## 3 Aip Array Platform Applications
### Investigating the Effectiveness of Calibration Methods on Large Phased Array  
The 8 \(\times\) 8 AiP array with 64 elements is a large array. In this part, this AiP array is used as a validation platform, and the effectiveness of three typical phased array calibration methods: 'on-off', 'inverse' and 'least squares' on large phased array calibration is investigated. Some work has been carried out to investigate the calibration accuracy of these three methods on small and medium phased arrays [22; 23; 36; 37]. For the 'inverse' calibration measurement, we first activate all antenna elements of the AiP and set their phase shifter and attenuator to 0\({}^{\circ}\) and 0 dB respectively. The S-parameter \(\vec{E}_{o}\) between the AiP and the chamber probe antenna is recorded. Then the phase shifter and attenuator of  
Figure 8: AiP beamforming patterns at different angles. Figure 7: AiP beamforming patterns at 0\({}^{\circ}\) without and with calibration. the \(m\)th element are set to \(-180^{\circ}\) and 0 dB in turn for \(m\in[1,64]\), while the phase shifter and attenuator of the remaining antenna elements are still set to \(0^{\circ}\) and 0 dB respectively. The S-parameter \(\vec{E_{m}}\) between the AiP and the chamber probe antenna is also recorded. Finally, the initial excitation of the \(m\)th element \(\vec{e_{m}}=\frac{\vec{E_{m}}-\vec{E_{m}}}{2}\) is obtained. In order to provide reference values for the calibration results, the phases of the first to fourth elements are set to \(22.5^{\circ}\), \(33.75^{\circ}\), \(45^{\circ}\) and \(56.25^{\circ}\), and the attenuation of the first to fourth elements is set to \(-2\) dB, \(-3\) dB, \(-4\) dB and \(-5\) dB, respectively. The remaining elements are set to \(0^{\circ}\) and 0 dB. The 'inverse' method is applied to calibrate the AiP with and without additional excitation assigned to the first four elements, and the difference between the two calibration results is shown in Figure 9. The amplitude differences of the first four elements are \(-1.1\) dB, \(-1.7\) dB, \(0.6\) dB and \(-1.4\) dB, respectively. And the phase differences are \(26.1^{\circ}\), \(18.7^{\circ}\), \(32.8^{\circ}\) and \(33.0^{\circ}\), respectively. Combining the reference values shows that the calibration results have large errors for the intended changed elements. In addition, there are large calibration errors of amplitude for the rest unchanged elements, where the amplitude calculated value of 0 dB. It indicates that the 'inverse' method fails to effectively calibrate the AiP with a large array. The AiP array calibration excitation matrix \(A\) of 'inverse' method can be denoted as (1), which the condition number is \(k(A)=31.3\). Therefore, the condition number of the 'inverse' calibration excitation matrix is large, which makes the calibration heavily influenced by measurement noise. For this reason the 'inverse' method is not suitable for calibration on large phased arrays. \[A=\left[ \begin{array}{cccc}1&1&\dots&1\\ -1&1&\dots&1\\ 1&-1&\dots&1\\ \dots&\dots&\dots&\dots\\ 1&1&\dots&-1\end{array} \right]_{9\times 8} \tag{1}\]  
Figure 9: 'Inverse’ calibration effectiveness measurement results. Further, the calibration method is replaced by the 'on-off' and 'least squares' methods, taking repeated calibration measurements as described above. The AiP array calibration excitation matrix of 'least squares' method is based on the Hadamard matrix [23; 36], and the condition number is 1, so the phased array calibration is less affected by the measurement noise. The obtained measurement results are shown in Figure 10 and Figure 11, respectively. The errors between the calibration results of these two methods for the four intended changed elements and the corresponding reference values are shown in Table 1. The measurement results show that both methods are able to perform effective measurements on the AiP array, though there are some errors as expected as well.