The clutter measurement experiment has been conducted by CRIRP in a period between January 2017 and March 2018 in the South China Sea. To acquire the sea clutter data in the open sea, the SSCMR was installed on a supply ship “Qiongsha 3.” This ship has been traveling between Hainan Province and Xisha Islands of China irregularly; therefore, the sea clutter was measured during the ship navigating.

The “Qiongsha 3” is 84-m-long and 13.8-m-wide, with a displacement of about 2500 tons, and it is shown in Fig. 1(a). The SSCMR was mounted on the bow port side, approximately 12 m above the sea surface; considering the height of the radar antenna, the total height of the radar was about 14.1 m above the sea surface. The depression angle of the radar was set to be °. Thus, according to the radar blind zone and the radar max power, the measurable grazing angle of the sea clutter was in a range from 0.3° to 1.1°, which is a relatively low grazing angle. The measurable azimuth angle of the sea clutter ranged from 190° to 350° (nose angle).

Fig. 1.

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	Fig. 1. Scene of shipborne sea clutter measurement system, showing (a) “Qiongsha 3” ship and (b) instruments mounted on deck.

The four other instruments installed on the ship deck as shown in Fig. 1(b), were used to collect assistant data necessary to support our investigation of the sea clutter characteristics. The instruments used were as follows: (i) an ultrasound micrometeorological observation system (LUFFT WS700) for collecting the meteorological data (e.g., temperature and wind speed), (ii) an attitude and heading reference system (MTi-G) of the ship for recording attitude and navigation data of the ship, (iii) a video monitoring system of the radar to assist in setting the radar azimuth, and (iv) a shipborne evaporation duct monitor system for acquiring the propagation conditions of the radiowave around the radar. During the experiment, these systems were functioning simultaneously with the SSCMR, proving complete data set for the sea clutter study.

The SSCMR system was equipped with a high-precision stabilization platform to maintain the stability of the radar beam pointing. By using a steerable pedestal, it was possible to conveniently steer the antenna in 360° azimuth and from 90° to –10° in elevation. The radar is a coherent, polarimetric system having 16 frequency points ranging from 3100 MHz to 3400 MHz, in steps of 20 MHz. In this study, we have used 3200-MHz frequency to measure the sea clutter. The radar design comprises four chirp bandwidths: 2.5, 5, 10, and 20 MHz, resulting in range resolutions of 60, 30, 15, and 7.5 m, respectively. Such a setup enables the investigation of the clutter in different radar resolutions. There are 794 range cells, corresponding to a maximum sampling distance of 5955 m. The detailed list of SSCMR parameters can be found in Table 1.

Table 1.

Table 1.

Table 1. Main parameters of SSCMR. . Number Parameter Values 1 frequency 3.1 GHz to 3.4 GHz 2 polarization HH 3 gain 56 dB 4 bandwidth 2.5 MHz, 5 MHz, 10 MHz, 20 MHz 5 PRF 500 Hz, 2 kHz, 5 kHz, 10 kHz 6 pulse width 3 μs 7 θdB 5.3° θdB = 3-dB antenna beamwidth

Table 1. Main parameters of SSCMR. .

During the two years of experimenting, having 18 voyages in total, many trials of the measurement have been carried out; the average radar measurement time was about 30 h per voyage. The acquired valid sea clutter data contained about 10784 sets or 6954 GB; the sea conditions varied from 2 to 5 (sea state scale, World Meteorological Organization). According to the sea state of each voyage and the number of data sets per voyage, the shares of the data volume with sea states 2, 3, 4, and 5 were about 33%, 23%, 32%, and 13%, respectively; there were relatively little data for sea state 5. The wave directions included upwave, downwave, and crosswave.

Figure 2 shows four typical range–pulse intensity plots of the sea clutter measured in different sea states; the radar parameters were the same. We see that the maximum measurable ranges of the sea clutter are different for the four sea states; as the sea state increases in the indicating number, the further sea echoes are received by the radar. This phenomenon complies with the known sea surface scattering mechanisms and indicates the validation of the measured clutter data.

Fig. 2.

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	Fig. 2. Range–pulse intensity plots of sea clutter in sea state of (a) 2, (b) 3, (c) 4, and (d) 5.

In the case of a shipborne radar looking at the sea surface, if the position of the scatterer on the sea surface is represented by (r_l,θ_m), the velocity is represented by (v_rl, v_θm), where(l,m) are the position indices in the slant-range and azimuth direction. The total sea clutter return measured by the radar in the spatial frequency (k_r,k_{θ) domain can be written as

Based on the expression of the sea clutter intensity given by Eq. (1), in which the ship motion is considered, the corresponding power spectral density of the sea clutter is given by

By transforming the spatial frequency k_θ into the Doppler frequency f, the power spectral density is given by Eq. (4) and can then be written as

The antenna beam pattern is a function of the azimuth angle, which is in the Gaussian form and can be expressed as

Figure 3 shows the geometry of calculating the Doppler components induced by the movement of the shipborne radar platform, where v_p is the velocity of the ship, φ is the angle between the moving direction of the ship and the projection of radar pointing direction (i.e., the azimuth angle), θ is the grazing angle, and θ_b is the 3-dB azimuthal bandwidth of the radar beam.

Fig. 3.

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	Fig. 3. Geometry of shipborne radar beam.

According to the geometry shown in Fig. 3, the Doppler shift induced by the ship movement can be calculated from^[16]

In calculating the Doppler bandwidth induced by the ship movement, we consider three scattering points P₁, P₂, P₃ on the sea surface, with all points being equally distant from the radar as shown in Fig. 3. Points P₁ and P₃ are placed at the 3-dB edge of the antenna beam and P₂ is located at the antenna boresight. Because the three scattering points are located on the same wavefront, the radar backscatter at a certain time delay is the sum of the backscatter from these scattering points, but the angles between the ship motion direction and the backscattering directions are different slightly. Let P₂ have the azimuth angle φ, P₁ and P₃ be φ ± θ_b/2; then the difference between the Doppler shift of the backscatter from P₁ and P₃ will be

The sea clutter Doppler spectrum measured by a moving ship-based platform is widened by the aspect dependent Doppler spread due to the antenna beam pattern, so it is referred to as the sea clutter “spread” spectrum in this paper. The above subsection gives the mapping relationship between the spread spectrum and the sea clutter inherent spectrum determined by the wave movement. If the inherent spectrum is known, and the relevant parameters such as moving velocity, radar pointing direction, radar beamwidth, and grazing angle are given, the spread spectrum is easily calculated through the convolution given by Eq. (5). However, our purpose is to understand the characteristics of the sea clutter inherent Doppler spectrum based on the sea clutter data collected by a moving ship-based radar, so we need to obtain the inherent spectrum from the spread spectrum; this comprises an inverse process.

Based on Eq. (5), rather than trying to deconvolve the radar beam pattern from the sea clutter spread spectrum, we first introduce a parametric model to describe the lineshape of the sea clutter inherent spectrum. Then we fit the model to the sea clutter spread spectrum to determine the model parameters with the best fit by using the particle swarm optimization (PSO) algorithm. Afterward, the estimated parameters are used to characterize the inherent spectrum model estimating of the inherent spectrum. The estimation process is given in Fig. 4.

Fig. 4.

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	Fig. 4. Estimation process of sea clutter inherent spectrum.

The ability of the Doppler model to describe the actual sea clutter Doppler spectrum determines the quality of the estimated shape of the inherent spectrum.^[17] In the modeling of the sea clutter Doppler spectrum, the Walker model^[9] and Ward model^[18] are two widely accepted and used models. Here in this work, the Walker model is adapted to describe the Doppler spectrum with the observation time longer than the period of the gravity sea waves (generally several seconds), which belongs to a long-time Doppler spectrum model. The Ward model is adapted for describing the Doppler spectrum with the observation time shorter than the period of the gravity sea waves but longer than the decorrelation times between the burst and whitecap scattering, which belongs to a short-time Doppler spectrum model.

The above two models have certain limitations in coping with the real sea clutter Doppler spectrum, so we use a suggested time-varying Doppler spectrum model for estimating the sea clutter inherent spectrum. This model is developed based on both the Walker model and Ward model. Thus, the real spectrum is described better by considering three different scattering mechanisms. The formula of the model can be written as

In the estimation process of the sea clutter inherent spectrum, nine parameters are required to be optimized by PSO, they are I_B, I_W, I_S, w_B, w_W, w_S, f_B, f_G, and Δ f_s. Their initial values are chosen as random numbers between x_min and x_max, which represent the possible minimum and maximum values of each parameter. The possible values are determined by analyzing the real spread spectrum of the shipborne sea clutter.

The method of estimating the sea clutter inherent Doppler spectrum was validated by the sea clutter data measured by SSCMR in the South China Sea in this section. The estimation process was as follows. First, we have chosen two sea clutter data sets with the same radar parameters, but one data set was acquired for the moving ship, and another data set was measured when the ship was static. To control the same sea conditions, the measurement time and sea area for the two data sets were made nearly equal. Secondly, based on the clutter data measured during the ship movement, we obtained the sea clutter spread spectrum by the Welch method, and then estimated the sea clutter inherent spectrum by using the method in this study. Finally, we have compared the estimated inherent spectrum with the Doppler spectrum yielded from the sea clutter data measured in the ship static state. If the two spectrum lineshapes have a good fit, it provee that the estimation method is valid.

Three validation tests were performed to evaluate the estimation method. Each test used two typical sets of clutter data: one corresponded to the static state of the ship and the other to the ship’s moving state. The measuring conditions of all the test data are given in Table 2. The radar parameters are shown in Table 1. The measurement intervals between the two clutter data in three tests were 8 min, 10 min, and 7 min respectively, which ensured that the sea wave conditions are identical when they are collected. In Table 2, φ represents the angle between the ship movement direction and the radar pointing direction as shown in Fig. 3. As can be seen from the clutter maps in Table 2, diagonal stripes are visible if the ship is moving, which is due to the relative movement between the radar platform and the sea surface scatterers. The relative movement makes the sea waves look like sea targets in radar eyes.

The comparisons among the sea clutter Doppler spectra measured by a moving ship-based platform, by a stationary ship-based platform, and the estimated clutter inherent spectrum are shown in Fig. 5, taking one range gate for example. Good agreement occurs between the estimated inherent spectrum and the actual sea clutter spectrum (i.e., the stationary platform clutter spectrum). The lineshapes of the clutter inherent spectrum are successfully reconstructed by the estimated ones.

Fig. 5.

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	Fig. 5. Comparison between clutter inherent spectrum and stationary platform clutter spectrum for range gate 190.

Table 2.

Table 2.

Table 2. Measuring conditions of sea clutter data. .

Table 2. Measuring conditions of sea clutter data. .

Table 3.

Table 3.

Table 3. Estimation errors (in unit Hz) of Doppler parameters of clutter inherent spectrum. . Range gate Test 1 Test 2 Test 3 Doppler mean shift Doppler bandwidth Doppler mean shift Doppler bandwidth Doppler mean shift Doppler bandwidth 130 1.77 0.54 1.32 0.36 2.23 0.20 150 2.26 2.43 1.07 2.10 0.51 1.78 170 2.57 0.56 0.63 3.23 1.26 1.75 190 2.72 2.11 2.67 1.84 1.87 2.10 210 1.12 0.16 0.61 1.13 1.04 1.77 230 3.07 2.47 0.67 2.65 0.69 4.79 250 4.36 0.74 2.79 0.36 2.78 1.29 Mean 2.55 1.29 1.39 1.67 1.48 1.95

Table 3. Estimation errors (in unit Hz) of Doppler parameters of clutter inherent spectrum. .

To evaluate the accuracy of the estimation method quantitatively, the estimation errors of the Doppler mean shift and bandwidth for the three tests were calculated, and are shown in Table 3. For each test, the inherent clutter spectra of 7 range gates were estimated, and the errors were counted. According to the results given in Table 3, it can be concluded that most of the mean estimation errors of the Doppler parameters are less than 2 Hz, except for the Doppler mean shift in test 1. Because the true values of these two Doppler parameters in S-band are on the order of tens of Hertz (refer to Fig. 5), the estimation errors shown in Table 3 are small and acceptable. This result validates the feasibility of the method of estimating the clutter inherent spectrum presented in this paper.

The typical range-Doppler maps of the sea clutter in the South China Sea estimated from the SSCMR clutter data in different sea states are presented in Fig. 6. By comparisons, the waves are of upwave direction for all sea states. The panels in the upper row are from the sea clutter “spread” spectra, and those in the lower row are from the sea clutter inherent spectra. As shown in the spread spectrum images, the Doppler mean shifts are about −100 Hz in sea states 2, 3, and 5. However, the shift is about +100 Hz for the sea state 4 spectrum. The spectra shapes indicate that in the two of the cases, the radar was looking backward and forward, relative to the ship moving direction. Although the Doppler shifts of the spread spectra exhibit different signs in the two cases, still all Doppler shifts of the corresponding inherent spectra share the same plus sign, proving that the wave directions are upwave for all the sea states, which coincide with the measuring condition of the clutter data.

Fig. 6.

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	Fig. 6. Range–Doppler maps of sea clutter in the South China Sea in sea states of (a) 2, (b) 3, (c) 4, and (d) 5.

By comparing the Doppler spectrum intensities shown in Fig. 6, as the sea state increases, the Doppler intensity of the clutter inherent spectrum clearly increases distinctly, indicating the growth of the clutter energy. As can be observed in the Doppler map, the Doppler intensity decreases as the range increases. Otherwise, by analyzing the fluctuation of the Doppler intensity versus range, the Doppler intensity clearly varies more significantly on the right side of the spectrum peak, and the spectrum spikes occur in these Doppler bins. This phenomenon can be attributed to the upwave conditions of the sea clutter data.

Figure 7 shows a typical comparison of the inherent spectrum lineshapes of the South China Sea in different sea states. The lineshapes are corresponding to the sea clutter data of the range gates 180 and 230 as shown in Figs. 6. Evidently, the Doppler mean shift and the bandwidth increase as the sea state increases; only the difference in Doppler mean shift is not remarkable for sea state 2 nor sea state 3, which is because the significant wave heights are similar for these clutter data. Moreover, as the sea state increases, the spectrum peak becomes increasingly complex, trending to exhibiting bimodal lineshapes.

Fig. 7.

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	Fig. 7. Comparison of inherent spectrum lineshapes of sea clutter in the South China Sea in different sea states: (a) gate = 180 and (b) gate = 230.

Figure 8 shows the typical range–Doppler maps of the sea clutter in the South China Sea for three different wave directions. The sea states were 3 in all these cases. From the sea clutter inherent spectra displayed in the lower row, we can observe that the wave direction has a significant influence on the Doppler mean shift, resulting in positive shift for upwave, negative shift for downwave, and near-zero shift for crosswave conditions. The Doppler mean shift is not strictly equal to zero for a crosswave case because the angle between the radar looking direction and the wave direction is not always equal to 90°. Further, as observed in the fluctuations of the spectrum intensity at each Doppler bin, under the upwave condition, the fluctuation is more intense for the Doppler bins on the side of positive Doppler shifts. However, under the downwave condition, the fluctuation is more intense on the side of negative Doppler shifts. Under the crosswave conditions, the fluctuations are comparable on both sides of the spectrum peak.

Fig. 8.

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	Fig. 8. Range–Doppler maps of sea clutter in the South China Sea in (a) upwave, (b) downwave, and (c) crosswave directions.

To illustrate the influence of wave direction on Doppler spectrum lineshape, figure 9 shows the lineshapes of the sea clutter inherent spectra obtained from the data of range gates 120 and 200 as shown in Fig. 8. Evidently, the symmetry of the lineshape and the Doppler mean shift are distinctly affected by the wave direction, but the influence on the Doppler bandwidth is not significant.

Fig. 9.

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	Fig. 9. Comparisons of sea clutter spectrum lineshapes of the South China Sea in different wave directions: (a) gate = 120 and (b) gate = 200.

The typical range–Doppler maps of the sea clutter in the South China Sea, estimated from the SSCMR clutter data with four different radar range resolutions, are displayed in Fig. 10. The sea conditions are sea state 3 and upwave. By comparing the Doppler maps in the four cases, the noticeable influence of the radar resolution can be observed in the variation degree of the spectrum intensity. When the resolution is 7.5 m, because the radar resolution cell is too small to cover a complete sea wave, the sea surface structure between different resolution cells changes remarkably; thus, the radar received clutter energy in each adjacent range gate exhibits considerable fluctuation. As a result, the Doppler spectrum exhibits a rapid fluctuation versus range. However, as the radar resolution decreases, the fluctuation of the spectrum weakens. When the resolution is 60 m, the Doppler spectrum exhibits a stable change with range increasing, owing to the small difference in clutter intensity between adjacent radar resolution cells, and this is further because a radar resolution cell contains multiple sea waves.

Fig. 10.

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	Fig. 10. Range–Doppler maps of sea clutter in the South China Sea for radar range resolutions of panel (a) 7.5 m, panel (b) 15 m, panel (c) 30 m, and panel (d) 60 m.

Based on the clutter data of range gates 130 and 220 shown in Figs. 10, figure 11 displays the comparisons of the lineshape of the sea clutter inherent spectrum among different radar range resolutions. For the radar resolution of 7.5 m, the Doppler bandwidth is relatively small, but for the other three cases, the Doppler bandwidths are larger and have approximately the same value. This phenomenon illustrates that as the radar resolution decreases to a critical value, knowing that a resolution cell can contain multiple sea waves and consequently the speed component of the sea wave reaches a stable state, the Doppler bandwidth does not change any further. For the Doppler mean shift, the influence of the radar resolution is not clear.

Fig. 11.

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	Fig. 11. Comparisons of sea clutter spectrum lineshape of the South China Sea in different radar range resolutions: panel (a) gate = 130 and panel (b) gate = 220.

In addition to the characteristics of Doppler spectrum lineshapes, the quantitative results of the Doppler spectrum parameters, including the Doppler mean shift and bandwidth, play an important role in suppressing the clutters of radar target detection. Based on the estimated inherent Doppler spectrum lineshapes from the large data sets in the experiment, we calculate and analyze the characteristics of the two Doppler spectrum parameters in the South China Sea, and the statistical results are shown in Table 4. The corresponding grazing angle is 0.8°, and the results are the mean values under different conditions.

Table 4.

Table 4.

Table 4. Statistics of Doppler spectrum parameters of radar sea clutter. . Sea state Wave direction Doppler mean shifts/Hz Doppler bandwidth/Hz 60 m 30 m 15 m 7.5 m 60 m 30 m 15 m 7.5 m 2 upwave 20.9 22.4 22.2 23.0 11.5 12.0 12.6 13.4 downwave −17.7 −17.0 −17.8 −17.6 7.5 7.4 8.0 8.9 3 upwave 27.1 30.8 25.7 28.4 14.9 15.5 14.9 15.3 downwave −21.9 −20.1 −21.3 −21.4 8.5 8.8 9.5 11.4 4 upwave 42.2 40.4 39.4 39.3 18.2 17.9 17.5 17.4 downwave −37.8 −36.8 −35.7 −33.9 13.0 12.7 13.1 13.6 5 upwave 49.0 46.4 46.4 44.9 24.6 23.9 23.5 23.5 downwave −46.5 −46.6 −47.4 −47.8 16.1 16.9 16.8 17.0

Table 4. Statistics of Doppler spectrum parameters of radar sea clutter. .

According to the results given in Table 4, we can conclude as follows.

(i) Under all measuring conditions, the variation trends of the Doppler mean shift and bandwidth as a function of sea state are very evident. The higher the sea state, the larger the absolute values of the two parameters are, which is in accordance with the scenario for faster wave speed and more complex sea wave components in higher sea states.

(ii) The sea wave direction has a distinct influence on the Doppler mean shift and bandwidth. The Doppler mean shift is positive in upwave and negative in downwave conditions, which meets the physical mechanism of the sea clutter Doppler spectrum. The Doppler bandwidth is wider for upwave and narrower in downwave cases, which indicates that there are more components of sea wave velocity in upwave conditions than in downwave conditions.

(iii) The radar range resolution has a little influence on the mean value of the Doppler mean shift and bandwidth. However, as shown in Fig. 10, we can deduce that with the increase of the radar range resolution, the distribution of the Doppler shift and bandwidth of sample becomes wider, that is, the variance of the sample increases. This is because the variation of the Doppler spectrum structure with range is more distinct for a smaller radar resolution.