【文章內(nèi)容簡(jiǎn)介】 wo antennas. In three dimensional coordinate, we recreate the descriptions of signals of Eq.(5) and (6), (9) (10)Repeat the similar steps implemented in previous 2D model, the simulation result without mutual coupling is shown in Figure 5 Correlation based on 3D without MCAs can be seen from , correlation of 3D for smaller antenna space is substantially bigger than 2D. Besides, correlation with different distribution of AoA is different. However, the correlation is still very high if the space is near, less than . The result is different with the experiments which has a lower correlation even if the distance is small. Hence, the effect factors are not considered far from enough.What39。s more, the problem about AoA still exists. According to [1], the ining waves39。 distribution has a standard deviation of 200 and the principal waves39。 incident at 200 above the horizontal plane (). Obviously, some negative angles will appear in the simulation, which are not consistent with the practical situations. Three methods are proposed to solve it. (Assume that the mean value is always 200).l Regard the negative angles of the ining waves as the waves which e from the opposite side, which are symmetric by zaxis.l Utilize 39。39。 principle39。39。 According to 39。39。 principle39。39。 with Eq.(4), we can easily obtain . Now it seems that the negative angles have been avoided. However, a new problem es out. There is almost no any wave in the domain from 400 to 900. Hence, it is also a little far from practice.l Redevelop another new distribution Since negative angles need to be avoided, and there is possibility that the waves from 00 to 900 exists. Then we can apply Gaussian distribution likewise with the mean of 200 and find a proper standard deviation of such that. . solve the following equation (11) Then, it’s easy to find the value of by solving the Eq.(11).4 Advanced Models Mutual CouplingFor MIMO antennas, limited by physical space, it will generate amount of mutual coupling between antenna elements. Mutual coupling is virtually the interchange of energy. As correlation analysis of antenna elements, mutual coupling (MC) should be taken into account. The effect of mutual coupling on spatial diversity and MIMO systems can be desirable depending on the antenna configuration and the environment.According to [5], there are some factors which will affect mutual coupling.l Distance between antennas It is the most important factor affecting mutual coupling. Some analytical studies showed that only if the distance between the antenna elements is more than half of the wavelength, there is minimal or almost no mutual coupling. Similarly, mutual coupling is also affected by the frequency since the signal is expressed in terms of wavelength.l Angle of Arrival (AoA)Even if mutual coupling is not taken into account, AoA is a critical parameter. Actually, AoA and mutual coupling are also strongly coupled. Different distribution of AoA will result in different mutual coupling.l NearField Scatterers (NFS) Besides, mutual coupling is strongly influenced by the surrounding objects in the nearfield of antenna elements. The reradiated signals from an antenna element could reflect back from the NFS and can be coupled back to other elements.Usually, we utilized numerical methods to measure mutual coupling. Naturally, it39。s almost difficult for us to conclude all the factors. Hence, no wonder that the simulation results will be always a little bit different from real behaviors of antenna element. 2D with Mutual CouplingSince the coupling effect is significant due to the reradiation of antennas for antenna spacings smaller than, the expression for the antenna electricity field with mutual coupling is developed.Figure 6 Wave propagation on 2D with MCThe electricity field part can be described as (12)whereand h is the length of an antenna.It39。s difficult to calculate the correlation using analytical equations. Hence, numerical method was employed. The equation (12) was rewritten into (13)The antenna pattern can be obtained using moment method by a simulation software called PLANCMM.With mutual coupling, we rewrite the descriptions of signals in Eq.(5) and (6), (14) (15)The correlation of the simulation result was shown in .Figure 7 correlation of the simulation Although only 2D model, it39。s obviously different from the situation without mutual coupling. The correlation at low distance is lower than the previous results. 3D with Mutual CouplingNaturally, 3D model with mutual coupling should be applied to simulate the correlation between antenna elements on the base of 2D.The situations between 2D and 3D are different mainly due to geometrical analysis. The 3D propagation model is shown in Figure 8 Wave propagation on 3D with MCCompared with 2D model, in order to measure R1 and R2, we had designed a virtual plane. Suppose any point at Antenna 1 is z1, and any point at Antenna 2 is z2. This virtual plane which passes zeropoint O, and the direction vector of wave is.And the analytic equation of the plane is,The distance between any point (x0,y0,z0) and the plain is (16)this point should be on the same side of the plane as normal vector and negative if it is on the opposite side.Hence, if we built a virtual plan, (17) (18)From the Eq.(12), the numerical calculation equation is(19)As the previous steps, the result is shown in Figure 9 Correlation based on 3D with MCCompared with 2D, the correlation of 3D is a little more lower.5 ComparisonThe validation by experiment is necessary. Some experiment showed that the correlation between antenna elements is under for diversity and MIMO configurations