# Low-Complexity Online Calibration for Large-Scale Multi-Beam Antennas
## 5 Implementation Results  
A S-band calibration receiver prototype is developed to further verify the proposed calibration method. Relevant calibration system parameters are summarized in Table 1. The calibration receiver operates at a center frequency of 2.199 GHz. We can calculate that the wavelength corresponding to this frequency is 13.6 cm. One wavelength corresponds to 360 degrees, thus the electrical length corresponding to 1 degree is 0.3 mm. In other words, only 0.3 mm electrical length change will bring about 1 degree phase change. The code sequence adopted for communication traffic is binary data randomly generated by MATLAB software. The length of calibration codes is 1023 and the chip rate is  
Figure 8: Calibration accuracy with different code lengths (\(K=10\)). (**a**) RMSE of the relative amplitude. (**b**) RMSE of the relative phase. Figure 7: Calibration accuracy with unequal power conditions (\(K=2\)). (**a**) RMSE of the relative amplitude. (**b**) RMSE of the relative phase. \(1\) Mcps. Since the acquisition of correlation peak requires a complete code length period, the correlation peak can be obtained every \(1.023\) ms, and then the amplitude and phase measurement results can be estimated. This measurement time is short enough to calibrate the amplitude and phase characteristics. In fact, the mission to calibrate time-varying amplitude and phase errors is typically required to be completed within 1 second. Therefore, we can average the results in exchange for improved accuracy with calibration time. To evaluate the calibration performance of different power and phase calibration signals, the relative power of different calibration signals is set to [0, 0, 0, \(-5\), \(-10\),\(-15\), \(-20\), \(-25\)] dB and the relative phase is set to [0, 90, 45, 30, 60, 170, 135, 160] deg where the first signal is considered as reference signal without losing generality. The total power level of calibration signals is \(-40\) dBm and the power level of commucation signal is \(0\)dBm. How to extract amplitude and phase characteristics from such strong communication signals is a difficult problem. The hardware connection of the experimental system is shown in Figure 9 and 10 shows the experiment system for calibration. The computer generates a mixed baseband calibration signal and sends it to the vector signal generator (E4438C) through Ethernet. The mixed baseband calibration signal is composed of several calibration signals with different amplitude and phase relationships. The amplitude and phase relationships are set by MATLAB software on the computer. Another signal generator (E8257D) generates the operating clock for the calibration receiver. The calibration receiver collects the calibration signal with unknown amplitude and phase relationships through analog to digital converter (ADC) chip, and performs code correlation operation through the field programmable gate array (FPGA). Amplitude and phase measurement results are returned to another computer for display through Ethernet. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values** \\ \hline Center frequency & S-band 2.199 GHz \\ Length of calibration codes & 1023 \\ Bandwidth & 2 MHz \\ Antenna beams & 8 beams \\ Relative power of different calibration signals & [0, 0, 0, \(-5\), \(-10\), \(-15\), \(-20\), \(-25\)] dB \\ Relative phase of different calibration signals & [0, 90, 45, 30, 60, 170, 135, 160] deg \\ Total power level of calibration signals & \(-40\) dBm \\ Power level of commucation signal & 0 dBm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters. Figure 9: Hardware connection of the experimental system. Hardware implementation results are shown in Figure 11. Because the experimental system is carried out under wired conditions, the relative amplitude and phase implementation results have high accuracy, close to the true values set by the signal generator (E4438C). The statistical results of means and RMSEs are shown in Tables 2 and 3. The lower the power, the worse the measurement accuracy.