## 4 Experiment Consequences and Discussion
The computational ECC of the proposed miniature eight-port antenna array is shown in Figure 11.  
\[\rho_{\mathrm{ij}}=\frac{\int[\mathrm{d}\pi\,\mathrm{A}_{\mathrm{ii}}(\theta, \phi)\sin(\theta)d\theta d\phi}{\sqrt{\int[\mathrm{d}\pi\,\mathrm{A}_{\mathrm{ ii}}(\theta,\phi)\sin(\theta)d\theta d\phi][\mathrm{d}\pi\,A_{\mathrm{jj}}(\theta, \phi)\sin(\theta)d\theta d\phi]}} \tag{1}\]  
The acceptable upper limit value of ECC in the general standard is 0.5. The ECC between Ant. i and Ant. j can be calculated by Equation (1), which uses far-field pattern data. The above method is calculated separately in MATLAB or EXCEL, which is also the measurement calculation in practice. In addition to ECC, channel capacity (CC) is also a critical parameter to assess the comprehensive MIMO performance of the proposed miniature eight-port antenna array. The CC is the total channel transmission rate of the MIMO antenna system, and the CC increases with the improvement of antenna element numbers and SNR. The CC can be computed by Equation (2):  
\[CC=E\bigg{\{}\mathrm{log}_{2}\bigg{[}\mathrm{det}\bigg{(}I_{N}+\frac{SNR}{N} \bigg{)}HH^{T}\bigg{]}\bigg{\}} \tag{2}\]  
\[\mathrm{H}= \begin{array}{cccc}\mathrm{h}_{11}&\mathrm{h}_{12}&\cdots& \mathrm{h}_{1\mathrm{Nt}}\\ \mathrm{h}_{21}&\mathrm{h}_{22}&\cdots&\mathrm{h}_{2\mathrm{Nt}}\\ \cdots&\cdots&\cdots&\cdots\\ \mathrm{h}_{N\mathrm{r}1}&\mathrm{h}_{N\mathrm{r}2}&\cdots&\mathrm{h}_{N\mathrm{ r}N\mathrm{t}}\end{array}  \tag{3}\]  
where \(SNR\) is the signal-noise ratio; \(E\) is the matrix expectation; \(N\) is the number of antenna elements; \(H\) is an Nr \(\times\) Nt identity matrix channel imitating practical space; and HT is the Hermitian transpose of the matrix. The element \(\mathrm{h}_{N\mathrm{r}N\mathrm{t}}\) of the H-matrix denotes the transmission channel gain between the transmitting antenna, Nt, and the receiving antenna, Nr. This data-adopted channel is a random array number with a value of 3000. Under the circumstance of best \(SNR\), the CC of the 4 \(\times\) 4 MIMO system is 25 bps/Hz, and the 8 \(\times\) 8 MIMO system is 46 bps/Hz. Code 1 is the channel capacity calculation in MATLAB. The singular value decomposition (SVD) function in code 1 is an orthogonal matrix decomposition method. In the return results, U and V represent two mutually orthogonal matrices, and S represents a diagonal matrix. When the SNR is 22 dB, in Figure 12a, the calculated CC is approximately 35-38 bps/Hz in the desired bands. Figure 12b shows a 3D rainbow mesh of the calculated channel capacity  
Figure 11: Computational ECC of the proposed miniature eight-port antenna array. as a function of the number of receiving and transmitting antennas. It can be observed that the channel capacity increases as the number of receiving or transmitting antennas increases. When the SNR is 22 dB, the 4 \(\times\) 4 antenna number is 22 bps/Hz, the 8 \(\times\) 8 antenna number is 37.6 bps/Hz, and the 10 \(\times\) 10 antenna number is 45.4 bps/Hz. Figure 12: Computational channel capacity as a function of the number of receiving antennas and transmitting antennas. (**a**) Two-dimensional rainbow mesh. (**b**) Three-dimensional rainbow mesh. Table 1 compares the MIMO performance of the presented miniature eight-port antenna array and other published papers. Compared with [15], the proposed MIMO antenna array shows smaller element volumes with similar operating frequency bands. The return loss parameter of the present antenna is \(-10\) dB at 3.3-5 GHz, whereas the antenna in [16] exhibits only \(-6\) dB at 3.3-7.1 GHz. This distinction underscores the superiority of the present antenna in terms of this key performance metric. Compared with [17], the proposed antenna has a smaller element volume of 47.6 mm\({}^{3}\). Compared with other references in Table 1, the smaller element volume is better suited to progressively miniaturize handset devices. The contribution of this work is that it shows wideband operation, small volume, high efficiency, low ECC, and a high CC handset antenna array.