## 4 Channel Capacity and Radiation Pattern Given by Calibration Method  
In this section, the performance is verified when considering the amplitude and phase errors shown in Figures 6 and 7. The \(C\) and radiation pattern given by the calibration method have been evaluated via simulation, when considering the amplitude and phase errors shown in Figures 6 and 7. This means that the correct transmission pattern cannot be created if there are amplitude and phase errors. In this evaluation, the ideal array factor is assumed and a mutual coupling effect between arrays is not considered. These effects should be evaluated in future work.  
Table 1 lists the simulation parameters. In order to evaluate the \(C\) and radiation pattern directly using the testbed described in Section 3, we assume a 16-element linear array with half-wavelength spacing. The weights for the array combinations are obtained via maximum ratio combining (MRC). Propagation is assumed to occur over an additive white Gaussian noise (AWGN) channel, and the signal-to-noise power ratio (SNR) is 20 dB per antenna element. The amplitude and phase are given both with and without calibration errors, and the signal-to-interference-plus-noise power ratio (SINR) is calculated. The channel capacity is given by  
\[C=\log_{2}(1+\text{SINR}) \tag{7}\]  
To verify the influence of the phase errors on \(C\), the cumulative density function (CDF) of \(C\) for different phase errors and \(C\) as a function of the phase-error range \(\Delta\theta\) are plotted in Figures 8 and 9, respectively; \(\Delta\theta\) is given by random numbers, and the number of trials is 10,000. We note that the \(C\) obtained for a CDF of 10% is plotted in Figure 9. Here, we have assumed that the desired signal and interference have directions of arrival (DoA) of \(\theta_{d}  
Next, we examine the radiation pattern given by the proposed calibration method using the testbed shown in Figure 5. Figure 10 shows the array patterns reflected by the phase errors in Figure 6. We note that the mutual coupling effect is not considered in Figure 10. The main beam directions in Figure 10a,b are \(0^{\circ}\) and \(45^{\circ}\), respectively, using MRC. As can be seen from this figure, the sidelobe level is very high without calibration, especially in the \(-30^{\circ}\) and \(60^{\circ}\) directions, because of the phase errors that occur in the absence of calibration. However, Figure 10 also shows that the ideal array pattern can be created when the calibration circuit is employed.  
Figure 10: Array patterns with and without calibration: (**a**) \(\theta_{d}=0^{\circ}\), and (**b**) \(\theta_{d}=45^{\circ}\).  
Figure 9: \(C\) vs. \(\Delta\theta\), with cumulative density function (CDF) of 10%.  
In Figure 11, the \(C\) with and without calibration is shown as a function of the difference in DoA; that is, \(\theta_{i}-\theta_{d}\), with \(\theta_{d}=0^{\circ}\) and \(\theta_{i}\) varying from \(10^{\circ}\) to \(60^{\circ}\). The phase errors shown in Figure 6 are considered. When calibration is not employed, \(C\) decreases significantly compared to that obtained without phase errors, regardless of \(\theta_{i}\). In contrast, the \(C\) with calibration is almost identical to that without phase errors (ideal). Because \(\theta_{i}=30^{\circ}\) is null when \(\theta_{d}=0^{\circ}\) with MRC, the \(C\) following calibration and without phase errors is 6 bit/s/Hz. It is clear that \(C\) decreases significantly when the null angle is considered for the interference.