4.3. Numerical Calculation Comparison
In this paper, 35 GHz and 76 GHz frequencies under horizontal–horizontal (H–H) and vertical–vertical (V–V) polarities are selected for simulation to verify the advantages of the proposed algorithm. The 35 GHz frequency is low, which is a common anti-collision frequency band for large and medium-sized helicopters. And 35 GHz has a stronger all-weather capability due to its lower frequency. The 76 GHz millimeter wave radar can be used as low-cost or on-chip radar [
30,
31]. Many basis functions need to be calculated because the wavelength of this frequency is very short.
- (1)
Simulation of incident wave frequency at 35 GHz
The length of power line 1 shown in
Table 2 is 184mm, with eight recurrences in total. The polarization mode of the incident wave is V–V polarization, and the frequency is set to 35 GHz. The ACA tolerance used in the SMWA is set to 1 × 10
−4. For the IEDG-CM-SMWA method in this paper, each interval can be divided into 2880 full RWGs and 152 half-RWGs. The CM-SMWA uses 23292 full RWGs. The power line is divided into eight segments using a three-level binary tree. The number of characteristic modes in each group is arranged as 700.
Use IEDG-CM-SMWA, CM-SMWA, and MoM to calculate the RCS of the power line, and the calculation results are shown in
Figure 7.
We can find from
Figure 7 that the RCS of the Bragg echo points of different algorithms under the V–V polarization condition is relatively consistent, and there is only a large relative error of about −40 dBsm. For the same absolute error, the relative error is relatively large, where the actual RCS value is small. However, when the power line RCS is about −40 dB, the RCS is generally smaller than the radar receiving noise in practice, which is easy to submerge by noise, and does not affect the effectiveness of RCS calculation.
The quantitative evaluation indexes in
Section 4.2 are used to analyze the RCS of power lines obtained by the three algorithms, as shown in
Table 3:
It can be seen from
Table 3 that the IEDG-CM-SMWA has greater advantages in terms of calculation speed under the same grouping conditions. We can find from the relative error column in
Table 3 that the IEDG-CM-SMWA is basically consistent with the results of the conventional MoM and CM-SMWA.
Further verification under different groups was carried out. The CM-SMWA is with 32 groups, and the characteristic modes in each group is 400. The IEDG-CM-SMWA method was still divided into eight groups. Use the IEDG-CM-SMWA, CM-SMWA, and MoM to calculate the RCS of the power line, and calculation results are given in
Figure 8.
We can see from
Figure 8 that under the V–V polarization condition, when the grouping is different, the RCS of the Bragg echo points of different algorithms is relatively consistent.
The quantitative evaluation indexes in
Section 4.2 are used to analyze the RCS of power lines obtained by the three algorithms, as shown in
Table 4:
Comparing the computational time of the CM-SMWA in
Table 3 and that of the CM-SMWA in
Table 4, we can find that the CM-SMWA divides the matrix into smaller parts, which will reduce the calculation time for this example. However, the IEDG-CM-SMWA proposed in this paper still saves time compared with the traditional CM-SMWA.
To illustrate the difference between the RCS of the power line and the PEC cylinder, we calculate the RCS of a cylinder with the same length and diameter as the power line LGJ50-8, as shown in
Figure 9.
We can see from
Figure 9 that the RCS of the cylinder is close to the RCS of the power line at the normal incidence (incidence angle 90°). However, the RCS of the power line has Bragg points at about 10.7° away from the normal incidence. The position of the Bragg point is determined by the stranding period of the power line. When the wave path difference of the incident waves, that reaches the adjacent strands, is an integral multiple of 0.5 λ, the scattering echoes will be enhanced [
19], but the smooth cylinder does not have Bragg points.
- (2)
Simulation of incident wave frequency at 76 GHz
For the same power line as in Example 1, under the condition of 76 GHz frequency, the target is discretized by RWG with an average size of 0.1 wavelength. Because of the high frequency, the grid is smaller, and 110,370 RWGs are used. The level of the binary tree of the CM-SMWA method is 7, and the power line is divided into 128 segments. The IEDG-CM-SMWA is also eight segments. The simulation results are given in
Figure 10.
We can see from
Figure 10 that the RCS of the Bragg echo points of the IEDG-CM-SMWA and the CM-SMWA are relatively consistent under the H–H polarization condition.
We can find from
Table 5 that the RCS relative error of the two methods is 2.8%, which is very close. The calculation time of the method proposed in this paper is still faster.
In order to further demonstrate the properties of power line with different polarizations, the V–V polarization RCS simulation is also carried out. The RCS results are shown in
Figure 11.
We can see from
Figure 11 that under the V–V polarization condition, the RCS of the Bragg echo points of the IEDG-CM-SMWA and the CM-SMWA are also relatively consistent.
It can be seen from
Table 6 that the IEDG-CM-SMWA can still maintain the leading speed under different polarization conditions. It shows that the proposed method has strong applicability, and is able to satisfy the requirements of power line detection, and has greater advantages in computational efficiency compared with the previous method.