**3. Fundamentals of compact design**

Section 2 has discussed the specific antennas and the corresponding compact techniques implicit in the design, but there are some methods leading to the compact design not only suit for one fixed structure, but also will be used into other types in the future. Thus, we discuss their applications in MIMO antennas and the related techniques in this section, including the detailed explanation of mode-cutting method, the fractal technique, the theory of characteristic mode, and the optimization algorithms.

#### **3.1 Mode-antenna analyses**

In Subsection 2.7, the mode-cutting methods for different antenna types has been shown, however, the cited references did not discuss the detailed modes so clear. Now we discuss the mode distributions according to the specific antenna types which have been studied in the MIMO antenna.

#### **Figure 15.**

*Current distributions of complete slot of [112]: (a) without CSR, (b) CSR at position 1, (c) CSR at position 2, and (d) CSR at position 3.*

If the mode-cutting method is implemented, the corresponding antenna has at least one integral modes, or we can say that the cutting method suits to the integral order mode of the related structures.

For the cutting of the semi-circle slot antenna, the authors in [112] discussed the current distribution of the complete slot as shown in **Figure 15**. Whether the complementary slot reflector exists or not, the current distributions are symmetrical. By optimizing the size and position of CSR, the cutting method can be implemented to get the half-loop slot, and the corresponding performances are affected rarely. Then, the two-element MIMO antenna is formed by symmetrical arrangement whose isolation less than 12 dB is achieved without any additional decoupling structure.

The literature [113] provides another way to design the cavity MIMO antenna which excites each sub-mode generated by the different shape cavities. The authors started the analysis for the closed circular cavity, then analyzed the characteristic modes for the open and sector cavities, and consequently obtained the methodology that the whole cavity can be divided into N sub-cavities. If a T-shape monopole is put at the proper position for each sub-cavity, the N-port MIMO antenna forms and high isolation is obtained. They took the 4-port circular open cavity as an example and fabricated an antenna prototype shown in **Figure 16**, whose measurements agree well with those of simulations. Thus, they continue discuss the related design for other shape cavity antennas.

## **3.2 Fractal techniques**

The fractal technique has been employed in the MIMO antennas as in subsection 2.6 owing to it can reduce the size for the compact design. As we know the fractal technique needs several iterations, it is effective to reduce the size in finite iterations, but when the iteration reaches to a certain number, the size reduction will not so obvious until it does not work. That's because as the iteration increases, the length of fractal shape will become smaller and can not be comparable with the wavelength. Therefore, we have to consider the iteration number depending on the specific requirement. In this subsection, we introduce two common simple fractal techniques, the Koch and the Sierpiński fractals [114, 115].

**Figure 16.** *4-Port MIMO antenna of [113].*
