k_{0} and q_{0} are the horizontal and vertical projections of the incident vector k_{i}. k and q are the horizontal and vertical projections of the scattering vector k_{s}. B(k, k_{0}) is a polarization matrix which can be referred in [4]. The SSA integral can be analytically solved upon the Bragg wave structure on each facet. This process is described in details in the ref. [5], which is not repeated here.

2.2. Echo Simulation Model

The echo simulation model is set up in this section for the radar detection scene of the semi-active seeker, which is described in Figure 1. The target is flying above the time-varying sea. The seeker is flying towards the target. The seeker is receiving the scattering return from the target scattering, multipath scattering and sea surface scattering, when they are illuminated by the radar. The radar is assumed to be the pulsed radar. In the pulse duration, the target and the seeker are assumed to be static. Considering the fact that the sea surface scattering and the multipath scattering is time varying, so the reflectivity of each scattering point at every position should be calculated at each pulses. The reflectivity of each scattering point is calculated at each time instant. The echo is obtained at each pulse instant by summing up the scattering energy from the scatterers in the simulation scene, which is presented as

${s}_{r}(k,t)={\displaystyle \underset{i=1}{\overset{N}{\sum}}{\gamma}_{i}\left(k\right)\xb7\text{rect}\left[\frac{t-2{R}_{i}\left(k\right)/c}{{T}_{r}}\right]\phi (t-\frac{2{R}_{i}\left(k\right)}{c})\mathrm{exp}\left\{-j\frac{4\pi {R}_{i}\left(k\right)}{\lambda}\right\}}$ (4)

In (4), rect(∙) is the envelope of the rectangular pulse. T_{r} is the pulse repetition time (PRT). R is the distance, which can reflect the time delay for the wave propagation.
${\gamma}_{i}$ is the reflectivity of each scattering point for each time instant, which is calculated by the model in the Section 2.1. The radar scattering returns collected from the facets in the same range bin are processed together.

In the echo simulations, the antenna pattern for the seeker and the ground radar should be considered, where the Gaussian Beam function is used as given by

${G}_{MB}\left(\theta \right)=\mathrm{exp}\left(-2\mathrm{ln}2{\theta}^{2}/{\theta}_{B}^{2}\right)\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\left|\theta \right|\le \mu $ (5)

θ_{B} is the half-power beam width of the main lobe. μ is the azimuth width , given by

$\mu ={\theta}_{B}\sqrt{\mathrm{ln}{g}_{3}/\left(-2\mathrm{ln}2\right)}$ (6)

The radiation from the first and second side-lobes are considered, whose beam function are similarly presented as

${G}_{B1}\left(\theta \right)={g}_{1}\mathrm{exp}\left(-2\mathrm{ln}2{\left(\theta \pm 1.5\mu \right)}^{2}/{\theta}_{B1}^{2}\right)\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\mu \le \left|\theta \right|\le 2\mu $ (7)

${G}_{B2}\left(\theta \right)={g}_{2}\mathrm{exp}\left(-2\mathrm{ln}2{\left(\theta \pm 2.5\mu \right)}^{2}/{\theta}_{B2}^{2}\right)\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}2\mu <\left|\theta \right|\le 3\mu $ (8)

g_{3} is the gain of the main beam. g_{1} is the peak gain of the first side-lobe. g_{2} is the peak gain of the second side-lobe. θ_{B}_{1} and θ_{B}_{2} are the beam width of the first and second side-lobe, whose value are given by

${\theta}_{B1}=0.5\mu \sqrt{\left(-2\mathrm{ln}2\right)/\mathrm{ln}\left({g}_{3}/{g}_{1}\right)}$ (9)

${\theta}_{B2}=0.5\mu \sqrt{\left(-2\mathrm{ln}2\right)/\mathrm{ln}\left({g}_{3}/{g}_{2}\right)}$ (10)

In the real scene, the target is flying above the infinite sea surface. The radar echo simulations, the target is moving and the sea surface is time varying. Once the echo is generated, the echo signal is handled by the following signal processing procedures [6] (Figure 3).

3. Numerical Results

In the numerical simulations, the working frequency of the ground radar is 10 GHz (X band). The sea state is chosen as low sea state, where the wind speed at 10 m high above the sea in the Elfouhaily’s sea spectrum is 3 m/s.

Figure 4 shows the bistatic scattering characteristics of a cruise missile target above the sea. The target is 5 m high above the sea, the incident angle is ${\theta}_{i}={45}^{\circ},{\phi}_{i}={0}^{\circ}$ . The results are compared with the target scattering and the sea scattering. It can be seen that the composite scattering is contributed by the target scattering, sea scattering as well as the multipath scattering, so it’s much stronger than each individual scattering component.

In the echo simulations, the bandwidth is 5 MHz. The antenna parameters are set as g_{1} = 10^{−2}, g_{2} = 10^{−2.5}, g_{3} = 10^{−3}, and θ_{B} = 5˚. The PRT is 10 μs. The pulse duration is 1 μs. The sampling frequency is 100 MHz (Figure 5).

Figure 5 shows the echo simulation results, where 512 pulses are used in a CPI. In Figure 5(a), the raw echo signal for. In Figure 5(b), the range-dopper map is obtained by employing the signal processing to the echo. The sea clutter has the strongest power in the map. The target has a velocity, so it has different Doppler value from the clutter. The multipath effect can be also identified in the map, which has broadened the target Doppler spectrum, but it is weak compared with the target and sea clutter.

Figure 3. Signal processing procedure.

Figure 4. Bistatic scattering characteristics of a cruise missile above the sea surface.

(a) (b)

Figure 5. Echo simulation results of the semi-active seeker. (a) Raw echo signal; (b) Range-Doppler map.

4. Conclusion

In this paper, the radar echo of the semi-active radar seeker against the sea skimming target is modelled and simulated. The scattering mechanisms are considered by a hybrid scheme based on the radar detection scene of the semi-active seeker. The echo after signal processing can show the spatial and Doppler characteristics of the target, sea clutter, and the multipath scattering.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No.61431010).

Cite this paper

Peng, P. , Guo, L. and Sun, H. (2018) The Echo Modelling and Simulation of the Semi-Active Radar Seeker against a Sea Skimming Target.*Journal of Computer and Communications*, **6**, 74-79. doi: 10.4236/jcc.2018.612007.

Peng, P. , Guo, L. and Sun, H. (2018) The Echo Modelling and Simulation of the Semi-Active Radar Seeker against a Sea Skimming Target.

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