# Rapid Simulation of Temporal-Spatial Correlated 3D Sea Clutter

Authors: Ye Zhao; Peng-Ju Yang; Xin-Cheng Ren; Xiao-Min Zhu
Journal: International Journal of Antennas and Propagation
 (2019)

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## Abstract

Due to the difficulties in actual measurement of sea clutter and uncertainties of experimental data, the electromagnetic (EM) scattering model becomes a better alternative means to acquire the sea clutter. However, the EM scattering model still faces the problems of huge memory consumption and low-computational efficiency when dealing with the large size of sea surface or the long time case. Thus, this paper presents a statistical model to simulate the temporal-spatial correlated three-dimensional (3D) sea clutter, which is based on the statistical properties obtained from the EM scattering model, such as probability density function and correlation function. The comparisons show that the texture feature, autocorrelation function, and PDF of the sea clutter simulated by the statistical model have a good agreement with the results given by the EM model. Furthermore, the statistical model is with high efficiency and can be used to simulate the large scene or long time temporal-spatial correlated 3D sea clutter.


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## Body

## 1. Introduction

It is the basic working mechanism of radar to discover and identify the target by using the electromagnetic (EM) scattering characteristics of the target. While the target exists or is hidden in the surrounding environment, the interference caused by the EM scattering of environment to the detection of the radar target signal is called radar clutter. Certainly, the radar echo from the sea surface environment is sea clutter. Because the sea surface is affected by the wind force, environmental humidity, surge, and other natural factors, the sea clutter signal has complex changes and high intensity. In addition, the sea surface is dynamic and constantly changing and the wave movement of sea surface has a rather complex relationship with the environmental factors, such as wave valley, ripple, vortex, and spray, all of which will affect the scattering characteristics of sea surface. Usually, in order to eliminate or reduce the influence of sea clutter, it is necessary to simulate sea clutter to obtain the distribution characteristics of sea clutter under various conditions before the radar detects the target on the sea surface. Moreover, the study on the characteristics of sea clutter is also of great significance for the natural mechanism explanation of the sea clutter and radar system design.At present, sea clutter modelling, suppression, and target detection under the background of sea clutter are one of the hotpots in the research of EM scattering of the sea surface [1, 2]. For the sea clutter modelling, a reasonable and practical sea clutter simulation model is very important, which can offset the difficulties in actual measurement of sea clutter and uncertainties of experimental data. Accordingly, many sea clutter simulation models based on the EM scattering model have been developed, such as Kirchhoff Approximation (KA) [3, 4], two-scale model (TSM) [5, 6], small slope approximation (SSA) [7–9], and some other facet-based models [10, 11]. Among these approaches, KA is just valid for the lower incident angle. TSM, as a famous and frequently-used tool, could only give an average of the scattering coefficient. The SSA method confronts the difficulties of huge memory consumption and low-computational efficiency, due to that the required sampling interval of sea surface in SSA is too small, such as less than one-eighth of the incident EM wavelength. Comparatively speaking, the facet-based asymptotical model (FBAM) [11] is a superior method and could give the scattering field information of single facet on sea surface which includes both amplitude and phase. In the FBAM, the sea surface is envisaged as a two-scale profile, in which the large-scale gravity wave is approximately decomposed by a mount of slightly rough facets with capillary waves as their microscopic random roughness. Because of considering the scattering of capillary waves, the computing time will increase when calculating the EM scattering from a sea surface with large area. In short, the EM scattering models mentioned above are harder to deal with the scattering of sea surface with large area or long time case.Another kind of sea clutter simulation models are based on the statistical model, such as the zero-memory nonlinear transform (ZMNL) [12, 13] and spherically invariant random process (SIRP) [14, 15]. And it is the core step of the sea clutter simulation based on the statistical model to generate the correlated non-Gaussian random process with the specified statistic and correlation properties [16–18], such as probability density function (PDF), correlation function, or spectral density function. In this paper, the FBAM is adopted as the EM scattering model to generate the sea clutter and then acquire the statistic and correlation properties for the establishment of a statistical model in the subsequent. However, in traditional sea clutter simulations, the sea clutter is always simulated as the time sequence or the two-dimensional (2D) sea clutter [17, 18] (in time-range dimensions or range-azimuth dimensions). With the development of the techniques of high-resolution imaging and target detection, the traditional time sequence or 2D sea clutter simulations cannot satisfy the practice requirement. Thus, the simulation of the temporal-spatial correlated three-dimensional (3D) (in range-azimuth-time dimensions) sea clutter will have a very important academic and realistic significance.The rest of this paper is organized as follows. Section2 gives two kinds of simulation models, namely, the EM scattering model and statistical model, to generate temporal-spatial correlated 3D sea clutter. And the statistical model is detailedly described here, which extends the ZMNL method to the 3D case. Section 3 gives some numerical results including the generation of 2D spatial correlated and 3D temporal-spatial correlated sea clutter. And then, the comparisons of the texture feature, statistical characteristics, and consumed time between the EM scattering model and the statistical model are shown. Section 4 forms the conclusion.


## 2. Simulation Models for 3D Sea Clutter

### 2.1. EM Scattering Model

For the simulation of 3D sea clutter, the FBAM proposed in our earlier work [11] is an available EM scattering model, which has been very well validated. It not only can be used to the RCS prediction and Doppler spectrum analysis of the sea surface [19], but also can be applied to the composite scattering and synthetic aperture radar (SAR) imagery simulation from a ship target over a sea surface [20].In FBAM, the sea surface is composed by a mount of tilted slightly rough facets. The scattering field from an arbitrary rough facet takes the following expression:(1)Ex,y,t=k21−ε2iReikR⋅F˜PQ⋅I⋅,where k is the wave number of electromagnetic waves; R is the position vector of facet; F˜PQ is the polarization factors related to the relative dielectric constant ε of sea water and Fresnel reflection coefficients (P,Q=H,V denote the polarization of incident and scattering waves, respectively); and I⋅ is an integral of the surface profile within a facet. The detailed expressions of F˜PQ and I⋅ can be found in [11], which are omitted here due to space limitations.


### 2.2. Statistical Model

In this part, the ZMNL method is extended to the 3D case for establishing a statistical model, which contains two major operational procedures, that is, the simulation of the correlated Gaussian process of zero mean and unit variance, and the generation of the desired non-Gaussian process using the nonlinear transformation.For the 3D case, the spectral density functionSkx,ky,ω and autocorrelation function Rρx,ρy,τ of the stochastic field consist of a pair of Wiener–Khintchine relationships, similar to the 2D case [21], which is given by(2)Rρx,ρy,τ=∫−∞∞∫−∞∞∫−∞∞Skx,ky,ωe−ikxρx+kyρy+ωτdkxdkydω,(3)Skx,ky,ω=12π3∫−∞∞∫−∞∞∫−∞∞Rρx,ρy,τ⋅eikxρx+kyρy+ωτdρxdρydτ,where kxandky are wave numbers, ρxandρy are separation distances in two directions. ω is angular frequency, and τ represents time interval. Then, the 3D correlated Gaussian process gx,y,t can be expressed by the following series as M, N, L ⟶ ∞, namely,(4)gx,y,t=∑m=−MM∑n=−NN∑l=−LLAmnl⋅coskxmx+kyny+ωlt+ϕmnl,where ϕmnl are independent random phase angles selected from a uniform distribution over 0,2π. Amnl is proportional to the square root of the spectral density function at km,kn,ωl:(5)Amnl=2Skxm,kyn,ωl⋅Δkx⋅Δky⋅Δω1/2,kxm=m⋅Δkx,m=−M,…,M,kyn=n⋅Δky,n=−N,…,N,ωl=l⋅Δω,l=−L,…,L,(6)Δkx=kuxM,Δky=kuyN,Δω=ωuL.In (6), kux, kuy, and ωu represent the upper cut-off wave numbers and frequency in corresponding dimensions of the kx−ky−ω coordinates, respectively.If a stochastic field (e.g.,Ex,y,t) is given, then the discretized version of spectral density function Skx,ky,ω of this field can readily be calculated by using the fast Fourier transform (FFT) algorithm. And the autocorrelation function of this stochastic field can be obtained easily based on (2) through the FFT algorithm. Namely, the correlation properties of an arbitrary stochastic field can be acquired by executing the FFT algorithm twice.So, assuming that the desired correlation properties (i.e., the correlation properties ofEx,y,t) are available, the correlated 3D Gaussian process gx,y,t of zero mean and unit variance can be generated according to (3) and (4). Then, the desired non-Gaussian process fx,y,t can be generated by executing nonlinear transformation from the correlated 3D Gaussian process, which takes the following calculation:(7)fx,y,t=Fnon−G−1FGgx,y,t,where FG⋅ represents the cumulative distribution function of Gaussian process gx,y,t and FGx=1/21+erfx/2. Fnon−G−1⋅ is the inverse cumulative distribution function of non-Gaussian process fx,y,t. If the non-Gaussian process fx,y,t follows the log-normal distribution with the shape parameter σ and scale parameter μ, the inverse cumulative distribution function of fx,y,t can be expressed as(8)Fnon−G−1x=exp2σ×erf−12x−1+μ.So, (7) can be rearranged to give the following expression:(9)fx,y,t=expσ×gx,y,t+μ.In theory, the stochastic fieldsEx,y,t and fx,y,t have consistent texture feature, correlation function, and PDF.


## 2.1. EM Scattering Model

For the simulation of 3D sea clutter, the FBAM proposed in our earlier work [11] is an available EM scattering model, which has been very well validated. It not only can be used to the RCS prediction and Doppler spectrum analysis of the sea surface [19], but also can be applied to the composite scattering and synthetic aperture radar (SAR) imagery simulation from a ship target over a sea surface [20].In FBAM, the sea surface is composed by a mount of tilted slightly rough facets. The scattering field from an arbitrary rough facet takes the following expression:(1)Ex,y,t=k21−ε2iReikR⋅F˜PQ⋅I⋅,where k is the wave number of electromagnetic waves; R is the position vector of facet; F˜PQ is the polarization factors related to the relative dielectric constant ε of sea water and Fresnel reflection coefficients (P,Q=H,V denote the polarization of incident and scattering waves, respectively); and I⋅ is an integral of the surface profile within a facet. The detailed expressions of F˜PQ and I⋅ can be found in [11], which are omitted here due to space limitations.


## 2.2. Statistical Model

In this part, the ZMNL method is extended to the 3D case for establishing a statistical model, which contains two major operational procedures, that is, the simulation of the correlated Gaussian process of zero mean and unit variance, and the generation of the desired non-Gaussian process using the nonlinear transformation.For the 3D case, the spectral density functionSkx,ky,ω and autocorrelation function Rρx,ρy,τ of the stochastic field consist of a pair of Wiener–Khintchine relationships, similar to the 2D case [21], which is given by(2)Rρx,ρy,τ=∫−∞∞∫−∞∞∫−∞∞Skx,ky,ωe−ikxρx+kyρy+ωτdkxdkydω,(3)Skx,ky,ω=12π3∫−∞∞∫−∞∞∫−∞∞Rρx,ρy,τ⋅eikxρx+kyρy+ωτdρxdρydτ,where kxandky are wave numbers, ρxandρy are separation distances in two directions. ω is angular frequency, and τ represents time interval. Then, the 3D correlated Gaussian process gx,y,t can be expressed by the following series as M, N, L ⟶ ∞, namely,(4)gx,y,t=∑m=−MM∑n=−NN∑l=−LLAmnl⋅coskxmx+kyny+ωlt+ϕmnl,where ϕmnl are independent random phase angles selected from a uniform distribution over 0,2π. Amnl is proportional to the square root of the spectral density function at km,kn,ωl:(5)Amnl=2Skxm,kyn,ωl⋅Δkx⋅Δky⋅Δω1/2,kxm=m⋅Δkx,m=−M,…,M,kyn=n⋅Δky,n=−N,…,N,ωl=l⋅Δω,l=−L,…,L,(6)Δkx=kuxM,Δky=kuyN,Δω=ωuL.In (6), kux, kuy, and ωu represent the upper cut-off wave numbers and frequency in corresponding dimensions of the kx−ky−ω coordinates, respectively.If a stochastic field (e.g.,Ex,y,t) is given, then the discretized version of spectral density function Skx,ky,ω of this field can readily be calculated by using the fast Fourier transform (FFT) algorithm. And the autocorrelation function of this stochastic field can be obtained easily based on (2) through the FFT algorithm. Namely, the correlation properties of an arbitrary stochastic field can be acquired by executing the FFT algorithm twice.So, assuming that the desired correlation properties (i.e., the correlation properties ofEx,y,t) are available, the correlated 3D Gaussian process gx,y,t of zero mean and unit variance can be generated according to (3) and (4). Then, the desired non-Gaussian process fx,y,t can be generated by executing nonlinear transformation from the correlated 3D Gaussian process, which takes the following calculation:(7)fx,y,t=Fnon−G−1FGgx,y,t,where FG⋅ represents the cumulative distribution function of Gaussian process gx,y,t and FGx=1/21+erfx/2. Fnon−G−1⋅ is the inverse cumulative distribution function of non-Gaussian process fx,y,t. If the non-Gaussian process fx,y,t follows the log-normal distribution with the shape parameter σ and scale parameter μ, the inverse cumulative distribution function of fx,y,t can be expressed as(8)Fnon−G−1x=exp2σ×erf−12x−1+μ.So, (7) can be rearranged to give the following expression:(9)fx,y,t=expσ×gx,y,t+μ.In theory, the stochastic fieldsEx,y,t and fx,y,t have consistent texture feature, correlation function, and PDF.


## 3. Results and Discussion

Figure1 is given here to validate the performance of the FBAM in the simulation of the PDF of the time series of sea clutter and the prediction of backscattering coefficient. The incident frequency is 14 GHz at VV polarization, and the wind is upwind at speed of 5 m/s. For the generation of the time series of sea clutter, the incident angle is θi=30°. Comparisons between the FBAM and experiment [22] indicate that the FBAM is a better EM model to generate the sea clutter and then acquire the statistical properties.Figure 1
Validations on the performance of the FBAM. (a) Backscattering coefficient. (b) PDF of the time series of sea clutter.
(a)
(b)Next, we simulate the sea clutter to verify the performance and efficiency of the statistical model.


### 3.1. Two-Dimensional Case

In order to verify the statistical model, Figure2 gives the comparisons of amplitude and autocorrelation function of 2D (in range-azimuth dimensions) spatial correlated sea clutter generated by statistical and EM models. For the EM model simulation, the incident frequency is 5 GHz slanting at the incident direction of θi=40°,ϕi=0°, and the results are completed in the backscattering case and for HH polarization. The 2D sea surface is generated based on the Monte Carlo method [23] using the Elfouhaily et al.’s spectrum [24], the sampling number along the x and y directions is M=N=128, the size of the facet is Δx=Δy=0.8m, the wind is upwind at speed of 5 m/s, the time t=0s, the relative dielectric constant of the sea water is calculated by the Klein model [25] at 20°C, and 35‰ salinity. In addition, the simulated 2D spatial correlated sea clutter by the EM model is of log-normal distribution and with the shape and scale parameters of 3.565560E − 01 and −4.407049, respectively. For ease of comparison, the desired correlation properties in the statistical model simulation should be consistent with the simulated 2D spatial correlated sea clutter by the EM model.Figure 2
Comparisons of amplitude and autocorrelation function of 2D sea clutter generated by statistical and EM models. (a) Statistical model. (b) EM model.
(a)
(b)From Figure2, it could be obviously found that the amplitude and autocorrelation function of 2D spatial correlated sea clutter generated based on the statistical and EM models have a consistent texture feature. In order to give a more intuitive comparison, the comparisons of 1D plot of the autocorrelation function and PDF are shown in Figure 3. It is seen that 1D plot of the autocorrelation function and PDF of 2D spatial correlated sea clutter generated by the statistical model agree well with the results simulated by the EM model.Figure 3
Comparisons of 1D plot of the autocorrelation function and PDF of 2D sea clutter generated by statistical and EM models. (a) 1D plot of the autocorrelation function. (b) PDF.
(a)
(b)Compared with the EM model, the major advantage of the statistical model is that it could quite efficiently generate sea clutter in a very large size of scene. Figure4 compares the amplitude and autocorrelation function of 2D spatial correlated sea clutter generated by the statistical model with different sizes of scenes. For clearer comparison, Figure 5 gives the comparisons of 1D plot of the autocorrelation function and PDF. From Figure 5, one can see that, the correlation in the edge of scene becomes smaller with the increase of scene and the middle area of the larger scene has a consistent correlation with the small scene. Besides, the sea clutter with different sizes of scenes has a consistent PDF (the amplitude and autocorrelation function of 100 m × 100 m are shown in Figure 2(a)).Figure 4
Comparisons of amplitude and autocorrelation function of 2D sea clutter by the statistical model with different sizes of scene. (a) 200 m × 200 m. (b) 400 m × 400 m.
(a)
(b)Figure 5
Comparisons of 1D plot of the autocorrelation function and PDF of 2D sea clutter by the statistical model with different sizes of scenes. (a) 1D plot of the autocorrelation function. (b) PDF.
(a)
(b)Furthermore, in order to contrast the efficiency between the statistical and EM models, Table1 gives the time taken by the above two models in the simulations of 2D sea clutter with different sizes of scenes. Obviously, the statistical model is with high efficiency, which is because that the FFT technique is used in the statistical model to generate the correlated sea clutter.Table 1
Comparison of the consumed time in the simulations of 2D sea clutter with different sizes of scenes.
The size of scene (m2)
100 × 100
200 × 200
400 × 400
Time (sec)
Statistical model
0.025
0.0765
3.0779
EM model
4.67
18.05
70.11
∗Calculated by a computer with Intel(R) Core(TM) i7-6700 CPU @ 3.40 GHz.


### 3.2. Three-Dimensional Case

The simulation of 3D temporal-spatial correlated sea clutter is similar to the simulation of 2D spatial correlated sea clutter. For the EM model simulation in the 3D case, the parameters are same with the 2D case except that the sampling number att direction is 128 and the time interval is 0.1 s. Besides, it should be explained that the simulated 3D temporal-spatial correlated sea clutter by the EM model is of log-normal distribution and with the shape and scale parameters of 3.563838E − 01 and −4.405951, respectively.Figure6 gives the amplitude and autocorrelation function of 3D temporal-spatial correlated sea clutter generated by the statistical model in xOt plane, xOy plane, and yOt plane, respectively. It is seen from Figure 6 that the amplitude and autocorrelation function in different planes have different textures. Figure 7 shows the comparison of 1D plots (i.e., at x, y, and t direction, respectively) of the autocorrelation function of 3D temporal-spatial correlated sea clutter between statistical and EM models. Accordingly, the comparison of PDF is illustrated in Figure 8. From Figures 7 and 8, it is seen that 1D plots of the autocorrelation function and PDF of 3D temporal-spatial correlated sea clutter generated by the statistical model agree well with the results simulated by the EM model.Figure 6
The amplitude and autocorrelation function of 3D sea clutter by the statistical model. (a)xOt plane. (b) xOy plane. (c) yOt plane.
(a)
(b)
(c)Figure 7
Comparison of 1D plots of the autocorrelation function of 3D sea clutter atx, y, and t direction between statistical and EM models.
(a)
(b)
(c)Figure 8
Comparisons of PDF of 3D sea clutter between statistical and EM models.In order to contrast the efficiency of the statistical and EM models in the simulations of 3D sea clutter, Table2 gives the comparison of the consumed time in the simulations of 3D sea clutter with different sizes of scenes and sampling number at t direction. As shown in Table 2, the statistical model increases efficiency about eight times.Table 2
Comparison of the consumed time in the simulations of 3D sea clutter with different sizes of scenes and sampling number att direction.
The size of scene (m2)
50 × 50
100 × 100
200 × 200
Sampling number att direction
128
256
512
128
128
Time (sec)
Statistical model
1.81
3.56
7.79
7.37
28.92
EM model
14.56
29.73
59.18
58.68
234.66
∗Calculated by a computer with Intel(R) Core(TM) i7-6700 CPU @ 3.40 GHz.The above simulation results of 2D and 3D cases could demonstrate that the statistical model is valid and can be used to quite efficiently generate the correlated sea clutter in a very large size of scene or the long time case.


## 3.1. Two-Dimensional Case

In order to verify the statistical model, Figure2 gives the comparisons of amplitude and autocorrelation function of 2D (in range-azimuth dimensions) spatial correlated sea clutter generated by statistical and EM models. For the EM model simulation, the incident frequency is 5 GHz slanting at the incident direction of θi=40°,ϕi=0°, and the results are completed in the backscattering case and for HH polarization. The 2D sea surface is generated based on the Monte Carlo method [23] using the Elfouhaily et al.’s spectrum [24], the sampling number along the x and y directions is M=N=128, the size of the facet is Δx=Δy=0.8m, the wind is upwind at speed of 5 m/s, the time t=0s, the relative dielectric constant of the sea water is calculated by the Klein model [25] at 20°C, and 35‰ salinity. In addition, the simulated 2D spatial correlated sea clutter by the EM model is of log-normal distribution and with the shape and scale parameters of 3.565560E − 01 and −4.407049, respectively. For ease of comparison, the desired correlation properties in the statistical model simulation should be consistent with the simulated 2D spatial correlated sea clutter by the EM model.Figure 2
Comparisons of amplitude and autocorrelation function of 2D sea clutter generated by statistical and EM models. (a) Statistical model. (b) EM model.
(a)
(b)From Figure2, it could be obviously found that the amplitude and autocorrelation function of 2D spatial correlated sea clutter generated based on the statistical and EM models have a consistent texture feature. In order to give a more intuitive comparison, the comparisons of 1D plot of the autocorrelation function and PDF are shown in Figure 3. It is seen that 1D plot of the autocorrelation function and PDF of 2D spatial correlated sea clutter generated by the statistical model agree well with the results simulated by the EM model.Figure 3
Comparisons of 1D plot of the autocorrelation function and PDF of 2D sea clutter generated by statistical and EM models. (a) 1D plot of the autocorrelation function. (b) PDF.
(a)
(b)Compared with the EM model, the major advantage of the statistical model is that it could quite efficiently generate sea clutter in a very large size of scene. Figure4 compares the amplitude and autocorrelation function of 2D spatial correlated sea clutter generated by the statistical model with different sizes of scenes. For clearer comparison, Figure 5 gives the comparisons of 1D plot of the autocorrelation function and PDF. From Figure 5, one can see that, the correlation in the edge of scene becomes smaller with the increase of scene and the middle area of the larger scene has a consistent correlation with the small scene. Besides, the sea clutter with different sizes of scenes has a consistent PDF (the amplitude and autocorrelation function of 100 m × 100 m are shown in Figure 2(a)).Figure 4
Comparisons of amplitude and autocorrelation function of 2D sea clutter by the statistical model with different sizes of scene. (a) 200 m × 200 m. (b) 400 m × 400 m.
(a)
(b)Figure 5
Comparisons of 1D plot of the autocorrelation function and PDF of 2D sea clutter by the statistical model with different sizes of scenes. (a) 1D plot of the autocorrelation function. (b) PDF.
(a)
(b)Furthermore, in order to contrast the efficiency between the statistical and EM models, Table1 gives the time taken by the above two models in the simulations of 2D sea clutter with different sizes of scenes. Obviously, the statistical model is with high efficiency, which is because that the FFT technique is used in the statistical model to generate the correlated sea clutter.Table 1
Comparison of the consumed time in the simulations of 2D sea clutter with different sizes of scenes.
The size of scene (m2)
100 × 100
200 × 200
400 × 400
Time (sec)
Statistical model
0.025
0.0765
3.0779
EM model
4.67
18.05
70.11
∗Calculated by a computer with Intel(R) Core(TM) i7-6700 CPU @ 3.40 GHz.


## 3.2. Three-Dimensional Case

The simulation of 3D temporal-spatial correlated sea clutter is similar to the simulation of 2D spatial correlated sea clutter. For the EM model simulation in the 3D case, the parameters are same with the 2D case except that the sampling number att direction is 128 and the time interval is 0.1 s. Besides, it should be explained that the simulated 3D temporal-spatial correlated sea clutter by the EM model is of log-normal distribution and with the shape and scale parameters of 3.563838E − 01 and −4.405951, respectively.Figure6 gives the amplitude and autocorrelation function of 3D temporal-spatial correlated sea clutter generated by the statistical model in xOt plane, xOy plane, and yOt plane, respectively. It is seen from Figure 6 that the amplitude and autocorrelation function in different planes have different textures. Figure 7 shows the comparison of 1D plots (i.e., at x, y, and t direction, respectively) of the autocorrelation function of 3D temporal-spatial correlated sea clutter between statistical and EM models. Accordingly, the comparison of PDF is illustrated in Figure 8. From Figures 7 and 8, it is seen that 1D plots of the autocorrelation function and PDF of 3D temporal-spatial correlated sea clutter generated by the statistical model agree well with the results simulated by the EM model.Figure 6
The amplitude and autocorrelation function of 3D sea clutter by the statistical model. (a)xOt plane. (b) xOy plane. (c) yOt plane.
(a)
(b)
(c)Figure 7
Comparison of 1D plots of the autocorrelation function of 3D sea clutter atx, y, and t direction between statistical and EM models.
(a)
(b)
(c)Figure 8
Comparisons of PDF of 3D sea clutter between statistical and EM models.In order to contrast the efficiency of the statistical and EM models in the simulations of 3D sea clutter, Table2 gives the comparison of the consumed time in the simulations of 3D sea clutter with different sizes of scenes and sampling number at t direction. As shown in Table 2, the statistical model increases efficiency about eight times.Table 2
Comparison of the consumed time in the simulations of 3D sea clutter with different sizes of scenes and sampling number att direction.
The size of scene (m2)
50 × 50
100 × 100
200 × 200
Sampling number att direction
128
256
512
128
128
Time (sec)
Statistical model
1.81
3.56
7.79
7.37
28.92
EM model
14.56
29.73
59.18
58.68
234.66
∗Calculated by a computer with Intel(R) Core(TM) i7-6700 CPU @ 3.40 GHz.The above simulation results of 2D and 3D cases could demonstrate that the statistical model is valid and can be used to quite efficiently generate the correlated sea clutter in a very large size of scene or the long time case.


## 4. Conclusions

In this paper, a statistical model extended from the ZMNL method to the 3D case is proposed to simulate the temporal-spatial correlated 3D sea clutter. And the statistical and correlation properties obtained from the EM scattering model are the foundations of the statistical model. The simulation results show that the texture feature, autocorrelation function, and PDF of the sea clutter simulated by the statistical model have a good agreement with the results given by the EM model. And the comparisons of the consumed time in the simulations of 2D and 3D sea clutter could demonstrate that the statistical model can quite efficiently simulate the large scene or long time temporal-spatial correlated 3D sea clutter. Besides, the proposed statistical model may facilitate the investigations on the natural mechanism explanation of sea surface scattering, sea clutter suppression, and target detection. These relevant studies will be under consideration in further research work.



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*Source: 9705406-2019-12-24.xml*