁed generalized RFI detection method (GRDM) is proposed to detect RFI applied to the ocean surface. Two RFI detection methods, the GRDM and the double-principal component analysis (DPCA) method, are used for cross-validation to obtain RFI recognition thresholds of DPCA in the Advanced Microwave Scanning Radiometer 2 (AMSR2) ocean data. In addition, in the present work the source and distribution characteristics of RFI over the ocean surface are also analyzed. The results show that the proposed scheme can e ﬀ ectively identify RFI signals from AMSR2 data, and only 7.3, 10.65, and 18.7 GHz channels are contaminated by RFI over the ocean surface. There are strong 7.3 GHz interference signals over the waters of East Asia (with the value of ∆ TB H mostly between 5 and 30 K and ∆ TBv mostly between 5 and 40 K), Europe (with the value of ∆ TB H mostly between 5 and 40 K and ∆ TBv mostly between 5 and 30 K), and North America (with the value of ∆ TB H mostly between 5 and 50 K and ∆ TBv mostly between 5 and 30 K). The RFI signals in 10.65 GHz data are mainly distributed over the Mediterranean and other European waters (with the value of ∆ TB H mostly between 5 and 35 K and ∆ TBv mostly between 5 and 20 K). The RFI signals at 18.7 GHz are mainly present over the o ﬀ shore marine areas of North America (with the value of ∆ TB H mostly between 5 and 50 K and ∆ TBv mostly between 5 and 40 K), with the strongest RFI distributed near the Great Lakes of America, and the RFI magnitudes over the east and west coasts are stronger than over the south coast. Satellite-borne microwave observations over the ocean su ﬀ er from interference mainly from stationary communication / television satellites. Due to the reﬂection of the sea surface, the range and intensity of RFI are strongly dependent on the relative geometric positions of stationary satellites and space-borne passive instruments. Therefore, RFI coverage area changes every day over the ocean in one 16-day period, which is very di ﬀ erent from that over the land.


Introduction
Passive thermal radiation received by satellite sensors from a natural Earth-atmosphere system is mixed with artificial signals from the Earth's surface, known as radio frequency interference (RFI). The latter, over the years, has become an increasingly serious problem in active and passive microwave

RFI Detection Methods
Over the ocean, because the microwave emissivity of the sea surface is much lower than that of the land, the sea surface conditions (e.g., wind speed and wind direction) and weather phenomena (e.g., water vapor, precipitation, and clouds) will also cause significant changes in TB, sometimes exceeding the impact of RFI [13]. When the spectral difference method is applied to ocean data, it cannot distinguish between weak RFI signals and weather changes, and there are certain errors in its use. Therefore, in this study, two independent interference detection methods, the GRDM and the DPCA method, are applied to identify RFI over the global ocean surface from AMSR2 low-frequency channel TB data and to perform cross-validation.

GRDM Method
A simplified GRDM was proposed to recognize C-band RFI, and its effectiveness was validated well by PCA method over the land [9]. Also, it is extended to RFI detection over the ocean in this study. The algorithm is written as Equation (1) [9]:

DPCA Method
The DPCA method consists of two PCA steps. Taking the RFI detection for the 7.3 GHz horizontal polarization (H-pol) channel as an example, the first PCA step is conducted for the TB vector V consisting of 10 channels. The matrix composed of observation field points for PCA is A 10×N [14]: TB7H  TB7V  TB10H  TB10V  TB18H  TB18V  TB23H  TB23V  TB37H TB37V where TB is the observed value of AMSR2 TB, subscripts H/V represent horizontal/vertical polarization, the subscript number represents the observed frequency, and N represents the sum of observed pixels. Construct the covariance matrix of A as: Its eigenvalue λ i (i = 1, 2, . . . , 10) and eigenvector e i = [e 1,i , e 2,i , . . . , e 10,i ] T satisfy: where e i represents the ith principal component (PC) and λ i is the contribution of the ith PC to the total variance. Project matrix A into the orthogonal space constructed by eigenvectors ( e 1 , e 2 , . . . , e 10 ) to obtain the PC coefficients: 10) represents the coefficient of the ith PC. Therefore, A can be expressed using e i and the PC coefficient u i : Based on the PC and PC coefficient, matrix A can be reconstructed into two parts A 1 and A 2 : where α is an integer constant, the value of which depends on the situation. Since the radiation observations from the natural Earth-atmosphere are highly correlated with the channels, the correlation of the observations between channels is captured by the first several principal components, namely A 1 . Matrix A 2 is the sum of TB from the (α + 1)th to the 10th PC, which is referred to as the residual data matrix. RFI only makes the observed value of the interfered channel abnormally high and is not related to other channels. Therefore, the RFI signal is contained in the residual matrix A 2 , and α is taken as 3 in this study. The second PCA step expands the residual matrix A 2 ; that is, it performs NPCA on A 2 . For example, the RFI detection in the 7.3 GHz H-pol channel: where µ and σ are the mean values and standard deviations of five RFI factors for each field of view.
Actually, both the first and the second step in DPCA method depends on the particular channel that is tested for RFI, which means that the two step is performed for a specific channel that is to be tested with regard to its RFI contamination. For RFI detection at 7.3, 10.65 and 18.7 GHz channels, the first steps in DPCA method, i.e., from Equation (2) to Equation (10), are the same, so the first step for these three-frequency channels only needs to be done once, the second steps (Equations (11)-(15)) are different.
Then, the data matrix B 5×N is reconstructed from R A 2 indices7H : The eigenvalue vector is expressed as the PC e 1 , e 2 , . . . , e 5 , and

RFI Detection by GRDM
According to Equation (1) and the coefficients in Table 1, the generalized RFI indices (∆Tb[i]) in Equation (1) for 6.925, 7.3, 10.65, and 18.7 GHz H-pol channels were obtained. As shown in the results, almost no RFI signal is detected in the observations of the 6.925, 23.8, 36.5, and 89.0 GHz channel over the global ocean (pictures omitted). The RFI signals detected in the 7.3 GHz channel are mainly distributed over the waters of East Asia, Europe, and North America. The RFI signals detected in the 10.65 GHz channel are distributed mainly over European waters. RFI signals detected in the 18.7 GHz channel are mainly distributed over North American waters. Figures 1-3 present the spatial distribution of 7.3 GHz-H RFI obtained by the GRDM over East Asian, European, and North American waters from 1 July to 16 July 2019. It can be seen from the figures that the greater the ∆Tb, the warmer the tones, the greater the probability of RFI and the stronger the intensity. Moreover, RFI generally appeared in a long, narrow strip, but the exact location and the length of the strip, and the strength of the RFI vary from day to day. Figure 1 illustrates the RFI signals in AMSR2 measurements for H-pol channels of 7.3 GHz over East Asian waters during 16 different days. On 1, 2, 5, 10, and 14 July, the detected RFI over East Asian waters is weak. And on 3,4,6,7,8,9,11,12,13, and 15 July, the detected RFI is much stronger, while on 16 July, almost no obvious RFI signal is detected. Figure 2 depicts the RFI signals in AMSR2 measurements for H-pol channels of 7.3 GHz over European waters during 16 different days. In general, the RFI strip has a northeast-southwest trend: for example, the North Sea-the English Channel-the Bay of Biscay (2,4,6,9,11, and 13 July), Adriatic Sea-Tyrrhenian Sea (2 July), the North Sea-the Gulf of Lion (3 July), the western waters of Corsica and Sardinia (5 July), the Irish sea to St. George's Channel and Bristol Bay (7 and 16 July), and the North Sea (8 and 15 July). Meanwhile, no significant RFI was detected on 12 or 14 July. Figure 3 shows the RFI signals in AMSR2 measurements for H-pol channels of 7.3 GHz over North American waters during 16 different days (1-16 July 2019). During the 16 days, almost no RFI signal is detected except on 1, 3, 5, 8, 13, and 15 July. RFI signals of different intensities are detected in the remaining 10 days. The longitude range of the RFI strip is usually between 140 • W and 153 • W, while the latitude range is usually between 25 • N and 37 • N. Figure 4 shows RFI signals in AMSR2 measurements for H-pol channels of 10.65 GHz over European waters on 16 different days. As can be observed in Figure 4, the RFI signals detected over the global ocean surface in the AMSR2 10.65 GHz channel are strongest over European waters. The RFI signals focus mainly on the North Sea, the English Channel, the Bay of Biscay, the Strait of Gibraltar, the Baltic Sea, the Mediterranean, the Black Sea and the Caspian Sea. Similarly, RFI in the AMSR2 10.65 GHz channel also generally appears in a long and narrow strip, while the location and the length of the strip and the strength of the RFI vary every day during the 16 different days. For example, North Sea-St. George's Channel-Bristol Bay-Atlantic Ocean (1, 10 July), Baltic Sea-Ligurian Sea-Mediterranean (1, 10 July), Black Sea-Levantine Sea (1, 10 July), North Sea-Alboran Sea (2 July), Baltic Sea-Adriatic Sea-Ionian Sea (2 July), Black Sea (2,4,9,11,13,16 July), North Sea-St George's Channel-Bristol Bay-Atlantic Ocean (3 July), Baltic Sea-Adriatic Sea-Tyrrhenian Sea (3, 5, 6, 7, 12, 14, 16 July), North Sea-Skagerrak-Balearic Sea-Alboran Sea (4, 6, 13, 15 July), Ionian Sea (4 July), North Sea-English Channel-Bay of Biscay-Strait of Gibraltar (5, 7, 14 July), in the southwest seas of the island of Briton and Ireland (8, 13, 15 July), Skagerrak Strait-Ligurian Sea-Balearic Sea (8 July), North Sea-Strait of Dover-Bay of Biscay-Strait of Gibraltar (9, 16 July), Baltic Sea-Adriatic Sea-Ionian Sea (9 July), Caspian Sea (10 July), North Sea-Balearic Sea (11 July), Strait of Otranto-Ionian Sea (11 July), North Sea-Bristol Bay-English Channel-Bay of Biscay-Atlantic Ocean (12 July).       Figure 5 shows RFI signals in AMSR2 measurements for H-pol channels of 18.7 GHz over North American waters on 16 different days. RFI at 18.7 GHz are mainly present over the offshore marine areas of North America. The strongest RFI are distributed near the Great Lakes of America, and the RFI magnitude over the east and west coasts is stronger than that over the south coast. For example, waters in the vicinity of Los Angeles (1, 6, 8, 15 July), a swath of the east coast from New York to east of the Florida Peninsula (1, 3, 8, 10 July), the northwest coast of the Gulf of Mexico (1, 3, 5, 10, 12 July), from Seaside in the US to the west coast of Cumbria (2, 11 July), the Great Lakes (2,4,5,7,9,11,12,13,14,16 July), the waters south of New Orleans (2,7,9,11,12,14,16 July), the waters west of Vancouver Island (3 July), the waters south of San Francisco (4, 13 July), the northeastern Gulf of Mexico (4, 11, 13 July), a swath of the eastern seaboard from Saint John in Canada to Beaufort in the US (5 July), the waters around the Florida Peninsula (6,8,15 July), the waters south of Vancouver Island (5,7,9,12,14,16 July), from the Gulf of Maine on the east side of Boston to the east side of New York (7, 14 July), the Gulf of St. Lawrence to the south of the Nova Scotia Peninsula (9, 16 July), and the Wells-Oak Island east coast strip (12 July).
Remote Sens. 2020, 12, x FOR PEER REVIEW 15 of 30 Figure 4 shows RFI signals in AMSR2 measurements for H-pol channels of 10.65 GHz over European waters on 16 different days. As can be observed in Figure 4, the RFI signals detected over the global ocean surface in the AMSR2 10.65 GHz channel are strongest over European waters. The RFI signals focus mainly on the North Sea, the English Channel, the Bay of Biscay, the Strait of Gibraltar, the Baltic Sea, the Mediterranean, the Black Sea and the Caspian Sea. Similarly, RFI in the AMSR2 10.65 GHz channel also generally appears in a long and narrow strip, while the location and the length of the strip and the strength of the RFI vary every day during the 16 different days. For example, North Sea-St. George's Channel-Bristol Bay-Atlantic Ocean (1, 10 July), Baltic Sea-Ligurian Sea-Mediterranean (1, 10 July), Black Sea-Levantine Sea (1, 10 July), North Sea-Alboran Sea (2 July), Baltic Sea-Adriatic Sea-Ionian Sea (2 July), Black Sea (2,4,9,11,13,16 July), North Sea-St George's Channel-Bristol Bay-Atlantic Ocean (3 July), Baltic Sea-Adriatic Sea-Tyrrhenian Sea (3,5,6,7,12,14,16      Gulf of Mexico (4, 11, 13 July), a swath of the eastern seaboard from Saint John in Canada to Beaufort in the US (5 July), the waters around the Florida Peninsula (6,8,15 July), the waters south of Vancouver Island (5,7,9,12,14,16 July), from the Gulf of Maine on the east side of Boston to the east side of New York (7, 14 July), the Gulf of St. Lawrence to the south of the Nova Scotia Peninsula (9, 16 July), and the Wells-Oak Island east coast strip (12 July). The results above show that the area of RFI coverage varies from day to day over the ocean, which is very different from that over the land. Figure 6 selects the spatial distribution of the RFI signals detected in H-pol and V-pol channels at 7.3 GHz, 10.65 GHz, and 18.7 GHz in typical areas. It can be seen that no matter which area is chosen, the RFI signals in H-pol channel are more widely distributed and stronger than those in V-pol channel. This is because the TB range of H-pol channel is much wider than that of V-pol channel, which also indicates that H-pol emissivity of different ground objects varies greater than those for vertical polarization [30]. The results above show that the area of RFI coverage varies from day to day over the ocean, which is very different from that over the land. Figure 6 selects the spatial distribution of the RFI signals detected in H-pol and V-pol channels at 7.3 GHz, 10.65 GHz, and 18.7 GHz in typical areas. It can be seen that no matter which area is chosen, the RFI signals in H-pol channel are more widely distributed and stronger than those in V-pol channel. This is because the TB range of H-pol channel is much wider than that of V-pol channel, which also indicates that H-pol emissivity of different ground objects varies greater than those for vertical polarization [30].  In order to further evaluate the differences between the two polarization modes, the number of RFI-contaminated pixels each day during the 16-day period is showed in Table 2. Since the TB range of H-pol channel is much wider than that of V-pol channel, it can be seen that, under normal circumstances, the number of RFI signals in H-pol channel is more than that in V-pol channel of the same frequency, which is consistent with the conclusion drawn from Figure 6.
Remote Sens. 2020, 12, x FOR PEER REVIEW 22 of 30 affected by the RFI detected by DPCA is similar to that detected by GRDM, and most of the RFI signals can be identified by the two methods.   Figure 6. According to the scatter diagram, the TB range of H-pol channel is much wider than that of V-pol channel, which also indicates that H-pol polarization is more sensitive to the underlying surface than the vertical polarization. As can be seen from the scatter diagram distribution, the 7.3 GHz RFI signal with good strength over East Asian waters exists mainly in the TB range of 80-120 K in H-pol channel (with the value of ΔTBH mostly between 5 and 30 K) and 170-200 K in V-pol channel (with the value of ΔTBV mostly between 5 and 40 K). The strong RFI signals over European waters exist mainly in the TB range of 75-125 K in H-pol channel (with the value of ΔTBH mostly between 5 and 40 K) and 160-190 K in V-pol channel (with the value of ΔTBV mostly between 5 and 30 K). The strong RFI signals over North American waters exist mainly in the TB range of 80-90 K in H-pol channel (with the value of ΔTBH mostly between 5 and 50 K) and 170-175 K in V-pol channel (with the value of ΔTBV mostly between 5 and 30 K). The strong RFI signal of 10.65 GHz over European waters is present mainly in the TB range of 80-120 K in H-pol channel (with the value of ΔTBH mostly between 5 and 35 K) and 170-190 K in V-pol channel (with the value of ΔTBV mostly between 5 and 20 K). The strong RFI signal of 18.7 GHz over North American waters exists mainly in the TB range of 100-250 K in H-pol channel (with the value of ΔTBH mostly between 5 and 50 K) and 180-250 K in V-pol channel (with the value of ΔTBV mostly between 5 and 40 K). In addition, the generalized RFI index of H-pol channel is generally larger than that of V-pol channel, up to more than 50 K, indicating that the RFI signal of H-pol channel is stronger than that of V-pol channel. The latter is consistent with the information information provided in Table 2.   Figure 6. According to the scatter diagram, the TB range of H-pol channel is much wider than that of V-pol channel, which also indicates that H-pol polarization is more sensitive to the underlying surface than the vertical polarization. As can be seen from the scatter diagram distribution, the 7.3 GHz RFI signal with good strength over East Asian waters exists mainly in the TB range of 80-120 K in H-pol channel (with the value of ∆TB H mostly between 5 and 30 K) and 170-200 K in V-pol channel (with the value of ∆TB V mostly between 5 and 40 K). The strong RFI signals over European waters exist mainly in the TB range of 75-125 K in H-pol channel (with the value of ∆TB H mostly between 5 and 40 K) and 160-190 K in V-pol channel (with the value of ∆TB V mostly between 5 and 30 K). The strong RFI signals over North American waters exist mainly in the TB range of 80-90 K in H-pol channel (with the value of ∆TB H mostly between 5 and 50 K) and 170-175 K in V-pol channel (with the value of ∆TB V mostly between 5 and 30 K). The strong RFI signal of 10.65 GHz over European waters is present mainly in the TB range of 80-120 K in H-pol channel (with the value of ∆TB H mostly between 5 and 35 K) and 170-190 K in V-pol channel (with the value of ∆TB V mostly between 5 and 20 K). The strong RFI signal of 18.7 GHz over North American waters exists mainly in the TB range of 100-250 K in H-pol channel (with the value of ∆TB H mostly between 5 and 50 K) and 180-250 K in V-pol channel (with the value of ∆TB V mostly between 5 and 40 K). In addition, the generalized RFI index of H-pol channel is generally larger than that of V-pol channel, up to more than 50 K, indicating that the RFI signal of H-pol channel is stronger than that of V-pol channel. The latter is consistent with the information information provided in Table 2. Remote Sens. 2020, 12, x FOR PEER REVIEW 25 of 30  However, DPCA is only a qualitative RFI signal detection method, i.e., a large value of the coefficients of the first PC (u1) of the residual data matrix A2 indicates the existence of RFI, and the larger the coefficient value of the first PC, the relative greater possibility of the existence of a strong RFI. Moreover, the ocean surface is not a completely smooth and flat mirror surface, especially when the ocean wind speed is high, and at the same time non-strict specular reflection causes the interference signal to have an angular spread. So, to effectively prevent a small-scale weather system from being mistaken for a false RFI signal, and to quantify RFI detection criteria using DPCA, the first PC coefficient u1 > u1threshold and the generalized RFI index > 5 K are combined into a threshold criterion for judging whether there is RFI from a geostationary satellite. And the values of recognition thresholds (u1threshold) in DPCA method developed for different channels are shown in Table 3.  However, DPCA is only a qualitative RFI signal detection method, i.e., a large value of the coefficients of the first PC (u 1 ) of the residual data matrix A 2 indicates the existence of RFI, and the larger the coefficient value of the first PC, the relative greater possibility of the existence of a strong RFI. Moreover, the ocean surface is not a completely smooth and flat mirror surface, especially when the ocean wind speed is high, and at the same time non-strict specular reflection causes the interference signal to have an angular spread. So, to effectively prevent a small-scale weather system from being mistaken for a false RFI signal, and to quantify RFI detection criteria using DPCA, the first PC coefficient u 1 > u 1threshold and the generalized RFI index > 5 K are combined into a threshold criterion for judging whether there is RFI from a geostationary satellite. And the values of recognition thresholds (u 1threshold ) in DPCA method developed for different channels are shown in Table 3. Remote Sens. 2020, 12, x FOR PEER REVIEW 27 of 30

RFI Source Analysis
During the 16-day orbital period, the location and intensity of RFI signals over the ocean are changing every day. It also has been proved that, the RFI of any AMSR2 channel from the ocean surface only appears during descending orbit observation in the northern hemisphere, while no RFI signal appears during ascending orbit observation. When the wind speed on the ocean surface is small, specular reflection occurs. Communications/TV signals coming from stationary satellites are reflected by the ocean surface, which is the main sources of interference with the observations of satellite-borne passive microwave radiometers on the ocean [25]. Thus, the RFI location and intensity depend highly upon the relative geometric positions of the stationary satellite and the space-borne passive instrument.

RFI Source Analysis
During the 16-day orbital period, the location and intensity of RFI signals over the ocean are changing every day. It also has been proved that, the RFI of any AMSR2 channel from the ocean surface only appears during descending orbit observation in the northern hemisphere, while no RFI signal appears during ascending orbit observation. When the wind speed on the ocean surface is small, specular reflection occurs. Communications/TV signals coming from stationary satellites are reflected by the ocean surface, which is the main sources of interference with the observations of satellite-borne passive microwave radiometers on the ocean [25]. Thus, the RFI location and intensity depend highly upon the relative geometric positions of the stationary satellite and the space-borne passive instrument.
Generally, stationary communication/TV satellites are fixed at a certain position over the Earth's equator and transmit signals continuously to designated areas [25,31]. Since the population density of coastal areas around the world is relatively high, static TV satellite antennas are designed to be directional and only intensively transmit to designated land areas. Although these geostationary satellite antennas are designed to focus on the land area, a small part of the strong radiation is still projected onto the ocean near the coastline, so there is a large-scale and strong RFI near the coastline [27]. In East Asia, Japan and other coastal areas have strong RFI. Over European waters, RFI signals are mainly distributed over the Mediterranean and other waters near Europe. Over North American waters, there are large-scale and strong RFIs near the coast, especially the east coast. Strong RFIs are also distributed over Lake Michigan, Lake Ontario, and Lake Erie of the Great Lakes. The closer to the inland, the stronger the RFI it becomes. The RFI is stronger over the north and west coasts, while the disturbance over the whole south coast is relatively weak.
In addition, AMSR2 C-band, X-band, and K-band channels have different RFI signal distribution areas over the ocean surface. This is caused by the different central frequencies currently used by the main stationary communication/TV satellites in different regions [27,32].

Conclusions
In this study, new coefficients which are applied to ocean surface were developed for a simplified GRDM. And the use of two independent identification methods is employed for cross-validation of the proposed technique, which allowed obtaining identification thresholds of the DPCA method. Meanwhile, the source and distribution characteristics of RFI over the ocean surface are analyzed. The results show that the proposed simplified GRDM works well over the ocean, which is a complement to the previous algorithm. Moreover, the detection results also show that the area of RFI coverage varies from day to day over the ocean, which is of big difference with that over the land. RFI signals over the waters are mainly distributed in Europe, East Asia, and North America, and the contaminated AMSR2 channels are in 7.3 GHz (C-band), 10.65 GHz (X-band), and 18.7 GHz (K-band). Moreover, RFI signals in H-pol channel are more widely distributed and stronger than those in V-pol channel of the same frequency. Furthermore, the generalized RFI index > 5 K and the first PC coefficient u 1 > u 1threshold after residual matrix principal component analysis are used as the threshold criteria for cross-verification of RFI signals. In the absence of reliable data about radio signals over the ocean, cross-validation results obtained by different identification methods are helpful for identifying frequency interference in ocean data. In addition, AMSR2 suffers interference from geostationary satellites when observing the ocean surface in a descending orbit, while observation in the ascending orbit is not affected by such interference.
The cross-validation RFI detection method proposed in this study makes use of the correlation between channels of the microwave radiometer. It also does not require any other data or models and its calculation is relatively simple and straightforward. Therefore, it can be easily transplanted to RFI detection in existing or future space-borne microwave radiometer observations. However, the regression coefficients in this method were determined by selecting the observed TB data of the ocean surface excluding snow cover and sea ice cover over a period of time as training data. The applicability to snow cover and sea ice surface with obvious scattering effect remains to be further verified. Moreover, RFI Signal in a pixel may come from multiple geostationary satellites simultaneously. Considering the specific space position of geostationary satellites and the radiometer (AMSR2 in this study), an attempt can be made to calculate the correlation between them and the signal strength. Maybe we can do this as part of this study's continuation in the future is to investigate the specific location of the geostationary satellite of which the downlink signals frequency is around at 7.3 GHz over East Asia, Europe, and North America, so as to do further research. These are subjects of ongoing work in our group.