## 2 Design of Matrix-Type Coding Metasurface
### Matrix-Type Random Coding Metasurface Arrangement  
As shown in Figure 2a, the basic unit based on SRR structure is designed, which is set as \"0\" unit. The SRR structure is rotated counterclockwise by 90\({}^{\circ}\) along the wave propagation direction (shown in Figure 2b), which is set as \"1\" unit. The whole basic unit is divided into three functional layers, where the period is \(p=10\) mm. The upper layer is copper film with SRR structure, which possesses a symmetric axis along 45\({}^{\circ}\) with respect to \(x\) or \(y\) direction. The length of outer radius is \(r=4.1\) mm, the ring width is \(s=0.2\) mm, and the split width of ring structure is \(w=1\) mm. The thickness of the FR4 substrate is 3.5 mm, with the dielectric constant of 4.3 and the loss tangent angle of 0.025. The back layer copper film and the upper layer copper film have the same thickness of 0.035 mm. Figure 2c presents the co-polarization (\(r_{xx}\) and \(r_{yy}\)) and cross-polarization (\(r_{yx}\) and \(r_{xy}\)) reflection coefficients; the high efficient and broadband polarization conversion features can be achieved in a broadband frequency range. The cross-polarization reflection coefficients (\(r_{yx}\) and \(r_{xy}\)) are greater than 0.8, while the co-polarization reflection coefficients (\(r_{xx}\) and \(r_{yy}\)) are substantially less than 0.35 in the frequency range of 6-15 GHz. The polarization conversion capability is defined as follows [47]: PCR\({}_{x}=1r_{yx}\,^{2}/(1\,r_{yx}\,^{2}+1\,r_{xx}\,^{2})\) and PCR\({}_{y}=1r_{xy}\,^{2}/(1\,r_{xy}\,^{2}+1\,r_{yy}\,^{2})\). As shown in  
Figure 2d, the linear polarization conversion ratio of the \(x\)- and \(y\)-polarized waves is as high as 85% and reached 99% at resonance frequencies. Figure 2e,f shows the cross-polarization phase and phase difference of \"0\" and \"1\" basic units, respectively. It can be observed that the phase of the \"0\" and \"1\" basic unit is different, although the magnitude of the reflection coefficients of co- and cross-polarization is the same. In addition, the phase gradient of designed MS is 180\({}^{\circ}\) in the frequency range of 5-16 GHz. Therefore, we use the characteristic of cross-polarization phase difference \(\pm\)180\({}^{\circ}\) to design the matrix-type random coding MS, which can be applied to achieve the broadband RCS reduction. To verify the proposed hypothesis and explore the RCS reduction characteristic of matrix-type random coding MSs, six kinds of arrangements with different ratio of \"0\" and \"1\" are designed, in which \(m_{0}\) and \(m_{1}\) are the number of \"0\" and \"1\" basic units. As for the two basic units, the reflection coefficients and polarization conversion rates are consistent, the units \"0\" and \"1\" can be interchanged, and the meaning of the expression is the same. Figure 3a,b presents the schematics of coding \(a\) and \(b\) with the ratio \(\alpha=m_{0}/m_{1}=1/1\). Figure 3c,d presents the schematics of coding \(c\) and \(d\) with the ratio \(\alpha=m_{0}/m_{1}=5/4\). Meanwhile, the coding \(e\) and \(f\) with the ratio \(\alpha=m_{0}/m_{1}=2/1\) are shown in Figure 3e,f. By applying the matrix-type random coding, the direction of energy scattering can be changed to form a diffuse reflection for the incident EM waves; it is possible to achieve the high efficient RCS reduction characteristic under normal incidence. Figure 2: (**a**) Basic unit “0”; (**b**) basic unit “1”; (**c**) the reflection coefficients of “0” and “1”; (**d**) the linear polarization conversion ratio for the normal incident \(x\)- and \(y\)-polarized wave; (**e**) the cross-polarization phase of “0” and “1”; and (**f**) the cross-polarization phase difference of “0” and “1”. To meet the periodic boundary conditions required of simulation, the \(5\times 5\) basic units are set as a supercell, and a series of coding arrangements are designed to explore the RCS reduction characteristic of MS.