## 3 Simulations and Measurements  
Table 1 exhibits seven operating states of the radiating patch array and its equivalent period length as well as the beam angle. With \(P_{0}\) of 1.75 mm, it can realize fixed-frequency beam scanning with 7 beams. The proposed antenna is simulated and optimized in the CST, and a RLC equivalent circuit is used to replace the pair of diodes in the simulation: a series circuit with \(R=4.2\)\(\Omega\) and \(L=20\) pH for state \"0\", and a parallel circuit with \(R=300\)\(\mathrm{k}\Omega\) and \(C=42\) fF for state \"1\". The developed antenna was fabricated and measured as shown in Figure 4. \begin{table}
\begin{tabular}{l l l l l} \hline \hline N & \multicolumn{2}{c}{**Operation States**} & \multicolumn{2}{c}{**Period Length**} & \multicolumn{1}{c}{\(\theta_{n}\)} \\ \hline
1 & 10010010010010010010010010010010010010010010010010010010010010010010010010010010 & \(P=3P_{0}\) & \(-13^{\circ}\) \\
2 & 110011001100110011001100110011001100110011001100110011001100110011001100110011001100 & \(P=4P_{0}\) & \(-8^{\circ}\) \\
3 & 110011000110001100011000110001100011000110001100011000110001100011000110001100 & \(P=4.75P_{0}\) & \(0^{\circ}\) \\
4 & 11000110001100011000110001100011000110001100011000110001100011000110001100011000 & \(P=5P_{0}\) & \(13^{\circ}\) \\
5 & 1100011100001110001110000111000111000111000011100011100011100011100011100011100011100011100011 & \(P=6.5P_{0}\) & \(21^{\circ}\) \\
6 & 1110000111100001111000011110000111100001111000011110000111100001111000011110000 & \(P=8P_{0}\) & \(32^{\circ}\) \\
7 & 111111000000111110000011111100000011111100000011111100000011111100000011111100000011111100 & \(P=12P_{0}\) & \(48^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Operation states of patch array. Figure 3: Surface currents on the patch within a time period T. (**a**) t = 0. (**b**) t = T/4. (**c**) t = 2T/4. (**d**) t = 3T/4. The simulated and measured results of \(S\)-parameters of this proposed antenna are respectively shown in Figure 5a,b. For a clear exhibition, the results for only three typical states are plotted, for the backward beam, broadside beam, and forward beam. It can be seen that the developed antenna has a good performance in transmission as well as in radiation, and the measured results show a good agreement with the simulated values. The simulated and measured results of the normalized radiation pattern for seven beams from 30 GHz to 33 GHz are respectively depicted in Figures 6a-d and 7a-d. It shows that a fixed-frequency beam scanning is generated, with a range from 61\({}^{\circ}\) to 63\({}^{\circ}\) in this band, and the measured results show a good agreement. Figure 4: Photographs of the fabricated antenna in measurement. Figure 5: Results of reflection and transmission coefficients from (**a**) simulation and (**b**) measurement. Figure 6: _Cont._  
Figure 8a,b, respectively, give the realized gains and axial ratios of state 4 for different frequencies from simulation and measurement, which indicate that good circular polarization is achieved within the main beam with a peak gain of 17.1 dBi in this band. The measured results show an agreement with an explainable gain degradation due to the machining tolerances and the uncertainty in the exact substrate permittivity. Figure 6: Results of the normalized radiation pattern of all the states from simulation for (**a**) 30 GHz, (**b**) 31 GHz, (**c**) 32 GHz, and (**d**) 33 GHz. Figure 7: Results of the normalized radiation pattern of all the states from measurement for (**a**) 30 GHz, (**b**) 31 GHz, (**c**) 32 GHz, and (**d**) 33 GHz. The simulated results of radiation efficiency for three typical states are given in Figure 9a. It indicates that the radiation efficiency is mainly between \(-0.5\) dB and \(-2\) dB in this observation band, with an average value of \(-1.2\) dB (87%). To clearly illustrate the beam-scanning property of the proposed antenna, the gains and main beam directions for different beams in this observation band are given in Figure 9b.